Finite Group Databasebeta

← #8743428

Subgroups — #8743428

Order 512.

6166 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58991C213yesmaximal, complemented
2#58924C213yesmaximal, complemented
3#58158C216yesmaximal, complemented
4#57964C216yesmaximal, complemented
5#56343C213yesmaximal, complemented
6#52912C213yesmaximal, complemented
7#52407C213yesmaximal, complemented
8#52395C213yesmaximal, complemented
9#47018C211yesmaximal, characteristic, complemented
10#46996C211yesmaximal, characteristic, complemented
11#43643C213yesmaximal, complemented
12#43101C216yesmaximal, complemented
13#40912C213yesmaximal, complemented
14#40842C216yesmaximal, complemented
15#40608C213yesmaximal, complemented
16#40593C213yesmaximal, complemented
17#37832C213yesmaximal, complemented
18C2×#2840C211yesmaximal, characteristic, complemented
19#36078C213yesmaximal, complemented
20C22×2−1+4C2211yescharacteristic, complemented
21C2×#548C2213yescomplemented
22C2×#546C2216yescomplemented
23C2×#546C2213yescomplemented
24C22×#120C2213yes—
25#2846C2211yescharacteristic
26#2841C2213yescomplemented
27#2840C2211yescharacteristic
28#2840C2213yes—
29#2840C2213yescomplemented
30#2840C2216yescomplemented
31#2840C2213yescomplemented
32#2838C2216yescomplemented
33#2832C2216yescomplemented
34#2830C2216yescomplemented
35#2824C2213yescomplemented
36#2824C2216yescomplemented
37#2824C2216yescomplemented
38#2819C2213yescomplemented
39#2816C2213yescomplemented
40#2804C2216yescomplemented
41#2784C2216yescomplemented
42#2784C2216yescomplemented
43#2763C2213yescomplemented
44#2760C2213yescomplemented
45#2760C2216yescomplemented
46#2760C2213yescomplemented
47#2759C2216yescomplemented
48#2759C2216yescomplemented
49#2751C2216yescomplemented
50#2742C2213yescomplemented
51#2737C2216yescomplemented
52#2737C2216yescomplemented
53#2737C2216yescomplemented
54#2712C2216yescomplemented
55#2710C2216yescomplemented
56#2700C2216yescomplemented
57#2697C2216yescomplemented
58#2696C2216yescomplemented
59#2696C2216yescomplemented
60#2696C2216yescomplemented
61#2692C2216yescomplemented
62#2692C2216yescomplemented
63#2686C2216yescomplemented
64#2686C2216yescomplemented
65#2684C2216yescomplemented
66#2684C2216yescomplemented
67#2681C2216yescomplemented
68#2678C2216yes—
69#2678C2216yescomplemented
70#2676C2216yescomplemented
71#2676C2216yescomplemented
72#2676C2216yescomplemented
73#2670C2213yes—
74#2670C2216yescomplemented
75#2668C2213yes—
76#2668C2216yescomplemented
77#2665C2216yescomplemented
78#2656C2211yescharacteristic, complemented
79#2653C2216yescomplemented
80#2643C2212yescomplemented
81#2639C2216yescomplemented
82#2632C2213yescomplemented
83#2631C2213yescomplemented
84#2631C2216yescomplemented
85#2626C2213yes—
86#2626C2213yescomplemented
87#2615C2213yescomplemented
88#2615C2213yescomplemented
89#2614C2213yescomplemented
90#2614C2213yescomplemented
91#2613C2213yes—
92#2607C2213yescomplemented
93#2580C2213yescomplemented
94#2572C2216yescomplemented
95#2564C2216yescomplemented
96#2561C2213yescomplemented
97#2557C2216yescomplemented
98#2539C2213yes—
99#2534C2213yescomplemented
100#2534C2216yescomplemented
101#2493C2216yescomplemented
102#2488C2216yescomplemented
103#2483C2213yescomplemented
104#2472C2216yescomplemented
105#2472C2216yescomplemented
106#2465C2216yescomplemented
107#2463C2213yescomplemented
108#2459C2216yescomplemented
109#2458C2216yescomplemented
110#2450C2216yescomplemented
111#2450C2216yescomplemented
112#2437C2213yes—
113#2437C2216yescomplemented
114#2436C2213yescomplemented
115#2436C2216yescomplemented
116#2436C2213yescomplemented
117#2430C2213yescomplemented
118#2430C2216yescomplemented
119#2430C2213yescomplemented
120#2430C2216yescomplemented
121#2430C2216yescomplemented
122#2425C2216yescomplemented
123#2424C2216yes—
124#2424C2216yescomplemented
125#2419C2216yescomplemented
126#2418C2216yescomplemented
127#2418C2216yescomplemented
128#2412C2216yescomplemented
129#2412C2213yescomplemented
130#2410C2216yescomplemented
131#2410C2213yescomplemented
132#2410C2216yescomplemented
133#2409C2213yescomplemented
134#2409C2216yescomplemented
135#2409C2216yescomplemented
136#2408C2216yescomplemented
137#2405C2213yescomplemented
138#2404C2213yes—
139#2404C2216yescomplemented
140#2404C2213yescomplemented
141#2404C2216yescomplemented
142#2404C2216yescomplemented
143#2404C2213yescomplemented
144#2403C2213yes—
145#2388C2213yescomplemented
146C2×#393C2216yescomplemented
147C2×#393C2213yescomplemented
148C2×#393C2213yescomplemented
149C2×#393C2213yescomplemented
150#2358C2216yescomplemented
151#2339C2216yescomplemented
152#2339C2213yescomplemented
153D4×C22⋊C4C2216yes—
154D4×C22⋊C4C2213yescomplemented
155#2325C2216yescomplemented
156#2321C2213yes—
157#2318C2213yescomplemented
158#2308C2213yes—
159C2×#379C2213yes—
160C26C2311yescharacteristic
161C2×2−1+4—412no—
162C22×#41C2313yes—
163C22×#41C2313yes—
164C22×#41C2313yescomplemented
165C22×#41C2311yescharacteristic, complemented
166C22×#41C2313yescomplemented
167C23×Q8C2311yescharacteristic
168C23×Q8C2313yes—
169C23×Q8C2313yescomplemented
170C23×Q8C2311yescharacteristic, complemented
171C23×D4C2313yes—
172C23×D4C2313yes—
173C23×D4C2313yes—
174#548—412no—
175#546—412no—
176#546—424no—
177C2×#124C2313yes—
178C2×#124C2316yes—
179C2×#124C2313yescomplemented
180C2×#124C2316yescomplemented
181C2×#124C2316yescomplemented
182C2×#123C2316yes—
183C2×#123C2316yes—
184C2×#123C2313yes—
185C2×#123C2313yes—
186C2×#123C2313yes—
187C2×#123C2316yes—
188C2×C22⋊Q8C2313yes—
189C2×C22⋊Q8C2316yes—
190C2×C22⋊Q8C2313yescomplemented
191C2×C22⋊Q8C2316yescomplemented
192C2×C22⋊Q8C2316yescomplemented
193C2×C22⋊Q8C2316yescomplemented
194C2×#121C2316yes—
195C2×#121C2313yes—
196C2×#121C2316yes—
197C2×#121C2313yes—
198C2×#121C2313yes—
199C2×#121C2313yes—
200C2×#121C2316yes—
201C2×#121C2316yes—
202C2×#121C2316yes—
203C2×#120—412no—
204C2×#120C2311yescharacteristic
205C2×#120C2316yes—
206C2×#120C2313yes—
207C2×#120C2313yes—
208C2×#120C2316yes—
209C2×#120C2316yes—
210C2×#120C2316yes—
211C2×#120C2316yes—
212C2×#120C2313yes—
213C2×#120C2316yes—
214C2×C4×Q8C2313yescomplemented
215C2×C4×D4C2313yes—
216C2×C4×D4C2313yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C22×C22⋊C4C2313yes—
222C22×C22⋊C4C2313yes—
223C22×C22⋊C4C2313yes—
224C22×C22⋊C4C2316yes—
225C22×C22⋊C4C2313yes—
226C22×C22⋊C4C2313yes—
227C22×C22⋊C4C2316yes—
228C22×C22⋊C4C2313yes—
229C22×C22⋊C4C2313yes—
230C22×C22⋊C4C2316yes—
231#401C2316yescomplemented
232#401C2312yescomplemented
233#400C2316yescomplemented
234#400C2316yescomplemented
235#400C2316yescomplemented
236#400C2316yescomplemented
237#400C2316yescomplemented
238#399C2313yes—
239#399C2316yes—
240#399C2313yes—
241#399C2311yescharacteristic, complemented
242#399C2313yescomplemented
243#398C2316yescomplemented
244#398C2316yescomplemented
245#397C2316yes—
246#397C2316yes—
247#397C2316yes—
248#397C2316yes—
249#397C2316yes—
250#397C2316yes—
251#397C2316yescomplemented
252#397C2316yescomplemented
253#397C2316yescomplemented
254#397C2316yescomplemented
255#396C2316yes—
256#396C2316yes—
257#396C2316yes—
258#396C2316yes—
259#396C2316yescomplemented
260#396C2312yescomplemented
261#395C2316yescomplemented
262#395C2313yescomplemented
263#395C2316yescomplemented
264#395C2313yescomplemented
265#395C2316yescomplemented
266#395C2316yescomplemented
267#395C2313yescomplemented
268#394C2316yes—
269#394C2316yes—
270#394C2316yes—
271#394C2316yes—
272#394C2316yes—
273#394C2316yes—
274#394C2316yes—
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2316yes—
279#394C2316yes—
280#394C2316yes—
281#394C2316yescomplemented
282#394C2316yescomplemented
283#394C2313yescomplemented
284#393C2313yes—
285#393C2316yes—
286#393C2316yes—
287#393C2316yes—
288#393C2316yes—
289#393C2313yes—
290#393C2313yes—
291#393C2313yes—
292#393C2313yes—
293#393C2316yes—
294#393C2316yes—
295#393C2313yes—
296#393C2316yes—
297#393C2316yes—
298#393C2316yes—
299#393C2313yes—
300#393C2313yes—
301#393C2316yes—
302#393C2316yes—
303#393C2316yes—
304#393C2316yes—
305#393C2313yes—
306#393C2313yes—
307#393C2316yes—
308#393C2313yescomplemented
309#393C2316yescomplemented
310#393C2313yescomplemented
311#393C2313yescomplemented
312#393C2313yescomplemented
313#393C2316yescomplemented
314#393C2316yescomplemented
315#393C2316yescomplemented
316#393C2313yescomplemented
317#393C2313yescomplemented
318#393C2313yescomplemented
319#392C2313yes—
320#392C2316yes—
321#392C2316yes—
322#392C2313yes—
323#392C2316yes—
324#392C2316yes—
325#392C2313yes—
326#392C2316yes—
327#392C2316yes—
328#392C2313yes—
329#392C2311yescharacteristic, complemented
330#392C2316yescomplemented
331#392C2313yescomplemented
332#392C2313yescomplemented
333#391C2316yescomplemented
334#391C2316yescomplemented
335#391C2316yescomplemented
336#391C2316yescomplemented
337#391C2316yescomplemented
338#391C2316yescomplemented
339#390C2316yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#389C2316yescomplemented
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yescomplemented
355#388C2316yescomplemented
356#388C2316yescomplemented
357#388C2316yescomplemented
358#387C2316yescomplemented
359#387C2316yescomplemented
360#387C2316yescomplemented
361#387C2316yescomplemented
362#387C2316yescomplemented
363#387C2316yescomplemented
364#387C2316yescomplemented
365#387C2316yescomplemented
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#386C2313yes—
377#386C2316yes—
378#386C2316yes—
379#386C2316yes—
380#386C2316yes—
381#386C2316yes—
382#386C2316yes—
383#386C2316yes—
384#386C2316yes—
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yescomplemented
389#386C2316yescomplemented
390#386C2316yescomplemented
391#386C2316yescomplemented
392#386C2316yescomplemented
393#386C2316yescomplemented
394#386C2316yescomplemented
395#386C2316yescomplemented
396#386C2316yescomplemented
397#385C2313yes—
398#385C2316yes—
399#385C2313yes—
400#385C2316yes—
401#385C2316yes—
402#385C2316yes—
403#385C2313yes—
404#385C2316yescomplemented
405#385C2316yescomplemented
406#385C2316yescomplemented
407#385C2316yescomplemented
408#385C2316yescomplemented
409#385C2316yescomplemented
410#383C2313yescomplemented
411#383C2316yescomplemented
412#382C2313yescomplemented
413#381C2313yes—
414#381C2313yes—
415#381C2313yes—
416#381C2313yes—
417#381C2316yes—
418#381C2313yescomplemented
419#381C2316yescomplemented
420#381C2313yescomplemented
421#381C2316yescomplemented
422#380C2316yes—
423#380C2316yes—
424#380C2313yes—
425#380C2316yes—
426#380C2313yescomplemented
427#380C2316yescomplemented
428#380C2313yescomplemented
429#380C2316yescomplemented
430#379C2313yes—
431#379C2313yes—
432#379C2311yescharacteristic
433#379C2313yes—
434#379C2313yes—
435#379C2313yes—
436#379C2316yes—
437#379C2316yes—
438#379C2313yes—
439#379C2316yes—
440#379C2313yes—
441C4×C22⋊C4C2313yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2313yes—
444C4×C22⋊C4C2316yescomplemented
445C4×C22⋊C4C2313yescomplemented
446C2×#95C2311yescharacteristic
447C2×#95C2312yes—
448C2×#95C2313yes—
449C2×#95C2316yes—
450C2×#95C2316yescomplemented
451C2×#95C2313yescomplemented
452C25—24no—
453C25—46no—
454C25—83no—
455C25C2413yes—
456C25C2413yes—
457C25C2413yes—
458C25C2411yescharacteristic
4592−1+4—464no—
460C2×#41—212no—
461C2×#41—224no—
462C2×#41—46no—
463C2×#41—46no—
464C2×#41—412no—
465C2×#41—46no—
466C2×#41—412no—
467C2×#41—46no—
468C2×#41—86no—
469C22×Q8—46no—
470C22×Q8—46no—
471C22×Q8—46no—
472C22×Q8—412no—
473C22×Q8—46no—
474C22×Q8—86no—
475C22×Q8C2413yes—
476C22×Q8C2413yes—
477C22×Q8C2413yes—
478C22×Q8C2413yes—
479C22×Q8C2416yes—
480C22×Q8C2413yes—
481C22×Q8C2411yescharacteristic
482C22×D4—212no—
483C22×D4—212no—
484C22×D4—46no—
485C22×D4—46no—
486C22×D4—412no—
487C22×D4—86no—
488C22×D4—83no—
489C22×D4C2413yes—
490C22×D4C2411yescharacteristic
491C22×D4C2416yes—
492C22×D4C2413yes—
493C22×D4C2413yes—
494C22×D4C2413yes—
495C22×D4C2416yes—
496C22×D4C2413yes—
497C22×D4C2416yes—
498C22×D4C2413yes—
499C22×D4C2416yes—
500C22×D4C2413yes—
501C22×D4C2413yes—
502C22×D4C2416yes—
503C22×D4C2413yes—
504C22×D4C2413yes—
505C23×C4C2413yes—
506C23×C4C2416yes—
507C23×C4C2416yes—
508C23×C4C2413yes—
509C23×C4C2413yes—
510C23×C4C2413yes—
511C23×C4C2413yes—
512C23×C4C2413yes—
513C23×C4C2413yes—
514C23×C4C2413yes—
515C23×C4C2416yes—
516C23×C4C2416yes—
517#124—46no—
518#124—46no—
519#124—412no—
520#124—412no—
521#124—86no—
522#123—412no—
523#123—412no—
524#123—46no—
525#123—46no—
526#123—86no—
527#123—83no—
528C22⋊Q8—46no—
529C22⋊Q8—412no—
530C22⋊Q8—412no—
531C22⋊Q8—46no—
532C22⋊Q8—86no—
533C22⋊Q8—86no—
534#121—224no—
535#121—412no—
536#121—46no—
537#121—412no—
538#121—46no—
539#121—46no—
540#121—46no—
541#121—86no—
542#121—86no—
543#120—24no—
544#120—224no—
545#120—412no—
546#120—412no—
547#120—46no—
548#120—46no—
549#120—412no—
550#120—412no—
551#120—86no—
552#120—83no—
553C4×Q8—46no—
554C4×D4—212no—
555C4×D4—46no—
556C4×D4—412no—
557C4×D4—412no—
558C4×D4—412no—
559C4×D4—86no—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C22⋊C4—46no—
577C2×C22⋊C4—46no—
578C2×C22⋊C4—412no—
579C2×C22⋊C4—46no—
580C2×C22⋊C4—46no—
581C2×C22⋊C4—46no—
582C2×C22⋊C4—412no—
583C2×C22⋊C4—83no—
584C2×C22⋊C4—83no—
585C2×C22⋊C4—86no—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2413yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2413yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2413yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2416yes—
633C2×C42C2413yes—
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2416yes—
637#95C2416yes—
638#95C2413yes—
639#95C2416yes—
640#95C2413yes—
641#95C2413yes—
642#95C2411yescharacteristic
643#95C2416yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C2412yes—
648#95C2413yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2413yes—
654#95C2416yes—
655#95C2413yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2413yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671C24—26no—
672C24—26no—
673C24—212no—
674C24—26no—
675C24—26no—
676C24—26no—
677C24—43no—
678C24—43no—
679C24—43no—
680C24—46no—
681C24—43no—
682C24—46no—
683C24—43no—
684C24—46no—
685C24—43no—
686C24—46no—
687C24—46no—
688C24—824no—
689C24—88no—
690C24—824no—
691C242−1+414yescomplemented
692C24C2513yes—
693C24C2513yes—
694C24C2511yescharacteristic
695C24C2513yes—
696C24C2513yes—
697C24C2511yescharacteristic
698#41—448no—
699#41—448no—
700#41—448no—
701#41—416no—
702#41—824no—
703C2×Q8—212no—
704C2×Q8—26no—
705C2×Q8—43no—
706C2×Q8—43no—
707C2×Q8—46no—
708C2×Q8—43no—
709C2×Q8—43no—
710C2×Q8—46no—
711C2×Q8—46no—
712C2×Q8—43no—
713C2×Q8—46no—
714C2×Q8—46no—
715C2×Q8—46no—
716C2×Q8—46no—
717C2×Q8—448no—
718C2×Q8—416no—
719C2×Q8—416no—
720C2×Q8—824no—
721C2×D4—212no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—26no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—26no—
731C2×D4—212no—
732C2×D4—26no—
733C2×D4—212no—
734C2×D4—26no—
735C2×D4—46no—
736C2×D4—43no—
737C2×D4—46no—
738C2×D4—43no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—43no—
742C2×D4—46no—
743C2×D4—46no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—43no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—46no—
753C2×D4—43no—
754C2×D4—43no—
755C2×D4—46no—
756C2×D4—46no—
757C2×D4—824no—
758C2×D4—824no—
759C2×D4—824no—
760C2×D4H(5,𝔽2)112yes—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—212no—
764C22×C4—212no—
765C22×C4—26no—
766C22×C4—26no—
767C22×C4—212no—
768C22×C4—26no—
769C22×C4—212no—
770C22×C4—26no—
771C22×C4—26no—
772C22×C4—46no—
773C22×C4—46no—
774C22×C4—46no—
775C22×C4—43no—
776C22×C4—43no—
777C22×C4—46no—
778C22×C4—46no—
779C22×C4—46no—
780C22×C4—46no—
781C22×C4—46no—
782C22×C4—46no—
783C22×C4—46no—
784C22×C4—46no—
785C22×C4—43no—
786C22×C4—46no—
787C22×C4—46no—
788C22×C4—46no—
789C22×C4—46no—
790C22×C4C2516yes—
791C22×C4C2513yes—
792C22×C4C2516yes—
793C22×C4C2513yes—
794C22×C4C2513yes—
795C22×C4C2511yescharacteristic
796C22×C4C2513yes—
797C22×C4C2513yes—
798C22×C4C2516yes—
799C22×C4C2516yes—
800C22×C4C2513yes—
801C22×C4C2513yes—
802C22×C4C2513yes—
803C4⋊C4—26no—
804C4⋊C4—212no—
805C4⋊C4—46no—
806C4⋊C4—46no—
807C4⋊C4—43no—
808C4⋊C4—46no—
809C4⋊C4—46no—
810C4⋊C4—43no—
811C4⋊C4—46no—
812C4⋊C4—43no—
813C4⋊C4—43no—
814C4⋊C4—46no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4—46no—
819C22⋊C4—212no—
820C22⋊C4—26no—
821C22⋊C4—26no—
822C22⋊C4—212no—
823C22⋊C4—26no—
824C22⋊C4—212no—
825C22⋊C4—212no—
826C22⋊C4—212no—
827C22⋊C4—43no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—43no—
834C22⋊C4—43no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—43no—
838C22⋊C4—43no—
839C22⋊C4—43no—
840C22⋊C4—43no—
841C22⋊C4—46no—
842C22⋊C4—43no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—43no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—43no—
850C22⋊C4—46no—
851C22⋊C4—46no—
852C22⋊C4—43no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—43no—
856C22⋊C4—43no—
857C22⋊C4—46no—
858C22⋊C4—46no—
859C22⋊C4—46no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C42—26no—
867C42—46no—
868C42—46no—
869C42—46no—
870C23—21no—
871C23—23no—
872C23—26no—
873C23—23no—
874C23—26no—
875C23—23no—
876C23—23no—
877C23—23no—
878C23—26no—
879C23—26no—
880C23—26no—
881C23—26no—
882C23—23no—
883C23—23no—
884C23—23no—
885C23—21no—
886C23—23no—
887C23—23no—
888C23—23no—
889C23—26no—
890C23—26no—
891C23—23no—
892C23—23no—
893C23—412no—
894C23—412no—
895C23—424no—
896C23—412no—
897C23—412no—
898C23—412no—
899C23—86no—
900C23—812no—
901C23—86no—
902C23—812no—
903C23—86no—
904C23—86no—
905C23—812no—
906C23—86no—
907C23—812no—
908C23—82no—
909C23—86no—
910C23—864no—
911C23—166no—
912C23C2×H(5,𝔽2)16yes—
913C23C2×H(5,𝔽2)16yes—
914C23C2×2−1+416yes—
915C23C2611yescharacteristic
916Q8—412no—
917Q8—412no—
918Q8—412no—
919Q8—44no—
920Q8—412no—
921Q8—86no—
922Q8—812no—
923D4—224no—
924D4—424no—
925D4—412no—
926D4—412no—
927D4—412no—
928D4—44no—
929D4—86no—
930D4—86no—
931D4—812no—
932D4—812no—
933D4—86no—
934D4—812no—
935D4—812no—
936D4—86no—
937D4—163no—
938D4—163no—
939C2×C4—26no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—26no—
943C2×C4—26no—
944C2×C4—26no—
945C2×C4—26no—
946C2×C4—26no—
947C2×C4—23no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—23no—
951C2×C4—26no—
952C2×C4—23no—
953C2×C4—26no—
954C2×C4—23no—
955C2×C4—23no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—23no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—424no—
969C2×C4—412no—
970C2×C4—412no—
971C2×C4—412no—
972C2×C4—86no—
973C2×C4—86no—
974C2×C4—812no—
975C2×C4—86no—
976C2×C4—86no—
977C2×C4—86no—
978C2×C4—812no—
979C2×C4—166no—
980C2×C4C2×H(5,𝔽2)16yes—
981C22—26no—
982C22—26no—
983C22—26no—
984C22—26no—
985C22—26no—
986C22—212no—
987C22—26no—
988C22—43no—
989C22—46no—
990C22—46no—
991C22—46no—
992C22—43no—
993C22—46no—
994C22—43no—
995C22—46no—
996C22—43no—
997C22—43no—
998C22—43no—
999C22—43no—
1000C22—46no—
1001C22—43no—
1002C22—46no—
1003C22—41no—
1004C22—43no—
1005C22—43no—
1006C22—824no—
1007C22—88no—
1008C22—824no—
1009C22—1612no—
1010C22#353214yes—
1011C22C22×H(5,𝔽2)13yes—
1012C22C22×2−1+411yescharacteristic
1013C22H(7,𝔽2)13yes—
1014C4—26no—
1015C4—43no—
1016C4—43no—
1017C4—46no—
1018C4—46no—
1019C4—46no—
1020C4—43no—
1021C4—46no—
1022C4—43no—
1023C4—43no—
1024C4—43no—
1025C4—41no—
1026C4—43no—
1027C2—24no—
1028C2—46no—
1029C2—46no—
1030C2—81no—
1031C2—83no—
1032C2—83no—
1033C2C2×#353211yescharacteristic
1034C2#6289413yes—
1035C2#6304513yes—
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. #58991C2semidirect
2. #58924C2semidirect
3. #58158C2semidirect
4. #57964C2semidirect
5. #56343C2semidirect
6. #52912C2semidirect
7. #52407C2semidirect
8. #52395C2semidirect
9. #47018C2semidirect
10. #46996C2semidirect
11. #43643C2semidirect
12. #43101C2semidirect
13. #40912C2semidirect
14. #40842C2semidirect
15. #40608C2semidirect
16. #40593C2semidirect
17. #37832C2semidirect
18. C2×#2840C2semidirect
19. #36078C2semidirect
20. C22×2−1+4C22semidirect
21. C2×#548C22semidirect
22. C2×#546C22semidirect
23. C2×#546C22semidirect
26. #2841C22semidirect
29. #2840C22semidirect
30. #2840C22semidirect
31. #2840C22semidirect
32. #2838C22semidirect
33. #2832C22semidirect
34. #2830C22semidirect
35. #2824C22semidirect
36. #2824C22semidirect
37. #2824C22semidirect
38. #2819C22semidirect
39. #2816C22semidirect
40. #2804C22semidirect
41. #2784C22semidirect
42. #2784C22semidirect
43. #2763C22semidirect
44. #2760C22semidirect
45. #2760C22semidirect
46. #2760C22semidirect
47. #2759C22semidirect
48. #2759C22semidirect
49. #2751C22semidirect
50. #2742C22semidirect
51. #2737C22semidirect
52. #2737C22semidirect
53. #2737C22semidirect
54. #2712C22semidirect
55. #2710C22semidirect
56. #2700C22semidirect
57. #2697C22semidirect
58. #2696C22semidirect
59. #2696C22semidirect
60. #2696C22semidirect
61. #2692C22semidirect
62. #2692C22semidirect
63. #2686C22semidirect
64. #2686C22semidirect
65. #2684C22semidirect
66. #2684C22semidirect
67. #2681C22semidirect
69. #2678C22semidirect
70. #2676C22semidirect
71. #2676C22semidirect
72. #2676C22semidirect
74. #2670C22semidirect
76. #2668C22semidirect
77. #2665C22semidirect
78. #2656C22semidirect
79. #2653C22semidirect
80. #2643C22semidirect
81. #2639C22semidirect
82. #2632C22semidirect
83. #2631C22semidirect
84. #2631C22semidirect
86. #2626C22semidirect
87. #2615C22semidirect
88. #2615C22semidirect
89. #2614C22semidirect
90. #2614C22semidirect
92. #2607C22semidirect
93. #2580C22semidirect
94. #2572C22semidirect
95. #2564C22semidirect
96. #2561C22semidirect
97. #2557C22semidirect
99. #2534C22semidirect
100. #2534C22semidirect
101. #2493C22semidirect
102. #2488C22semidirect
103. #2483C22semidirect
104. #2472C22semidirect
105. #2472C22semidirect
106. #2465C22semidirect
107. #2463C22semidirect
108. #2459C22semidirect
109. #2458C22semidirect
110. #2450C22semidirect
111. #2450C22semidirect
113. #2437C22semidirect
114. #2436C22semidirect
115. #2436C22semidirect
116. #2436C22semidirect
117. #2430C22semidirect
118. #2430C22semidirect
119. #2430C22semidirect
120. #2430C22semidirect
121. #2430C22semidirect
122. #2425C22semidirect
124. #2424C22semidirect
125. #2419C22semidirect
126. #2418C22semidirect
127. #2418C22semidirect
128. #2412C22semidirect
129. #2412C22semidirect
130. #2410C22semidirect
131. #2410C22semidirect
132. #2410C22semidirect
133. #2409C22semidirect
134. #2409C22semidirect
135. #2409C22semidirect
136. #2408C22semidirect
137. #2405C22semidirect
139. #2404C22semidirect
140. #2404C22semidirect
141. #2404C22semidirect
142. #2404C22semidirect
143. #2404C22semidirect
145. #2388C22semidirect
146. C2×#393C22semidirect
147. C2×#393C22semidirect
148. C2×#393C22semidirect
149. C2×#393C22semidirect
150. #2358C22semidirect
151. #2339C22semidirect
152. #2339C22semidirect
154. D4×C22⋊C4C22semidirect
155. #2325C22semidirect
157. #2318C22semidirect
164. C22×#41C23semidirect
165. C22×#41C23semidirect
166. C22×#41C23semidirect
169. C23×Q8C23semidirect
170. C23×Q8C23semidirect
179. C2×#124C23semidirect
180. C2×#124C23semidirect
181. C2×#124C23semidirect
190. C2×C22⋊Q8C23semidirect
191. C2×C22⋊Q8C23semidirect
192. C2×C22⋊Q8C23semidirect
193. C2×C22⋊Q8C23semidirect
214. C2×C4×Q8C23semidirect
231. #401C23semidirect
232. #401C23semidirect
233. #400C23semidirect
234. #400C23semidirect
235. #400C23semidirect
236. #400C23semidirect
237. #400C23semidirect
241. #399C23semidirect
242. #399C23semidirect
243. #398C23semidirect
244. #398C23semidirect
251. #397C23semidirect
252. #397C23semidirect
253. #397C23semidirect
254. #397C23semidirect
259. #396C23semidirect
260. #396C23semidirect
261. #395C23semidirect
262. #395C23semidirect
263. #395C23semidirect
264. #395C23semidirect
265. #395C23semidirect
266. #395C23semidirect
267. #395C23semidirect
281. #394C23semidirect
282. #394C23semidirect
283. #394C23semidirect
308. #393C23semidirect
309. #393C23semidirect
310. #393C23semidirect
311. #393C23semidirect
312. #393C23semidirect
313. #393C23semidirect
314. #393C23semidirect
315. #393C23semidirect
316. #393C23semidirect
317. #393C23semidirect
318. #393C23semidirect
329. #392C23semidirect
330. #392C23semidirect
331. #392C23semidirect
332. #392C23semidirect
333. #391C23semidirect
334. #391C23semidirect
335. #391C23semidirect
336. #391C23semidirect
337. #391C23semidirect
338. #391C23semidirect
345. #389C23semidirect
354. #388C23semidirect
355. #388C23semidirect
356. #388C23semidirect
357. #388C23semidirect
358. #387C23semidirect
359. #387C23semidirect
360. #387C23semidirect
361. #387C23semidirect
362. #387C23semidirect
363. #387C23semidirect
364. #387C23semidirect
365. #387C23semidirect
388. #386C23semidirect
389. #386C23semidirect
390. #386C23semidirect
391. #386C23semidirect
392. #386C23semidirect
393. #386C23semidirect
394. #386C23semidirect
395. #386C23semidirect
396. #386C23semidirect
404. #385C23semidirect
405. #385C23semidirect
406. #385C23semidirect
407. #385C23semidirect
408. #385C23semidirect
409. #385C23semidirect
410. #383C23semidirect
411. #383C23semidirect
412. #382C23semidirect
418. #381C23semidirect
419. #381C23semidirect
420. #381C23semidirect
421. #381C23semidirect
426. #380C23semidirect
427. #380C23semidirect
428. #380C23semidirect
429. #380C23semidirect
444. C4×C22⋊C4C23semidirect
445. C4×C22⋊C4C23semidirect
450. C2×#95C23semidirect
451. C2×#95C23semidirect
691. C242−1+4semidirect

Maximal subgroups

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

subgroupindex
#589912
#589242
#581582
#579642
#563432
#529122
#524072
#523952
#470182
#469962
#436432
#431012
#409122
#408422
#406082
#405932
#378322
C2×#28402
#360782