Finite Group Databasebeta

← #8932791

Subgroups — #8932791

Order 512.

5413 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#47607C216yesmaximal, complemented
2#47223C213yesmaximal, complemented
3#47213C213yesmaximal, complemented
4#46854C213yesmaximal, complemented
5#46813C213yesmaximal, complemented
6#46716C216yesmaximal, complemented
7#46661C216yesmaximal, complemented
8#46600C216yesmaximal, complemented
9#46425C213yesmaximal, complemented
10#46354C213yesmaximal, complemented
11#35534C213yesmaximal, complemented
12#35530C213yesmaximal, complemented
13#35504C211yesmaximal, characteristic, complemented
14#35474C213yesmaximal, complemented
15#35463C211yesmaximal, characteristic, complemented
16#35438C213yesmaximal, complemented
17#35438C211yesmaximal, characteristic, complemented
18#35394C213yesmaximal, complemented
19#35356C213yesmaximal, complemented
20C2×#540C2213yes—
21C2×#538C2213yescomplemented
22C2×#537C2213yes—
23C2×#534C2213yes—
24C22×#123C2213yes—
25C2×#520C2213yescomplemented
26#2837C2216yescomplemented
27#2825C2212yescomplemented
28#2816C2213yes—
29#2815C2213yes—
30#2797C2216yescomplemented
31#2796C2216yescomplemented
32#2793C2216yescomplemented
33#2791C2216yescomplemented
34#2780C2216yescomplemented
35#2754C2216yescomplemented
36#2746C2216yescomplemented
37#2740C2216yescomplemented
38#2730C2216yescomplemented
39#2721C2216yescomplemented
40#2714C2216yescomplemented
41#2710C2216yescomplemented
42#2706C2216yescomplemented
43#2706C2216yescomplemented
44#2703C2216yescomplemented
45#2699C2216yes—
46#2696C2216yescomplemented
47#2694C2216yescomplemented
48#2688C2216yes—
49#2687C2216yescomplemented
50#2682C2216yes—
51#2678C2216yescomplemented
52#2676C2216yescomplemented
53#2673C2216yescomplemented
54#2671C2216yes—
55#2669C2216yescomplemented
56#2669C2216yescomplemented
57#2668C2216yescomplemented
58#2607C2216yescomplemented
59#2607C2213yescomplemented
60#2607C2213yescomplemented
61#2579C2213yescomplemented
62#2579C2213yescomplemented
63#2575C2216yescomplemented
64#2566C2213yescomplemented
65#2565C2213yescomplemented
66#2561C2213yes—
67#2560C2216yescomplemented
68#2557C2216yescomplemented
69#2557C2216yescomplemented
70#2557C2216yescomplemented
71#2557C2216yescomplemented
72#2557C2216yescomplemented
73#2553C2216yescomplemented
74#2553C2216yescomplemented
75#2548C2213yescomplemented
76#2541C2213yescomplemented
77#2539C2216yes—
78#2539C2213yes—
79#2539C2213yes—
80#2539C2213yes—
81#2539C2216yescomplemented
82#2531C2216yescomplemented
83#2527C2216yescomplemented
84#2517C2216yescomplemented
85#2504C2213yescomplemented
86#2502C2213yescomplemented
87#2502C2213yescomplemented
88#2501C2213yes—
89#2501C2216yes—
90#2501C2213yes—
91#2501C2213yescomplemented
92#2500C2213yes—
93#2500C2213yescomplemented
94#2499C2213yescomplemented
95#2499C2213yescomplemented
96#2482C2213yes—
97#2482C2213yescomplemented
98#2472C2216yescomplemented
99#2471C2216yescomplemented
100#2471C2216yescomplemented
101#2471C2216yescomplemented
102#2471C2216yescomplemented
103#2471C2216yescomplemented
104#2471C2216yescomplemented
105#2467C2216yescomplemented
106#2464C2216yescomplemented
107#2464C2216yescomplemented
108#2464C2216yescomplemented
109#2458C2216yescomplemented
110#2458C2216yescomplemented
111#2456C2216yescomplemented
112#2456C2216yescomplemented
113#2456C2216yescomplemented
114#2443C2216yescomplemented
115#2443C2216yescomplemented
116#2443C2216yescomplemented
117#2443C2216yescomplemented
118#2443C2216yescomplemented
119#2443C2216yescomplemented
120#2431C2213yes—
121#2431C2216yescomplemented
122#2431C2213yescomplemented
123#2423C2216yescomplemented
124#2423C2216yescomplemented
125#2422C2216yescomplemented
126#2422C2216yescomplemented
127#2422C2216yescomplemented
128#2418C2216yescomplemented
129#2412C2216yescomplemented
130#2410C2216yes—
131#2408C2213yes—
132#2408C2213yes—
133#2404C2213yes—
134#2404C2216yescomplemented
135#2404C2213yescomplemented
136#2335C2216yescomplemented
137#2333C2213yes—
138#2333C2213yes—
139#2333C2213yescomplemented
140#2333C2216yescomplemented
141#2332C2213yescomplemented
142#2328C2213yescomplemented
143#2326C2213yescomplemented
144#2322C2216yescomplemented
145#2321C2213yescomplemented
146#2321C2213yescomplemented
147#2317C2213yescomplemented
148#2313C2213yescomplemented
149#2311C2213yescomplemented
150C4×#127C2211yescharacteristic, complemented
151C4×#124C2213yescomplemented
152C4×#120C2211yescharacteristic
153C4×#120C2213yes—
154#2298C2213yescomplemented
155#2297C2213yescomplemented
156#2297C2213yescomplemented
157C2×#384C2211yescharacteristic, complemented
158#2273C2211yescharacteristic
159#2273C2213yescomplemented
160C22×#41C2313yes—
161C22×#41C2313yes—
162C23×D4C2313yes—
163C24×C4C2311yescharacteristic
164#540—412no—
165#538—412no—
166#537—412no—
167#534—412no—
168C2×#127C2311yescharacteristic
169C2×#127C2313yes—
170C2×#127C2313yes—
171C2×#126C2316yes—
172C2×#125C2313yes—
173C2×#124C2313yes—
174C2×#124C2316yes—
175C2×#124C2313yes—
176C2×#123—412no—
177C2×#123C2316yes—
178C2×#123C2316yes—
179C2×#123C2316yes—
180C2×#123C2316yes—
181C2×#123C2316yes—
182C2×#123C2316yes—
183C2×#123C2316yes—
184C2×#123C2316yes—
185C2×#123C2316yes—
186C2×#123C2316yes—
187C2×#123C2316yes—
188C2×C22⋊Q8C2313yes—
189C2×C22⋊Q8C2316yes—
190C2×C22⋊Q8C2313yes—
191C2×#121C2313yes—
192C2×#121C2313yes—
193C2×#121C2313yes—
194C2×#121C2316yes—
195C2×#121C2316yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2316yes—
199C2×#121C2313yes—
200C2×#121C2316yes—
201C2×#121C2316yes—
202C2×#121C2316yes—
203C2×#120C2313yes—
204C2×#120C2313yes—
205C2×#120C2311yescharacteristic
206C2×#120C2313yes—
207C2×#120C2316yes—
208C2×#120C2316yes—
209C2×#120C2316yes—
210#520—412no—
211C2×C4×Q8C2313yes—
212C2×C4×Q8C2313yes—
213C2×C4×D4C2313yes—
214C2×C4×D4C2313yes—
215C2×C4×D4C2313yes—
216C2×C4×D4C2313yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2313yes—
221C2×C4×D4C2313yes—
222C2×#117C2313yes—
223C2×#117C2313yes—
224C2×#117C2313yes—
225C2×#117C2313yes—
226C22×C4⋊C4C2313yes—
227C22×C4⋊C4C2313yes—
228C22×C4⋊C4C2313yes—
229C22×C4⋊C4C2313yes—
230C22×C4⋊C4C2313yes—
231C22×C22⋊C4C2313yes—
232C22×C22⋊C4C2313yes—
233C22×C22⋊C4C2313yes—
234C22×C22⋊C4C2316yes—
235C22×C42C2311yescharacteristic
236#401C2312yes—
237#400C2316yes—
238#400C2316yes—
239#399C2316yes—
240#399C2316yes—
241#399C2316yes—
242#399C2316yes—
243#399C2316yes—
244#399C2316yes—
245#399C2316yes—
246#399C2316yes—
247#399C2316yes—
248#398C2316yes—
249#398C2316yes—
250#398C2316yes—
251#398C2316yes—
252#398C2316yes—
253#398C2316yes—
254#398C2316yes—
255#397C2316yes—
256#397C2316yes—
257#397C2316yes—
258#397C2316yes—
259#397C2316yes—
260#397C2316yes—
261#397C2316yes—
262#397C2316yes—
263#397C2316yes—
264#397C2316yes—
265#397C2316yes—
266#397C2316yes—
267#396C2316yes—
268#396C2316yes—
269#396C2312yes—
270#396C2316yes—
271#396C2316yes—
272#394C2316yes—
273#394C2316yes—
274#394C2316yes—
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2316yes—
279#394C2316yes—
280#394C2316yes—
281#394C2316yes—
282#394C2316yes—
283#394C2316yes—
284#393C2316yes—
285#393C2316yes—
286#393C2316yes—
287#393C2316yes—
288#392C2316yes—
289#392C2312yes—
290#392C2316yes—
291#392C2316yes—
292#392C2316yes—
293#392C2316yes—
294#392C2316yes—
295#392C2316yes—
296#392C2316yes—
297#392C2316yes—
298#392C2316yes—
299#392C2316yes—
300#392C2316yes—
301#392C2316yes—
302#391C2313yes—
303#391C2313yes—
304#391C2313yes—
305#391C2313yes—
306#391C2316yes—
307#391C2316yes—
308#391C2313yes—
309#391C2313yes—
310#390C2313yes—
311#390C2313yes—
312#390C2313yes—
313#390C2313yes—
314#390C2313yes—
315#390C2313yes—
316#390C2316yes—
317#390C2316yes—
318#390C2313yes—
319#390C2313yes—
320#390C2316yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2313yes—
329#389C2316yes—
330#389C2316yes—
331#389C2316yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C2316yes—
336#388C2316yes—
337#388C2316yes—
338#388C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#387C2316yes—
352#387C2316yes—
353#387C2316yes—
354#387C2316yes—
355#387C2316yes—
356#387C2316yes—
357#387C2316yes—
358#387C2316yes—
359#387C2316yes—
360#387C2316yes—
361#387C2316yes—
362#387C2316yes—
363#387C2316yes—
364#387C2316yes—
365#387C2316yes—
366#387C2316yes—
367#387C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2313yes—
372#386C2313yes—
373#386C2316yes—
374#386C2316yes—
375#386C2313yes—
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#386C2316yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#385C2316yes—
396#385C2316yes—
397#385C2316yes—
398#385C2313yes—
399#385C2313yes—
400#385C2316yes—
401#385C2316yes—
402#385C2316yes—
403#385C2313yes—
404#385C2313yes—
405#385C2316yes—
406#385C2316yes—
407#385C2316yes—
408#384C2311yescharacteristic
409#384C2313yes—
410#384C2313yes—
411#384C2313yes—
412#384C2313yes—
413#384C2313yes—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#382C2313yes—
417#382C2313yes—
418#382C2313yes—
419#382C2313yes—
420#381C2313yes—
421#381C2316yes—
422#381C2313yes—
423#381C2316yes—
424#380C2316yes—
425#380C2316yes—
426#380C2313yes—
427#380C2313yes—
428#380C2316yes—
429#379C2313yes—
430#379C2313yes—
431#379C2313yes—
432#379C2311yescharacteristic
433C4×C4⋊C4C2313yes—
434C4×C4⋊C4C2313yes—
435C4×C22⋊C4C2316yes—
436C4×C22⋊C4C2313yes—
437C4×C22⋊C4C2313yes—
438C4×C22⋊C4C2313yes—
439C4×C22⋊C4C2316yes—
440C4×C22⋊C4C2316yes—
441C4×C22⋊C4C2313yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2316yes—
444C4×C22⋊C4C2313yes—
445C4×C22⋊C4C2313yes—
446C4×C22⋊C4C2313yes—
447C4×C22⋊C4C2313yes—
448C4×C22⋊C4C2316yes—
449C4×C22⋊C4C2316yes—
450C4×C22⋊C4C2316yes—
451#376C2313yes—
452C43C2311yescharacteristic
453C25C2411yescharacteristic
454C25C2413yes—
455C2×#41—212no—
456C2×#41—46no—
457C2×#41—46no—
458C2×#41—46no—
459C2×#41—46no—
460C2×#41—46no—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×D4—46no—
464C22×D4—412no—
465C22×D4C2413yes—
466C22×D4C2413yes—
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2413yes—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C23×C4—46no—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C2416yes—
485C23×C4C2413yes—
486C23×C4C2413yes—
487C23×C4C2416yes—
488C23×C4C2411yescharacteristic
489C23×C4C2413yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2413yes—
493#127—46no—
494#127—42no—
495#127—46no—
496#126—412no—
497#125—46no—
498#124—46no—
499#124—46no—
500#124—412no—
501#123—412no—
502#123—412no—
503#123—412no—
504#123—412no—
505#123—412no—
506#123—412no—
507#123—412no—
508#123—412no—
509#123—412no—
510#123—412no—
511#123—412no—
512C22⋊Q8—212no—
513C22⋊Q8—412no—
514C22⋊Q8—46no—
515#121—212no—
516#121—212no—
517#121—212no—
518#121—412no—
519#121—412no—
520#121—412no—
521#121—412no—
522#121—412no—
523#121—412no—
524#121—412no—
525#121—46no—
526#121—412no—
527#120—46no—
528#120—46no—
529#120—412no—
530#120—412no—
531#120—412no—
532#120—42no—
533#120—46no—
534C4×Q8—46no—
535C4×Q8—46no—
536C4×D4—46no—
537C4×D4—46no—
538C4×D4—46no—
539C4×D4—46no—
540C4×D4—46no—
541C4×D4—46no—
542C4×D4—46no—
543C4×D4—46no—
544C4×D4—412no—
545#117—212no—
546#117—46no—
547#117—46no—
548#117—46no—
549C2×C4⋊C4—212no—
550C2×C4⋊C4—46no—
551C2×C4⋊C4—46no—
552C2×C4⋊C4—46no—
553C2×C4⋊C4—46no—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C22⋊C4—212no—
582C2×C22⋊C4—212no—
583C2×C22⋊C4—412no—
584C2×C22⋊C4—46no—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C42—42no—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635C2×C42C2416yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2411yescharacteristic
639C2×C42C2413yes—
640C2×C42C2411yescharacteristic
641C2×C42C2413yes—
642#95C2416yes—
643#95C2416yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C2412yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668C24—26no—
669C24—26no—
670C24—46no—
671C24—43no—
672C24—41no—
673C24—46no—
674C24—43no—
675C24—43no—
676C24C2516yes—
677C24C2513yes—
678C24C2513yes—
679C24C2511yescharacteristic
680#41—448no—
681#41—824no—
682C2×Q8—26no—
683C2×Q8—26no—
684C2×Q8—26no—
685C2×Q8—43no—
686C2×Q8—43no—
687C2×Q8—43no—
688C2×D4—26no—
689C2×D4—26no—
690C2×D4—26no—
691C2×D4—26no—
692C2×D4—212no—
693C2×D4—212no—
694C2×D4—212no—
695C2×D4—212no—
696C2×D4—26no—
697C2×D4—26no—
698C2×D4—26no—
699C2×D4—26no—
700C2×D4—26no—
701C2×D4—43no—
702C2×D4—43no—
703C2×D4—43no—
704C2×D4—46no—
705C2×D4—46no—
706C2×D4—46no—
707C2×D4—46no—
708C2×D4—46no—
709C2×D4—46no—
710C2×D4—46no—
711C2×D4—43no—
712C2×D4—43no—
713C2×D4—43no—
714C2×D4—43no—
715C2×D4—43no—
716C2×D4—43no—
717C2×D4—46no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—46no—
730C2×D4—824no—
731C22×C4—26no—
732C22×C4—26no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—26no—
739C22×C4—212no—
740C22×C4—43no—
741C22×C4—43no—
742C22×C4—43no—
743C22×C4—43no—
744C22×C4—46no—
745C22×C4—46no—
746C22×C4—46no—
747C22×C4—46no—
748C22×C4—46no—
749C22×C4—46no—
750C22×C4—46no—
751C22×C4—43no—
752C22×C4—43no—
753C22×C4—43no—
754C22×C4—43no—
755C22×C4—46no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4—88no—
761C22×C4H(5,𝔽2)112yes—
762C22×C4C2516yes—
763C22×C4C2513yes—
764C22×C4C2513yes—
765C22×C4C2513yes—
766C22×C4C2516yes—
767C22×C4C2516yes—
768C22×C4C2511yescharacteristic
769C22×C4C2513yes—
770C22×C4C2511yescharacteristic
771C22×C4C2513yes—
772C22×C4C2513yes—
773C22×C4C2513yes—
774C22×C4C2513yes—
775C22×C4C2513yes—
776C22×C4C2513yes—
777C4⋊C4—26no—
778C4⋊C4—26no—
779C4⋊C4—26no—
780C4⋊C4—26no—
781C4⋊C4—26no—
782C4⋊C4—26no—
783C4⋊C4—26no—
784C4⋊C4—26no—
785C4⋊C4—26no—
786C4⋊C4—26no—
787C4⋊C4—212no—
788C4⋊C4—212no—
789C4⋊C4—43no—
790C4⋊C4—43no—
791C4⋊C4—43no—
792C4⋊C4—43no—
793C4⋊C4—46no—
794C4⋊C4—46no—
795C4⋊C4—46no—
796C4⋊C4—46no—
797C4⋊C4—46no—
798C4⋊C4—46no—
799C4⋊C4—46no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4—46no—
804C22⋊C4—26no—
805C22⋊C4—26no—
806C22⋊C4—212no—
807C22⋊C4—212no—
808C22⋊C4—212no—
809C22⋊C4—212no—
810C22⋊C4—212no—
811C22⋊C4—212no—
812C22⋊C4—212no—
813C22⋊C4—212no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—46no—
819C22⋊C4—46no—
820C22⋊C4—46no—
821C22⋊C4—46no—
822C22⋊C4—46no—
823C22⋊C4—43no—
824C22⋊C4—43no—
825C22⋊C4—43no—
826C22⋊C4—43no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—43no—
831C22⋊C4—46no—
832C22⋊C4—43no—
833C22⋊C4—43no—
834C22⋊C4—43no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C22⋊C4—46no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C42—26no—
846C42—26no—
847C42—41no—
848C42—43no—
849C42—43no—
850C42—43no—
851C42—43no—
852C42—43no—
853C42—43no—
854C42—43no—
855C42—46no—
856C42—43no—
857C42—43no—
858C42—41no—
859C42—43no—
860C23—28no—
861C23—26no—
862C23—23no—
863C23—26no—
864C23—23no—
865C23—23no—
866C23—23no—
867C23—26no—
868C23—26no—
869C23—26no—
870C23—26no—
871C23—23no—
872C23—26no—
873C23—26no—
874C23—26no—
875C23—26no—
876C23—26no—
877C23—23no—
878C23—23no—
879C23—412no—
880C23—86no—
881C23—86no—
882C23—86no—
883C23—86no—
884C23—166no—
885C23—166no—
886C23C2×H(5,𝔽2)16yes—
887C23#58512yes—
888C23C2611yescharacteristic
889Q8—412no—
890Q8—86no—
891D4—412no—
892D4—412no—
893D4—412no—
894D4—86no—
895D4—86no—
896D4—86no—
897D4—812no—
898D4—812no—
899D4—812no—
900D4—812no—
901D4—166no—
902D4—166no—
903D4—166no—
904D4—166no—
905C2×C4—224no—
906C2×C4—23no—
907C2×C4—23no—
908C2×C4—23no—
909C2×C4—23no—
910C2×C4—23no—
911C2×C4—23no—
912C2×C4—23no—
913C2×C4—23no—
914C2×C4—23no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—26no—
918C2×C4—26no—
919C2×C4—26no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—23no—
923C2×C4—23no—
924C2×C4—26no—
925C2×C4—26no—
926C2×C4—26no—
927C2×C4—26no—
928C2×C4—26no—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—26no—
934C2×C4—26no—
935C2×C4—23no—
936C2×C4—23no—
937C2×C4—26no—
938C2×C4—412no—
939C2×C4—412no—
940C2×C4—812no—
941C2×C4—86no—
942C2×C4—86no—
943C2×C4—86no—
944C2×C4—86no—
945C2×C4—161no—
946C2×C4—163no—
947C2×C4—163no—
948C2×C4—163no—
949C2×C4—166no—
950C2×C4C2×H(5,𝔽2)16yes—
951C2×C4C2×H(5,𝔽2)16yes—
952C2×C4#58516yes—
953C22—26no—
954C22—26no—
955C22—26no—
956C22—26no—
957C22—46no—
958C22—41no—
959C22—43no—
960C22—46no—
961C22—43no—
962C22—46no—
963C22—46no—
964C22—46no—
965C22—46no—
966C22—43no—
967C22—46no—
968C22—46no—
969C22—46no—
970C22—46no—
971C22—43no—
972C22—46no—
973C22—88no—
974C22—1612no—
975C22C22×H(5,𝔽2)13yes—
976C22C2×#58511yescharacteristic
977C22C2×#58513yes—
978C4—26no—
979C4—26no—
980C4—26no—
981C4—43no—
982C4—46no—
983C4—43no—
984C4—41no—
985C4—43no—
986C4—43no—
987C4—41no—
988C4—43no—
989C4—46no—
990C4—43no—
991C4—46no—
992C4—43no—
993C2—42no—
994C2—46no—
995C2—83no—
996C2—86no—
997C2#6282013yes—
998C2#6283211yescharacteristic
999C2#6283613yes—
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. #47607C2semidirect
2. #47223C2semidirect
3. #47213C2semidirect
4. #46854C2semidirect
5. #46813C2semidirect
6. #46716C2semidirect
7. #46661C2semidirect
8. #46600C2semidirect
9. #46425C2semidirect
10. #46354C2semidirect
11. #35534C2semidirect
12. #35530C2semidirect
13. #35504C2semidirect
14. #35474C2semidirect
15. #35463C2semidirect
16. #35438C2semidirect
17. #35438C2semidirect
18. #35394C2semidirect
19. #35356C2semidirect
21. C2×#538C22semidirect
25. C2×#520C22semidirect
26. #2837C22semidirect
27. #2825C22semidirect
30. #2797C22semidirect
31. #2796C22semidirect
32. #2793C22semidirect
33. #2791C22semidirect
34. #2780C22semidirect
35. #2754C22semidirect
36. #2746C22semidirect
37. #2740C22semidirect
38. #2730C22semidirect
39. #2721C22semidirect
40. #2714C22semidirect
41. #2710C22semidirect
42. #2706C22semidirect
43. #2706C22semidirect
44. #2703C22semidirect
46. #2696C22semidirect
47. #2694C22semidirect
49. #2687C22semidirect
51. #2678C22semidirect
52. #2676C22semidirect
53. #2673C22semidirect
55. #2669C22semidirect
56. #2669C22semidirect
57. #2668C22semidirect
58. #2607C22semidirect
59. #2607C22semidirect
60. #2607C22semidirect
61. #2579C22semidirect
62. #2579C22semidirect
63. #2575C22semidirect
64. #2566C22semidirect
65. #2565C22semidirect
67. #2560C22semidirect
68. #2557C22semidirect
69. #2557C22semidirect
70. #2557C22semidirect
71. #2557C22semidirect
72. #2557C22semidirect
73. #2553C22semidirect
74. #2553C22semidirect
75. #2548C22semidirect
76. #2541C22semidirect
81. #2539C22semidirect
82. #2531C22semidirect
83. #2527C22semidirect
84. #2517C22semidirect
85. #2504C22semidirect
86. #2502C22semidirect
87. #2502C22semidirect
91. #2501C22semidirect
93. #2500C22semidirect
94. #2499C22semidirect
95. #2499C22semidirect
97. #2482C22semidirect
98. #2472C22semidirect
99. #2471C22semidirect
100. #2471C22semidirect
101. #2471C22semidirect
102. #2471C22semidirect
103. #2471C22semidirect
104. #2471C22semidirect
105. #2467C22semidirect
106. #2464C22semidirect
107. #2464C22semidirect
108. #2464C22semidirect
109. #2458C22semidirect
110. #2458C22semidirect
111. #2456C22semidirect
112. #2456C22semidirect
113. #2456C22semidirect
114. #2443C22semidirect
115. #2443C22semidirect
116. #2443C22semidirect
117. #2443C22semidirect
118. #2443C22semidirect
119. #2443C22semidirect
121. #2431C22semidirect
122. #2431C22semidirect
123. #2423C22semidirect
124. #2423C22semidirect
125. #2422C22semidirect
126. #2422C22semidirect
127. #2422C22semidirect
128. #2418C22semidirect
129. #2412C22semidirect
134. #2404C22semidirect
135. #2404C22semidirect
136. #2335C22semidirect
139. #2333C22semidirect
140. #2333C22semidirect
141. #2332C22semidirect
142. #2328C22semidirect
143. #2326C22semidirect
144. #2322C22semidirect
145. #2321C22semidirect
146. #2321C22semidirect
147. #2317C22semidirect
148. #2313C22semidirect
149. #2311C22semidirect
150. C4×#127C22semidirect
151. C4×#124C22semidirect
154. #2298C22semidirect
155. #2297C22semidirect
156. #2297C22semidirect
157. C2×#384C22semidirect
159. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#476072
#472232
#472132
#468542
#468132
#467162
#466612
#466002
#464252
#463542
#355342
#355302
#355042
#354742
#354632
#354382
#353942
#353562