Finite Group Databasebeta

← #7732515

Subgroups — #7732515

Order 512.

8894 conjugacy classes of subgroups.

The subgroup lattice has 2047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic, complemented
2C2×#3459C211yesmaximal, characteristic, complemented
3#47844C214yesmaximal, complemented
4#47843C214yesmaximal, complemented
5#46368C214yesmaximal, complemented
6#46367C214yesmaximal, complemented
7#42998C214yesmaximal, complemented
8#42996C214yesmaximal, complemented
9#38909C212yesmaximal, complemented
10#38902C212yesmaximal, complemented
11#38026C212yesmaximal, complemented
12#38025C212yesmaximal, complemented
13#37768C212yesmaximal, complemented
14#37752C212yesmaximal, complemented
15#37692C212yesmaximal, complemented
16#37672C212yesmaximal, complemented
17#37657C212yesmaximal, complemented
18#37648C212yesmaximal, complemented
19#37439C211yesmaximal, characteristic, complemented
20#37278C212yesmaximal, complemented
21#37268C212yesmaximal, complemented
22#36097C212yesmaximal, complemented
23D4×#121C212yesmaximal, complemented
24#35520C212yesmaximal, complemented
25#35512C212yesmaximal, complemented
26#35251C211yesmaximal, characteristic, complemented
27#35000C211yesmaximal, characteristic, complemented
28C2×#2407C211yesmaximal, characteristic, complemented
29#34360C211yesmaximal, characteristic, complemented
30C22×H(5,𝔽2)C2211yescharacteristic, complemented
31C23×#41C2211yescharacteristic, complemented
32#3488—216no—
33C2×#550C2212yescomplemented
34C2×#548C2212yescomplemented
35C2×#546C2212yescomplemented
36C2×#546C2214yescomplemented
37C2×D42C2212yescomplemented
38C2×D42C2214yescomplemented
39C2×D42C2214yescomplemented
40#3459—216no—
41C2×#543C2211yescharacteristic, complemented
42C2×#539C2212yescomplemented
43C2×#539C2211yescharacteristic, complemented
44C2×#539C2211yescharacteristic, complemented
45C2×#539C2212yescomplemented
46C2×#538C2212yescomplemented
47C2×#538C2212yescomplemented
48C2×#538C2212yescomplemented
49C2×#537C2212yescomplemented
50C2×#537C2211yescharacteristic, complemented
51C2×#537C2211yescharacteristic, complemented
52C2×#537C2211yescharacteristic, complemented
53C2×#535C2212yescomplemented
54C2×#535C2211yescharacteristic, complemented
55C2×#534C2211yescharacteristic, complemented
56C2×#534C2212yescomplemented
57C2×#534C2212yescomplemented
58C2×#529C2212yescomplemented
59C2×#529C2212yescomplemented
60C2×#529C2212yescomplemented
61C2×#525C2211yescharacteristic
62C2×#525C2212yescomplemented
63C2×#525C2211yescharacteristic, complemented
64C2×#525C2212yescomplemented
65C2×#525C2212yescomplemented
66C2×#525C2212yescomplemented
67C22×C22⋊Q8C2211yescharacteristic, complemented
68C22×#121C2212yes—
69C22×#121C2211yescharacteristic, complemented
70C22×#121C2212yescomplemented
71C22×#121C2211yescharacteristic, complemented
72C2×#520C2211yescharacteristic, complemented
73C22×C4×D4C2212yescomplemented
74C22×C4×D4C2211yescharacteristic, complemented
75#2856C2212yescomplemented
76#2854C2212yescomplemented
77#2850C2212yescomplemented
78#2848C2212yescomplemented
79#2848C2212yescomplemented
80#2847C2212yescomplemented
81#2847C2212yescomplemented
82#2847C2212yescomplemented
83#2813C2214yescomplemented
84#2732C2214yescomplemented
85#2728C2214yescomplemented
86#2715C2214yescomplemented
87#2714C2214yescomplemented
88#2714C2214yescomplemented
89#2712C2214yescomplemented
90#2711C2214yescomplemented
91#2711C2214yescomplemented
92#2708C2214yescomplemented
93#2704C2214yescomplemented
94#2702C2214yescomplemented
95#2701C2214yescomplemented
96#2696C2214yescomplemented
97#2694C2214yescomplemented
98#2691C2214yescomplemented
99#2691C2214yescomplemented
100#2688C2214yescomplemented
101#2685C2214yescomplemented
102#2685C2214yescomplemented
103#2684C2214yescomplemented
104#2682C2214yescomplemented
105#2681C2214yescomplemented
106#2681C2214yescomplemented
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2676C2214yescomplemented
110#2675C2214yescomplemented
111#2673C2214yescomplemented
112#2673C2214yescomplemented
113#2671C2214yescomplemented
114#2671C2214yescomplemented
115#2671C2214yescomplemented
116#2671C2214yescomplemented
117#2670C2214yescomplemented
118#2670C2214yescomplemented
119#2669C2214yescomplemented
120#2669C2214yescomplemented
121#2669C2214yescomplemented
122#2668C2214yescomplemented
123#2668C2214yescomplemented
124#2656C2212yescomplemented
125#2639C2212yescomplemented
126#2626C2212yescomplemented
127#2625C2212yescomplemented
128#2624C2212yescomplemented
129#2624C2212yescomplemented
130#2620C2212yescomplemented
131#2619C2212yescomplemented
132#2618C2212yescomplemented
133#2617C2212yescomplemented
134#2617C2212yescomplemented
135#2616C2212yescomplemented
136#2615C2212yescomplemented
137#2615C2212yescomplemented
138#2592C2212yescomplemented
139#2582C2212yescomplemented
140#2580C2212yescomplemented
141#2559C2214yescomplemented
142#2548C2212yescomplemented
143#2544C2214yescomplemented
144#2543C2214yescomplemented
145#2543C2214yescomplemented
146#2541C2212yescomplemented
147#2540C2212yescomplemented
148#2539C2214yescomplemented
149#2537C2212yescomplemented
150#2536C2212yescomplemented
151#2534C2214yescomplemented
152#2487C2212yescomplemented
153#2486C2212yescomplemented
154#2480C2214yescomplemented
155#2479C2214yescomplemented
156#2477C2214yescomplemented
157#2473C2214yescomplemented
158#2472C2214yescomplemented
159#2472C2214yescomplemented
160#2468C2214yescomplemented
161#2464C2214yescomplemented
162#2464C2214yescomplemented
163#2464C2214yescomplemented
164#2463C2214yescomplemented
165#2463C2214yescomplemented
166#2461C2214yescomplemented
167#2459C2214yescomplemented
168#2456C2214yescomplemented
169#2455C2214yescomplemented
170#2454C2214yescomplemented
171#2450C2214yescomplemented
172#2449C2214yescomplemented
173#2443C2214yescomplemented
174#2443C2214yescomplemented
175#2437C2214yescomplemented
176#2430C2214yescomplemented
177#2428C2214yescomplemented
178#2428C2214yescomplemented
179#2428C2214yescomplemented
180#2427C2214yescomplemented
181#2425C2214yescomplemented
182#2425C2214yescomplemented
183#2424C2214yescomplemented
184#2424C2214yescomplemented
185#2424C2214yescomplemented
186#2418C2214yescomplemented
187#2417C2212yescomplemented
188#2416C2212yescomplemented
189#2416C2212yescomplemented
190#2416C2212yescomplemented
191#2416C2214yescomplemented
192#2416C2212yescomplemented
193#2416C2212yescomplemented
194#2415C2212yescomplemented
195#2414C2212yescomplemented
196#2410C2214yescomplemented
197#2410C2214yescomplemented
198#2410C2214yescomplemented
199#2410C2214yescomplemented
200#2410C2214yescomplemented
201#2410C2214yescomplemented
202#2410C2214yescomplemented
203#2409C2212yescomplemented
204#2408C2214yescomplemented
205#2408C2212yescomplemented
206#2408C2212yescomplemented
207#2408C2212yescomplemented
208#2408C2212yescomplemented
209#2408C2214yescomplemented
210#2408C2214yescomplemented
211#2408C2212yescomplemented
212#2407C2212yescomplemented
213#2407C2212yescomplemented
214#2407C2212yescomplemented
215#2407C2212yescomplemented
216#2407C2214yescomplemented
217#2407C2214yescomplemented
218#2407C2214yescomplemented
219#2407C2212yescomplemented
220#2407C2212yescomplemented
221#2407C2212yescomplemented
222#2407C2214yescomplemented
223#2407C2212yescomplemented
224#2405C2214yescomplemented
225#2405C2214yescomplemented
226#2405C2214yescomplemented
227#2403C2214yescomplemented
228#2403C2214yescomplemented
229C2×#394C2212yescomplemented
230C2×#392C2212yescomplemented
231#2376C2214yescomplemented
232#2361C2214yescomplemented
233#2358C2214yescomplemented
234#2358C2214yescomplemented
235#2352C2212yescomplemented
236#2352C2212yescomplemented
237D4×C4⋊C4C2212yescomplemented
238D4×C4⋊C4C2212yescomplemented
239D4×C22⋊C4C2214yescomplemented
240#2329C2212yescomplemented
241#2329C2212yescomplemented
242#2325C2212yescomplemented
243#2325C2212yescomplemented
244#2324C2212yescomplemented
245#2323C2212yescomplemented
246#2314C2212yescomplemented
247#2311C2212yescomplemented
248#2311C2212yescomplemented
249#2311C2211yescharacteristic, complemented
250#2311C2211yescharacteristic, complemented
251#2309C2212yescomplemented
252#2308C2212yescomplemented
253C4×C22⋊Q8C2212yescomplemented
254C4×#121C2212yescomplemented
255C2×#391C2211yescharacteristic, complemented
256C2×#390C2211yescharacteristic, complemented
257C2×#386C2212yescomplemented
258C2×#385C2212yescomplemented
259C2×#380C2211yescharacteristic, complemented
260C2×#380C2211yescharacteristic, complemented
261C2×H(5,𝔽2)—28no—
262C2×H(5,𝔽2)—44no—
263C2×H(5,𝔽2)—44no—
264C22×#41—28no—
265C22×#41—44no—
266C22×#41—44no—
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C22×#41C2311yescharacteristic
270C22×#41C2312yes—
271C22×#41C2312yes—
272C22×#41C2311yescharacteristic
273C22×#41C2312yes—
274C22×#41C2312yes—
275C22×#41C2311yescharacteristic
276C22×#41C2311yescharacteristic
277C23×Q8C2311yescharacteristic
278C23×D4C2312yes—
279C23×D4C2311yescharacteristic
280C23×D4C2311yescharacteristic
281C23×D4C2312yes—
282C23×D4C2312yes—
283C23×D4C2312yes—
284C23×D4C2312yes—
285C23×D4C2314yes—
286C23×D4C2311yescharacteristic
287C23×D4C2314yes—
288C23×D4C2312yes—
289C23×D4C2314yes—
290C24×C4C2312yes—
291C24×C4C2311yescharacteristic
292C24×C4C2312yes—
293C24×C4C2311yescharacteristic
294#550—216no—
295#548—216no—
296#546—232no—
297#546—216no—
298D42—232no—
299D42—216no—
300D42—416no—
301#543—28no—
302#539—216no—
303#539—28no—
304#539—216no—
305#539—28no—
306#538—216no—
307#538—216no—
308#538—216no—
309#537—28no—
310#537—216no—
311#537—44no—
312#537—44no—
313#535—216no—
314#535—28no—
315#534—28no—
316#534—216no—
317#534—48no—
318C2×#127C2312yes—
319C2×#127C2314yes—
320C2×#127C2314yes—
321#529—216no—
322#529—216no—
323#529—216no—
324C2×#126C2312yes—
325C2×#126C2312yes—
326C2×#126C2312yes—
327C2×#126C2312yes—
328C2×#126C2312yes—
329C2×#126C2312yes—
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#125C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2314yes—
339#525—216no—
340#525—28no—
341#525—216no—
342#525—216no—
343#525—48no—
344#525D4116yescomplemented
345C2×#123C2312yes—
346C2×#123C2312yes—
347C2×#123C2312yes—
348C2×#123C2312yes—
349C2×#123C2314yes—
350C2×#123C2312yes—
351C2×#123C2312yes—
352C2×#123C2312yes—
353C2×#123C2312yes—
354C2×#123C2312yes—
355C2×#123C2312yes—
356C2×#123C2312yes—
357C2×#123C2314yes—
358C2×#123C2314yes—
359C2×#123C2314yes—
360C2×#123C2312yes—
361C2×C22⋊Q8—44no—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2311yescharacteristic
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2311yescharacteristic
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2312yes—
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2312yes—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2314yes—
376C2×C22⋊Q8C2312yes—
377C2×C22⋊Q8C2312yes—
378C2×C22⋊Q8C2312yes—
379C2×C22⋊Q8C2312yes—
380C2×C22⋊Q8C2314yes—
381C2×C22⋊Q8C2311yescharacteristic
382C2×C22⋊Q8C2311yescharacteristic
383C2×#121—28no—
384C2×#121—216no—
385C2×#121—44no—
386C2×#121—48no—
387C2×#121C2312yes—
388C2×#121C2311yescharacteristic
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2311yescharacteristic
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2312yes—
395C2×#121C2312yes—
396C2×#121C2312yes—
397C2×#121C2314yes—
398C2×#121C2312yes—
399C2×#121C2314yes—
400C2×#121C2312yes—
401C2×#121C2312yes—
402C2×#121C2312yes—
403C2×#121C2312yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2312yes—
407C2×#121C2312yes—
408C2×#121C2314yes—
409C2×#121C2314yes—
410C2×#121C2314yes—
411C2×#121C2314yes—
412C2×#121C2312yes—
413C2×#121C2312yes—
414C2×#121C2312yes—
415C2×#121C2312yes—
416C2×#121C2312yes—
417C2×#121C2312yes—
418C2×#121C2314yes—
419C2×#121C2312yes—
420C2×#121C2312yes—
421C2×#121C2314yes—
422C2×#121C2314yes—
423C2×#121C2314yes—
424C2×#121C2314yes—
425C2×#121C2314yes—
426C2×#121C2314yes—
427C2×#121C2314yes—
428C2×#121C2314yes—
429C2×#121C2314yes—
430C2×#121C2314yes—
431C2×#121C2314yes—
432C2×#121C2314yes—
433C2×#121C2311yescharacteristic
434C2×#121C2311yescharacteristic
435C2×#120C2314yes—
436C2×#120C2312yes—
437C2×#120C2312yes—
438C2×#120C2312yes—
439C2×#120C2314yes—
440C2×#120C2312yes—
441C2×#120C2312yes—
442C2×#120C2314yes—
443C2×#120C2314yes—
444C2×#120C2314yes—
445C2×#120C2314yes—
446C2×#120C2314yes—
447C2×#120C2314yes—
448C2×#120C2314yes—
449C2×#120C2314yes—
450C2×#120C2314yes—
451C2×#120C2314yes—
452C2×#120C2312yes—
453#520—28no—
454C2×C4×Q8C2312yes—
455C2×C4×Q8C2312yes—
456C2×C4×D4—28no—
457C2×C4×D4—216no—
458C2×C4×D4C2312yes—
459C2×C4×D4C2312yes—
460C2×C4×D4C2314yes—
461C2×C4×D4C2312yes—
462C2×C4×D4C2312yes—
463C2×C4×D4C2312yes—
464C2×C4×D4C2312yes—
465C2×C4×D4C2312yes—
466C2×C4×D4C2312yes—
467C2×C4×D4C2312yes—
468C2×C4×D4C2312yes—
469C2×C4×D4C2312yes—
470C2×C4×D4C2312yes—
471C2×C4×D4C2314yes—
472C2×C4×D4C2312yes—
473C2×C4×D4C2312yes—
474C2×C4×D4C2314yes—
475C2×C4×D4C2314yes—
476C2×C4×D4C2314yes—
477C2×C4×D4C2314yes—
478C2×C4×D4C2314yes—
479C2×C4×D4C2314yes—
480C2×C4×D4C2312yes—
481C2×C4×D4C2312yes—
482C2×#117C2312yes—
483C2×#117C2311yescharacteristic
484C2×#117C2312yes—
485C2×#117C2312yes—
486C2×#117C2312yes—
487C2×#117C2311yescharacteristic
488C22×C4⋊C4C2311yescharacteristic
489C22×C4⋊C4C2312yes—
490C22×C4⋊C4C2312yes—
491C22×C4⋊C4C2311yescharacteristic
492C22×C4⋊C4C2312yes—
493C22×C4⋊C4C2311yescharacteristic
494C22×C4⋊C4C2311yescharacteristic
495C22×C4⋊C4C2311yescharacteristic
496C22×C4⋊C4C2311yescharacteristic
497C22×C4⋊C4C2312yes—
498C22×C22⋊C4C2311yescharacteristic
499C22×C22⋊C4C2312yes—
500C22×C22⋊C4C2311yescharacteristic
501C22×C22⋊C4C2312yes—
502C22×C22⋊C4C2312yes—
503C22×C22⋊C4C2314yes—
504C22×C22⋊C4C2312yes—
505C22×C22⋊C4C2312yes—
506C22×C22⋊C4C2314yes—
507C22×C22⋊C4C2312yes—
508C22×C22⋊C4C2312yes—
509C22×C22⋊C4C2312yes—
510C22×C22⋊C4C2312yes—
511C22×C42C2312yes—
512C22×C42C2311yescharacteristic
513#400C2314yes—
514#400C2314yes—
515#399C2314yes—
516#399C2314yes—
517#399C2314yes—
518#399C2314yes—
519#399C2314yes—
520#398C2314yes—
521#398C2314yes—
522#398C2314yes—
523#398C2314yes—
524#398C2314yes—
525#398C2314yes—
526#397C2314yes—
527#397C2314yes—
528#397C2314yes—
529#397C2314yes—
530#397C2314yes—
531#397C2314yes—
532#397C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2314yes—
536#396C2314yes—
537#396C2314yes—
538#396C2314yes—
539#396C2314yes—
540#396C2314yes—
541#395C2314yes—
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#394C2314yes—
567#394C2314yes—
568#394C2314yes—
569#394C2314yes—
570#394C2314yes—
571#394C2314yes—
572#394C2314yes—
573#394C2314yes—
574#394C2314yes—
575#393C2314yes—
576#393C2314yes—
577#393C2314yes—
578#393C2314yes—
579#392C2314yes—
580#392C2314yes—
581#392C2314yes—
582#392C2314yes—
583#392C2314yes—
584#392C2314yes—
585#392C2314yes—
586#392C2314yes—
587#392C2314yes—
588#392C2314yes—
589#392C2314yes—
590#392C2314yes—
591#392C2314yes—
592#392C2314yes—
593#392C2314yes—
594#392C2314yes—
595#392C2314yes—
596#392C2314yes—
597#392C2314yes—
598#392C2314yes—
599#392C2314yes—
600#392C2314yes—
601#391C2312yes—
602#391C2312yes—
603#391C2314yes—
604#391C2312yes—
605#391C2314yes—
606#391C2312yes—
607#391C2314yes—
608#390C2312yes—
609#390C2312yes—
610#390C2312yes—
611#390C2312yes—
612#390C2314yes—
613#390C2314yes—
614#390C2312yes—
615#390C2312yes—
616#390C2312yes—
617#390C2314yes—
618#390C2314yes—
619#390C2314yes—
620#390C2314yes—
621#390C2314yes—
622#390C2314yes—
623#390C2314yes—
624#390C2312yes—
625#390C2314yes—
626#390C2314yes—
627#390C2314yes—
628#389C2312yes—
629#389C2314yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2314yes—
634#389C2314yes—
635#389C2314yes—
636#389C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#384C2312yes—
718#382C2312yes—
719#381C2314yes—
720#380C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2314yes—
729#380C2314yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#379C2314yes—
743#379C2314yes—
744#379C2314yes—
745#379C2314yes—
746#379C2314yes—
747#379C2314yes—
748#379C2314yes—
749#379C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C22⋊C4C2314yes—
754C4×C22⋊C4C2314yes—
755C4×C22⋊C4C2314yes—
756C4×C22⋊C4C2314yes—
757C2×#95C2312yes—
758C2×#95C2312yes—
759C2×#95C2312yes—
760C2×#95C2312yes—
761C25C2412yes—
762C25C2414yes—
763C25C2412yes—
764C25C2411yescharacteristic
765C25C2411yescharacteristic
766C25C2412yes—
767H(5,𝔽2)—464no—
768C2×#41—28no—
769C2×#41—24no—
770C2×#41—28no—
771C2×#41—24no—
772C2×#41—24no—
773C2×#41—24no—
774C2×#41—24no—
775C2×#41—28no—
776C2×#41—24no—
777C2×#41—24no—
778C2×#41—28no—
779C2×#41—28no—
780C2×#41—24no—
781C2×#41—24no—
782C2×#41—42no—
783C2×#41—42no—
784C2×#41—44no—
785C2×#41—42no—
786C2×#41—42no—
787C2×#41—44no—
788C2×#41—44no—
789C2×#41—44no—
790C2×#41—42no—
791C2×#41—42no—
792C2×#41—42no—
793C2×#41—42no—
794C2×#41—44no—
795C2×#41—44no—
796C2×#41—44no—
797C2×#41—464no—
798C2×#41C2×D418yescomplemented
799C22×Q8—24no—
800C22×Q8—24no—
801C22×Q8—42no—
802C22×Q8C2411yescharacteristic
803C22×Q8C2412yes—
804C22×Q8C2411yescharacteristic
805C22×Q8C2412yes—
806C22×Q8C2411yescharacteristic
807C22×Q8C2411yescharacteristic
808C22×D4—24no—
809C22×D4—28no—
810C22×D4—24no—
811C22×D4—28no—
812C22×D4—28no—
813C22×D4—28no—
814C22×D4—28no—
815C22×D4—28no—
816C22×D4—216no—
817C22×D4—24no—
818C22×D4—28no—
819C22×D4—216no—
820C22×D4—24no—
821C22×D4—24no—
822C22×D4—28no—
823C22×D4—42no—
824C22×D4—44no—
825C22×D4—44no—
826C22×D4—44no—
827C22×D4—42no—
828C22×D4—42no—
829C22×D4—48no—
830C22×D4—42no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—44no—
834C22×D4—48no—
835C22×D4—44no—
836C22×D4—48no—
837C22×D4—44no—
838C22×D4—48no—
839C22×D4—48no—
840C22×D4—48no—
841C22×D4—44no—
842C22×D4—82no—
843C22×D4—84no—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2412yes—
848C22×D4C2411yescharacteristic
849C22×D4C2412yes—
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C22×D4C2412yes—
860C22×D4C2411yescharacteristic
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2412yes—
866C22×D4C2411yescharacteristic
867C22×D4C2414yes—
868C22×D4C2414yes—
869C22×D4C2414yes—
870C22×D4C2412yes—
871C22×D4C2414yes—
872C22×D4C2414yes—
873C22×D4C2414yes—
874C22×D4C2412yes—
875C22×D4C2414yes—
876C22×D4C2414yes—
877C22×D4C2414yes—
878C22×D4C2412yes—
879C22×D4C2411yescharacteristic
880C22×D4C2412yes—
881C23×C4—28no—
882C23×C4—24no—
883C23×C4—28no—
884C23×C4—42no—
885C23×C4—42no—
886C23×C4—44no—
887C23×C4—42no—
888C23×C4—44no—
889C23×C4—42no—
890C23×C4—44no—
891C23×C4—44no—
892C23×C4C2×D418yescomplemented
893C23×C4C2411yescharacteristic
894C23×C4C2412yes—
895C23×C4C2412yes—
896C23×C4C2412yes—
897C23×C4C2412yes—
898C23×C4C2412yes—
899C23×C4C2412yes—
900C23×C4C2414yes—
901C23×C4C2412yes—
902C23×C4C2411yescharacteristic
903C23×C4C2411yescharacteristic
904C23×C4C2412yes—
905C23×C4C2411yescharacteristic
906C23×C4C2412yes—
907C23×C4C2411yescharacteristic
908C23×C4C2411yescharacteristic
909C23×C4C2412yes—
910C23×C4C2412yes—
911C23×C4C2412yes—
912C23×C4C2412yes—
913C23×C4C2414yes—
914C23×C4C2412yes—
915C23×C4C2412yes—
916C23×C4C2412yes—
917C23×C4C2412yes—
918C23×C4C2412yes—
919C23×C4C2414yes—
920C23×C4C2412yes—
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2411yescharacteristic
924#127—216no—
925#127—28no—
926#127—48no—
927#126—28no—
928#126—28no—
929#126—28no—
930#126—28no—
931#126—28no—
932#126—28no—
933#125—28no—
934#125—28no—
935#125—28no—
936#124—28no—
937#124—28no—
938#124—28no—
939#124—216no—
940#124—28no—
941#124—84no—
942#123—28no—
943#123—28no—
944#123—28no—
945#123—28no—
946#123—28no—
947#123—216no—
948#123—28no—
949#123—28no—
950#123—28no—
951#123—28no—
952#123—28no—
953#123—28no—
954#123—48no—
955#123—48no—
956#123—48no—
957#123C2×D4116yescomplemented
958C22⋊Q8—28no—
959C22⋊Q8—28no—
960C22⋊Q8—28no—
961C22⋊Q8—28no—
962C22⋊Q8—28no—
963C22⋊Q8—24no—
964C22⋊Q8—24no—
965C22⋊Q8—28no—
966C22⋊Q8—28no—
967C22⋊Q8—28no—
968C22⋊Q8—28no—
969C22⋊Q8—216no—
970C22⋊Q8—28no—
971C22⋊Q8—28no—
972C22⋊Q8—44no—
973C22⋊Q8—48no—
974C22⋊Q8—44no—
975C22⋊Q8—44no—
976C22⋊Q8—44no—
977C22⋊Q8C2×D418yescomplemented
978C22⋊Q8C2×D418yescomplemented
979#121—28no—
980#121—216no—
981#121—28no—
982#121—28no—
983#121—28no—
984#121—28no—
985#121—28no—
986#121—216no—
987#121—28no—
988#121—28no—
989#121—28no—
990#121—28no—
991#121—28no—
992#121—28no—
993#121—24no—
994#121—24no—
995#121—28no—
996#121—28no—
997#121—28no—
998#121—216no—
999#121—216no—
1000#121—28no—
1001#121—28no—
1002#121—216no—
1003#121—216no—
1004#121—44no—
1005#121—48no—
1006#121—48no—
1007#121—48no—
1008#121—48no—
1009#121—48no—
1010#121—48no—
1011#121—48no—
1012#121—48no—
1013#121—48no—
1014#121—44no—
1015#121—44no—
1016#121—44no—
1017#121—44no—
1018#121—44no—
1019#121—44no—
1020#121—48no—
1021#121—44no—
1022#121—48no—
1023#121—48no—
1024#121—84no—
1025#121C2×D418yes—
1026#121C2×D418yescomplemented
1027#120—28no—
1028#120—216no—
1029#120—28no—
1030#120—28no—
1031#120—28no—
1032#120—216no—
1033#120—28no—
1034#120—216no—
1035#120—216no—
1036#120—216no—
1037#120—48no—
1038#120—48no—
1039#120—48no—
1040#120—48no—
1041#120—48no—
1042#120—84no—
1043#120—84no—
1044#120C2×D4116yescomplemented
1045C4×Q8—28no—
1046C4×Q8—28no—
1047C4×D4—28no—
1048C4×D4—28no—
1049C4×D4—28no—
1050C4×D4—28no—
1051C4×D4—28no—
1052C4×D4—28no—
1053C4×D4—28no—
1054C4×D4—28no—
1055C4×D4—28no—
1056C4×D4—28no—
1057C4×D4—216no—
1058C4×D4—28no—
1059C4×D4—28no—
1060C4×D4—216no—
1061C4×D4—216no—
1062C4×D4—28no—
1063C4×D4—28no—
1064C4×D4—48no—
1065C4×D4—48no—
1066C4×D4—48no—
1067C4×D4—48no—
1068C4×D4—84no—
1069C4×D4C2×D4116yescomplemented
1070C4×D4C2×D4116yescomplemented
1071#117—24no—
1072#117—28no—
1073#117—28no—
1074#117—28no—
1075#117—44no—
1076#117C2×D418yescomplemented
1077C2×C4⋊C4—24no—
1078C2×C4⋊C4—24no—
1079C2×C4⋊C4—28no—
1080C2×C4⋊C4—28no—
1081C2×C4⋊C4—42no—
1082C2×C4⋊C4—44no—
1083C2×C4⋊C4—42no—
1084C2×C4⋊C4—44no—
1085C2×C4⋊C4—42no—
1086C2×C4⋊C4—42no—
1087C2×C4⋊C4C2412yes—
1088C2×C4⋊C4C2412yes—
1089C2×C4⋊C4C2412yes—
1090C2×C4⋊C4C2412yes—
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2412yes—
1093C2×C4⋊C4C2412yes—
1094C2×C4⋊C4C2412yes—
1095C2×C4⋊C4C2412yes—
1096C2×C4⋊C4C2412yes—
1097C2×C4⋊C4C2412yes—
1098C2×C4⋊C4C2414yes—
1099C2×C4⋊C4C2414yes—
1100C2×C4⋊C4C2411yescharacteristic
1101C2×C4⋊C4C2412yes—
1102C2×C4⋊C4C2412yes—
1103C2×C4⋊C4C2411yescharacteristic
1104C2×C4⋊C4C2412yes—
1105C2×C4⋊C4C2412yes—
1106C2×C4⋊C4C2414yes—
1107C2×C4⋊C4C2414yes—
1108C2×C4⋊C4C2412yes—
1109C2×C4⋊C4C2412yes—
1110C2×C4⋊C4C2412yes—
1111C2×C4⋊C4C2412yes—
1112C2×C4⋊C4C2412yes—
1113C2×C4⋊C4C2414yes—
1114C2×C4⋊C4C2412yes—
1115C2×C4⋊C4C2412yes—
1116C2×C4⋊C4C2412yes—
1117C2×C4⋊C4C2412yes—
1118C2×C4⋊C4C2414yes—
1119C2×C4⋊C4C2414yes—
1120C2×C4⋊C4C2414yes—
1121C2×C4⋊C4C2414yes—
1122C2×C4⋊C4C2414yes—
1123C2×C4⋊C4C2414yes—
1124C2×C4⋊C4C2414yes—
1125C2×C4⋊C4C2414yes—
1126C2×C4⋊C4C2411yescharacteristic
1127C2×C4⋊C4C2412yes—
1128C2×C4⋊C4C2411yescharacteristic
1129C2×C4⋊C4C2412yes—
1130C2×C22⋊C4—24no—
1131C2×C22⋊C4—24no—
1132C2×C22⋊C4—28no—
1133C2×C22⋊C4—28no—
1134C2×C22⋊C4—28no—
1135C2×C22⋊C4—216no—
1136C2×C22⋊C4—44no—
1137C2×C22⋊C4—44no—
1138C2×C22⋊C4—48no—
1139C2×C22⋊C4—44no—
1140C2×C22⋊C4—44no—
1141C2×C22⋊C4—82no—
1142C2×C22⋊C4—82no—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2412yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2412yes—
1148C2×C22⋊C4C2412yes—
1149C2×C22⋊C4C2412yes—
1150C2×C22⋊C4C2412yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2412yes—
1153C2×C22⋊C4C2412yes—
1154C2×C22⋊C4C2412yes—
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2414yes—
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2412yes—
1163C2×C22⋊C4C2412yes—
1164C2×C22⋊C4C2412yes—
1165C2×C22⋊C4C2412yes—
1166C2×C22⋊C4C2412yes—
1167C2×C22⋊C4C2414yes—
1168C2×C22⋊C4C2414yes—
1169C2×C22⋊C4C2414yes—
1170C2×C22⋊C4C2414yes—
1171C2×C22⋊C4C2412yes—
1172C2×C22⋊C4C2412yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2412yes—
1175C2×C22⋊C4C2414yes—
1176C2×C22⋊C4C2414yes—
1177C2×C22⋊C4C2414yes—
1178C2×C22⋊C4C2414yes—
1179C2×C22⋊C4C2414yes—
1180C2×C22⋊C4C2414yes—
1181C2×C22⋊C4C2414yes—
1182C2×C22⋊C4C2414yes—
1183C2×C22⋊C4C2414yes—
1184C2×C22⋊C4C2414yes—
1185C2×C22⋊C4C2414yes—
1186C2×C22⋊C4C2414yes—
1187C2×C22⋊C4C2414yes—
1188C2×C22⋊C4C2414yes—
1189C2×C22⋊C4C2414yes—
1190C2×C22⋊C4C2414yes—
1191C2×C22⋊C4C2414yes—
1192C2×C22⋊C4C2414yes—
1193C2×C22⋊C4C2414yes—
1194C2×C22⋊C4C2414yes—
1195C2×C22⋊C4C2414yes—
1196C2×C22⋊C4C2414yes—
1197C2×C22⋊C4C2414yes—
1198C2×C22⋊C4C2414yes—
1199C2×C22⋊C4C2414yes—
1200C2×C22⋊C4C2414yes—
1201C2×C22⋊C4C2414yes—
1202C2×C22⋊C4C2414yes—
1203C2×C22⋊C4C2414yes—
1204C2×C22⋊C4C2414yes—
1205C2×C22⋊C4C2414yes—
1206C2×C22⋊C4C2414yes—
1207C2×C22⋊C4C2414yes—
1208C2×C22⋊C4C2412yes—
1209C2×C22⋊C4C2412yes—
1210C2×C22⋊C4C2412yes—
1211C2×C22⋊C4C2412yes—
1212C2×C22⋊C4C2412yes—
1213C2×C42—24no—
1214C2×C42—28no—
1215C2×C42C2412yes—
1216C2×C42C2412yes—
1217C2×C42C2414yes—
1218C2×C42C2412yes—
1219C2×C42C2412yes—
1220C2×C42C2412yes—
1221C2×C42C2414yes—
1222C2×C42C2414yes—
1223C2×C42C2414yes—
1224C2×C42C2412yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228#95C2414yes—
1229#95C2414yes—
1230#95C2414yes—
1231#95C2414yes—
1232#95C2414yes—
1233#95C2414yes—
1234#95C2414yes—
1235#95C2414yes—
1236#95C2414yes—
1237#95C2414yes—
1238#95C2414yes—
1239#95C2414yes—
1240#95C2414yes—
1241#95C2414yes—
1242#95C2414yes—
1243#95C2414yes—
1244#95C2414yes—
1245#95C2414yes—
1246#95C2414yes—
1247#95C2414yes—
1248#95C2414yes—
1249#95C2414yes—
1250#95C2414yes—
1251C24—22no—
1252C24—22no—
1253C24—22no—
1254C24—22no—
1255C24—24no—
1256C24—24no—
1257C24—24no—
1258C24—24no—
1259C24—24no—
1260C24—24no—
1261C24—28no—
1262C24—24no—
1263C24—28no—
1264C24—41no—
1265C24—41no—
1266C24—42no—
1267C24—41no—
1268C24—42no—
1269C24—41no—
1270C24—41no—
1271C24—42no—
1272C24—42no—
1273C24—41no—
1274C24—42no—
1275C24—42no—
1276C24—41no—
1277C24—41no—
1278C24—44no—
1279C24—42no—
1280C24—42no—
1281C24—42no—
1282C24—42no—
1283C24—44no—
1284C24—44no—
1285C24—44no—
1286C24—44no—
1287C24—42no—
1288C24—42no—
1289C24—42no—
1290C24—42no—
1291C24C22×D414yes—
1292C24H(5,𝔽2)14yescomplemented
1293C24C2514yes—
1294C24C2512yes—
1295C24C2512yes—
1296C24C2511yescharacteristic
1297C24C2512yes—
1298C24C2511yescharacteristic
1299C24C2512yes—
1300C24C2512yes—
1301C24C2511yescharacteristic
1302#41—232no—
1303#41—416no—
1304#41—416no—
1305#41—416no—
1306#41—432no—
1307#41—432no—
1308#41—416no—
1309#41—432no—
1310#41—432no—
1311#41—88no—
1312C2×Q8—22no—
1313C2×Q8—24no—
1314C2×Q8—22no—
1315C2×Q8—24no—
1316C2×Q8—22no—
1317C2×Q8—22no—
1318C2×Q8—24no—
1319C2×Q8—22no—
1320C2×Q8—22no—
1321C2×Q8—42no—
1322C2×Q8—41no—
1323C2×Q8—41no—
1324C2×Q8—41no—
1325C2×Q8—41no—
1326C2×Q8—42no—
1327C2×Q8—42no—
1328C2×Q8—416no—
1329C2×Q8C22×D414yes—
1330C2×Q8H(5,𝔽2)14yes—
1331C2×D4—24no—
1332C2×D4—24no—
1333C2×D4—24no—
1334C2×D4—24no—
1335C2×D4—24no—
1336C2×D4—24no—
1337C2×D4—24no—
1338C2×D4—24no—
1339C2×D4—28no—
1340C2×D4—24no—
1341C2×D4—24no—
1342C2×D4—28no—
1343C2×D4—24no—
1344C2×D4—28no—
1345C2×D4—28no—
1346C2×D4—24no—
1347C2×D4—24no—
1348C2×D4—24no—
1349C2×D4—28no—
1350C2×D4—24no—
1351C2×D4—24no—
1352C2×D4—28no—
1353C2×D4—24no—
1354C2×D4—24no—
1355C2×D4—24no—
1356C2×D4—28no—
1357C2×D4—24no—
1358C2×D4—24no—
1359C2×D4—24no—
1360C2×D4—28no—
1361C2×D4—28no—
1362C2×D4—28no—
1363C2×D4—28no—
1364C2×D4—28no—
1365C2×D4—28no—
1366C2×D4—22no—
1367C2×D4—24no—
1368C2×D4—24no—
1369C2×D4—28no—
1370C2×D4—24no—
1371C2×D4—24no—
1372C2×D4—22no—
1373C2×D4—28no—
1374C2×D4—22no—
1375C2×D4—28no—
1376C2×D4—24no—
1377C2×D4—22no—
1378C2×D4—28no—
1379C2×D4—24no—
1380C2×D4—22no—
1381C2×D4—24no—
1382C2×D4—24no—
1383C2×D4—22no—
1384C2×D4—416no—
1385C2×D4—432no—
1386C2×D4—42no—
1387C2×D4—42no—
1388C2×D4—44no—
1389C2×D4—42no—
1390C2×D4—41no—
1391C2×D4—41no—
1392C2×D4—42no—
1393C2×D4—42no—
1394C2×D4—44no—
1395C2×D4—42no—
1396C2×D4—42no—
1397C2×D4—42no—
1398C2×D4—42no—
1399C2×D4—42no—
1400C2×D4—42no—
1401C2×D4—42no—
1402C2×D4—42no—
1403C2×D4—42no—
1404C2×D4—44no—
1405C2×D4—42no—
1406C2×D4—432no—
1407C2×D4—416no—
1408C2×D4—44no—
1409C2×D4—44no—
1410C2×D4—44no—
1411C2×D4—44no—
1412C2×D4—44no—
1413C2×D4—42no—
1414C2×D4—42no—
1415C2×D4—44no—
1416C2×D4—44no—
1417C2×D4—44no—
1418C2×D4—44no—
1419C2×D4—44no—
1420C2×D4—44no—
1421C2×D4—41no—
1422C2×D4—41no—
1423C2×D4—42no—
1424C2×D4—42no—
1425C2×D4—44no—
1426C2×D4—44no—
1427C2×D4—44no—
1428C2×D4—44no—
1429C2×D4—44no—
1430C2×D4—44no—
1431C2×D4—44no—
1432C2×D4—44no—
1433C2×D4—44no—
1434C2×D4—44no—
1435C2×D4—44no—
1436C2×D4—42no—
1437C2×D4—42no—
1438C2×D4—44no—
1439C2×D4—44no—
1440C2×D4—44no—
1441C2×D4—432no—
1442C2×D4—432no—
1443C2×D4—464no—
1444C2×D4—416no—
1445C2×D4—832no—
1446C2×D4—816no—
1447C2×D4—816no—
1448C2×D4—832no—
1449C2×D4C22×D418yes—
1450C2×D4C22×D418yes—
1451C2×D4C22×D414yes—
1452C2×D4C22×D418yes—
1453C2×D4H(5,𝔽2)14yes—
1454C22×C4—24no—
1455C22×C4—24no—
1456C22×C4—22no—
1457C22×C4—22no—
1458C22×C4—24no—
1459C22×C4—22no—
1460C22×C4—22no—
1461C22×C4—24no—
1462C22×C4—24no—
1463C22×C4—22no—
1464C22×C4—22no—
1465C22×C4—22no—
1466C22×C4—24no—
1467C22×C4—24no—
1468C22×C4—24no—
1469C22×C4—22no—
1470C22×C4—22no—
1471C22×C4—22no—
1472C22×C4—22no—
1473C22×C4—24no—
1474C22×C4—24no—
1475C22×C4—24no—
1476C22×C4—24no—
1477C22×C4—24no—
1478C22×C4—24no—
1479C22×C4—24no—
1480C22×C4—24no—
1481C22×C4—24no—
1482C22×C4—28no—
1483C22×C4—24no—
1484C22×C4—24no—
1485C22×C4—28no—
1486C22×C4—24no—
1487C22×C4—24no—
1488C22×C4—24no—
1489C22×C4—24no—
1490C22×C4—24no—
1491C22×C4—24no—
1492C22×C4—24no—
1493C22×C4—28no—
1494C22×C4—24no—
1495C22×C4—24no—
1496C22×C4—416no—
1497C22×C4—41no—
1498C22×C4—41no—
1499C22×C4—42no—
1500C22×C4—41no—
1501C22×C4—41no—
1502C22×C4—42no—
1503C22×C4—42no—
1504C22×C4—41no—
1505C22×C4—41no—
1506C22×C4—42no—
1507C22×C4—42no—
1508C22×C4—42no—
1509C22×C4—44no—
1510C22×C4—41no—
1511C22×C4—42no—
1512C22×C4—42no—
1513C22×C4—44no—
1514C22×C4—42no—
1515C22×C4—42no—
1516C22×C4—41no—
1517C22×C4—42no—
1518C22×C4—41no—
1519C22×C4—42no—
1520C22×C4—42no—
1521C22×C4—44no—
1522C22×C4—44no—
1523C22×C4—44no—
1524C22×C4—42no—
1525C22×C4—42no—
1526C22×C4—42no—
1527C22×C4—42no—
1528C22×C4—42no—
1529C22×C4—42no—
1530C22×C4—42no—
1531C22×C4—42no—
1532C22×C4—41no—
1533C22×C4—44no—
1534C22×C4—42no—
1535C22×C4—42no—
1536C22×C4—42no—
1537C22×C4—42no—
1538C22×C4—42no—
1539C22×C4—42no—
1540C22×C4—42no—
1541C22×C4—432no—
1542C22×C4—88no—
1543C22×C4—816no—
1544C22×C4C22×D414yes—
1545C22×C4C22×D414yes—
1546C22×C4C22×D414yes—
1547C22×C4C22×D418yes—
1548C22×C4C22×D414yes—
1549C22×C4C22×D414yes—
1550C22×C4C22×D414yes—
1551C22×C4C2514yes—
1552C22×C4C2514yes—
1553C22×C4C2514yes—
1554C22×C4C2512yes—
1555C22×C4C2512yes—
1556C22×C4C2514yes—
1557C22×C4C2514yes—
1558C22×C4C2512yes—
1559C22×C4C2512yes—
1560C22×C4C2512yes—
1561C22×C4C2512yes—
1562C22×C4C2512yes—
1563C22×C4C2511yescharacteristic
1564C22×C4C2512yes—
1565C22×C4C2512yes—
1566C22×C4C2511yescharacteristic
1567C22×C4C2512yes—
1568C22×C4C2511yescharacteristic
1569C22×C4C2512yes—
1570C22×C4C2511yescharacteristic
1571C4⋊C4—24no—
1572C4⋊C4—24no—
1573C4⋊C4—24no—
1574C4⋊C4—24no—
1575C4⋊C4—24no—
1576C4⋊C4—24no—
1577C4⋊C4—28no—
1578C4⋊C4—24no—
1579C4⋊C4—22no—
1580C4⋊C4—24no—
1581C4⋊C4—24no—
1582C4⋊C4—22no—
1583C4⋊C4—24no—
1584C4⋊C4—24no—
1585C4⋊C4—28no—
1586C4⋊C4—24no—
1587C4⋊C4—24no—
1588C4⋊C4—24no—
1589C4⋊C4—24no—
1590C4⋊C4—24no—
1591C4⋊C4—24no—
1592C4⋊C4—24no—
1593C4⋊C4—24no—
1594C4⋊C4—24no—
1595C4⋊C4—28no—
1596C4⋊C4—28no—
1597C4⋊C4—44no—
1598C4⋊C4—42no—
1599C4⋊C4—42no—
1600C4⋊C4—42no—
1601C4⋊C4—42no—
1602C4⋊C4—44no—
1603C4⋊C4—44no—
1604C4⋊C4—44no—
1605C4⋊C4—44no—
1606C4⋊C4—44no—
1607C4⋊C4—44no—
1608C4⋊C4—44no—
1609C4⋊C4—44no—
1610C4⋊C4C22×D414yes—
1611C4⋊C4C22×D418yes—
1612C4⋊C4C22×D414yes—
1613C4⋊C4C22×D418yes—
1614C22⋊C4—24no—
1615C22⋊C4—24no—
1616C22⋊C4—24no—
1617C22⋊C4—24no—
1618C22⋊C4—28no—
1619C22⋊C4—24no—
1620C22⋊C4—24no—
1621C22⋊C4—24no—
1622C22⋊C4—24no—
1623C22⋊C4—24no—
1624C22⋊C4—28no—
1625C22⋊C4—28no—
1626C22⋊C4—28no—
1627C22⋊C4—28no—
1628C22⋊C4—28no—
1629C22⋊C4—28no—
1630C22⋊C4—24no—
1631C22⋊C4—24no—
1632C22⋊C4—24no—
1633C22⋊C4—24no—
1634C22⋊C4—24no—
1635C22⋊C4—24no—
1636C22⋊C4—28no—
1637C22⋊C4—28no—
1638C22⋊C4—28no—
1639C22⋊C4—24no—
1640C22⋊C4—24no—
1641C22⋊C4—28no—
1642C22⋊C4—28no—
1643C22⋊C4—24no—
1644C22⋊C4—24no—
1645C22⋊C4—28no—
1646C22⋊C4—28no—
1647C22⋊C4—44no—
1648C22⋊C4—44no—
1649C22⋊C4—44no—
1650C22⋊C4—44no—
1651C22⋊C4—44no—
1652C22⋊C4—44no—
1653C22⋊C4—44no—
1654C22⋊C4—44no—
1655C22⋊C4—44no—
1656C22⋊C4—44no—
1657C22⋊C4—44no—
1658C22⋊C4—44no—
1659C22⋊C4—44no—
1660C22⋊C4—44no—
1661C22⋊C4—44no—
1662C22⋊C4—44no—
1663C22⋊C4—44no—
1664C22⋊C4—44no—
1665C22⋊C4—44no—
1666C22⋊C4—44no—
1667C22⋊C4—44no—
1668C22⋊C4—44no—
1669C22⋊C4—44no—
1670C22⋊C4—44no—
1671C22⋊C4—44no—
1672C22⋊C4—44no—
1673C22⋊C4—44no—
1674C22⋊C4—44no—
1675C22⋊C4—44no—
1676C22⋊C4—44no—
1677C22⋊C4—44no—
1678C22⋊C4—44no—
1679C22⋊C4C22×D418yes—
1680C22⋊C4C22×D418yes—
1681C22⋊C4C22×D418yes—
1682C22⋊C4C22×D418yes—
1683C22⋊C4C22×D418yes—
1684C42—24no—
1685C42—24no—
1686C42—24no—
1687C42—24no—
1688C42—24no—
1689C42—28no—
1690C42—44no—
1691C42—44no—
1692C42—44no—
1693C42C22×D418yes—
1694C23—21no—
1695C23—21no—
1696C23—21no—
1697C23—21no—
1698C23—22no—
1699C23—22no—
1700C23—22no—
1701C23—21no—
1702C23—22no—
1703C23—22no—
1704C23—22no—
1705C23—21no—
1706C23—21no—
1707C23—22no—
1708C23—22no—
1709C23—21no—
1710C23—21no—
1711C23—22no—
1712C23—21no—
1713C23—22no—
1714C23—21no—
1715C23—22no—
1716C23—22no—
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—22no—
1721C23—22no—
1722C23—22no—
1723C23—22no—
1724C23—21no—
1725C23—22no—
1726C23—22no—
1727C23—21no—
1728C23—28no—
1729C23—28no—
1730C23—22no—
1731C23—24no—
1732C23—22no—
1733C23—22no—
1734C23—24no—
1735C23—22no—
1736C23—22no—
1737C23—24no—
1738C23—22no—
1739C23—24no—
1740C23—22no—
1741C23—22no—
1742C23—22no—
1743C23—22no—
1744C23—24no—
1745C23—22no—
1746C23—24no—
1747C23—22no—
1748C23—24no—
1749C23—22no—
1750C23—22no—
1751C23—44no—
1752C23—44no—
1753C23—44no—
1754C23—44no—
1755C23—48no—
1756C23—48no—
1757C23—48no—
1758C23—48no—
1759C23—416no—
1760C23—48no—
1761C23—48no—
1762C23—48no—
1763C23—82no—
1764C23—84no—
1765C23—82no—
1766C23—84no—
1767C23—82no—
1768C23—82no—
1769C23—84no—
1770C23—82no—
1771C23—82no—
1772C23—82no—
1773C23—82no—
1774C23—84no—
1775C23—84no—
1776C23—84no—
1777C23—84no—
1778C23—88no—
1779C23—88no—
1780C23—88no—
1781C23—84no—
1782C23—88no—
1783C23—84no—
1784C23—84no—
1785C23—162no—
1786C23—164no—
1787C23—162no—
1788C23—162no—
1789C23—164no—
1790C23—162no—
1791C23C23×D414yes—
1792C23C23×D412yes—
1793C23C23×D412yes—
1794C23C23×D412yes—
1795C23C2×H(5,𝔽2)14yes—
1796C23C2×H(5,𝔽2)14yes—
1797C23C2×H(5,𝔽2)12yes—
1798C23#58512yes—
1799C23C2611yescharacteristic
1800Q8—28no—
1801Q8—44no—
1802Q8—48no—
1803Q8—44no—
1804Q8—84no—
1805Q8—82no—
1806D4—216no—
1807D4—216no—
1808D4—28no—
1809D4—44no—
1810D4—48no—
1811D4—48no—
1812D4—48no—
1813D4—416no—
1814D4—416no—
1815D4—48no—
1816D4—48no—
1817D4—48no—
1818D4—48no—
1819D4—48no—
1820D4—48no—
1821D4—48no—
1822D4—416no—
1823D4—48no—
1824D4—48no—
1825D4—416no—
1826D4—48no—
1827D4—44no—
1828D4—88no—
1829D4—88no—
1830D4—82no—
1831D4—84no—
1832D4—84no—
1833D4—88no—
1834D4—88no—
1835D4—88no—
1836D4—88no—
1837D4—88no—
1838D4—88no—
1839D4—84no—
1840D4—88no—
1841D4—88no—
1842D4—164no—
1843C2×C4—216no—
1844C2×C4—22no—
1845C2×C4—22no—
1846C2×C4—22no—
1847C2×C4—21no—
1848C2×C4—21no—
1849C2×C4—22no—
1850C2×C4—21no—
1851C2×C4—21no—
1852C2×C4—21no—
1853C2×C4—21no—
1854C2×C4—22no—
1855C2×C4—22no—
1856C2×C4—22no—
1857C2×C4—22no—
1858C2×C4—28no—
1859C2×C4—28no—
1860C2×C4—28no—
1861C2×C4—216no—
1862C2×C4—22no—
1863C2×C4—22no—
1864C2×C4—22no—
1865C2×C4—22no—
1866C2×C4—22no—
1867C2×C4—24no—
1868C2×C4—22no—
1869C2×C4—22no—
1870C2×C4—24no—
1871C2×C4—24no—
1872C2×C4—24no—
1873C2×C4—24no—
1874C2×C4—22no—
1875C2×C4—24no—
1876C2×C4—22no—
1877C2×C4—24no—
1878C2×C4—24no—
1879C2×C4—24no—
1880C2×C4—22no—
1881C2×C4—22no—
1882C2×C4—22no—
1883C2×C4—22no—
1884C2×C4—22no—
1885C2×C4—22no—
1886C2×C4—24no—
1887C2×C4—22no—
1888C2×C4—22no—
1889C2×C4—24no—
1890C2×C4—24no—
1891C2×C4—24no—
1892C2×C4—22no—
1893C2×C4—22no—
1894C2×C4—24no—
1895C2×C4—24no—
1896C2×C4—22no—
1897C2×C4—22no—
1898C2×C4—44no—
1899C2×C4—44no—
1900C2×C4—44no—
1901C2×C4—48no—
1902C2×C4—416no—
1903C2×C4—48no—
1904C2×C4—48no—
1905C2×C4—48no—
1906C2×C4—48no—
1907C2×C4—44no—
1908C2×C4—48no—
1909C2×C4—48no—
1910C2×C4—84no—
1911C2×C4—84no—
1912C2×C4—84no—
1913C2×C4—84no—
1914C2×C4—88no—
1915C2×C4—82no—
1916C2×C4—84no—
1917C2×C4—82no—
1918C2×C4—84no—
1919C2×C4—84no—
1920C2×C4—84no—
1921C2×C4—88no—
1922C2×C4—162no—
1923C2×C4—162no—
1924C2×C4C23×D414yes—
1925C2×C4C23×D412yes—
1926C2×C4C23×D414yes—
1927C2×C4C23×D412yes—
1928C2×C4C23×D414yes—
1929C2×C4C23×D412yes—
1930C2×C4C23×D412yes—
1931C2×C4C2×H(5,𝔽2)14yes—
1932C2×C4C2×H(5,𝔽2)12yes—
1933C2×C4C2×H(5,𝔽2)12yes—
1934C22—22no—
1935C22—22no—
1936C22—22no—
1937C22—22no—
1938C22—22no—
1939C22—22no—
1940C22—22no—
1941C22—24no—
1942C22—22no—
1943C22—24no—
1944C22—24no—
1945C22—22no—
1946C22—24no—
1947C22—22no—
1948C22—22no—
1949C22—24no—
1950C22—22no—
1951C22—24no—
1952C22—24no—
1953C22—24no—
1954C22—24no—
1955C22—42no—
1956C22—42no—
1957C22—42no—
1958C22—42no—
1959C22—42no—
1960C22—41no—
1961C22—41no—
1962C22—41no—
1963C22—41no—
1964C22—42no—
1965C22—42no—
1966C22—41no—
1967C22—42no—
1968C22—42no—
1969C22—41no—
1970C22—41no—
1971C22—42no—
1972C22—42no—
1973C22—42no—
1974C22—41no—
1975C22—42no—
1976C22—42no—
1977C22—44no—
1978C22—42no—
1979C22—44no—
1980C22—42no—
1981C22—42no—
1982C22—42no—
1983C22—44no—
1984C22—42no—
1985C22—42no—
1986C22—44no—
1987C22—44no—
1988C22—42no—
1989C22—42no—
1990C22—42no—
1991C22—42no—
1992C22—44no—
1993C22—42no—
1994C22—44no—
1995C22—42no—
1996C22—88no—
1997C22—88no—
1998C22—816no—
1999C22—816no—
2000C22—1616no—
2001C22—168no—
2002C22#348814yes—
2003C22C24×D411yescharacteristic
2004C22C22×H(5,𝔽2)11yescharacteristic
2005C22C22×H(5,𝔽2)11yescharacteristic
2006C22C22×H(5,𝔽2)11yescharacteristic
2007C22C2×#58511yescharacteristic
2008C22H(7,𝔽2)11yescharacteristic
2009C222−1+611yescharacteristic
2010C4—22no—
2011C4—22no—
2012C4—24no—
2013C4—24no—
2014C4—22no—
2015C4—24no—
2016C4—24no—
2017C4—42no—
2018C4—42no—
2019C4—42no—
2020C4—42no—
2021C4—42no—
2022C4—44no—
2023C4—42no—
2024C4—42no—
2025C4—44no—
2026C4—44no—
2027C4—44no—
2028C4—44no—
2029C4#348414yes—
2030C2—24no—
2031C2—42no—
2032C2—44no—
2033C2—42no—
2034C2—44no—
2035C2—44no—
2036C2—82no—
2037C2—82no—
2038C2—84no—
2039C2C2×#348411yescharacteristic
2040C2C2×#348811yescharacteristic
2041C2#6285311yescharacteristic
2042C2#6289211yescharacteristic
2043C2#6289511yescharacteristic
2044C2#6289811yescharacteristic
2045C2#6289911yescharacteristic
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×#3488C2semidirect
2. C2×#3459C2semidirect
3. #47844C2semidirect
4. #47843C2semidirect
5. #46368C2semidirect
6. #46367C2semidirect
7. #42998C2semidirect
8. #42996C2semidirect
9. #38909C2semidirect
10. #38902C2semidirect
11. #38026C2semidirect
12. #38025C2semidirect
13. #37768C2semidirect
14. #37752C2semidirect
15. #37692C2semidirect
16. #37672C2semidirect
17. #37657C2semidirect
18. #37648C2semidirect
19. #37439C2semidirect
20. #37278C2semidirect
21. #37268C2semidirect
22. #36097C2semidirect
23. D4×#121C2semidirect
24. #35520C2semidirect
25. #35512C2semidirect
26. #35251C2semidirect
27. #35000C2semidirect
28. C2×#2407C2semidirect
29. #34360C2semidirect
30. C22×H(5,𝔽2)C22semidirect
31. C23×#41C22semidirect
33. C2×#550C22semidirect
34. C2×#548C22semidirect
35. C2×#546C22semidirect
36. C2×#546C22semidirect
37. C2×D42C22semidirect
38. C2×D42C22semidirect
39. C2×D42C22semidirect
41. C2×#543C22semidirect
42. C2×#539C22semidirect
43. C2×#539C22semidirect
44. C2×#539C22semidirect
45. C2×#539C22semidirect
46. C2×#538C22semidirect
47. C2×#538C22semidirect
48. C2×#538C22semidirect
49. C2×#537C22semidirect
50. C2×#537C22semidirect
51. C2×#537C22semidirect
52. C2×#537C22semidirect
53. C2×#535C22semidirect
54. C2×#535C22semidirect
55. C2×#534C22semidirect
56. C2×#534C22semidirect
57. C2×#534C22semidirect
58. C2×#529C22semidirect
59. C2×#529C22semidirect
60. C2×#529C22semidirect
62. C2×#525C22semidirect
63. C2×#525C22semidirect
64. C2×#525C22semidirect
65. C2×#525C22semidirect
66. C2×#525C22semidirect
67. C22×C22⋊Q8C22semidirect
69. C22×#121C22semidirect
70. C22×#121C22semidirect
71. C22×#121C22semidirect
72. C2×#520C22semidirect
73. C22×C4×D4C22semidirect
74. C22×C4×D4C22semidirect
75. #2856C22semidirect
76. #2854C22semidirect
77. #2850C22semidirect
78. #2848C22semidirect
79. #2848C22semidirect
80. #2847C22semidirect
81. #2847C22semidirect
82. #2847C22semidirect
83. #2813C22semidirect
84. #2732C22semidirect
85. #2728C22semidirect
86. #2715C22semidirect
87. #2714C22semidirect
88. #2714C22semidirect
89. #2712C22semidirect
90. #2711C22semidirect
91. #2711C22semidirect
92. #2708C22semidirect
93. #2704C22semidirect
94. #2702C22semidirect
95. #2701C22semidirect
96. #2696C22semidirect
97. #2694C22semidirect
98. #2691C22semidirect
99. #2691C22semidirect
100. #2688C22semidirect
101. #2685C22semidirect
102. #2685C22semidirect
103. #2684C22semidirect
104. #2682C22semidirect
105. #2681C22semidirect
106. #2681C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2676C22semidirect
110. #2675C22semidirect
111. #2673C22semidirect
112. #2673C22semidirect
113. #2671C22semidirect
114. #2671C22semidirect
115. #2671C22semidirect
116. #2671C22semidirect
117. #2670C22semidirect
118. #2670C22semidirect
119. #2669C22semidirect
120. #2669C22semidirect
121. #2669C22semidirect
122. #2668C22semidirect
123. #2668C22semidirect
124. #2656C22semidirect
125. #2639C22semidirect
126. #2626C22semidirect
127. #2625C22semidirect
128. #2624C22semidirect
129. #2624C22semidirect
130. #2620C22semidirect
131. #2619C22semidirect
132. #2618C22semidirect
133. #2617C22semidirect
134. #2617C22semidirect
135. #2616C22semidirect
136. #2615C22semidirect
137. #2615C22semidirect
138. #2592C22semidirect
139. #2582C22semidirect
140. #2580C22semidirect
141. #2559C22semidirect
142. #2548C22semidirect
143. #2544C22semidirect
144. #2543C22semidirect
145. #2543C22semidirect
146. #2541C22semidirect
147. #2540C22semidirect
148. #2539C22semidirect
149. #2537C22semidirect
150. #2536C22semidirect
151. #2534C22semidirect
152. #2487C22semidirect
153. #2486C22semidirect
154. #2480C22semidirect
155. #2479C22semidirect
156. #2477C22semidirect
157. #2473C22semidirect
158. #2472C22semidirect
159. #2472C22semidirect
160. #2468C22semidirect
161. #2464C22semidirect
162. #2464C22semidirect
163. #2464C22semidirect
164. #2463C22semidirect
165. #2463C22semidirect
166. #2461C22semidirect
167. #2459C22semidirect
168. #2456C22semidirect
169. #2455C22semidirect
170. #2454C22semidirect
171. #2450C22semidirect
172. #2449C22semidirect
173. #2443C22semidirect
174. #2443C22semidirect
175. #2437C22semidirect
176. #2430C22semidirect
177. #2428C22semidirect
178. #2428C22semidirect
179. #2428C22semidirect
180. #2427C22semidirect
181. #2425C22semidirect
182. #2425C22semidirect
183. #2424C22semidirect
184. #2424C22semidirect
185. #2424C22semidirect
186. #2418C22semidirect
187. #2417C22semidirect
188. #2416C22semidirect
189. #2416C22semidirect
190. #2416C22semidirect
191. #2416C22semidirect
192. #2416C22semidirect
193. #2416C22semidirect
194. #2415C22semidirect
195. #2414C22semidirect
196. #2410C22semidirect
197. #2410C22semidirect
198. #2410C22semidirect
199. #2410C22semidirect
200. #2410C22semidirect
201. #2410C22semidirect
202. #2410C22semidirect
203. #2409C22semidirect
204. #2408C22semidirect
205. #2408C22semidirect
206. #2408C22semidirect
207. #2408C22semidirect
208. #2408C22semidirect
209. #2408C22semidirect
210. #2408C22semidirect
211. #2408C22semidirect
212. #2407C22semidirect
213. #2407C22semidirect
214. #2407C22semidirect
215. #2407C22semidirect
216. #2407C22semidirect
217. #2407C22semidirect
218. #2407C22semidirect
219. #2407C22semidirect
220. #2407C22semidirect
221. #2407C22semidirect
222. #2407C22semidirect
223. #2407C22semidirect
224. #2405C22semidirect
225. #2405C22semidirect
226. #2405C22semidirect
227. #2403C22semidirect
228. #2403C22semidirect
229. C2×#394C22semidirect
230. C2×#392C22semidirect
231. #2376C22semidirect
232. #2361C22semidirect
233. #2358C22semidirect
234. #2358C22semidirect
235. #2352C22semidirect
236. #2352C22semidirect
237. D4×C4⋊C4C22semidirect
238. D4×C4⋊C4C22semidirect
239. D4×C22⋊C4C22semidirect
240. #2329C22semidirect
241. #2329C22semidirect
242. #2325C22semidirect
243. #2325C22semidirect
244. #2324C22semidirect
245. #2323C22semidirect
246. #2314C22semidirect
247. #2311C22semidirect
248. #2311C22semidirect
249. #2311C22semidirect
250. #2311C22semidirect
251. #2309C22semidirect
252. #2308C22semidirect
253. C4×C22⋊Q8C22semidirect
254. C4×#121C22semidirect
255. C2×#391C22semidirect
256. C2×#390C22semidirect
257. C2×#386C22semidirect
258. C2×#385C22semidirect
259. C2×#380C22semidirect
260. C2×#380C22semidirect
344. #525D4semidirect
798. C2×#41C2×D4semidirect
892. C23×C4C2×D4semidirect
957. #123C2×D4semidirect
977. C22⋊Q8C2×D4semidirect
978. C22⋊Q8C2×D4semidirect
1026. #121C2×D4semidirect
1044. #120C2×D4semidirect
1069. C4×D4C2×D4semidirect
1070. C4×D4C2×D4semidirect
1076. #117C2×D4semidirect
1292. C24H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×#34592
#478442
#478432
#463682
#463672
#429982
#429962
#389092
#389022
#380262
#380252
#377682
#377522
#376922
#376722
#376572
#376482
#374392
#372782
#372682
#360972
D4×#1212
#355202
#355122
#352512
#350002
C2×#24072
#343602