Finite Group Databasebeta

← #7689018

Subgroups — #7689018

Order 512.

11467 conjugacy classes of subgroups.

The subgroup lattice has 1955 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C212yesmaximal, complemented
2C2×#3496C212yesmaximal, complemented
3#59818C211yesmaximal, characteristic, complemented
4#59814C212yesmaximal, complemented
5#59131C212yesmaximal, complemented
6#59128C212yesmaximal, complemented
7#59123C214yesmaximal, complemented
8#59122C214yesmaximal, complemented
9#45244C211yesmaximal, characteristic, complemented
10#45091C212yesmaximal, complemented
11#44870C211yesmaximal, characteristic, complemented
12#44758C212yesmaximal, complemented
13#43886C214yesmaximal, complemented
14#43017C212yesmaximal, complemented
15#39335C212yesmaximal, complemented
16#39334C212yesmaximal, complemented
17#39333C214yesmaximal, complemented
18#39332C214yesmaximal, complemented
19#36260C211yesmaximal, characteristic, complemented
20#36218C212yesmaximal, complemented
21#36214C212yesmaximal, complemented
22#36124C212yesmaximal, complemented
23#36123C214yesmaximal, complemented
24#36085C211yesmaximal, characteristic, complemented
25#35750C211yesmaximal, characteristic, complemented
26#35680C212yesmaximal, complemented
27#34925C211yesmaximal, characteristic, complemented
28C2×#2555C212yesmaximal, complemented
29C4×#546C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic, complemented
31C22×H(5,𝔽2)C2211yescharacteristic
32C22×H(5,𝔽2)C2212yescomplemented
33#3500—232no—
34#3496—232no—
35C2×#548C2212yescomplemented
36C2×#548C2212yescomplemented
37C2×#548C2212yescomplemented
38C2×#548C2212yescomplemented
39C2×#547C2212yescomplemented
40C2×#547C2212yescomplemented
41C2×#547C2214yescomplemented
42C2×#547C2211yescharacteristic, complemented
43C2×#546C2212yes—
44C2×#546C2214yescomplemented
45C2×#546C2214yescomplemented
46C2×#546C2214yescomplemented
47C2×#546C2212yescomplemented
48C2×#546C2212yescomplemented
49C2×#546C2214yescomplemented
50C2×#546C2212yescomplemented
51C2×#546C2212yescomplemented
52C2×#546C2214yescomplemented
53C2×#546C2212yescomplemented
54C2×#546C2212yescomplemented
55C2×#546C2214yescomplemented
56C2×D42C2212yes—
57C2×D42C2212yescomplemented
58C2×D42C2214yescomplemented
59C2×D42C2211yescharacteristic, complemented
60C2×#537C2212yescomplemented
61C2×#537C2212yescomplemented
62C2×#536C2212yescomplemented
63C2×#536C2214yescomplemented
64C2×#535C2212yescomplemented
65C2×#535C2214yescomplemented
66C2×#534C2214yescomplemented
67C2×#534C2214yescomplemented
68C2×#532C2214yescomplemented
69C2×#532C2212yescomplemented
70C2×#532C2212yescomplemented
71C2×#532C2212yescomplemented
72C22×#124C2214yescomplemented
73C22×#124C2212yescomplemented
74C22×#121C2214yescomplemented
75C22×#121C2214yescomplemented
76C2×C4×#41C2212yescomplemented
77C22×C4×D4C2212yescomplemented
78#2858C2211yescharacteristic, complemented
79#2856C2212yescomplemented
80#2854C2214yescomplemented
81#2850C2212yescomplemented
82#2850C2212yescomplemented
83#2847C2214yescomplemented
84#2683C2212yescomplemented
85#2682C2214yescomplemented
86#2680C2212yescomplemented
87#2679C2212yescomplemented
88#2677C2214yescomplemented
89#2676C2214yescomplemented
90#2676C2214yescomplemented
91#2675C2214yescomplemented
92#2675C2212yescomplemented
93#2674C2214yescomplemented
94#2674C2214yescomplemented
95#2673C2214yescomplemented
96#2673C2214yescomplemented
97#2672C2214yescomplemented
98#2672C2214yescomplemented
99#2672C2214yescomplemented
100#2671C2214yescomplemented
101#2671C2214yescomplemented
102#2670C2212yescomplemented
103#2670C2214yescomplemented
104#2669C2214yescomplemented
105#2669C2212yescomplemented
106#2669C2214yescomplemented
107#2668C2214yescomplemented
108#2616C2211yescharacteristic, complemented
109#2616C2211yescharacteristic, complemented
110#2615C2212yescomplemented
111#2614C2212yescomplemented
112#2613C2214yescomplemented
113#2613C2212yescomplemented
114#2555C2211yescharacteristic, complemented
115#2555C2212yescomplemented
116#2555C2214yescomplemented
117#2555C2214yescomplemented
118#2555C2212yescomplemented
119#2555C2214yescomplemented
120#2555C2214yescomplemented
121#2555C2212yescomplemented
122#2555C2214yescomplemented
123#2555C2214yescomplemented
124#2555C2212yescomplemented
125#2555C2214yescomplemented
126#2555C2211yescharacteristic, complemented
127#2551C2211yescharacteristic, complemented
128#2545C2212yescomplemented
129#2544C2212yescomplemented
130#2543C2214yescomplemented
131#2543C2214yescomplemented
132#2542C2211yescharacteristic, complemented
133#2541C2211yescharacteristic, complemented
134#2541C2212yescomplemented
135#2540C2212yescomplemented
136#2540C2212yescomplemented
137#2539C2214yescomplemented
138#2539C2214yescomplemented
139#2537C2211yescharacteristic, complemented
140#2536C2212yescomplemented
141#2535C2212yescomplemented
142#2534C2214yescomplemented
143#2534C2214yescomplemented
144#2501C2212yescomplemented
145#2491C2214yescomplemented
146#2491C2212yescomplemented
147#2491C2212yescomplemented
148#2472C2214yescomplemented
149#2472C2214yescomplemented
150#2472C2214yescomplemented
151#2464C2214yescomplemented
152#2464C2214yescomplemented
153#2464C2214yescomplemented
154#2463C2212yescomplemented
155#2461C2214yescomplemented
156#2461C2214yescomplemented
157#2461C2214yescomplemented
158#2461C2214yescomplemented
159#2456C2214yescomplemented
160#2449C2214yescomplemented
161#2443C2214yescomplemented
162#2440C2214yescomplemented
163#2435C2211yescharacteristic, complemented
164#2434C2212yescomplemented
165#2434C2211yescharacteristic, complemented
166#2433C2214yescomplemented
167#2433C2212yescomplemented
168#2433C2212yescomplemented
169#2432C2212yescomplemented
170#2431C2212yescomplemented
171#2431C2212yescomplemented
172#2430C2214yescomplemented
173#2430C2214yescomplemented
174#2430C2212yescomplemented
175#2430C2212yescomplemented
176#2429C2212yescomplemented
177#2428C2214yescomplemented
178#2428C2214yescomplemented
179#2428C2212yescomplemented
180#2428C2212yescomplemented
181#2428C2212yescomplemented
182#2427C2212yescomplemented
183#2426C2212yescomplemented
184#2425C2214yescomplemented
185#2425C2214yescomplemented
186#2424C2214yescomplemented
187#2424C2214yescomplemented
188#2424C2214yescomplemented
189#2424C2214yescomplemented
190#2424C2214yescomplemented
191#2424C2214yescomplemented
192#2422C2214yescomplemented
193#2418C2214yescomplemented
194#2417C2212yescomplemented
195#2416C2212yescomplemented
196#2415C2212yescomplemented
197#2414C2212yescomplemented
198#2413C2214yescomplemented
199#2412C2214yescomplemented
200#2411C2214yescomplemented
201#2410C2214yescomplemented
202#2410C2214yescomplemented
203#2410C2214yescomplemented
204#2410C2214yescomplemented
205#2410C2214yescomplemented
206#2409C2212yescomplemented
207#2409C2211yescharacteristic, complemented
208#2408C2211yescharacteristic, complemented
209#2408C2212yescomplemented
210#2407C2212yescomplemented
211#2407C2212yescomplemented
212#2407C2212yescomplemented
213#2406C2212yescomplemented
214#2406C2214yescomplemented
215#2406C2212yescomplemented
216#2405C2214yescomplemented
217#2404C2214yescomplemented
218#2403C2212yescomplemented
219#2403C2214yescomplemented
220#2403C2214yescomplemented
221#2388C2212yescomplemented
222#2388C2211yescharacteristic, complemented
223#2388C2211yescharacteristic, complemented
224C2×#395C2212yescomplemented
225C2×#394C2212yescomplemented
226C2×#392C2214yescomplemented
227#2367C2212yescomplemented
228#2364C2214yescomplemented
229#2363C2212yescomplemented
230#2361C2214yescomplemented
231#2360C2212yescomplemented
232#2359C2214yescomplemented
233#2358C2214yescomplemented
234#2358C2212yescomplemented
235#2358C2214yescomplemented
236#2358C2214yescomplemented
237#2352C2212yescomplemented
238#2349C2212yescomplemented
239#2342C2214yescomplemented
240#2339C2212yescomplemented
241#2339C2211yescharacteristic, complemented
242#2339C2211yescharacteristic, complemented
243D4×C22⋊C4C2214yescomplemented
244D4×C22⋊C4C2212yescomplemented
245D4×C22⋊C4C2212yescomplemented
246C4×#127C2211yescharacteristic, complemented
247C4×#124C2212yescomplemented
248C4×C22⋊Q8C2212yescomplemented
249C4×#123C2214yescomplemented
250C4×#121C2214yescomplemented
251C4×#121C2212yescomplemented
252C4×#121C2212yescomplemented
253C4×#121C2212yescomplemented
254C4×#120C2214yescomplemented
255C2×#390C2212yescomplemented
256C2×#388C2214yescomplemented
257C2×#386C2214yescomplemented
258C42×D4C2212yescomplemented
259C42×D4C2211yescharacteristic, complemented
260C2×C4×C22⋊C4C2214yescomplemented
261C2×2−1+4—216no—
262C2×2−1+4—44no—
263C2×H(5,𝔽2)—216no—
264C2×H(5,𝔽2)—216no—
265C2×H(5,𝔽2)—216no—
266C2×H(5,𝔽2)—44no—
267C2×H(5,𝔽2)—48no—
268C22×#41C2311yescharacteristic
269C22×#41C2311yescharacteristic
270C22×#41C2311yescharacteristic
271C22×#41C2312yes—
272C22×#41C2312yes—
273C22×#41C2312yes—
274C22×#41C2314yes—
275C22×#41C2312yes—
276C22×#41C2312yes—
277C22×#41C2311yescharacteristic
278C22×#41C2314yes—
279C22×#41C2312yes—
280C22×#41C2312yes—
281C23×Q8C2312yes—
282C23×Q8C2312yes—
283C23×Q8C2311yescharacteristic
284C23×D4C2312yes—
285C23×D4C2312yes—
286C23×D4C2314yes—
287C23×D4C2311yescharacteristic
288C23×D4C2314yes—
289C23×D4C2314yes—
290C23×D4C2314yes—
291C23×D4C2312yes—
292C23×D4C2312yes—
293C23×D4C2314yes—
294C23×D4C2314yes—
295C23×D4C2312yes—
296C24×C4C2314yes—
297#548—216no—
298#548—216no—
299#548—216no—
300#548—216no—
301#547—216no—
302#547—232no—
303#547—216no—
304#547—44no—
305#546—216no—
306#546—216no—
307#546—216no—
308#546—232no—
309#546—232no—
310#546—232no—
311#546—232no—
312#546—216no—
313#546—216no—
314#546—216no—
315#546—232no—
316#546—232no—
317#546D4132yescomplemented
318D42—216no—
319D42—216no—
320D42—232no—
321D42—44no—
322#537—216no—
323#537—216no—
324#536—232no—
325#536—216no—
326#535—216no—
327#535—232no—
328#534—232no—
329#534—232no—
330#532—216no—
331#532—232no—
332#532—216no—
333#532—216no—
334C2×C4⋊Q8C2312yes—
335C2×C4⋊Q8C2314yes—
336C2×C4⋊Q8C2312yes—
337C2×C4⋊Q8C2312yes—
338C2×C4⋊Q8C2311yescharacteristic
339C2×#127C2312yes—
340C2×#127C2314yes—
341C2×#127C2312yes—
342C2×#127C2312yes—
343C2×#127C2311yescharacteristic
344C2×#127C2311yescharacteristic
345C2×#127C2312yes—
346C2×#124—216no—
347C2×#124—232no—
348C2×#124C2312yes—
349C2×#124C2312yes—
350C2×#124C2314yes—
351C2×#124C2312yes—
352C2×#124C2314yes—
353C2×#124C2314yes—
354C2×#124C2314yes—
355C2×#124C2314yes—
356C2×#124C2314yes—
357C2×#124C2312yes—
358C2×#124C2312yes—
359C2×#124C2314yes—
360C2×#124C2314yes—
361C2×#124C2312yes—
362C2×#124C2312yes—
363C2×#124C2312yes—
364C2×#124C2312yes—
365C2×#123C2314yes—
366C2×#123C2314yes—
367C2×#123C2314yes—
368C2×#123C2314yes—
369C2×#123C2314yes—
370C2×#123C2314yes—
371C2×#123C2314yes—
372C2×#123C2314yes—
373C2×#123C2314yes—
374C2×#123C2314yes—
375C2×#123C2314yes—
376C2×#123C2314yes—
377C2×#123C2312yes—
378C2×#123C2312yes—
379C2×#123C2314yes—
380C2×C22⋊Q8C2312yes—
381C2×C22⋊Q8C2312yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2312yes—
384C2×C22⋊Q8C2312yes—
385C2×C22⋊Q8C2314yes—
386C2×C22⋊Q8C2314yes—
387C2×C22⋊Q8C2312yes—
388C2×C22⋊Q8C2314yes—
389C2×C22⋊Q8C2314yes—
390C2×C22⋊Q8C2314yes—
391C2×C22⋊Q8C2314yes—
392C2×C22⋊Q8C2311yescharacteristic
393C2×C22⋊Q8C2311yescharacteristic
394C2×C22⋊Q8C2312yes—
395C2×#121—232no—
396C2×#121—232no—
397C2×#121C2314yes—
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2314yes—
401C2×#121C2312yes—
402C2×#121C2312yes—
403C2×#121C2314yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2314yes—
407C2×#121C2314yes—
408C2×#121C2314yes—
409C2×#121C2314yes—
410C2×#121C2314yes—
411C2×#121C2314yes—
412C2×#121C2314yes—
413C2×#121C2314yes—
414C2×#121C2314yes—
415C2×#121C2314yes—
416C2×#121C2314yes—
417C2×#121C2314yes—
418C2×#121C2314yes—
419C2×#121C2312yes—
420C2×#121C2314yes—
421C2×#121C2312yes—
422C2×#121C2312yes—
423C2×#121C2314yes—
424C2×#121C2312yes—
425C2×#121C2314yes—
426C2×#121C2312yes—
427C2×#121C2314yes—
428C2×#121C2312yes—
429C2×#121C2312yes—
430C2×#121C2312yes—
431C2×#121C2314yes—
432C2×#121C2314yes—
433C2×#121C2314yes—
434C2×#121C2312yes—
435C2×#121C2312yes—
436C2×#121C2312yes—
437C2×#121C2312yes—
438C2×#121C2312yes—
439C2×#121C2314yes—
440C2×#121C2312yes—
441C2×#121C2314yes—
442C2×#120C2314yes—
443C2×#120C2314yes—
444C2×#120C2314yes—
445C2×#120C2314yes—
446C2×#120C2314yes—
447C2×#120C2314yes—
448C2×#120C2314yes—
449C2×#120C2314yes—
450C2×#120C2314yes—
451C2×#120C2314yes—
452C2×#120C2314yes—
453C2×#120C2314yes—
454C2×#120C2314yes—
455C2×#120C2314yes—
456C2×#120C2314yes—
457C2×#120C2312yes—
458C2×#120C2314yes—
459C2×#120C2314yes—
460C4×#41—216no—
461C2×C4×Q8C2312yes—
462C2×C4×Q8C2312yes—
463C2×C4×D4—216no—
464C2×C4×D4C2312yes—
465C2×C4×D4C2312yes—
466C2×C4×D4C2311yescharacteristic
467C2×C4×D4C2312yes—
468C2×C4×D4C2312yes—
469C2×C4×D4C2314yes—
470C2×C4×D4C2314yes—
471C2×C4×D4C2314yes—
472C2×C4×D4C2314yes—
473C2×C4×D4C2314yes—
474C2×C4×D4C2314yes—
475C2×C4×D4C2314yes—
476C2×C4×D4C2314yes—
477C2×C4×D4C2312yes—
478C2×C4×D4C2312yes—
479C2×C4×D4C2312yes—
480C2×C4×D4C2312yes—
481C2×C4×D4C2312yes—
482C2×C4×D4C2314yes—
483C2×C4×D4C2312yes—
484C2×C4×D4C2314yes—
485C2×C4×D4C2311yescharacteristic
486C2×C4×D4C2311yescharacteristic
487C2×C4×D4C2312yes—
488C2×C4×D4C2312yes—
489C2×C4×D4C2314yes—
490C2×C4×D4C2312yes—
491C2×C4×D4C2312yes—
492C2×#117C2314yes—
493C2×#117C2312yes—
494C22×C4⋊C4C2312yes—
495C22×C4⋊C4C2314yes—
496C22×C4⋊C4C2314yes—
497C22×C4⋊C4C2312yes—
498C22×C22⋊C4C2314yes—
499C22×C22⋊C4C2314yes—
500C22×C22⋊C4C2314yes—
501C22×C22⋊C4C2314yes—
502C22×C22⋊C4C2314yes—
503C22×C22⋊C4C2314yes—
504C22×C22⋊C4C2314yes—
505C22×C22⋊C4C2314yes—
506C22×C22⋊C4C2314yes—
507C22×C22⋊C4C2314yes—
508C22×C22⋊C4C2314yes—
509C22×C22⋊C4C2314yes—
510C22×C42C2312yes—
511C22×C42C2312yes—
512C22×C42C2314yes—
513C22×C42C2312yes—
514#399C2314yes—
515#399C2314yes—
516#399C2314yes—
517#398C2314yes—
518#398C2314yes—
519#398C2314yes—
520#397C2314yes—
521#397C2314yes—
522#397C2314yes—
523#396C2314yes—
524#396C2314yes—
525#396C2314yes—
526#396C2314yes—
527#396C2314yes—
528#396C2314yes—
529#395C2312yes—
530#395C2312yes—
531#395C2314yes—
532#395C2312yes—
533#395C2311yescharacteristic
534#395C2314yes—
535#395C2312yes—
536#395C2314yes—
537#395C2312yes—
538#395C2311yescharacteristic
539#395C2312yes—
540#394C2312yes—
541#394C2312yes—
542#394C2314yes—
543#394C2312yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2312yes—
549#394C2314yes—
550#394C2311yescharacteristic
551#394C2314yes—
552#394C2312yes—
553#394C2314yes—
554#394C2312yes—
555#394C2312yes—
556#394C2312yes—
557#394C2311yescharacteristic
558#394C2312yes—
559#394C2312yes—
560#394C2314yes—
561#394C2314yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#394C2314yes—
566#394C2314yes—
567#394C2314yes—
568#394C2314yes—
569#393C2311yescharacteristic
570#393C2314yes—
571#393C2312yes—
572#393C2314yes—
573#393C2312yes—
574#393C2311yescharacteristic
575#392C2311yescharacteristic
576#392C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2314yes—
580#392C2314yes—
581#392C2312yes—
582#392C2314yes—
583#392C2314yes—
584#392C2312yes—
585#392C2314yes—
586#392C2314yes—
587#392C2314yes—
588#392C2314yes—
589#392C2314yes—
590#392C2314yes—
591#392C2312yes—
592#392C2312yes—
593#392C2311yescharacteristic
594#392C2312yes—
595#392C2312yes—
596#392C2314yes—
597#392C2312yes—
598#392C2314yes—
599#392C2314yes—
600#392C2314yes—
601#392C2312yes—
602#392C2314yes—
603#391C2312yes—
604#391C2312yes—
605#391C2312yes—
606#391C2312yes—
607#390C2311yescharacteristic
608#390C2312yes—
609#390C2312yes—
610#390C2311yescharacteristic
611#390C2312yes—
612#390C2312yes—
613#390C2314yes—
614#390C2314yes—
615#390C2312yes—
616#390C2312yes—
617#390C2314yes—
618#390C2312yes—
619#390C2314yes—
620#390C2314yes—
621#390C2312yes—
622#390C2314yes—
623#390C2312yes—
624#390C2312yes—
625#390C2312yes—
626#390C2314yes—
627#390C2314yes—
628#390C2312yes—
629#389C2314yes—
630#389C2314yes—
631#389C2312yes—
632#389C2312yes—
633#389C2314yes—
634#389C2312yes—
635#389C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2312yes—
657#388C2314yes—
658#388C2312yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2312yes—
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#386C2312yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2312yes—
696#386C2314yes—
697#386C2312yes—
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#385C2312yes—
713#384C2311yescharacteristic
714#384C2312yes—
715#382C2312yes—
716#381C2314yes—
717#381C2312yes—
718#381C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2311yescharacteristic
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#379C2314yes—
730#379C2314yes—
731#379C2314yes—
732#379C2314yes—
733#379C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2314yes—
739C4×C4⋊C4C2312yes—
740C4×C22⋊C4C2312yes—
741C4×C22⋊C4C2314yes—
742C4×C22⋊C4C2312yes—
743C4×C22⋊C4C2312yes—
744C4×C22⋊C4C2311yescharacteristic
745C4×C22⋊C4C2311yescharacteristic
746C4×C22⋊C4C2312yes—
747C4×C22⋊C4C2314yes—
748C4×C22⋊C4C2314yes—
749C4×C22⋊C4C2312yes—
750C4×C22⋊C4C2312yes—
751C4×C22⋊C4C2314yes—
752C4×C22⋊C4C2312yes—
753C4×C22⋊C4C2314yes—
754C4×C22⋊C4C2314yes—
755C4×C22⋊C4C2314yes—
756C4×C22⋊C4C2314yes—
757C4×C22⋊C4C2314yes—
758C4×C22⋊C4C2312yes—
759C2×#95C2314yes—
760C2×#95C2312yes—
761C2×#95C2312yes—
762C2×#95C2314yes—
763C43C2311yescharacteristic
764C25C2414yes—
765C25C2414yes—
766C25C2412yes—
767C25C2414yes—
7682−1+4—464no—
769H(5,𝔽2)—464no—
770H(5,𝔽2)—4128no—
771C2×#41—28no—
772C2×#41—28no—
773C2×#41—28no—
774C2×#41—216no—
775C2×#41—216no—
776C2×#41—28no—
777C2×#41—28no—
778C2×#41—216no—
779C2×#41—28no—
780C2×#41—216no—
781C2×#41—28no—
782C2×#41—28no—
783C2×#41—24no—
784C2×#41—24no—
785C2×#41—28no—
786C2×#41—28no—
787C2×#41—28no—
788C2×#41—28no—
789C2×#41—216no—
790C2×#41—28no—
791C2×#41—216no—
792C2×#41—28no—
793C2×#41—42no—
794C2×#41—44no—
795C2×#41—42no—
796C2×#41—48no—
797C2×#41—44no—
798C2×#41—48no—
799C2×#41—44no—
800C2×#41—44no—
801C2×#41—44no—
802C2×#41—44no—
803C2×#41C2×D4116yescomplemented
804C22×Q8—28no—
805C22×Q8—28no—
806C22×Q8—216no—
807C22×Q8—28no—
808C22×Q8—44no—
809C22×Q8—44no—
810C22×Q8—42no—
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2412yes—
814C22×Q8C2411yescharacteristic
815C22×Q8C2414yes—
816C22×Q8C2412yes—
817C22×Q8C2411yescharacteristic
818C22×Q8C2412yes—
819C22×D4—28no—
820C22×D4—28no—
821C22×D4—216no—
822C22×D4—216no—
823C22×D4—216no—
824C22×D4—216no—
825C22×D4—216no—
826C22×D4—216no—
827C22×D4—216no—
828C22×D4—28no—
829C22×D4—216no—
830C22×D4—28no—
831C22×D4—28no—
832C22×D4—216no—
833C22×D4—28no—
834C22×D4—28no—
835C22×D4—216no—
836C22×D4—216no—
837C22×D4—28no—
838C22×D4—44no—
839C22×D4—42no—
840C22×D4—44no—
841C22×D4—48no—
842C22×D4—48no—
843C22×D4—48no—
844C22×D4—44no—
845C22×D4—44no—
846C22×D4—48no—
847C22×D4—48no—
848C22×D4—48no—
849C22×D4—82no—
850C22×D4—84no—
851C22×D4—84no—
852C22×D4C2×D4116yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C22×D4C2412yes—
860C22×D4C2411yescharacteristic
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C22×D4C2411yescharacteristic
867C22×D4C2412yes—
868C22×D4C2414yes—
869C22×D4C2412yes—
870C22×D4C2412yes—
871C22×D4C2412yes—
872C22×D4C2414yes—
873C22×D4C2414yes—
874C22×D4C2412yes—
875C22×D4C2414yes—
876C22×D4C2412yes—
877C22×D4C2414yes—
878C22×D4C2412yes—
879C22×D4C2414yes—
880C22×D4C2412yes—
881C22×D4C2414yes—
882C22×D4C2412yes—
883C22×D4C2411yescharacteristic
884C22×D4C2411yescharacteristic
885C22×D4C2414yes—
886C22×D4C2414yes—
887C22×D4C2414yes—
888C22×D4C2412yes—
889C22×D4C2412yes—
890C22×D4C2414yes—
891C22×D4C2412yes—
892C22×D4C2414yes—
893C22×D4C2411yescharacteristic
894C23×C4—216no—
895C23×C4—48no—
896C23×C4—84no—
897C23×C4C2412yes—
898C23×C4C2412yes—
899C23×C4C2411yescharacteristic
900C23×C4C2411yescharacteristic
901C23×C4C2412yes—
902C23×C4C2412yes—
903C23×C4C2414yes—
904C23×C4C2414yes—
905C23×C4C2414yes—
906C23×C4C2414yes—
907C23×C4C2414yes—
908C23×C4C2412yes—
909C23×C4C2414yes—
910C23×C4C2412yes—
911C23×C4C2414yes—
912C23×C4C2412yes—
913C23×C4C2412yes—
914C23×C4C2414yes—
915C23×C4C2412yes—
916C23×C4C2412yes—
917C23×C4C2414yes—
918C23×C4C2412yes—
919C23×C4C2414yes—
920C23×C4C2414yes—
921C4⋊Q8—28no—
922C4⋊Q8—216no—
923C4⋊Q8—28no—
924C4⋊Q8—28no—
925C4⋊Q8—42no—
926#127—216no—
927#127—28no—
928#127—28no—
929#127—28no—
930#127—42no—
931#127—42no—
932#127—82no—
933#124—28no—
934#124—28no—
935#124—216no—
936#124—28no—
937#124—216no—
938#124—216no—
939#124—216no—
940#124—216no—
941#124—216no—
942#124—216no—
943#124—216no—
944#124—28no—
945#124—28no—
946#124—28no—
947#124—28no—
948#124—28no—
949#124C2×D4116yescomplemented
950#123—216no—
951#123—216no—
952#123—216no—
953#123—216no—
954#123—216no—
955#123—216no—
956#123—216no—
957#123—216no—
958#123—216no—
959#123—216no—
960#123—216no—
961#123—216no—
962#123—44no—
963#123—44no—
964#123C2×D4132yescomplemented
965C22⋊Q8—28no—
966C22⋊Q8—28no—
967C22⋊Q8—28no—
968C22⋊Q8—28no—
969C22⋊Q8—216no—
970C22⋊Q8—216no—
971C22⋊Q8—28no—
972C22⋊Q8—216no—
973C22⋊Q8—28no—
974C22⋊Q8—216no—
975C22⋊Q8—216no—
976C22⋊Q8—216no—
977C22⋊Q8—42no—
978C22⋊Q8—42no—
979C22⋊Q8C2×D4116yescomplemented
980#121—216no—
981#121—216no—
982#121—216no—
983#121—28no—
984#121—28no—
985#121—216no—
986#121—216no—
987#121—28no—
988#121—216no—
989#121—216no—
990#121—28no—
991#121—216no—
992#121—216no—
993#121—216no—
994#121—28no—
995#121—28no—
996#121—216no—
997#121—28no—
998#121—28no—
999#121—28no—
1000#121—28no—
1001#121—216no—
1002#121—28no—
1003#121—28no—
1004#121—216no—
1005#121—216no—
1006#121—216no—
1007#121—216no—
1008#121—216no—
1009#121—216no—
1010#121—216no—
1011#121—28no—
1012#121—28no—
1013#121—216no—
1014#121—216no—
1015#121—216no—
1016#121—48no—
1017#121—44no—
1018#121—44no—
1019#121—44no—
1020#121—44no—
1021#121—44no—
1022#121—84no—
1023#121C2×D4132yescomplemented
1024#121C2×D4116yescomplemented
1025#120—216no—
1026#120—216no—
1027#120—216no—
1028#120—216no—
1029#120—216no—
1030#120—216no—
1031#120—216no—
1032#120—216no—
1033#120—216no—
1034#120—216no—
1035#120—216no—
1036#120—216no—
1037#120—44no—
1038#120—48no—
1039#120—48no—
1040#120—48no—
1041#120—84no—
1042#120C2×D4132yescomplemented
1043C4×Q8—28no—
1044C4×Q8—28no—
1045C4×D4—28no—
1046C4×D4—28no—
1047C4×D4—216no—
1048C4×D4—24no—
1049C4×D4—216no—
1050C4×D4—216no—
1051C4×D4—28no—
1052C4×D4—28no—
1053C4×D4—28no—
1054C4×D4—28no—
1055C4×D4—28no—
1056C4×D4—216no—
1057C4×D4—216no—
1058C4×D4—216no—
1059C4×D4—216no—
1060C4×D4—216no—
1061C4×D4—216no—
1062C4×D4—216no—
1063C4×D4—28no—
1064C4×D4—28no—
1065C4×D4—28no—
1066C4×D4—44no—
1067C4×D4—42no—
1068C4×D4—42no—
1069C4×D4—44no—
1070C4×D4—84no—
1071C4×D4C2×D4116yescomplemented
1072C4×D4C2×D4116yescomplemented
1073#117—28no—
1074#117—216no—
1075C2×C4⋊C4—216no—
1076C2×C4⋊C4—28no—
1077C2×C4⋊C4—216no—
1078C2×C4⋊C4—44no—
1079C2×C4⋊C4C2414yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2412yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2414yes—
1084C2×C4⋊C4C2414yes—
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2414yes—
1087C2×C4⋊C4C2412yes—
1088C2×C4⋊C4C2414yes—
1089C2×C4⋊C4C2414yes—
1090C2×C4⋊C4C2411yescharacteristic
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2414yes—
1093C2×C4⋊C4C2412yes—
1094C2×C4⋊C4C2414yes—
1095C2×C4⋊C4C2414yes—
1096C2×C4⋊C4C2412yes—
1097C2×C4⋊C4C2412yes—
1098C2×C4⋊C4C2412yes—
1099C2×C4⋊C4C2414yes—
1100C2×C4⋊C4C2411yescharacteristic
1101C2×C4⋊C4C2412yes—
1102C2×C4⋊C4C2412yes—
1103C2×C4⋊C4C2412yes—
1104C2×C4⋊C4C2411yescharacteristic
1105C2×C4⋊C4C2414yes—
1106C2×C4⋊C4C2412yes—
1107C2×C4⋊C4C2414yes—
1108C2×C4⋊C4C2412yes—
1109C2×C4⋊C4C2412yes—
1110C2×C4⋊C4C2414yes—
1111C2×C4⋊C4C2412yes—
1112C2×C22⋊C4—216no—
1113C2×C22⋊C4—216no—
1114C2×C22⋊C4—216no—
1115C2×C22⋊C4—216no—
1116C2×C22⋊C4—216no—
1117C2×C22⋊C4—216no—
1118C2×C22⋊C4—216no—
1119C2×C22⋊C4—216no—
1120C2×C22⋊C4—216no—
1121C2×C22⋊C4—48no—
1122C2×C22⋊C4—48no—
1123C2×C22⋊C4C2×D4132yescomplemented
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2412yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2412yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2412yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1158C2×C22⋊C4C2412yes—
1159C2×C22⋊C4C2412yes—
1160C2×C22⋊C4C2412yes—
1161C2×C22⋊C4C2412yes—
1162C2×C22⋊C4C2412yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2412yes—
1165C2×C22⋊C4C2412yes—
1166C2×C22⋊C4C2412yes—
1167C2×C22⋊C4C2412yes—
1168C2×C22⋊C4C2412yes—
1169C2×C22⋊C4C2414yes—
1170C2×C22⋊C4C2414yes—
1171C2×C22⋊C4C2414yes—
1172C2×C22⋊C4C2414yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2414yes—
1175C2×C22⋊C4C2414yes—
1176C2×C22⋊C4C2411yescharacteristic
1177C2×C22⋊C4C2411yescharacteristic
1178C2×C22⋊C4C2412yes—
1179C2×C22⋊C4C2414yes—
1180C2×C22⋊C4C2414yes—
1181C2×C22⋊C4C2414yes—
1182C2×C22⋊C4C2412yes—
1183C2×C22⋊C4C2414yes—
1184C2×C22⋊C4C2412yes—
1185C2×C22⋊C4C2412yes—
1186C2×C22⋊C4C2412yes—
1187C2×C22⋊C4C2412yes—
1188C2×C22⋊C4C2412yes—
1189C2×C22⋊C4C2414yes—
1190C2×C22⋊C4C2412yes—
1191C2×C22⋊C4C2412yes—
1192C2×C22⋊C4C2414yes—
1193C2×C22⋊C4C2414yes—
1194C2×C22⋊C4C2414yes—
1195C2×C22⋊C4C2414yes—
1196C2×C42—216no—
1197C2×C42—28no—
1198C2×C42—28no—
1199C2×C42—82no—
1200C2×C42C2414yes—
1201C2×C42C2412yes—
1202C2×C42C2412yes—
1203C2×C42C2412yes—
1204C2×C42C2412yes—
1205C2×C42C2414yes—
1206C2×C42C2412yes—
1207C2×C42C2414yes—
1208C2×C42C2411yescharacteristic
1209C2×C42C2411yescharacteristic
1210C2×C42C2412yes—
1211C2×C42C2412yes—
1212C2×C42C2414yes—
1213C2×C42C2412yes—
1214C2×C42C2411yescharacteristic
1215C2×C42C2412yes—
1216#95C2412yes—
1217#95C2412yes—
1218#95C2411yescharacteristic
1219#95C2411yescharacteristic
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226#95C2412yes—
1227#95C2412yes—
1228#95C2414yes—
1229#95C2414yes—
1230#95C2412yes—
1231#95C2412yes—
1232#95C2412yes—
1233#95C2412yes—
1234#95C2412yes—
1235#95C2414yes—
1236#95C2411yescharacteristic
1237#95C2412yes—
1238#95C2412yes—
1239#95C2411yescharacteristic
1240#95C2414yes—
1241#95C2414yes—
1242#95C2414yes—
1243#95C2414yes—
1244#95C2414yes—
1245#95C2414yes—
1246#95C2414yes—
1247C24—28no—
1248C24—28no—
1249C24—28no—
1250C24—28no—
1251C24—28no—
1252C24—28no—
1253C24—28no—
1254C24—28no—
1255C24—44no—
1256C24—44no—
1257C24—44no—
1258C24—44no—
1259C24—44no—
1260C24—42no—
1261C24—44no—
1262C24—44no—
1263C24—44no—
1264C24—44no—
1265C24—42no—
1266C24—44no—
1267C24—44no—
1268C24—44no—
1269C24—44no—
1270C24—44no—
1271C24—42no—
1272C24C22×D4116yes—
1273C24C2512yes—
1274C24C2514yes—
1275C24C2511yescharacteristic
1276C24C2511yescharacteristic
1277C24C2514yes—
1278C24C2512yes—
1279C24C2512yes—
1280C24C2512yes—
1281#41—264no—
1282#41—416no—
1283#41—432no—
1284#41—416no—
1285#41—464no—
1286#41—432no—
1287#41—464no—
1288#41—432no—
1289#41—432no—
1290#41—432no—
1291#41—432no—
1292#41—416no—
1293#41—416no—
1294C2×Q8—24no—
1295C2×Q8—28no—
1296C2×Q8—28no—
1297C2×Q8—24no—
1298C2×Q8—24no—
1299C2×Q8—24no—
1300C2×Q8—24no—
1301C2×Q8—28no—
1302C2×Q8—24no—
1303C2×Q8—24no—
1304C2×Q8—24no—
1305C2×Q8—22no—
1306C2×Q8—22no—
1307C2×Q8—41no—
1308C2×Q8—44no—
1309C2×Q8—42no—
1310C2×Q8—42no—
1311C2×Q8—41no—
1312C2×Q8—432no—
1313C2×Q8—432no—
1314C2×Q8—416no—
1315C2×Q8C22×D418yes—
1316C2×D4—28no—
1317C2×D4—28no—
1318C2×D4—28no—
1319C2×D4—28no—
1320C2×D4—264no—
1321C2×D4—28no—
1322C2×D4—24no—
1323C2×D4—24no—
1324C2×D4—24no—
1325C2×D4—28no—
1326C2×D4—28no—
1327C2×D4—28no—
1328C2×D4—28no—
1329C2×D4—28no—
1330C2×D4—28no—
1331C2×D4—24no—
1332C2×D4—24no—
1333C2×D4—24no—
1334C2×D4—28no—
1335C2×D4—28no—
1336C2×D4—28no—
1337C2×D4—24no—
1338C2×D4—24no—
1339C2×D4—28no—
1340C2×D4—24no—
1341C2×D4—24no—
1342C2×D4—28no—
1343C2×D4—24no—
1344C2×D4—24no—
1345C2×D4—28no—
1346C2×D4—24no—
1347C2×D4—28no—
1348C2×D4—28no—
1349C2×D4—24no—
1350C2×D4—28no—
1351C2×D4—28no—
1352C2×D4—24no—
1353C2×D4—24no—
1354C2×D4—28no—
1355C2×D4—28no—
1356C2×D4—28no—
1357C2×D4—24no—
1358C2×D4—24no—
1359C2×D4—24no—
1360C2×D4—24no—
1361C2×D4—24no—
1362C2×D4—24no—
1363C2×D4—24no—
1364C2×D4—28no—
1365C2×D4—28no—
1366C2×D4—24no—
1367C2×D4—24no—
1368C2×D4—28no—
1369C2×D4—24no—
1370C2×D4—24no—
1371C2×D4—22no—
1372C2×D4—22no—
1373C2×D4—24no—
1374C2×D4—432no—
1375C2×D4—41no—
1376C2×D4—42no—
1377C2×D4—42no—
1378C2×D4—44no—
1379C2×D4—42no—
1380C2×D4—44no—
1381C2×D4—42no—
1382C2×D4—42no—
1383C2×D4—44no—
1384C2×D4—44no—
1385C2×D4—42no—
1386C2×D4—41no—
1387C2×D4—42no—
1388C2×D4—44no—
1389C2×D4—44no—
1390C2×D4—41no—
1391C2×D4—42no—
1392C2×D4—44no—
1393C2×D4—42no—
1394C2×D4—42no—
1395C2×D4—41no—
1396C2×D4—464no—
1397C2×D4—41no—
1398C2×D4—44no—
1399C2×D4—44no—
1400C2×D4—44no—
1401C2×D4—44no—
1402C2×D4—44no—
1403C2×D4—42no—
1404C2×D4—44no—
1405C2×D4—44no—
1406C2×D4—42no—
1407C2×D4—42no—
1408C2×D4—42no—
1409C2×D4—44no—
1410C2×D4—44no—
1411C2×D4—44no—
1412C2×D4—42no—
1413C2×D4—42no—
1414C2×D4—42no—
1415C2×D4—44no—
1416C2×D4—44no—
1417C2×D4—42no—
1418C2×D4—42no—
1419C2×D4—41no—
1420C2×D4—42no—
1421C2×D4—44no—
1422C2×D4—44no—
1423C2×D4—44no—
1424C2×D4—44no—
1425C2×D4—44no—
1426C2×D4—42no—
1427C2×D4—44no—
1428C2×D4—464no—
1429C2×D4—416no—
1430C2×D4—464no—
1431C2×D4—464no—
1432C2×D4—432no—
1433C2×D4—432no—
1434C2×D4—832no—
1435C2×D4—832no—
1436C2×D4—816no—
1437C2×D4C22×D4116yes—
1438C2×D4C22×D4116yes—
1439C2×D4C22×D418yes—
1440C2×D4C22×D4116yes—
1441C2×D4C22×D418yes—
1442C2×D4C22×D418yes—
1443C2×D4H(5,𝔽2)14yes—
1444C22×C4—28no—
1445C22×C4—28no—
1446C22×C4—24no—
1447C22×C4—24no—
1448C22×C4—24no—
1449C22×C4—24no—
1450C22×C4—28no—
1451C22×C4—28no—
1452C22×C4—28no—
1453C22×C4—28no—
1454C22×C4—28no—
1455C22×C4—28no—
1456C22×C4—24no—
1457C22×C4—24no—
1458C22×C4—24no—
1459C22×C4—28no—
1460C22×C4—24no—
1461C22×C4—28no—
1462C22×C4—28no—
1463C22×C4—28no—
1464C22×C4—28no—
1465C22×C4—28no—
1466C22×C4—24no—
1467C22×C4—28no—
1468C22×C4—24no—
1469C22×C4—24no—
1470C22×C4—28no—
1471C22×C4—24no—
1472C22×C4—24no—
1473C22×C4—22no—
1474C22×C4—22no—
1475C22×C4—24no—
1476C22×C4—28no—
1477C22×C4—24no—
1478C22×C4—28no—
1479C22×C4—24no—
1480C22×C4—24no—
1481C22×C4—24no—
1482C22×C4—28no—
1483C22×C4—28no—
1484C22×C4—44no—
1485C22×C4—42no—
1486C22×C4—44no—
1487C22×C4—42no—
1488C22×C4—44no—
1489C22×C4—44no—
1490C22×C4—44no—
1491C22×C4—44no—
1492C22×C4—44no—
1493C22×C4—42no—
1494C22×C4—44no—
1495C22×C4—44no—
1496C22×C4—44no—
1497C22×C4—42no—
1498C22×C4—42no—
1499C22×C4—42no—
1500C22×C4—42no—
1501C22×C4—44no—
1502C22×C4—42no—
1503C22×C4—42no—
1504C22×C4—44no—
1505C22×C4—44no—
1506C22×C4—44no—
1507C22×C4—832no—
1508C22×C4C22×D4116yes—
1509C22×C4C22×D418yes—
1510C22×C4C22×D418yes—
1511C22×C4C22×D4116yes—
1512C22×C4C2511yescharacteristic
1513C22×C4C2512yes—
1514C22×C4C2514yes—
1515C22×C4C2512yes—
1516C22×C4C2512yes—
1517C22×C4C2514yes—
1518C22×C4C2512yes—
1519C22×C4C2511yescharacteristic
1520C22×C4C2512yes—
1521C22×C4C2511yescharacteristic
1522C22×C4C2512yes—
1523C22×C4C2512yes—
1524C22×C4C2512yes—
1525C22×C4C2512yes—
1526C22×C4C2514yes—
1527C22×C4C2512yes—
1528C22×C4C2514yes—
1529C22×C4C2512yes—
1530C22×C4C2512yes—
1531C22×C4C2511yescharacteristic
1532C22×C4C2511yescharacteristic
1533C4⋊C4—28no—
1534C4⋊C4—24no—
1535C4⋊C4—24no—
1536C4⋊C4—28no—
1537C4⋊C4—24no—
1538C4⋊C4—28no—
1539C4⋊C4—28no—
1540C4⋊C4—28no—
1541C4⋊C4—28no—
1542C4⋊C4—28no—
1543C4⋊C4—24no—
1544C4⋊C4—28no—
1545C4⋊C4—24no—
1546C4⋊C4—28no—
1547C4⋊C4—24no—
1548C4⋊C4—24no—
1549C4⋊C4—28no—
1550C4⋊C4—28no—
1551C4⋊C4—24no—
1552C4⋊C4—22no—
1553C4⋊C4—24no—
1554C4⋊C4—41no—
1555C4⋊C4—42no—
1556C4⋊C4—42no—
1557C4⋊C4—42no—
1558C4⋊C4—42no—
1559C4⋊C4—41no—
1560C4⋊C4—44no—
1561C4⋊C4—44no—
1562C4⋊C4—42no—
1563C4⋊C4C22×D418yes—
1564C4⋊C4C22×D4116yes—
1565C4⋊C4C22×D418yes—
1566C22⋊C4—28no—
1567C22⋊C4—24no—
1568C22⋊C4—28no—
1569C22⋊C4—28no—
1570C22⋊C4—28no—
1571C22⋊C4—28no—
1572C22⋊C4—28no—
1573C22⋊C4—28no—
1574C22⋊C4—28no—
1575C22⋊C4—24no—
1576C22⋊C4—24no—
1577C22⋊C4—24no—
1578C22⋊C4—24no—
1579C22⋊C4—24no—
1580C22⋊C4—28no—
1581C22⋊C4—24no—
1582C22⋊C4—28no—
1583C22⋊C4—24no—
1584C22⋊C4—24no—
1585C22⋊C4—28no—
1586C22⋊C4—28no—
1587C22⋊C4—28no—
1588C22⋊C4—28no—
1589C22⋊C4—28no—
1590C22⋊C4—28no—
1591C22⋊C4—28no—
1592C22⋊C4—28no—
1593C22⋊C4—28no—
1594C22⋊C4—28no—
1595C22⋊C4—28no—
1596C22⋊C4—28no—
1597C22⋊C4—28no—
1598C22⋊C4—28no—
1599C22⋊C4—24no—
1600C22⋊C4—24no—
1601C22⋊C4—24no—
1602C22⋊C4—24no—
1603C22⋊C4—28no—
1604C22⋊C4—24no—
1605C22⋊C4—24no—
1606C22⋊C4—28no—
1607C22⋊C4—28no—
1608C22⋊C4—24no—
1609C22⋊C4—24no—
1610C22⋊C4—24no—
1611C22⋊C4—44no—
1612C22⋊C4—44no—
1613C22⋊C4—44no—
1614C22⋊C4—44no—
1615C22⋊C4—42no—
1616C22⋊C4—42no—
1617C22⋊C4—41no—
1618C22⋊C4—41no—
1619C22⋊C4—44no—
1620C22⋊C4—44no—
1621C22⋊C4—44no—
1622C22⋊C4—42no—
1623C22⋊C4—44no—
1624C22⋊C4—44no—
1625C22⋊C4—44no—
1626C22⋊C4—42no—
1627C22⋊C4—42no—
1628C22⋊C4—42no—
1629C22⋊C4—42no—
1630C22⋊C4—42no—
1631C22⋊C4C22×D4116yes—
1632C22⋊C4C22×D418yes—
1633C22⋊C4C22×D4116yes—
1634C22⋊C4C22×D4116yes—
1635C22⋊C4C22×D418yes—
1636C22⋊C4C22×D4116yes—
1637C22⋊C4C22×D4116yes—
1638C42—24no—
1639C42—24no—
1640C42—28no—
1641C42—24no—
1642C42—24no—
1643C42—24no—
1644C42—28no—
1645C42—28no—
1646C42—24no—
1647C42—22no—
1648C42—22no—
1649C42—41no—
1650C42—44no—
1651C42—42no—
1652C42—42no—
1653C42C22×D418yes—
1654C23—24no—
1655C23—22no—
1656C23—22no—
1657C23—22no—
1658C23—24no—
1659C23—22no—
1660C23—22no—
1661C23—22no—
1662C23—24no—
1663C23—22no—
1664C23—24no—
1665C23—22no—
1666C23—22no—
1667C23—22no—
1668C23—24no—
1669C23—24no—
1670C23—22no—
1671C23—22no—
1672C23—22no—
1673C23—24no—
1674C23—22no—
1675C23—232no—
1676C23—24no—
1677C23—22no—
1678C23—22no—
1679C23—24no—
1680C23—22no—
1681C23—22no—
1682C23—21no—
1683C23—21no—
1684C23—22no—
1685C23—24no—
1686C23—22no—
1687C23—24no—
1688C23—22no—
1689C23—21no—
1690C23—22no—
1691C23—22no—
1692C23—24no—
1693C23—21no—
1694C23—24no—
1695C23—22no—
1696C23—21no—
1697C23—24no—
1698C23—21no—
1699C23—22no—
1700C23—416no—
1701C23—416no—
1702C23—416no—
1703C23—48no—
1704C23—416no—
1705C23—88no—
1706C23—88no—
1707C23—88no—
1708C23—88no—
1709C23—88no—
1710C23—88no—
1711C23—88no—
1712C23—88no—
1713C23—88no—
1714C23—88no—
1715C23—88no—
1716C23—88no—
1717C23—88no—
1718C23—88no—
1719C23—88no—
1720C23—88no—
1721C23—162no—
1722C23—164no—
1723C23—162no—
1724C23—164no—
1725C23C23×D418yes—
1726C23C23×D414yes—
1727C23C23×D414yes—
1728C23C23×D418yes—
1729C23C2×H(5,𝔽2)14yes—
1730C23C2611yescharacteristic
1731Q8—216no—
1732Q8—44no—
1733Q8—416no—
1734Q8—48no—
1735Q8—48no—
1736Q8—44no—
1737Q8—44no—
1738Q8—44no—
1739D4—232no—
1740D4—232no—
1741D4—216no—
1742D4—416no—
1743D4—48no—
1744D4—48no—
1745D4—416no—
1746D4—48no—
1747D4—48no—
1748D4—416no—
1749D4—416no—
1750D4—48no—
1751D4—416no—
1752D4—48no—
1753D4—48no—
1754D4—44no—
1755D4—48no—
1756D4—44no—
1757D4—416no—
1758D4—48no—
1759D4—44no—
1760D4—48no—
1761D4—416no—
1762D4—48no—
1763D4—48no—
1764D4—88no—
1765D4—84no—
1766D4—84no—
1767D4—82no—
1768D4—88no—
1769D4—84no—
1770D4—84no—
1771D4—84no—
1772D4—88no—
1773D4—88no—
1774D4—88no—
1775D4—88no—
1776D4—88no—
1777D4—88no—
1778D4—162no—
1779D4D42116yes—
1780C2×C4—22no—
1781C2×C4—22no—
1782C2×C4—22no—
1783C2×C4—24no—
1784C2×C4—21no—
1785C2×C4—22no—
1786C2×C4—22no—
1787C2×C4—24no—
1788C2×C4—22no—
1789C2×C4—22no—
1790C2×C4—22no—
1791C2×C4—24no—
1792C2×C4—22no—
1793C2×C4—21no—
1794C2×C4—24no—
1795C2×C4—22no—
1796C2×C4—232no—
1797C2×C4—216no—
1798C2×C4—216no—
1799C2×C4—22no—
1800C2×C4—22no—
1801C2×C4—22no—
1802C2×C4—24no—
1803C2×C4—24no—
1804C2×C4—22no—
1805C2×C4—24no—
1806C2×C4—22no—
1807C2×C4—24no—
1808C2×C4—22no—
1809C2×C4—22no—
1810C2×C4—21no—
1811C2×C4—22no—
1812C2×C4—22no—
1813C2×C4—21no—
1814C2×C4—21no—
1815C2×C4—22no—
1816C2×C4—22no—
1817C2×C4—22no—
1818C2×C4—22no—
1819C2×C4—24no—
1820C2×C4—22no—
1821C2×C4—24no—
1822C2×C4—22no—
1823C2×C4—22no—
1824C2×C4—22no—
1825C2×C4—22no—
1826C2×C4—24no—
1827C2×C4—22no—
1828C2×C4—22no—
1829C2×C4—24no—
1830C2×C4—416no—
1831C2×C4—48no—
1832C2×C4—416no—
1833C2×C4—416no—
1834C2×C4—48no—
1835C2×C4—416no—
1836C2×C4—416no—
1837C2×C4—416no—
1838C2×C4—48no—
1839C2×C4—416no—
1840C2×C4—48no—
1841C2×C4—48no—
1842C2×C4—44no—
1843C2×C4—48no—
1844C2×C4—44no—
1845C2×C4—84no—
1846C2×C4—84no—
1847C2×C4—84no—
1848C2×C4—88no—
1849C2×C4—88no—
1850C2×C4—88no—
1851C2×C4C23×D414yes—
1852C2×C4C23×D414yes—
1853C2×C4C23×D418yes—
1854C2×C4C23×D418yes—
1855C2×C4C23×D414yes—
1856C2×C4C23×D414yes—
1857C2×C4C23×D414yes—
1858C2×C4C2×H(5,𝔽2)12yes—
1859C2×C4#58512yes—
1860C2×C4#58514yes—
1861C22—28no—
1862C22—24no—
1863C22—28no—
1864C22—24no—
1865C22—24no—
1866C22—28no—
1867C22—24no—
1868C22—24no—
1869C22—24no—
1870C22—28no—
1871C22—24no—
1872C22—24no—
1873C22—28no—
1874C22—42no—
1875C22—44no—
1876C22—42no—
1877C22—42no—
1878C22—44no—
1879C22—42no—
1880C22—42no—
1881C22—42no—
1882C22—44no—
1883C22—42no—
1884C22—44no—
1885C22—42no—
1886C22—42no—
1887C22—44no—
1888C22—42no—
1889C22—42no—
1890C22—44no—
1891C22—42no—
1892C22—44no—
1893C22—41no—
1894C22—42no—
1895C22—41no—
1896C22—42no—
1897C22—42no—
1898C22—42no—
1899C22—42no—
1900C22—44no—
1901C22—44no—
1902C22—42no—
1903C22—44no—
1904C22—41no—
1905C22—41no—
1906C22—41no—
1907C22—44no—
1908C22—42no—
1909C22—41no—
1910C22—832no—
1911C22—1616no—
1912C22—168no—
1913C22—1616no—
1914C22C2×D4218yes—
1915C22C24×D412yes—
1916C22C22×H(5,𝔽2)11yescharacteristic
1917C22C2×#58512yes—
1918C22C2×#58511yescharacteristic
1919C22H(7,𝔽2)11yescharacteristic
1920C4—24no—
1921C4—24no—
1922C4—28no—
1923C4—24no—
1924C4—22no—
1925C4—24no—
1926C4—24no—
1927C4—28no—
1928C4—44no—
1929C4—42no—
1930C4—41no—
1931C4—42no—
1932C4—42no—
1933C4—44no—
1934C4—42no—
1935C4—41no—
1936C4—42no—
1937C4—42no—
1938C4—41no—
1939C4—42no—
1940C4C2×D4214yes—
1941C2—28no—
1942C2—44no—
1943C2—48no—
1944C2—44no—
1945C2—81no—
1946C2—81no—
1947C2—84no—
1948C2—82no—
1949C2C22×D4211yescharacteristic
1950C2#6281212yes—
1951C2#6291811yescharacteristic
1952C2#6298712yes—
1953C2#6302411yescharacteristic
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×#3500C2semidirect
2. C2×#3496C2semidirect
3. #59818C2semidirect
4. #59814C2semidirect
5. #59131C2semidirect
6. #59128C2semidirect
7. #59123C2semidirect
8. #59122C2semidirect
9. #45244C2semidirect
10. #45091C2semidirect
11. #44870C2semidirect
12. #44758C2semidirect
13. #43886C2semidirect
14. #43017C2semidirect
15. #39335C2semidirect
16. #39334C2semidirect
17. #39333C2semidirect
18. #39332C2semidirect
19. #36260C2semidirect
20. #36218C2semidirect
21. #36214C2semidirect
22. #36124C2semidirect
23. #36123C2semidirect
24. #36085C2semidirect
25. #35750C2semidirect
26. #35680C2semidirect
27. #34925C2semidirect
28. C2×#2555C2semidirect
29. C4×#546C2semidirect
30. C22×2−1+4C22semidirect
32. C22×H(5,𝔽2)C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
39. C2×#547C22semidirect
40. C2×#547C22semidirect
41. C2×#547C22semidirect
42. C2×#547C22semidirect
44. C2×#546C22semidirect
45. C2×#546C22semidirect
46. C2×#546C22semidirect
47. C2×#546C22semidirect
48. C2×#546C22semidirect
49. C2×#546C22semidirect
50. C2×#546C22semidirect
51. C2×#546C22semidirect
52. C2×#546C22semidirect
53. C2×#546C22semidirect
54. C2×#546C22semidirect
55. C2×#546C22semidirect
57. C2×D42C22semidirect
58. C2×D42C22semidirect
59. C2×D42C22semidirect
60. C2×#537C22semidirect
61. C2×#537C22semidirect
62. C2×#536C22semidirect
63. C2×#536C22semidirect
64. C2×#535C22semidirect
65. C2×#535C22semidirect
66. C2×#534C22semidirect
67. C2×#534C22semidirect
68. C2×#532C22semidirect
69. C2×#532C22semidirect
70. C2×#532C22semidirect
71. C2×#532C22semidirect
72. C22×#124C22semidirect
73. C22×#124C22semidirect
74. C22×#121C22semidirect
75. C22×#121C22semidirect
76. C2×C4×#41C22semidirect
77. C22×C4×D4C22semidirect
78. #2858C22semidirect
79. #2856C22semidirect
80. #2854C22semidirect
81. #2850C22semidirect
82. #2850C22semidirect
83. #2847C22semidirect
84. #2683C22semidirect
85. #2682C22semidirect
86. #2680C22semidirect
87. #2679C22semidirect
88. #2677C22semidirect
89. #2676C22semidirect
90. #2676C22semidirect
91. #2675C22semidirect
92. #2675C22semidirect
93. #2674C22semidirect
94. #2674C22semidirect
95. #2673C22semidirect
96. #2673C22semidirect
97. #2672C22semidirect
98. #2672C22semidirect
99. #2672C22semidirect
100. #2671C22semidirect
101. #2671C22semidirect
102. #2670C22semidirect
103. #2670C22semidirect
104. #2669C22semidirect
105. #2669C22semidirect
106. #2669C22semidirect
107. #2668C22semidirect
108. #2616C22semidirect
109. #2616C22semidirect
110. #2615C22semidirect
111. #2614C22semidirect
112. #2613C22semidirect
113. #2613C22semidirect
114. #2555C22semidirect
115. #2555C22semidirect
116. #2555C22semidirect
117. #2555C22semidirect
118. #2555C22semidirect
119. #2555C22semidirect
120. #2555C22semidirect
121. #2555C22semidirect
122. #2555C22semidirect
123. #2555C22semidirect
124. #2555C22semidirect
125. #2555C22semidirect
126. #2555C22semidirect
127. #2551C22semidirect
128. #2545C22semidirect
129. #2544C22semidirect
130. #2543C22semidirect
131. #2543C22semidirect
132. #2542C22semidirect
133. #2541C22semidirect
134. #2541C22semidirect
135. #2540C22semidirect
136. #2540C22semidirect
137. #2539C22semidirect
138. #2539C22semidirect
139. #2537C22semidirect
140. #2536C22semidirect
141. #2535C22semidirect
142. #2534C22semidirect
143. #2534C22semidirect
144. #2501C22semidirect
145. #2491C22semidirect
146. #2491C22semidirect
147. #2491C22semidirect
148. #2472C22semidirect
149. #2472C22semidirect
150. #2472C22semidirect
151. #2464C22semidirect
152. #2464C22semidirect
153. #2464C22semidirect
154. #2463C22semidirect
155. #2461C22semidirect
156. #2461C22semidirect
157. #2461C22semidirect
158. #2461C22semidirect
159. #2456C22semidirect
160. #2449C22semidirect
161. #2443C22semidirect
162. #2440C22semidirect
163. #2435C22semidirect
164. #2434C22semidirect
165. #2434C22semidirect
166. #2433C22semidirect
167. #2433C22semidirect
168. #2433C22semidirect
169. #2432C22semidirect
170. #2431C22semidirect
171. #2431C22semidirect
172. #2430C22semidirect
173. #2430C22semidirect
174. #2430C22semidirect
175. #2430C22semidirect
176. #2429C22semidirect
177. #2428C22semidirect
178. #2428C22semidirect
179. #2428C22semidirect
180. #2428C22semidirect
181. #2428C22semidirect
182. #2427C22semidirect
183. #2426C22semidirect
184. #2425C22semidirect
185. #2425C22semidirect
186. #2424C22semidirect
187. #2424C22semidirect
188. #2424C22semidirect
189. #2424C22semidirect
190. #2424C22semidirect
191. #2424C22semidirect
192. #2422C22semidirect
193. #2418C22semidirect
194. #2417C22semidirect
195. #2416C22semidirect
196. #2415C22semidirect
197. #2414C22semidirect
198. #2413C22semidirect
199. #2412C22semidirect
200. #2411C22semidirect
201. #2410C22semidirect
202. #2410C22semidirect
203. #2410C22semidirect
204. #2410C22semidirect
205. #2410C22semidirect
206. #2409C22semidirect
207. #2409C22semidirect
208. #2408C22semidirect
209. #2408C22semidirect
210. #2407C22semidirect
211. #2407C22semidirect
212. #2407C22semidirect
213. #2406C22semidirect
214. #2406C22semidirect
215. #2406C22semidirect
216. #2405C22semidirect
217. #2404C22semidirect
218. #2403C22semidirect
219. #2403C22semidirect
220. #2403C22semidirect
221. #2388C22semidirect
222. #2388C22semidirect
223. #2388C22semidirect
224. C2×#395C22semidirect
225. C2×#394C22semidirect
226. C2×#392C22semidirect
227. #2367C22semidirect
228. #2364C22semidirect
229. #2363C22semidirect
230. #2361C22semidirect
231. #2360C22semidirect
232. #2359C22semidirect
233. #2358C22semidirect
234. #2358C22semidirect
235. #2358C22semidirect
236. #2358C22semidirect
237. #2352C22semidirect
238. #2349C22semidirect
239. #2342C22semidirect
240. #2339C22semidirect
241. #2339C22semidirect
242. #2339C22semidirect
243. D4×C22⋊C4C22semidirect
244. D4×C22⋊C4C22semidirect
245. D4×C22⋊C4C22semidirect
246. C4×#127C22semidirect
247. C4×#124C22semidirect
248. C4×C22⋊Q8C22semidirect
249. C4×#123C22semidirect
250. C4×#121C22semidirect
251. C4×#121C22semidirect
252. C4×#121C22semidirect
253. C4×#121C22semidirect
254. C4×#120C22semidirect
255. C2×#390C22semidirect
256. C2×#388C22semidirect
257. C2×#386C22semidirect
258. C42×D4C22semidirect
259. C42×D4C22semidirect
260. C2×C4×C22⋊C4C22semidirect
317. #546D4semidirect
803. C2×#41C2×D4semidirect
949. #124C2×D4semidirect
964. #123C2×D4semidirect
979. C22⋊Q8C2×D4semidirect
1023. #121C2×D4semidirect
1024. #121C2×D4semidirect
1042. #120C2×D4semidirect
1071. C4×D4C2×D4semidirect
1072. C4×D4C2×D4semidirect
1123. 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×#35002
C2×#34962
#598182
#598142
#591312
#591282
#591232
#591222
#452442
#450912
#448702
#447582
#438862
#430172
#393352
#393342
#393332
#393322
#362602
#362182
#362142
#361242
#361232
#360852
#357502
#356802
#349252
C2×#25552
C4×#5462