Finite Group Databasebeta

← #7715879

Subgroups — #7715879

Order 512.

7806 conjugacy classes of subgroups.

The subgroup lattice has 1901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3534C211yesmaximal, characteristic, complemented
2C22×#551C211yesmaximal, characteristic, complemented
3#50179C214yesmaximal, complemented
4#48835C214yesmaximal, complemented
5#48830C214yesmaximal, complemented
6#48790C214yesmaximal, complemented
7#44020C214yesmaximal, complemented
8#44001C214yesmaximal, complemented
9#43959C214yesmaximal, complemented
10#43932C214yesmaximal, complemented
11#39722C212yesmaximal, complemented
12#39129C212yesmaximal, complemented
13#38023C212yesmaximal, complemented
14#38021C212yesmaximal, complemented
15#37654C212yesmaximal, complemented
16#37644C212yesmaximal, complemented
17#36971C211yesmaximal, characteristic, complemented
18#36967C211yesmaximal, characteristic, complemented
19#36961C211yesmaximal, characteristic, complemented
20#36957C211yesmaximal, characteristic, complemented
21#36236C212yesmaximal, complemented
22#36098C212yesmaximal, complemented
23#35263C211yesmaximal, characteristic, complemented
24#35262C211yesmaximal, characteristic, complemented
25#35150C211yesmaximal, characteristic, complemented
26#35094C211yesmaximal, characteristic, complemented
27#35050C211yesmaximal, characteristic, complemented
28#34986C211yesmaximal, characteristic, complemented
29#34984C211yesmaximal, characteristic, complemented
30C2×#2617C211yesmaximal, characteristic, complemented
31#34376C211yesmaximal, characteristic, complemented
32#3534—216no—
33C2×#562C2212yescomplemented
34C2×#560C2212yescomplemented
35C2×#553C2212yescomplemented
36C2×#551—216no—
37C2×#551C2214yescomplemented
38C2×#551C2214yescomplemented
39C2×#551C2214yescomplemented
40C2×#551C2214yescomplemented
41C2×#551C2212yescomplemented
42C2×#546C2212yes—
43C2×#546C2212yescomplemented
44C2×#546C2212yescomplemented
45C2×D42C2212yes—
46C2×#540C2212yescomplemented
47C2×#539C2211yescharacteristic, complemented
48C2×#539C2212yescomplemented
49C2×#538C2211yescharacteristic, complemented
50C2×#538C2212yescomplemented
51C2×#537C2211yescharacteristic, complemented
52C2×#534C2212yescomplemented
53C2×#534C2212yescomplemented
54C2×#534C2211yescharacteristic, complemented
55C22×#126C2211yescharacteristic, complemented
56C22×#126C2211yescharacteristic, complemented
57C22×#124C2211yescharacteristic, complemented
58C2×#525C2211yescharacteristic
59C2×#525C2212yescomplemented
60C22×#123C2211yescharacteristic
61C22×#123C2211yescharacteristic, complemented
62C22×#123C2211yescharacteristic, complemented
63C22×C22⋊Q8C2211yescharacteristic, complemented
64C22×C22⋊Q8C2211yescharacteristic, complemented
65C22×#121C2211yescharacteristic
66C22×#120C2211yescharacteristic
67C22×#120C2212yescomplemented
68C22×C4×D4C2211yescharacteristic
69C22×C4×D4C2211yescharacteristic, complemented
70C22×#117C2211yescharacteristic, complemented
71C22×#117C2211yescharacteristic, complemented
72C23×C22⋊C4C2211yescharacteristic, complemented
73C23×C22⋊C4C2211yescharacteristic, complemented
74#2855C2211yescharacteristic, complemented
75#2855C2211yescharacteristic, complemented
76#2854C2211yescharacteristic, complemented
77#2854C2211yescharacteristic, complemented
78#2854C2211yescharacteristic, complemented
79#2854C2212yescomplemented
80#2854C2211yescharacteristic, complemented
81#2854C2211yescharacteristic, complemented
82#2854C2211yescharacteristic, complemented
83#2849C2212yescomplemented
84#2849C2212yescomplemented
85#2849C2212yescomplemented
86#2847C2212yescomplemented
87#2846C2212yescomplemented
88#2727C2214yescomplemented
89#2727C2214yescomplemented
90#2725C2214yescomplemented
91#2723C2214yescomplemented
92#2723C2214yescomplemented
93#2723C2214yescomplemented
94#2723C2214yescomplemented
95#2721C2214yescomplemented
96#2715C2214yescomplemented
97#2714C2214yescomplemented
98#2714C2214yescomplemented
99#2714C2214yescomplemented
100#2712C2214yescomplemented
101#2710C2214yescomplemented
102#2710C2214yescomplemented
103#2710C2214yescomplemented
104#2706C2214yescomplemented
105#2705C2214yescomplemented
106#2705C2214yescomplemented
107#2703C2214yescomplemented
108#2703C2214yescomplemented
109#2702C2214yescomplemented
110#2700C2214yescomplemented
111#2696C2214yescomplemented
112#2696C2214yescomplemented
113#2687C2214yescomplemented
114#2681C2214yescomplemented
115#2680C2214yescomplemented
116#2679C2214yescomplemented
117#2678C2214yescomplemented
118#2678C2214yescomplemented
119#2676C2214yescomplemented
120#2672C2214yescomplemented
121#2672C2214yescomplemented
122#2672C2214yescomplemented
123#2671C2214yescomplemented
124#2670C2214yescomplemented
125#2670C2214yescomplemented
126#2669C2214yescomplemented
127#2668C2214yescomplemented
128#2626C2211yescharacteristic, complemented
129#2626C2211yescharacteristic, complemented
130#2625C2212yescomplemented
131#2624C2212yescomplemented
132#2624C2212yescomplemented
133#2624C2212yescomplemented
134#2623C2212yescomplemented
135#2618C2212yescomplemented
136#2617C2211yescharacteristic
137#2617C2211yescharacteristic
138#2617C2212yescomplemented
139#2617C2212yescomplemented
140#2617C2212yescomplemented
141#2617C2211yescharacteristic, complemented
142#2617C2211yescharacteristic, complemented
143#2617C2211yescharacteristic, complemented
144#2617C2211yescharacteristic, complemented
145#2617C2212yescomplemented
146#2617C2212yescomplemented
147#2617C2214yescomplemented
148#2613C2212yescomplemented
149#2561C2212yescomplemented
150#2554C2214yescomplemented
151#2549C2214yescomplemented
152#2540C2214yescomplemented
153#2539C2212yescomplemented
154#2539C2212yescomplemented
155#2539C2212yescomplemented
156#2539C2214yescomplemented
157#2534C2212yescomplemented
158#2534C2214yescomplemented
159#2534C2212yescomplemented
160#2512C2214yescomplemented
161#2504C2212yescomplemented
162#2504C2212yescomplemented
163#2501C2212yescomplemented
164#2500C2214yescomplemented
165#2498C2214yescomplemented
166#2489C2214yescomplemented
167#2488C2214yescomplemented
168#2487C2212yescomplemented
169#2487C2212yescomplemented
170#2486C2212yescomplemented
171#2485C2214yescomplemented
172#2482C2212yescomplemented
173#2482C2214yescomplemented
174#2479C2214yescomplemented
175#2479C2214yescomplemented
176#2477C2214yescomplemented
177#2475C2214yescomplemented
178#2472C2214yescomplemented
179#2472C2214yescomplemented
180#2471C2214yescomplemented
181#2467C2214yescomplemented
182#2466C2214yescomplemented
183#2464C2214yescomplemented
184#2459C2214yescomplemented
185#2456C2214yescomplemented
186#2455C2214yescomplemented
187#2455C2214yescomplemented
188#2450C2214yescomplemented
189#2445C2214yescomplemented
190#2444C2214yescomplemented
191#2444C2214yescomplemented
192#2437C2214yescomplemented
193#2437C2214yescomplemented
194#2436C2212yescomplemented
195#2427C2214yescomplemented
196#2425C2214yescomplemented
197#2425C2214yescomplemented
198#2425C2214yescomplemented
199#2424C2214yes—
200#2424C2214yescomplemented
201#2424C2214yescomplemented
202#2424C2214yescomplemented
203#2424C2214yescomplemented
204#2422C2214yescomplemented
205#2420C2214yescomplemented
206#2418C2214yescomplemented
207#2418C2214yescomplemented
208#2418C2214yescomplemented
209#2418C2214yescomplemented
210#2418C2214yescomplemented
211#2415C2214yescomplemented
212#2415C2214yescomplemented
213#2415C2214yescomplemented
214#2414C2214yescomplemented
215#2414C2214yescomplemented
216#2413C2212yescomplemented
217#2412C2212yescomplemented
218#2412C2212yescomplemented
219#2412C2212yescomplemented
220#2412C2214yescomplemented
221#2411C2212yescomplemented
222#2411C2214yescomplemented
223#2410C2214yescomplemented
224#2410C2212yescomplemented
225#2409C2212yescomplemented
226#2408C2214yes—
227#2406C2212yescomplemented
228#2405C2212yescomplemented
229#2405C2212yescomplemented
230#2405C2212yescomplemented
231#2404C2212yescomplemented
232#2404C2212yescomplemented
233#2403C2212yescomplemented
234#2403C2214yescomplemented
235C2×#397C2212yescomplemented
236C2×#394C2214yescomplemented
237C2×#392C2212yescomplemented
238#2376C2214yescomplemented
239#2359C2214yescomplemented
240#2358C2214yescomplemented
241#2349C2214yescomplemented
242#2345C2212yescomplemented
243#2342C2212yescomplemented
244#2342C2212yescomplemented
245D4×C22⋊C4C2212yes—
246D4×C22⋊C4C2214yescomplemented
247D4×C22⋊C4C2214yescomplemented
248#2335C2214yescomplemented
249#2322C2214yescomplemented
250#2322C2212yescomplemented
251#2321C2212yescomplemented
252#2321C2212yescomplemented
253#2321C2212yescomplemented
254#2317C2212yescomplemented
255#2316C2211yescharacteristic, complemented
256#2316C2212yescomplemented
257#2315C2211yescharacteristic, complemented
258#2313C2211yescharacteristic, complemented
259#2312C2211yescharacteristic, complemented
260#2311C2212yescomplemented
261#2311C2212yescomplemented
262#2309C2212yescomplemented
263C4×#123C2212yescomplemented
264C4×#120C2212yescomplemented
265C2×#386C2212yescomplemented
266C2×#386C2212yescomplemented
267#2280C2211yescharacteristic, complemented
268C2×#380C2211yescharacteristic, complemented
269C26C2311yescharacteristic
270C22×#41C2311yescharacteristic
271C22×#41C2312yes—
272C23×Q8C2311yescharacteristic
273C23×D4C2311yescharacteristic
274C23×D4C2311yescharacteristic
275C23×D4C2312yes—
276C23×D4C2312yes—
277C23×D4C2312yes—
278C23×D4C2311yescharacteristic
279C23×D4C2314yes—
280C23×D4C2311yescharacteristic
281C24×C4C2311yescharacteristic
282C24×C4C2311yescharacteristic
283C24×C4C2311yescharacteristic
284C24×C4C2311yescharacteristic
285C24×C4C2311yescharacteristic
286#562—216no—
287#560—216no—
288#553—216no—
289#551—232no—
290#551—232no—
291#551—216no—
292#551—232no—
293#551—232no—
294#546—216no—
295#546—216no—
296#546—216no—
297D42—216no—
298#540—216no—
299#539—216no—
300#539—28no—
301#538—216no—
302#538—28no—
303#537—28no—
304#534—216no—
305#534—28no—
306#534—48no—
307C2×#127C2312yes—
308C2×#126—28no—
309C2×#126—28no—
310C2×#126C2314yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#126C2312yescomplemented
315C2×#126C2312yescomplemented
316C2×#126C2312yescomplemented
317C2×#126C2312yescomplemented
318C2×#125C2312yescomplemented
319C2×#125C2312yescomplemented
320C2×#124—28no—
321C2×#124C2314yes—
322C2×#124C2314yes—
323C2×#124C2312yes—
324C2×#124C2312yescomplemented
325C2×#124C2312yescomplemented
326C2×#124C2314yescomplemented
327#525—28no—
328#525—48no—
329C2×#123—28no—
330C2×#123—28no—
331C2×#123D4116yescomplemented
332C2×#123C2312yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2312yes—
340C2×#123C2312yes—
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2312yes—
348C2×#123C2312yes—
349C2×#123C2312yes—
350C2×#123C2312yes—
351C2×#123C2312yescomplemented
352C2×#123C2312yescomplemented
353C2×#123C2312yescomplemented
354C2×#123C2312yescomplemented
355C2×#123C2312yescomplemented
356C2×#123C2312yescomplemented
357C2×#123C2312yescomplemented
358C2×#123C2314yescomplemented
359C2×C22⋊Q8—28no—
360C2×C22⋊Q8—28no—
361C2×C22⋊Q8C2311yescharacteristic
362C2×C22⋊Q8C2311yescharacteristic
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2314yes—
369C2×C22⋊Q8C2312yescomplemented
370C2×C22⋊Q8C2312yescomplemented
371C2×C22⋊Q8C2312yescomplemented
372C2×C22⋊Q8C2312yescomplemented
373C2×C22⋊Q8C2314yescomplemented
374C2×#121—28no—
375C2×#121C2312yes—
376C2×#121C2311yescharacteristic
377C2×#121C2311yescharacteristic
378C2×#121C2311yescharacteristic
379C2×#121C2312yes—
380C2×#121C2311yescharacteristic
381C2×#121C2311yescharacteristic
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2311yescharacteristic
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2314yes—
391C2×#121C2314yes—
392C2×#121C2314yes—
393C2×#121C2314yes—
394C2×#121C2314yes—
395C2×#121C2312yescomplemented
396C2×#121C2312yescomplemented
397C2×#121C2312yescomplemented
398C2×#121C2312yescomplemented
399C2×#121C2312yescomplemented
400C2×#121C2312yescomplemented
401C2×#120—28no—
402C2×#120—48no—
403C2×#120C2312yes—
404C2×#120C2312yes—
405C2×#120C2312yes—
406C2×#120C2312yes—
407C2×#120C2312yes—
408C2×#120C2314yes—
409C2×#120C2314yes—
410C2×#120C2312yes—
411C2×#120C2312yes—
412C2×#120C2312yes—
413C2×#120C2312yes—
414C2×#120C2314yes—
415C2×#120C2312yes—
416C2×#120C2312yes—
417C2×#120C2314yes—
418C2×#120C2314yes—
419C2×#120C2314yes—
420C2×#120C2314yes—
421C2×#120C2314yes—
422C2×#120C2312yescomplemented
423C2×#120C2312yescomplemented
424C2×#120C2312yescomplemented
425C2×C4×D4—28no—
426C2×C4×D4—28no—
427C2×C4×D4C2312yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2312yes—
430C2×C4×D4C2314yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2314yes—
434C2×C4×D4C2314yes—
435C2×C4×D4C2314yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2314yes—
438C2×C4×D4C2314yes—
439C2×C4×D4C2314yes—
440C2×C4×D4C2314yes—
441C2×C4×D4C2312yescomplemented
442C2×C4×D4C2312yescomplemented
443C2×#117—28no—
444C2×#117—28no—
445C2×#117C2312yes—
446C2×#117C2312yes—
447C2×#117C2311yescharacteristic
448C2×#117C2312yes—
449C2×#117C2312yes—
450C2×#117C2314yes—
451C2×#117C2314yes—
452C2×#117C2312yes—
453C2×#117C2312yes—
454C2×#117C2312yescomplemented
455C22×C4⋊C4C2311yescharacteristic
456C22×C4⋊C4C2311yescharacteristic
457C22×C4⋊C4C2311yescharacteristic
458C22×C4⋊C4C2311yescharacteristic
459C22×C4⋊C4C2311yescharacteristic
460C22×C4⋊C4C2311yescharacteristic
461C22×C4⋊C4C2311yescharacteristic
462C22×C4⋊C4C2312yes—
463C22×C4⋊C4C2311yescharacteristic
464C22×C4⋊C4C2311yescharacteristic
465C22×C22⋊C4—28no—
466C22×C22⋊C4—28no—
467C22×C22⋊C4C2312yes—
468C22×C22⋊C4C2311yescharacteristic
469C22×C22⋊C4C2311yescharacteristic
470C22×C22⋊C4C2311yescharacteristic
471C22×C22⋊C4C2312yes—
472C22×C22⋊C4C2314yes—
473C22×C22⋊C4C2311yescharacteristic
474C22×C22⋊C4C2311yescharacteristic
475C22×C22⋊C4C2312yes—
476C22×C22⋊C4C2312yes—
477C22×C22⋊C4C2312yes—
478C22×C22⋊C4C2312yes—
479C22×C22⋊C4C2311yescharacteristic
480C22×C22⋊C4C2311yescharacteristic
481C22×C22⋊C4C2311yescharacteristic
482C22×C22⋊C4C2314yes—
483C22×C22⋊C4C2311yescharacteristic
484C22×C22⋊C4C2311yescharacteristic
485C22×C22⋊C4C2311yescharacteristic
486C22×C22⋊C4C2312yes—
487C22×C22⋊C4C2312yes—
488C22×C22⋊C4C2314yes—
489C22×C22⋊C4C2314yes—
490C22×C22⋊C4C2311yescharacteristic
491C22×C22⋊C4C2311yescharacteristic
492C22×C22⋊C4C2311yescharacteristic
493C22×C22⋊C4C2312yescomplemented
494C22×C22⋊C4C2314yescomplemented
495C22×C42C2311yescharacteristic
496C22×C42C2311yescharacteristic
497C22×C42C2311yescharacteristic
498#400C2314yescomplemented
499#400C2314yescomplemented
500#400C2314yescomplemented
501#399C2312yes—
502#399C2312yes—
503#399C2314yes—
504#399C2314yes—
505#399C2314yescomplemented
506#399C2314yescomplemented
507#399C2314yescomplemented
508#399C2314yescomplemented
509#399C2314yescomplemented
510#398C2314yescomplemented
511#398C2314yescomplemented
512#398C2314yescomplemented
513#398C2314yescomplemented
514#397C2312yes—
515#397C2312yes—
516#397C2312yes—
517#397C2312yes—
518#397C2312yes—
519#397C2314yes—
520#397C2314yes—
521#397C2312yes—
522#397C2314yes—
523#397C2314yes—
524#397C2314yes—
525#397C2314yescomplemented
526#397C2314yescomplemented
527#397C2314yescomplemented
528#397C2314yescomplemented
529#397C2314yescomplemented
530#397C2314yescomplemented
531#397C2314yescomplemented
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2314yes—
536#396C2314yes—
537#396C2314yescomplemented
538#396C2314yescomplemented
539#396C2314yescomplemented
540#395C2314yescomplemented
541#395C2314yescomplemented
542#394C2314yes—
543#394C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#394C2314yes—
559#394C2314yes—
560#394C2314yes—
561#394C2314yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#394C2314yes—
566#394C2314yescomplemented
567#394C2314yescomplemented
568#394C2314yescomplemented
569#394C2314yescomplemented
570#394C2314yescomplemented
571#393C2312yes—
572#393C2312yes—
573#393C2314yes—
574#393C2314yescomplemented
575#393C2314yescomplemented
576#393C2314yescomplemented
577#392C2314yes—
578#392C2314yes—
579#392C2312yes—
580#392C2312yes—
581#392C2312yes—
582#392C2312yes—
583#392C2314yes—
584#392C2314yes—
585#392C2314yes—
586#392C2312yes—
587#392C2312yes—
588#392C2314yes—
589#392C2314yes—
590#392C2314yes—
591#392C2314yes—
592#392C2314yes—
593#392C2314yes—
594#391C2312yescomplemented
595#391C2312yescomplemented
596#391C2314yescomplemented
597#391C2314yescomplemented
598#391C2314yescomplemented
599#390C2314yes—
600#390C2314yes—
601#390C2314yes—
602#390C2314yes—
603#390C2314yes—
604#390C2314yes—
605#390C2314yes—
606#390C2314yes—
607#390C2314yes—
608#390C2312yescomplemented
609#390C2312yescomplemented
610#390C2312yescomplemented
611#390C2312yescomplemented
612#390C2314yescomplemented
613#390C2314yescomplemented
614#390C2312yescomplemented
615#390C2312yescomplemented
616#390C2314yescomplemented
617#390C2314yescomplemented
618#390C2314yescomplemented
619#389C2314yescomplemented
620#389C2312yescomplemented
621#389C2312yescomplemented
622#389C2312yescomplemented
623#389C2312yescomplemented
624#389C2314yescomplemented
625#389C2314yescomplemented
626#389C2314yescomplemented
627#389C2312yescomplemented
628#389C2312yescomplemented
629#389C2312yescomplemented
630#389C2312yescomplemented
631#389C2314yescomplemented
632#389C2314yescomplemented
633#389C2314yescomplemented
634#389C2314yescomplemented
635#389C2314yescomplemented
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yescomplemented
648#388C2314yescomplemented
649#388C2314yescomplemented
650#388C2314yescomplemented
651#388C2314yescomplemented
652#388C2314yescomplemented
653#388C2314yescomplemented
654#388C2314yescomplemented
655#388C2314yescomplemented
656#388C2314yescomplemented
657#388C2314yescomplemented
658#388C2314yescomplemented
659#388C2314yescomplemented
660#388C2314yescomplemented
661#388C2314yescomplemented
662#387C2314yescomplemented
663#387C2314yescomplemented
664#387C2314yescomplemented
665#387C2314yescomplemented
666#387C2314yescomplemented
667#387C2314yescomplemented
668#387C2314yescomplemented
669#387C2314yescomplemented
670#386C2312yes—
671#386C2312yes—
672#386C2314yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#386C2312yes—
677#386C2312yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2312yes—
685#386C2312yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2312yes—
695#386C2312yes—
696#386C2312yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yescomplemented
704#386C2314yescomplemented
705#386C2314yescomplemented
706#386C2314yescomplemented
707#385C2314yes—
708#385C2314yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#385C2314yes—
713#385C2312yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yescomplemented
719#385C2314yescomplemented
720#385C2314yescomplemented
721#385C2314yescomplemented
722#385C2314yescomplemented
723#385C2314yescomplemented
724#385C2314yescomplemented
725#385C2314yescomplemented
726#384C2314yescomplemented
727#382C2314yescomplemented
728#382C2314yescomplemented
729#381C2314yes—
730#381C2312yes—
731#381C2312yes—
732#381C2312yes—
733#381C2312yes—
734#381C2314yescomplemented
735#380C2311yescharacteristic
736#380C2311yescharacteristic
737#380C2311yescharacteristic
738#380C2311yescharacteristic
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2314yes—
743#380C2312yes—
744#380C2314yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2314yescomplemented
749#380C2314yescomplemented
750#380C2314yescomplemented
751#380C2314yescomplemented
752#380C2314yescomplemented
753#380C2314yescomplemented
754#379C2314yes—
755#379C2314yes—
756#379C2314yes—
757#379C2312yes—
758#379C2312yes—
759#379C2312yes—
760#379C2312yes—
761#379C2314yes—
762#379C2314yescomplemented
763C4×C4⋊C4C2314yescomplemented
764C4×C4⋊C4C2314yescomplemented
765C4×C22⋊C4C2312yes—
766C4×C22⋊C4C2312yes—
767C4×C22⋊C4C2312yes—
768C4×C22⋊C4C2312yes—
769C4×C22⋊C4C2314yes—
770C4×C22⋊C4C2314yes—
771C4×C22⋊C4C2314yescomplemented
772C4×C22⋊C4C2314yescomplemented
773C2×#95C2314yes—
774C2×#95C2312yes—
775C2×#95C2314yescomplemented
776C25—24no—
777C25—24no—
778C25—42no—
779C25—44no—
780C25—82no—
781C25C2412yes—
782C25C2411yescharacteristic
783C25C2411yescharacteristic
784C25C2412yes—
785C25C2412yes—
786C25C2411yescharacteristic
787C25C2411yescharacteristic
788C25C2412yes—
789C2×#41—24no—
790C2×#41—28no—
791C2×#41—44no—
792C2×#41—44no—
793C2×#41—44no—
794C22×Q8—24no—
795C22×Q8—82no—
796C22×Q8C2414yes—
797C22×Q8C2412yes—
798C22×Q8C2411yescharacteristic
799C22×D4—24no—
800C22×D4—24no—
801C22×D4—24no—
802C22×D4—28no—
803C22×D4—28no—
804C22×D4—28no—
805C22×D4—24no—
806C22×D4—42no—
807C22×D4—44no—
808C22×D4—48no—
809C22×D4—44no—
810C22×D4—48no—
811C22×D4—44no—
812C22×D4—44no—
813C22×D4—48no—
814C22×D4—44no—
815C22×D4—44no—
816C22×D4—82no—
817C22×D4—84no—
818C22×D4C2×D418yes—
819C22×D4C2412yes—
820C22×D4C2412yes—
821C22×D4C2412yes—
822C22×D4C2412yes—
823C22×D4C2414yes—
824C22×D4C2412yes—
825C22×D4C2414yes—
826C22×D4C2412yes—
827C22×D4C2414yes—
828C22×D4C2412yes—
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2414yes—
832C22×D4C2414yes—
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2412yes—
847C23×C4—24no—
848C23×C4—24no—
849C23×C4—24no—
850C23×C4—24no—
851C23×C4—24no—
852C23×C4—44no—
853C23×C4—42no—
854C23×C4—82no—
855C23×C4—82no—
856C23×C4—82no—
857C23×C4C2×D418yes—
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2414yes—
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2412yes—
867C23×C4C2414yes—
868C23×C4C2411yescharacteristic
869C23×C4C2411yescharacteristic
870C23×C4C2411yescharacteristic
871C23×C4C2414yes—
872C23×C4C2412yes—
873C23×C4C2412yes—
874C23×C4C2412yes—
875C23×C4C2414yes—
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2412yes—
879C23×C4C2412yes—
880C23×C4C2414yes—
881C23×C4C2411yescharacteristic
882C23×C4C2411yescharacteristic
883C23×C4C2411yescharacteristic
884C23×C4C2411yescharacteristic
885C23×C4C2411yescharacteristic
886C23×C4C2411yescharacteristic
887#127—28no—
888#126—216no—
889#126—216no—
890#126—216no—
891#126—216no—
892#126—28no—
893#126—28no—
894#126—28no—
895#126—28no—
896#125—28no—
897#125—28no—
898#124—216no—
899#124—216no—
900#124—28no—
901#124—28no—
902#124—28no—
903#124—84no—
904#123—28no—
905#123—28no—
906#123—28no—
907#123—28no—
908#123—28no—
909#123—216no—
910#123—216no—
911#123—216no—
912#123—216no—
913#123—28no—
914#123—28no—
915#123—28no—
916#123—28no—
917#123—28no—
918#123—48no—
919#123—44no—
920#123—44no—
921#123—44no—
922#123—44no—
923#123—44no—
924#123—44no—
925#123—84no—
926#123—84no—
927#123C2×D4116yes—
928#123C2×D4116yes—
929#123C2×D4116yescomplemented
930#123C2×D4116yescomplemented
931C22⋊Q8—24no—
932C22⋊Q8—24no—
933C22⋊Q8—216no—
934C22⋊Q8—216no—
935C22⋊Q8—28no—
936C22⋊Q8—28no—
937C22⋊Q8—28no—
938C22⋊Q8—216no—
939C22⋊Q8—216no—
940C22⋊Q8—28no—
941C22⋊Q8—28no—
942C22⋊Q8—48no—
943C22⋊Q8—84no—
944#121—28no—
945#121—28no—
946#121—28no—
947#121—24no—
948#121—24no—
949#121—24no—
950#121—24no—
951#121—28no—
952#121—28no—
953#121—24no—
954#121—24no—
955#121—28no—
956#121—28no—
957#121—28no—
958#121—28no—
959#121—28no—
960#121—28no—
961#121—28no—
962#121—28no—
963#121—28no—
964#121—28no—
965#121—48no—
966#121—48no—
967#121—48no—
968#121—84no—
969#121—84no—
970#120—28no—
971#120—28no—
972#120—28no—
973#120—28no—
974#120—28no—
975#120—216no—
976#120—216no—
977#120—28no—
978#120—28no—
979#120—28no—
980#120—28no—
981#120—28no—
982#120—28no—
983#120—44no—
984#120—44no—
985#120—48no—
986#120—48no—
987#120—48no—
988#120—44no—
989#120—48no—
990#120—84no—
991#120—84no—
992C4×D4—216no—
993C4×D4—216no—
994C4×D4—28no—
995C4×D4—28no—
996C4×D4—28no—
997C4×D4—28no—
998C4×D4—28no—
999C4×D4—28no—
1000C4×D4—216no—
1001C4×D4—216no—
1002C4×D4—28no—
1003C4×D4—28no—
1004C4×D4—48no—
1005C4×D4—48no—
1006C4×D4—48no—
1007C4×D4—84no—
1008#117—28no—
1009#117—28no—
1010#117—28no—
1011#117—28no—
1012#117—24no—
1013#117—216no—
1014#117—216no—
1015#117—28no—
1016#117—44no—
1017#117—44no—
1018C2×C4⋊C4—24no—
1019C2×C4⋊C4—24no—
1020C2×C4⋊C4—24no—
1021C2×C4⋊C4—24no—
1022C2×C4⋊C4—24no—
1023C2×C4⋊C4—24no—
1024C2×C4⋊C4—24no—
1025C2×C4⋊C4—44no—
1026C2×C4⋊C4C2×D418yescomplemented
1027C2×C4⋊C4C2×D418yescomplemented
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2411yescharacteristic
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2411yescharacteristic
1040C2×C4⋊C4C2411yescharacteristic
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2414yes—
1062C2×C4⋊C4C2414yes—
1063C2×C4⋊C4C2414yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2414yes—
1067C2×C4⋊C4C2412yes—
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2412yes—
1071C2×C22⋊C4—24no—
1072C2×C22⋊C4—24no—
1073C2×C22⋊C4—24no—
1074C2×C22⋊C4—24no—
1075C2×C22⋊C4—24no—
1076C2×C22⋊C4—24no—
1077C2×C22⋊C4—24no—
1078C2×C22⋊C4—24no—
1079C2×C22⋊C4—24no—
1080C2×C22⋊C4—28no—
1081C2×C22⋊C4—28no—
1082C2×C22⋊C4—28no—
1083C2×C22⋊C4—28no—
1084C2×C22⋊C4—24no—
1085C2×C22⋊C4—24no—
1086C2×C22⋊C4—28no—
1087C2×C22⋊C4—216no—
1088C2×C22⋊C4—216no—
1089C2×C22⋊C4—28no—
1090C2×C22⋊C4—28no—
1091C2×C22⋊C4—44no—
1092C2×C22⋊C4—48no—
1093C2×C22⋊C4—44no—
1094C2×C22⋊C4—84no—
1095C2×C22⋊C4—84no—
1096C2×C22⋊C4C2×D418yes—
1097C2×C22⋊C4C2×D418yescomplemented
1098C2×C22⋊C4C2×D418yescomplemented
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2412yes—
1128C2×C22⋊C4C2412yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2412yes—
1132C2×C22⋊C4C2412yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2412yes—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2414yes—
1149C2×C22⋊C4C2414yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2414yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2414yes—
1154C2×C22⋊C4C2414yes—
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2414yes—
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2414yes—
1167C2×C22⋊C4C2414yes—
1168C2×C22⋊C4C2414yes—
1169C2×C22⋊C4C2414yes—
1170C2×C22⋊C4C2414yes—
1171C2×C22⋊C4C2414yes—
1172C2×C22⋊C4C2414yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2412yes—
1175C2×C22⋊C4C2412yes—
1176C2×C22⋊C4C2412yes—
1177C2×C22⋊C4C2412yes—
1178C2×C22⋊C4C2412yes—
1179C2×C42—24no—
1180C2×C42—24no—
1181C2×C42—24no—
1182C2×C42C2412yes—
1183C2×C42C2412yes—
1184C2×C42C2414yes—
1185C2×C42C2412yes—
1186C2×C42C2412yes—
1187C2×C42C2412yes—
1188C2×C42C2412yes—
1189C2×C42C2412yes—
1190C2×C42C2414yes—
1191C2×C42C2414yes—
1192C2×C42C2414yes—
1193C2×C42C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226C24—22no—
1227C24—22no—
1228C24—24no—
1229C24—22no—
1230C24—22no—
1231C24—22no—
1232C24—22no—
1233C24—22no—
1234C24—24no—
1235C24—24no—
1236C24—24no—
1237C24—28no—
1238C24—24no—
1239C24—24no—
1240C24—22no—
1241C24—22no—
1242C24—28no—
1243C24—24no—
1244C24—42no—
1245C24—42no—
1246C24—42no—
1247C24—42no—
1248C24—42no—
1249C24—42no—
1250C24—44no—
1251C24—42no—
1252C24—42no—
1253C24—44no—
1254C24—42no—
1255C24—44no—
1256C24—44no—
1257C24—42no—
1258C24—42no—
1259C24—42no—
1260C24—44no—
1261C24—44no—
1262C24—42no—
1263C24—416no—
1264C24—416no—
1265C24—816no—
1266C24—88no—
1267C24—816no—
1268C24C22×D414yes—
1269C24C22×D414yes—
1270C24H(5,𝔽2)14yes—
1271C24C2512yes—
1272C24C2512yes—
1273C24C2512yes—
1274C24C2512yes—
1275C24C2511yescharacteristic
1276C24C2512yes—
1277C24C2512yes—
1278C24C2511yescharacteristic
1279C24C2511yescharacteristic
1280#41—88no—
1281#41—816no—
1282C2×Q8—28no—
1283C2×Q8—22no—
1284C2×Q8—24no—
1285C2×Q8—42no—
1286C2×Q8—44no—
1287C2×Q8—44no—
1288C2×Q8—42no—
1289C2×Q8—42no—
1290C2×Q8—88no—
1291C2×D4—28no—
1292C2×D4—28no—
1293C2×D4—24no—
1294C2×D4—24no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—28no—
1298C2×D4—24no—
1299C2×D4—24no—
1300C2×D4—24no—
1301C2×D4—28no—
1302C2×D4—28no—
1303C2×D4—24no—
1304C2×D4—24no—
1305C2×D4—24no—
1306C2×D4—24no—
1307C2×D4—24no—
1308C2×D4—24no—
1309C2×D4—28no—
1310C2×D4—24no—
1311C2×D4—24no—
1312C2×D4—24no—
1313C2×D4—24no—
1314C2×D4—28no—
1315C2×D4—28no—
1316C2×D4—24no—
1317C2×D4—22no—
1318C2×D4—24no—
1319C2×D4—22no—
1320C2×D4—24no—
1321C2×D4—22no—
1322C2×D4—24no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—44no—
1328C2×D4—44no—
1329C2×D4—42no—
1330C2×D4—42no—
1331C2×D4—44no—
1332C2×D4—44no—
1333C2×D4—44no—
1334C2×D4—44no—
1335C2×D4—44no—
1336C2×D4—42no—
1337C2×D4—42no—
1338C2×D4—42no—
1339C2×D4—44no—
1340C2×D4—44no—
1341C2×D4—44no—
1342C2×D4—44no—
1343C2×D4—44no—
1344C2×D4—44no—
1345C2×D4—44no—
1346C2×D4—42no—
1347C2×D4—42no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—42no—
1352C2×D4—44no—
1353C2×D4—42no—
1354C2×D4—42no—
1355C2×D4—42no—
1356C2×D4—42no—
1357C2×D4—42no—
1358C2×D4—44no—
1359C2×D4—44no—
1360C2×D4—44no—
1361C2×D4—416no—
1362C2×D4—416no—
1363C2×D4—88no—
1364C2×D4—88no—
1365C2×D4—816no—
1366C2×D4—816no—
1367C2×D4—816no—
1368C2×D4—832no—
1369C2×D4C22×D418yes—
1370C2×D4C22×D418yes—
1371C22×C4—22no—
1372C22×C4—24no—
1373C22×C4—24no—
1374C22×C4—22no—
1375C22×C4—22no—
1376C22×C4—22no—
1377C22×C4—22no—
1378C22×C4—22no—
1379C22×C4—22no—
1380C22×C4—22no—
1381C22×C4—28no—
1382C22×C4—22no—
1383C22×C4—22no—
1384C22×C4—22no—
1385C22×C4—22no—
1386C22×C4—24no—
1387C22×C4—24no—
1388C22×C4—24no—
1389C22×C4—28no—
1390C22×C4—24no—
1391C22×C4—28no—
1392C22×C4—28no—
1393C22×C4—28no—
1394C22×C4—24no—
1395C22×C4—24no—
1396C22×C4—24no—
1397C22×C4—24no—
1398C22×C4—24no—
1399C22×C4—416no—
1400C22×C4—42no—
1401C22×C4—42no—
1402C22×C4—42no—
1403C22×C4—42no—
1404C22×C4—44no—
1405C22×C4—42no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—42no—
1409C22×C4—42no—
1410C22×C4—42no—
1411C22×C4—44no—
1412C22×C4—42no—
1413C22×C4—44no—
1414C22×C4—44no—
1415C22×C4—44no—
1416C22×C4—42no—
1417C22×C4—42no—
1418C22×C4—44no—
1419C22×C4—44no—
1420C22×C4—44no—
1421C22×C4—42no—
1422C22×C4—44no—
1423C22×C4—44no—
1424C22×C4—44no—
1425C22×C4—42no—
1426C22×C4—42no—
1427C22×C4—44no—
1428C22×C4—42no—
1429C22×C4—42no—
1430C22×C4—44no—
1431C22×C4—44no—
1432C22×C4—44no—
1433C22×C4—416no—
1434C22×C4—88no—
1435C22×C4—88no—
1436C22×C4—88no—
1437C22×C4C22×D414yes—
1438C22×C4C22×D414yes—
1439C22×C4C22×D414yes—
1440C22×C4C22×D414yes—
1441C22×C4C22×D414yes—
1442C22×C4C22×D414yes—
1443C22×C4C22×D414yes—
1444C22×C4C22×D414yes—
1445C22×C4C22×D414yes—
1446C22×C4C2514yes—
1447C22×C4C2512yes—
1448C22×C4C2514yes—
1449C22×C4C2514yes—
1450C22×C4C2514yes—
1451C22×C4C2512yes—
1452C22×C4C2512yes—
1453C22×C4C2512yes—
1454C22×C4C2512yes—
1455C22×C4C2512yes—
1456C22×C4C2512yes—
1457C22×C4C2512yes—
1458C22×C4C2512yes—
1459C22×C4C2512yes—
1460C22×C4C2512yes—
1461C22×C4C2512yes—
1462C22×C4C2511yescharacteristic
1463C22×C4C2511yescharacteristic
1464C22×C4C2511yescharacteristic
1465C22×C4C2512yes—
1466C22×C4C2511yescharacteristic
1467C22×C4C2512yes—
1468C4⋊C4—24no—
1469C4⋊C4—24no—
1470C4⋊C4—28no—
1471C4⋊C4—24no—
1472C4⋊C4—24no—
1473C4⋊C4—28no—
1474C4⋊C4—28no—
1475C4⋊C4—22no—
1476C4⋊C4—24no—
1477C4⋊C4—22no—
1478C4⋊C4—28no—
1479C4⋊C4—22no—
1480C4⋊C4—24no—
1481C4⋊C4—22no—
1482C4⋊C4—24no—
1483C4⋊C4—24no—
1484C4⋊C4—24no—
1485C4⋊C4—24no—
1486C4⋊C4—24no—
1487C4⋊C4—24no—
1488C4⋊C4—24no—
1489C4⋊C4—44no—
1490C4⋊C4—42no—
1491C4⋊C4—42no—
1492C4⋊C4—42no—
1493C4⋊C4—42no—
1494C4⋊C4—44no—
1495C4⋊C4—44no—
1496C4⋊C4—44no—
1497C4⋊C4—44no—
1498C4⋊C4—44no—
1499C4⋊C4—44no—
1500C4⋊C4—44no—
1501C4⋊C4—44no—
1502C4⋊C4—44no—
1503C4⋊C4—44no—
1504C4⋊C4—44no—
1505C4⋊C4—44no—
1506C4⋊C4—44no—
1507C4⋊C4C22×D418yes—
1508C4⋊C4C22×D418yes—
1509C4⋊C4C22×D418yes—
1510C4⋊C4C22×D418yes—
1511C22⋊C4—24no—
1512C22⋊C4—24no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—24no—
1516C22⋊C4—28no—
1517C22⋊C4—24no—
1518C22⋊C4—24no—
1519C22⋊C4—24no—
1520C22⋊C4—24no—
1521C22⋊C4—24no—
1522C22⋊C4—24no—
1523C22⋊C4—24no—
1524C22⋊C4—28no—
1525C22⋊C4—28no—
1526C22⋊C4—28no—
1527C22⋊C4—28no—
1528C22⋊C4—24no—
1529C22⋊C4—24no—
1530C22⋊C4—24no—
1531C22⋊C4—24no—
1532C22⋊C4—24no—
1533C22⋊C4—24no—
1534C22⋊C4—24no—
1535C22⋊C4—28no—
1536C22⋊C4—28no—
1537C22⋊C4—24no—
1538C22⋊C4—24no—
1539C22⋊C4—24no—
1540C22⋊C4—28no—
1541C22⋊C4—24no—
1542C22⋊C4—28no—
1543C22⋊C4—24no—
1544C22⋊C4—24no—
1545C22⋊C4—24no—
1546C22⋊C4—24no—
1547C22⋊C4—24no—
1548C22⋊C4—24no—
1549C22⋊C4—24no—
1550C22⋊C4—24no—
1551C22⋊C4—24no—
1552C22⋊C4—24no—
1553C22⋊C4—24no—
1554C22⋊C4—24no—
1555C22⋊C4—44no—
1556C22⋊C4—44no—
1557C22⋊C4—44no—
1558C22⋊C4—44no—
1559C22⋊C4—44no—
1560C22⋊C4—44no—
1561C22⋊C4—44no—
1562C22⋊C4—44no—
1563C22⋊C4—44no—
1564C22⋊C4—44no—
1565C22⋊C4—44no—
1566C22⋊C4—44no—
1567C22⋊C4—44no—
1568C22⋊C4—44no—
1569C22⋊C4—44no—
1570C22⋊C4—44no—
1571C22⋊C4—44no—
1572C22⋊C4—44no—
1573C22⋊C4—44no—
1574C22⋊C4—44no—
1575C22⋊C4—44no—
1576C22⋊C4—44no—
1577C22⋊C4—44no—
1578C22⋊C4—44no—
1579C22⋊C4—44no—
1580C22⋊C4—44no—
1581C22⋊C4—44no—
1582C22⋊C4—44no—
1583C22⋊C4—44no—
1584C22⋊C4—44no—
1585C22⋊C4C22×D418yes—
1586C22⋊C4C22×D418yes—
1587C22⋊C4C22×D418yes—
1588C22⋊C4C22×D418yes—
1589C22⋊C4C22×D418yes—
1590C22⋊C4C22×D418yes—
1591C42—24no—
1592C42—24no—
1593C42—28no—
1594C42—24no—
1595C42—24no—
1596C42—24no—
1597C42—24no—
1598C42—24no—
1599C42—44no—
1600C42—44no—
1601C42—44no—
1602C42—44no—
1603C23—21no—
1604C23—22no—
1605C23—21no—
1606C23—22no—
1607C23—22no—
1608C23—22no—
1609C23—21no—
1610C23—22no—
1611C23—24no—
1612C23—24no—
1613C23—22no—
1614C23—22no—
1615C23—22no—
1616C23—21no—
1617C23—22no—
1618C23—24no—
1619C23—24no—
1620C23—28no—
1621C23—28no—
1622C23—28no—
1623C23—28no—
1624C23—22no—
1625C23—22no—
1626C23—22no—
1627C23—22no—
1628C23—22no—
1629C23—22no—
1630C23—22no—
1631C23—22no—
1632C23—22no—
1633C23—22no—
1634C23—22no—
1635C23—24no—
1636C23—24no—
1637C23—22no—
1638C23—24no—
1639C23—24no—
1640C23—24no—
1641C23—24no—
1642C23—24no—
1643C23—24no—
1644C23—44no—
1645C23—48no—
1646C23—44no—
1647C23—44no—
1648C23—48no—
1649C23—48no—
1650C23—416no—
1651C23—48no—
1652C23—48no—
1653C23—44no—
1654C23—44no—
1655C23—48no—
1656C23—44no—
1657C23—44no—
1658C23—48no—
1659C23—48no—
1660C23—44no—
1661C23—48no—
1662C23—84no—
1663C23—84no—
1664C23—84no—
1665C23—84no—
1666C23—84no—
1667C23—88no—
1668C23—84no—
1669C23—88no—
1670C23—84no—
1671C23—88no—
1672C23—84no—
1673C23—84no—
1674C23—84no—
1675C23—88no—
1676C23—84no—
1677C23—88no—
1678C23—88no—
1679C23—864no—
1680C23—164no—
1681C23C23×D412yes—
1682C23C23×D414yes—
1683C23C23×D412yes—
1684C23C23×D412yes—
1685C23C2×H(5,𝔽2)14yes—
1686C23C2×H(5,𝔽2)12yes—
1687C23#58514yes—
1688C23#58512yes—
1689C23C2611yescharacteristic
1690Q8—88no—
1691Q8—82no—
1692Q8—84no—
1693D4—216no—
1694D4—48no—
1695D4—416no—
1696D4—416no—
1697D4—48no—
1698D4—48no—
1699D4—48no—
1700D4—48no—
1701D4—84no—
1702D4—82no—
1703D4—84no—
1704D4—82no—
1705D4—84no—
1706D4—82no—
1707D4—84no—
1708D4—84no—
1709D4—84no—
1710D4—88no—
1711D4—84no—
1712D4—84no—
1713D4—84no—
1714D4—84no—
1715D4—84no—
1716D4—88no—
1717D4—88no—
1718D4—88no—
1719D4—88no—
1720D4—164no—
1721C2×C4—22no—
1722C2×C4—22no—
1723C2×C4—24no—
1724C2×C4—22no—
1725C2×C4—22no—
1726C2×C4—22no—
1727C2×C4—22no—
1728C2×C4—24no—
1729C2×C4—28no—
1730C2×C4—28no—
1731C2×C4—28no—
1732C2×C4—22no—
1733C2×C4—22no—
1734C2×C4—22no—
1735C2×C4—22no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—22no—
1739C2×C4—22no—
1740C2×C4—22no—
1741C2×C4—22no—
1742C2×C4—22no—
1743C2×C4—24no—
1744C2×C4—24no—
1745C2×C4—24no—
1746C2×C4—22no—
1747C2×C4—22no—
1748C2×C4—22no—
1749C2×C4—22no—
1750C2×C4—22no—
1751C2×C4—24no—
1752C2×C4—24no—
1753C2×C4—24no—
1754C2×C4—24no—
1755C2×C4—22no—
1756C2×C4—22no—
1757C2×C4—24no—
1758C2×C4—22no—
1759C2×C4—24no—
1760C2×C4—22no—
1761C2×C4—22no—
1762C2×C4—24no—
1763C2×C4—24no—
1764C2×C4—24no—
1765C2×C4—22no—
1766C2×C4—22no—
1767C2×C4—24no—
1768C2×C4—24no—
1769C2×C4—24no—
1770C2×C4—24no—
1771C2×C4—22no—
1772C2×C4—22no—
1773C2×C4—44no—
1774C2×C4—44no—
1775C2×C4—44no—
1776C2×C4—44no—
1777C2×C4—44no—
1778C2×C4—44no—
1779C2×C4—416no—
1780C2×C4—44no—
1781C2×C4—44no—
1782C2×C4—44no—
1783C2×C4—44no—
1784C2×C4—44no—
1785C2×C4—44no—
1786C2×C4—84no—
1787C2×C4—88no—
1788C2×C4—84no—
1789C2×C4—84no—
1790C2×C4—84no—
1791C2×C4—84no—
1792C2×C4—88no—
1793C2×C4—84no—
1794C2×C4—84no—
1795C2×C4—84no—
1796C2×C4—84no—
1797C2×C4—88no—
1798C2×C4—164no—
1799C2×C4C23×D412yes—
1800C2×C4C23×D412yes—
1801C2×C4C23×D414yes—
1802C2×C4C23×D412yes—
1803C2×C4C23×D414yes—
1804C2×C4C23×D412yes—
1805C2×C4C23×D414yes—
1806C22—22no—
1807C22—22no—
1808C22—22no—
1809C22—22no—
1810C22—24no—
1811C22—24no—
1812C22—24no—
1813C22—24no—
1814C22—22no—
1815C22—24no—
1816C22—24no—
1817C22—24no—
1818C22—22no—
1819C22—24no—
1820C22—22no—
1821C22—28no—
1822C22—416no—
1823C22—416no—
1824C22—42no—
1825C22—42no—
1826C22—44no—
1827C22—42no—
1828C22—44no—
1829C22—42no—
1830C22—44no—
1831C22—42no—
1832C22—42no—
1833C22—42no—
1834C22—42no—
1835C22—42no—
1836C22—42no—
1837C22—42no—
1838C22—42no—
1839C22—42no—
1840C22—42no—
1841C22—42no—
1842C22—42no—
1843C22—44no—
1844C22—44no—
1845C22—44no—
1846C22—44no—
1847C22—44no—
1848C22—44no—
1849C22—44no—
1850C22—44no—
1851C22—88no—
1852C22—816no—
1853C22—88no—
1854C22—816no—
1855C22—168no—
1856C22—168no—
1857C22#348514yes—
1858C22#348814yes—
1859C22C24×D411yescharacteristic
1860C22C22×H(5,𝔽2)11yescharacteristic
1861C22C2×#58512yes—
1862C22C2×#58511yescharacteristic
1863C22H(7,𝔽2)12yes—
1864C4—22no—
1865C4—22no—
1866C4—22no—
1867C4—22no—
1868C4—24no—
1869C4—24no—
1870C4—24no—
1871C4—42no—
1872C4—42no—
1873C4—42no—
1874C4—42no—
1875C4—42no—
1876C4—42no—
1877C4—42no—
1878C4—42no—
1879C4—42no—
1880C4—42no—
1881C4—42no—
1882C4—44no—
1883C4—44no—
1884C4—44no—
1885C4—44no—
1886C2—24no—
1887C2—24no—
1888C2—42no—
1889C2—44no—
1890C2—44no—
1891C2—82no—
1892C2—82no—
1893C2—82no—
1894C2—82no—
1895C2C2×#348511yescharacteristic
1896C2C2×#348811yescharacteristic
1897C2#6285211yescharacteristic
1898C2#6290012yes—
1899C2#6293312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3534C2semidirect
2. C22×#551C2semidirect
3. #50179C2semidirect
4. #48835C2semidirect
5. #48830C2semidirect
6. #48790C2semidirect
7. #44020C2semidirect
8. #44001C2semidirect
9. #43959C2semidirect
10. #43932C2semidirect
11. #39722C2semidirect
12. #39129C2semidirect
13. #38023C2semidirect
14. #38021C2semidirect
15. #37654C2semidirect
16. #37644C2semidirect
17. #36971C2semidirect
18. #36967C2semidirect
19. #36961C2semidirect
20. #36957C2semidirect
21. #36236C2semidirect
22. #36098C2semidirect
23. #35263C2semidirect
24. #35262C2semidirect
25. #35150C2semidirect
26. #35094C2semidirect
27. #35050C2semidirect
28. #34986C2semidirect
29. #34984C2semidirect
30. C2×#2617C2semidirect
31. #34376C2semidirect
33. C2×#562C22semidirect
34. C2×#560C22semidirect
35. C2×#553C22semidirect
37. C2×#551C22semidirect
38. C2×#551C22semidirect
39. C2×#551C22semidirect
40. C2×#551C22semidirect
41. C2×#551C22semidirect
43. C2×#546C22semidirect
44. C2×#546C22semidirect
46. C2×#540C22semidirect
47. C2×#539C22semidirect
48. C2×#539C22semidirect
49. C2×#538C22semidirect
50. C2×#538C22semidirect
51. C2×#537C22semidirect
52. C2×#534C22semidirect
53. C2×#534C22semidirect
54. C2×#534C22semidirect
55. C22×#126C22semidirect
56. C22×#126C22semidirect
57. C22×#124C22semidirect
59. C2×#525C22semidirect
61. C22×#123C22semidirect
62. C22×#123C22semidirect
63. C22×C22⋊Q8C22semidirect
64. C22×C22⋊Q8C22semidirect
67. C22×#120C22semidirect
69. C22×C4×D4C22semidirect
70. C22×#117C22semidirect
71. C22×#117C22semidirect
72. C23×C22⋊C4C22semidirect
73. C23×C22⋊C4C22semidirect
74. #2855C22semidirect
75. #2855C22semidirect
76. #2854C22semidirect
77. #2854C22semidirect
78. #2854C22semidirect
79. #2854C22semidirect
80. #2854C22semidirect
81. #2854C22semidirect
82. #2854C22semidirect
83. #2849C22semidirect
84. #2849C22semidirect
85. #2849C22semidirect
86. #2847C22semidirect
87. #2846C22semidirect
88. #2727C22semidirect
89. #2727C22semidirect
90. #2725C22semidirect
91. #2723C22semidirect
92. #2723C22semidirect
93. #2723C22semidirect
94. #2723C22semidirect
95. #2721C22semidirect
96. #2715C22semidirect
97. #2714C22semidirect
98. #2714C22semidirect
99. #2714C22semidirect
100. #2712C22semidirect
101. #2710C22semidirect
102. #2710C22semidirect
103. #2710C22semidirect
104. #2706C22semidirect
105. #2705C22semidirect
106. #2705C22semidirect
107. #2703C22semidirect
108. #2703C22semidirect
109. #2702C22semidirect
110. #2700C22semidirect
111. #2696C22semidirect
112. #2696C22semidirect
113. #2687C22semidirect
114. #2681C22semidirect
115. #2680C22semidirect
116. #2679C22semidirect
117. #2678C22semidirect
118. #2678C22semidirect
119. #2676C22semidirect
120. #2672C22semidirect
121. #2672C22semidirect
122. #2672C22semidirect
123. #2671C22semidirect
124. #2670C22semidirect
125. #2670C22semidirect
126. #2669C22semidirect
127. #2668C22semidirect
128. #2626C22semidirect
129. #2626C22semidirect
130. #2625C22semidirect
131. #2624C22semidirect
132. #2624C22semidirect
133. #2624C22semidirect
134. #2623C22semidirect
135. #2618C22semidirect
138. #2617C22semidirect
139. #2617C22semidirect
140. #2617C22semidirect
141. #2617C22semidirect
142. #2617C22semidirect
143. #2617C22semidirect
144. #2617C22semidirect
145. #2617C22semidirect
146. #2617C22semidirect
147. #2617C22semidirect
148. #2613C22semidirect
149. #2561C22semidirect
150. #2554C22semidirect
151. #2549C22semidirect
152. #2540C22semidirect
153. #2539C22semidirect
154. #2539C22semidirect
155. #2539C22semidirect
156. #2539C22semidirect
157. #2534C22semidirect
158. #2534C22semidirect
159. #2534C22semidirect
160. #2512C22semidirect
161. #2504C22semidirect
162. #2504C22semidirect
163. #2501C22semidirect
164. #2500C22semidirect
165. #2498C22semidirect
166. #2489C22semidirect
167. #2488C22semidirect
168. #2487C22semidirect
169. #2487C22semidirect
170. #2486C22semidirect
171. #2485C22semidirect
172. #2482C22semidirect
173. #2482C22semidirect
174. #2479C22semidirect
175. #2479C22semidirect
176. #2477C22semidirect
177. #2475C22semidirect
178. #2472C22semidirect
179. #2472C22semidirect
180. #2471C22semidirect
181. #2467C22semidirect
182. #2466C22semidirect
183. #2464C22semidirect
184. #2459C22semidirect
185. #2456C22semidirect
186. #2455C22semidirect
187. #2455C22semidirect
188. #2450C22semidirect
189. #2445C22semidirect
190. #2444C22semidirect
191. #2444C22semidirect
192. #2437C22semidirect
193. #2437C22semidirect
194. #2436C22semidirect
195. #2427C22semidirect
196. #2425C22semidirect
197. #2425C22semidirect
198. #2425C22semidirect
200. #2424C22semidirect
201. #2424C22semidirect
202. #2424C22semidirect
203. #2424C22semidirect
204. #2422C22semidirect
205. #2420C22semidirect
206. #2418C22semidirect
207. #2418C22semidirect
208. #2418C22semidirect
209. #2418C22semidirect
210. #2418C22semidirect
211. #2415C22semidirect
212. #2415C22semidirect
213. #2415C22semidirect
214. #2414C22semidirect
215. #2414C22semidirect
216. #2413C22semidirect
217. #2412C22semidirect
218. #2412C22semidirect
219. #2412C22semidirect
220. #2412C22semidirect
221. #2411C22semidirect
222. #2411C22semidirect
223. #2410C22semidirect
224. #2410C22semidirect
225. #2409C22semidirect
227. #2406C22semidirect
228. #2405C22semidirect
229. #2405C22semidirect
230. #2405C22semidirect
231. #2404C22semidirect
232. #2404C22semidirect
233. #2403C22semidirect
234. #2403C22semidirect
235. C2×#397C22semidirect
236. C2×#394C22semidirect
237. C2×#392C22semidirect
238. #2376C22semidirect
239. #2359C22semidirect
240. #2358C22semidirect
241. #2349C22semidirect
242. #2345C22semidirect
243. #2342C22semidirect
244. #2342C22semidirect
246. D4×C22⋊C4C22semidirect
247. D4×C22⋊C4C22semidirect
248. #2335C22semidirect
249. #2322C22semidirect
250. #2322C22semidirect
251. #2321C22semidirect
252. #2321C22semidirect
253. #2321C22semidirect
254. #2317C22semidirect
255. #2316C22semidirect
256. #2316C22semidirect
257. #2315C22semidirect
258. #2313C22semidirect
259. #2312C22semidirect
260. #2311C22semidirect
261. #2311C22semidirect
262. #2309C22semidirect
263. C4×#123C22semidirect
264. C4×#120C22semidirect
265. C2×#386C22semidirect
266. C2×#386C22semidirect
267. #2280C22semidirect
268. C2×#380C22semidirect
314. C2×#126C23semidirect
315. C2×#126C23semidirect
316. C2×#126C23semidirect
317. C2×#126C23semidirect
318. C2×#125C23semidirect
319. C2×#125C23semidirect
324. C2×#124C23semidirect
325. C2×#124C23semidirect
326. C2×#124C23semidirect
331. C2×#123D4semidirect
351. C2×#123C23semidirect
352. C2×#123C23semidirect
353. C2×#123C23semidirect
354. C2×#123C23semidirect
355. C2×#123C23semidirect
356. C2×#123C23semidirect
357. C2×#123C23semidirect
358. C2×#123C23semidirect
369. C2×C22⋊Q8C23semidirect
370. C2×C22⋊Q8C23semidirect
371. C2×C22⋊Q8C23semidirect
372. C2×C22⋊Q8C23semidirect
373. C2×C22⋊Q8C23semidirect
395. C2×#121C23semidirect
396. C2×#121C23semidirect
397. C2×#121C23semidirect
398. C2×#121C23semidirect
399. C2×#121C23semidirect
400. C2×#121C23semidirect
422. C2×#120C23semidirect
423. C2×#120C23semidirect
424. C2×#120C23semidirect
441. C2×C4×D4C23semidirect
442. C2×C4×D4C23semidirect
454. C2×#117C23semidirect
493. C22×C22⋊C4C23semidirect
494. C22×C22⋊C4C23semidirect
498. #400C23semidirect
499. #400C23semidirect
500. #400C23semidirect
505. #399C23semidirect
506. #399C23semidirect
507. #399C23semidirect
508. #399C23semidirect
509. #399C23semidirect
510. #398C23semidirect
511. #398C23semidirect
512. #398C23semidirect
513. #398C23semidirect
525. #397C23semidirect
526. #397C23semidirect
527. #397C23semidirect
528. #397C23semidirect
529. #397C23semidirect
530. #397C23semidirect
531. #397C23semidirect
537. #396C23semidirect
538. #396C23semidirect
539. #396C23semidirect
540. #395C23semidirect
541. #395C23semidirect
566. #394C23semidirect
567. #394C23semidirect
568. #394C23semidirect
569. #394C23semidirect
570. #394C23semidirect
574. #393C23semidirect
575. #393C23semidirect
576. #393C23semidirect
594. #391C23semidirect
595. #391C23semidirect
596. #391C23semidirect
597. #391C23semidirect
598. #391C23semidirect
608. #390C23semidirect
609. #390C23semidirect
610. #390C23semidirect
611. #390C23semidirect
612. #390C23semidirect
613. #390C23semidirect
614. #390C23semidirect
615. #390C23semidirect
616. #390C23semidirect
617. #390C23semidirect
618. #390C23semidirect
619. #389C23semidirect
620. #389C23semidirect
621. #389C23semidirect
622. #389C23semidirect
623. #389C23semidirect
624. #389C23semidirect
625. #389C23semidirect
626. #389C23semidirect
627. #389C23semidirect
628. #389C23semidirect
629. #389C23semidirect
630. #389C23semidirect
631. #389C23semidirect
632. #389C23semidirect
633. #389C23semidirect
634. #389C23semidirect
635. #389C23semidirect
647. #388C23semidirect
648. #388C23semidirect
649. #388C23semidirect
650. #388C23semidirect
651. #388C23semidirect
652. #388C23semidirect
653. #388C23semidirect
654. #388C23semidirect
655. #388C23semidirect
656. #388C23semidirect
657. #388C23semidirect
658. #388C23semidirect
659. #388C23semidirect
660. #388C23semidirect
661. #388C23semidirect
662. #387C23semidirect
663. #387C23semidirect
664. #387C23semidirect
665. #387C23semidirect
666. #387C23semidirect
667. #387C23semidirect
668. #387C23semidirect
669. #387C23semidirect
703. #386C23semidirect
704. #386C23semidirect
705. #386C23semidirect
706. #386C23semidirect
718. #385C23semidirect
719. #385C23semidirect
720. #385C23semidirect
721. #385C23semidirect
722. #385C23semidirect
723. #385C23semidirect
724. #385C23semidirect
725. #385C23semidirect
726. #384C23semidirect
727. #382C23semidirect
728. #382C23semidirect
734. #381C23semidirect
748. #380C23semidirect
749. #380C23semidirect
750. #380C23semidirect
751. #380C23semidirect
752. #380C23semidirect
753. #380C23semidirect
762. #379C23semidirect
763. C4×C4⋊C4C23semidirect
764. C4×C4⋊C4C23semidirect
771. C4×C22⋊C4C23semidirect
772. C4×C22⋊C4C23semidirect
775. C2×#95C23semidirect
929. #123C2×D4semidirect
930. #123C2×D4semidirect
1026. C2×C4⋊C4C2×D4semidirect
1027. C2×C4⋊C4C2×D4semidirect
1097. C2×C22⋊C4C2×D4semidirect
1098. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35342
C22×#5512
#501792
#488352
#488302
#487902
#440202
#440012
#439592
#439322
#397222
#391292
#380232
#380212
#376542
#376442
#369712
#369672
#369612
#369572
#362362
#360982
#352632
#352622
#351502
#350942
#350502
#349862
#349842
C2×#26172
#343762