Finite Group Databasebeta

← #8429352

Subgroups — #8429352

Order 512.

5321 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60045C211yesmaximal, characteristic, complemented
2#59620C213yesmaximal, complemented
3#59537C213yesmaximal, complemented
4#58989C211yesmaximal, characteristic, complemented
5#58621C213yesmaximal, complemented
6#54852C213yesmaximal, complemented
7#53493C211yesmaximal, characteristic, complemented
8#52916C213yesmaximal, complemented
9#52712C213yesmaximal, complemented
10#52325C216yesmaximal, complemented
11#42303C213yesmaximal, complemented
12#41945C213yesmaximal, complemented
13#40501C216yesmaximal, complemented
14#39457C216yesmaximal, complemented
15#39443C216yesmaximal, complemented
16#37611C213yesmaximal, complemented
17#37513C213yesmaximal, complemented
18#36412C213yesmaximal, complemented
19#34962C213yesmaximal, complemented
20C2×#555C2213yescomplemented
21C2×#550C2213yes—
22C2×#542C2213yes—
23C2×#540C2213yes—
24C2×#538C2216yescomplemented
25#2858C2213yes—
26#2856C2213yes—
27#2856C2211yescharacteristic, complemented
28#2844C2213yescomplemented
29#2832C2216yescomplemented
30#2828C2213yes—
31#2828C2213yescomplemented
32#2824C2216yescomplemented
33#2820C2213yescomplemented
34#2819C2213yes—
35#2819C2213yes—
36#2819C2216yescomplemented
37#2818C2216yes—
38#2816C2213yescomplemented
39#2815C2213yes—
40#2813C2216yes—
41#2812C2212yescomplemented
42#2804C2213yes—
43#2785C2213yes—
44#2784C2213yescomplemented
45#2775C2216yescomplemented
46#2769C2213yescomplemented
47#2723C2216yes—
48#2720C2216yescomplemented
49#2718C2216yescomplemented
50#2706C2216yescomplemented
51#2699C2213yes—
52#2686C2216yescomplemented
53#2679C2211yescharacteristic
54#2677C2216yescomplemented
55#2676C2216yescomplemented
56#2676C2216yescomplemented
57#2675C2216yescomplemented
58#2674C2216yescomplemented
59#2673C2216yes—
60#2673C2216yes—
61#2673C2216yescomplemented
62#2672C2216yes—
63#2672C2216yescomplemented
64#2671C2216yescomplemented
65#2670C2216yes—
66#2669C2216yes—
67#2669C2216yes—
68#2669C2216yes—
69#2669C2216yescomplemented
70#2658C2211yescharacteristic, complemented
71#2657C2213yes—
72#2656C2213yes—
73#2656C2211yescharacteristic, complemented
74#2635C2216yes—
75#2635C2213yes—
76#2635C2216yescomplemented
77#2635C2216yescomplemented
78#2635C2213yescomplemented
79#2632C2216yescomplemented
80#2632C2216yescomplemented
81#2632C2213yescomplemented
82#2631C2216yes—
83#2631C2213yescomplemented
84#2628C2213yescomplemented
85#2619C2213yes—
86#2615C2216yescomplemented
87#2611C2213yescomplemented
88#2610C2213yes—
89#2604C2216yescomplemented
90#2598C2213yes—
91#2598C2213yes—
92#2593C2213yes—
93#2586C2213yescomplemented
94#2574C2216yescomplemented
95#2572C2213yes—
96#2572C2213yes—
97#2572C2216yescomplemented
98#2572C2213yescomplemented
99#2572C2216yescomplemented
100#2567C2213yescomplemented
101#2564C2213yescomplemented
102#2560C2216yescomplemented
103#2559C2216yes—
104#2558C2216yescomplemented
105#2557C2216yes—
106#2555C2216yes—
107#2555C2213yes—
108#2555C2216yescomplemented
109#2555C2216yescomplemented
110#2555C2216yescomplemented
111#2555C2216yescomplemented
112#2555C2216yescomplemented
113#2554C2216yes—
114#2543C2213yes—
115#2541C2213yes—
116#2540C2213yes—
117#2540C2213yes—
118#2539C2216yescomplemented
119#2518C2216yescomplemented
120#2500C2213yes—
121#2500C2213yescomplemented
122#2495C2216yescomplemented
123#2491C2216yescomplemented
124#2479C2216yescomplemented
125#2472C2216yescomplemented
126#2471C2216yescomplemented
127#2467C2216yes—
128#2467C2216yescomplemented
129#2464C2216yes—
130#2461C2216yes—
131#2459C2216yescomplemented
132#2456C2216yes—
133#2456C2216yescomplemented
134#2431C2213yes—
135#2431C2213yescomplemented
136#2430C2216yescomplemented
137#2428C2216yes—
138#2428C2216yescomplemented
139#2428C2216yescomplemented
140#2424C2216yescomplemented
141#2420C2216yescomplemented
142#2404C2216yes—
143#2396C2213yescomplemented
144#2392C2213yescomplemented
145#2388C2216yes—
146#2363C2216yescomplemented
147#2363C2216yescomplemented
148#2358C2216yes—
149#2353C2216yescomplemented
150#2343C2213yescomplemented
151#2343C2213yescomplemented
152C4×#126C2216yescomplemented
153C4×#124C2216yescomplemented
154C4×#124C2213yescomplemented
155C4×#123C2216yescomplemented
156C4×#121C2216yescomplemented
157#2297C2213yes—
158#2297C2213yescomplemented
159C42×D4C2213yescomplemented
160C22×#41C2313yes—
161C22×#41C2313yes—
162#555—412no—
163#550—412no—
164#542—412no—
165#540—412no—
166#538—424no—
167C2×C4⋊Q8C2313yes—
168C2×C4⋊Q8C2313yes—
169C2×#127C2316yes—
170C2×#127C2313yes—
171C2×#127C2313yes—
172C2×#127C2313yes—
173C2×#127C2311yescharacteristic
174C2×#126C2316yes—
175C2×#126C2316yes—
176C2×#125C2313yes—
177C2×#124C2316yes—
178C2×#124C2313yes—
179C2×#124C2313yes—
180C2×#124C2313yes—
181C2×#124C2313yes—
182C2×#124C2316yes—
183C2×#124C2316yes—
184C2×#124C2313yes—
185C2×#124C2316yes—
186C2×#124C2313yes—
187C2×#123C2316yes—
188C2×#123C2316yes—
189C2×#123C2316yes—
190C2×#123C2316yes—
191C2×C22⋊Q8C2313yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2316yes—
194C2×#121C2313yes—
195C2×#121C2316yes—
196C2×#121C2316yes—
197C2×#121C2313yes—
198C2×#121C2313yes—
199C2×#121C2313yes—
200C2×#121C2313yes—
201C2×#121C2316yes—
202C2×#121C2316yes—
203C2×#121C2316yes—
204C2×#121C2316yes—
205C2×#121C2313yes—
206C2×#121C2313yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2313yes—
210C2×#121C2313yes—
211C2×#121C2316yes—
212C2×#121C2316yes—
213C2×#121C2316yes—
214C2×#120C2316yes—
215C2×#120C2316yes—
216C2×#120C2316yes—
217C2×#120C2312yes—
218C2×#120C2312yes—
219C2×C4×Q8C2313yes—
220C2×C4×Q8C2313yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2313yes—
224C2×C4×D4C2313yes—
225C2×C4×D4C2313yes—
226C2×C4×D4C2316yes—
227C2×C4×D4C2313yes—
228C2×C4×D4C2316yes—
229C2×C4×D4C2316yes—
230C2×#117C2313yes—
231C2×#117C2313yes—
232C2×#117C2313yes—
233C2×#117C2313yes—
234C22×C22⋊C4C2316yes—
235C22×C42C2313yes—
236C22×C42C2311yescharacteristic
237#400C2313yes—
238#400C2316yes—
239#400C2316yes—
240#400C2313yes—
241#400C2313yes—
242#400C2316yes—
243#399C2311yescharacteristic
244#399C2313yes—
245#399C2313yes—
246#399C2311yescharacteristic
247#399C2313yes—
248#399C2316yes—
249#399C2313yes—
250#399C2313yes—
251#399C2311yescharacteristic
252#399C2316yes—
253#399C2313yes—
254#398C2316yes—
255#398C2316yes—
256#398C2313yes—
257#397C2316yes—
258#397C2313yes—
259#397C2313yes—
260#397C2313yes—
261#397C2316yes—
262#397C2316yes—
263#396C2316yes—
264#396C2316yes—
265#396C2316yes—
266#396C2316yes—
267#395C2313yes—
268#395C2316yes—
269#395C2316yes—
270#395C2316yes—
271#395C2316yes—
272#395C2316yes—
273#394C2316yes—
274#394C2316yes—
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2316yes—
279#394C2316yes—
280#394C2313yes—
281#394C2313yes—
282#394C2316yes—
283#394C2316yes—
284#394C2316yes—
285#394C2316yes—
286#394C2316yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yes—
290#394C2313yes—
291#394C2316yes—
292#394C2316yes—
293#394C2316yes—
294#394C2316yes—
295#394C2316yes—
296#393C2316yes—
297#393C2313yes—
298#393C2313yes—
299#393C2313yes—
300#393C2316yes—
301#393C2316yes—
302#393C2316yes—
303#393C2316yes—
304#393C2316yes—
305#393C2316yes—
306#392C2313yes—
307#392C2316yes—
308#392C2316yes—
309#392C2316yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#392C2313yes—
314#392C2316yes—
315#392C2316yes—
316#392C2316yes—
317#392C2316yes—
318#392C2316yes—
319#392C2316yes—
320#392C2316yes—
321#392C2316yes—
322#392C2316yes—
323#392C2313yes—
324#392C2313yes—
325#392C2313yes—
326#392C2311yescharacteristic
327#392C2313yes—
328#392C2316yes—
329#392C2316yes—
330#392C2313yes—
331#392C2313yes—
332#392C2316yes—
333#391C2316yes—
334#391C2313yes—
335#391C2313yes—
336#391C2313yes—
337#390C2316yes—
338#390C2313yes—
339#390C2313yes—
340#390C2313yes—
341#390C2313yes—
342#390C2316yes—
343#390C2316yes—
344#390C2313yes—
345#390C2316yes—
346#390C2313yes—
347#390C2313yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#389C2316yes—
352#389C2316yes—
353#389C2316yes—
354#389C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#388C2316yes—
371#388C2316yes—
372#388C2316yes—
373#388C2316yes—
374#388C2316yes—
375#388C2316yes—
376#388C2316yes—
377#388C2316yes—
378#387C2316yes—
379#387C2316yes—
380#387C2316yes—
381#387C2316yes—
382#387C2316yes—
383#387C2316yes—
384#387C2316yes—
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#386C2316yes—
396#386C2316yes—
397#386C2316yes—
398#386C2316yes—
399#386C2316yes—
400#386C2316yes—
401#386C2316yes—
402#386C2316yes—
403#386C2316yes—
404#386C2316yes—
405#385C2316yes—
406#385C2316yes—
407#385C2316yes—
408#385C2316yes—
409#385C2316yes—
410#385C2316yes—
411#384C2311yescharacteristic
412#384C2313yes—
413#383C2316yes—
414#383C2316yes—
415#383C2313yes—
416#383C2313yes—
417#382C2313yes—
418#382C2313yes—
419#382C2316yes—
420#382C2313yes—
421#381C2313yes—
422#381C2316yes—
423#381C2313yes—
424#381C2316yes—
425#380C2316yes—
426#380C2316yes—
427#380C2316yes—
428#379C2312yes—
429C4×C4⋊C4C2313yes—
430C4×C4⋊C4C2316yes—
431C4×C4⋊C4C2316yes—
432C4×C4⋊C4C2313yes—
433C4×C4⋊C4C2313yes—
434C4×C22⋊C4C2316yes—
435C4×C22⋊C4C2316yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2316yes—
438C4×C22⋊C4C2316yes—
439C4×C22⋊C4C2316yes—
440C4×C22⋊C4C2316yes—
441C4×C22⋊C4C2316yes—
442C4×C22⋊C4C2313yes—
443C4×C22⋊C4C2316yes—
444C4×C22⋊C4C2316yes—
445C4×C22⋊C4C2316yes—
446C4×C22⋊C4C2313yes—
447#376C2311yescharacteristic
448#376C2313yes—
449C2×#95C2313yes—
450C2×#95C2311yescharacteristic
451C43C2313yes—
452C25C2412yes—
453C2×#41—46no—
454C2×#41—46no—
455C2×#41—46no—
456C2×#41—46no—
457C2×#41—83no—
458C2×#41—83no—
459C22×Q8C2413yes—
460C22×Q8C2413yes—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×D4C2413yes—
464C22×D4C2416yes—
465C22×D4C2416yes—
466C22×D4C2413yes—
467C22×D4C2413yes—
468C22×D4C2413yes—
469C22×D4C2413yes—
470C22×D4C2413yes—
471C22×D4C2416yes—
472C22×D4C2413yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C2416yes—
478C22×D4C2413yes—
479C22×D4C2413yes—
480C22×D4C2411yescharacteristic
481C22×D4C2413yes—
482C22×D4C2416yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C23×C4C2413yes—
488C23×C4C2416yes—
489C23×C4C2416yes—
490C23×C4C2416yes—
491C4⋊Q8—46no—
492C4⋊Q8—46no—
493#127—46no—
494#127—46no—
495#127—412no—
496#127—81no—
497#127—83no—
498#126—224no—
499#126—412no—
500#125—46no—
501#124—412no—
502#124—412no—
503#124—412no—
504#124—46no—
505#124—412no—
506#124—46no—
507#124—46no—
508#124—46no—
509#124—46no—
510#124—46no—
511#123—224no—
512#123—412no—
513#123—412no—
514#123—412no—
515C22⋊Q8—412no—
516C22⋊Q8—412no—
517C22⋊Q8—46no—
518#121—412no—
519#121—412no—
520#121—412no—
521#121—46no—
522#121—46no—
523#121—46no—
524#121—46no—
525#121—412no—
526#121—46no—
527#121—412no—
528#121—46no—
529#121—46no—
530#121—412no—
531#121—412no—
532#121—412no—
533#121—412no—
534#121—412no—
535#121—46no—
536#121—46no—
537#121—86no—
538#120—412no—
539#120—412no—
540#120—412no—
541#120—82no—
542#120—82no—
543C4×Q8—46no—
544C4×Q8—46no—
545C4×D4—224no—
546C4×D4—212no—
547C4×D4—46no—
548C4×D4—46no—
549C4×D4—412no—
550C4×D4—46no—
551C4×D4—46no—
552C4×D4—412no—
553C4×D4—86no—
554#117—212no—
555#117—212no—
556#117—46no—
557#117—46no—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2413yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2413yes—
580C2×C22⋊C4—412no—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2413yes—
584C2×C22⋊C4C2413yes—
585C2×C22⋊C4C2413yes—
586C2×C22⋊C4C2413yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2413yes—
590C2×C22⋊C4C2413yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2413yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C42—81no—
625C2×C42—83no—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2416yes—
632C2×C42C2416yes—
633C2×C42C2413yes—
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2411yescharacteristic
637C2×C42C2413yes—
638C2×C42C2413yes—
639#95C2416yes—
640#95C2413yes—
641#95C2413yes—
642#95C2413yes—
643#95C2411yescharacteristic
644#95C2413yes—
645#95C2411yescharacteristic
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C2416yes—
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#95C2413yes—
663#95C2413yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668C24—46no—
669C24—46no—
670C24—42no—
671C24C2516yes—
672C24C2513yes—
673C24C2511yescharacteristic
674C24C2513yes—
675C24C2511yescharacteristic
676#41—824no—
677#41—824no—
678C2×Q8—26no—
679C2×Q8—43no—
680C2×Q8—43no—
681C2×Q8—43no—
682C2×Q8—46no—
683C2×Q8—46no—
684C2×Q8—46no—
685C2×Q8—43no—
686C2×Q8—43no—
687C2×D4—26no—
688C2×D4—212no—
689C2×D4—212no—
690C2×D4—26no—
691C2×D4—26no—
692C2×D4—26no—
693C2×D4—46no—
694C2×D4—46no—
695C2×D4—43no—
696C2×D4—43no—
697C2×D4—43no—
698C2×D4—43no—
699C2×D4—46no—
700C2×D4—46no—
701C2×D4—46no—
702C2×D4—46no—
703C2×D4—43no—
704C2×D4—43no—
705C2×D4—46no—
706C2×D4—46no—
707C2×D4—46no—
708C2×D4—46no—
709C2×D4—46no—
710C2×D4—46no—
711C2×D4—46no—
712C2×D4—46no—
713C2×D4—46no—
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—43no—
727C2×D4—43no—
728C2×D4—43no—
729C2×D4—43no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—46no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C22×C4—26no—
739C22×C4—26no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—212no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—212no—
746C22×C4—212no—
747C22×C4—43no—
748C22×C4—43no—
749C22×C4—46no—
750C22×C4—46no—
751C22×C4—46no—
752C22×C4—46no—
753C22×C4—46no—
754C22×C4—46no—
755C22×C4—46no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4C2516yes—
761C22×C4C2513yes—
762C22×C4C2513yes—
763C22×C4C2516yes—
764C22×C4C2516yes—
765C22×C4C2511yescharacteristic
766C22×C4C2513yes—
767C22×C4C2513yes—
768C22×C4C2513yes—
769C22×C4C2513yes—
770C22×C4C2513yes—
771C22×C4C2513yes—
772C22×C4C2513yes—
773C22×C4C2513yes—
774C4⋊C4—26no—
775C4⋊C4—26no—
776C4⋊C4—212no—
777C4⋊C4—212no—
778C4⋊C4—212no—
779C4⋊C4—212no—
780C4⋊C4—43no—
781C4⋊C4—43no—
782C4⋊C4—43no—
783C4⋊C4—43no—
784C4⋊C4—43no—
785C4⋊C4—43no—
786C4⋊C4—46no—
787C4⋊C4—46no—
788C4⋊C4—43no—
789C4⋊C4—46no—
790C4⋊C4—43no—
791C4⋊C4—46no—
792C4⋊C4—46no—
793C4⋊C4—46no—
794C4⋊C4—46no—
795C4⋊C4H(5,𝔽2)112yes—
796C22⋊C4—212no—
797C22⋊C4—212no—
798C22⋊C4—26no—
799C22⋊C4—26no—
800C22⋊C4—26no—
801C22⋊C4—26no—
802C22⋊C4—212no—
803C22⋊C4—212no—
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—46no—
814C22⋊C4—46no—
815C22⋊C4—43no—
816C22⋊C4—43no—
817C22⋊C4—43no—
818C22⋊C4—43no—
819C22⋊C4—46no—
820C22⋊C4—46no—
821C22⋊C4—46no—
822C22⋊C4—46no—
823C22⋊C4—43no—
824C22⋊C4—43no—
825C22⋊C4—46no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—46no—
834C22⋊C4—46no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C42—26no—
840C42—26no—
841C42—26no—
842C42—26no—
843C42—26no—
844C42—212no—
845C42—212no—
846C42—26no—
847C42—43no—
848C42—46no—
849C42—41no—
850C42—43no—
851C42—46no—
852C23—26no—
853C23—23no—
854C23—26no—
855C23—23no—
856C23—23no—
857C23—23no—
858C23—26no—
859C23—26no—
860C23—26no—
861C23—26no—
862C23—26no—
863C23—26no—
864C23—23no—
865C23—23no—
866C23—23no—
867C23—26no—
868C23—26no—
869C23—23no—
870C23—23no—
871C23—26no—
872C23—21no—
873C23—23no—
874C23—21no—
875C23—812no—
876C23—162no—
877C23—166no—
878C23C2611yescharacteristic
879Q8—412no—
880Q8—86no—
881Q8—163no—
882Q8—163no—
883D4—412no—
884D4—812no—
885D4—86no—
886D4—812no—
887D4—86no—
888D4—86no—
889D4—86no—
890D4—86no—
891D4—86no—
892D4—812no—
893D4—812no—
894D4—812no—
895D4—163no—
896D4—163no—
897D4—166no—
898D4—163no—
899D4—166no—
900D4—161no—
901D4—166no—
902D4—166no—
903C2×C4—23no—
904C2×C4—23no—
905C2×C4—26no—
906C2×C4—23no—
907C2×C4—23no—
908C2×C4—23no—
909C2×C4—23no—
910C2×C4—23no—
911C2×C4—23no—
912C2×C4—23no—
913C2×C4—26no—
914C2×C4—26no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—26no—
918C2×C4—23no—
919C2×C4—23no—
920C2×C4—26no—
921C2×C4—26no—
922C2×C4—26no—
923C2×C4—26no—
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—412no—
933C2×C4—412no—
934C2×C4—86no—
935C2×C4—86no—
936C2×C4—812no—
937C2×C4—812no—
938C2×C4—812no—
939C2×C4—166no—
940C2×C4C2×H(5,𝔽2)16yes—
941C2×C4C2×H(5,𝔽2)16yes—
942C2×C4C2×H(5,𝔽2)16yes—
943C2×C4#58516yes—
944C22—43no—
945C22—43no—
946C22—43no—
947C22—43no—
948C22—46no—
949C22—46no—
950C22—46no—
951C22—46no—
952C22—46no—
953C22—46no—
954C22—43no—
955C22—41no—
956C22—41no—
957C22—43no—
958C22—43no—
959C22—43no—
960C22—46no—
961C22—46no—
962C22—46no—
963C22—43no—
964C22—46no—
965C22—43no—
966C22—46no—
967C22—168no—
968C22C22×H(5,𝔽2)13yes—
969C22C2×#58513yes—
970C22H(7,𝔽2)11yescharacteristic
971C4—26no—
972C4—26no—
973C4—26no—
974C4—26no—
975C4—43no—
976C4—43no—
977C4—46no—
978C4—43no—
979C4—43no—
980C4—43no—
981C4—43no—
982C4—41no—
983C4—46no—
984C4—46no—
985C2—81no—
986C2—83no—
987C2—81no—
988C2—83no—
989C2—86no—
990C2#6275913yes—
991C2#6291813yes—
992C2#6304011yescharacteristic
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. #60045C2semidirect
2. #59620C2semidirect
3. #59537C2semidirect
4. #58989C2semidirect
5. #58621C2semidirect
6. #54852C2semidirect
7. #53493C2semidirect
8. #52916C2semidirect
9. #52712C2semidirect
10. #52325C2semidirect
11. #42303C2semidirect
12. #41945C2semidirect
13. #40501C2semidirect
14. #39457C2semidirect
15. #39443C2semidirect
16. #37611C2semidirect
17. #37513C2semidirect
18. #36412C2semidirect
19. #34962C2semidirect
20. C2×#555C22semidirect
24. C2×#538C22semidirect
27. #2856C22semidirect
28. #2844C22semidirect
29. #2832C22semidirect
31. #2828C22semidirect
32. #2824C22semidirect
33. #2820C22semidirect
36. #2819C22semidirect
38. #2816C22semidirect
41. #2812C22semidirect
44. #2784C22semidirect
45. #2775C22semidirect
46. #2769C22semidirect
48. #2720C22semidirect
49. #2718C22semidirect
50. #2706C22semidirect
52. #2686C22semidirect
54. #2677C22semidirect
55. #2676C22semidirect
56. #2676C22semidirect
57. #2675C22semidirect
58. #2674C22semidirect
61. #2673C22semidirect
63. #2672C22semidirect
64. #2671C22semidirect
69. #2669C22semidirect
70. #2658C22semidirect
73. #2656C22semidirect
76. #2635C22semidirect
77. #2635C22semidirect
78. #2635C22semidirect
79. #2632C22semidirect
80. #2632C22semidirect
81. #2632C22semidirect
83. #2631C22semidirect
84. #2628C22semidirect
86. #2615C22semidirect
87. #2611C22semidirect
89. #2604C22semidirect
93. #2586C22semidirect
94. #2574C22semidirect
97. #2572C22semidirect
98. #2572C22semidirect
99. #2572C22semidirect
100. #2567C22semidirect
101. #2564C22semidirect
102. #2560C22semidirect
104. #2558C22semidirect
108. #2555C22semidirect
109. #2555C22semidirect
110. #2555C22semidirect
111. #2555C22semidirect
112. #2555C22semidirect
118. #2539C22semidirect
119. #2518C22semidirect
121. #2500C22semidirect
122. #2495C22semidirect
123. #2491C22semidirect
124. #2479C22semidirect
125. #2472C22semidirect
126. #2471C22semidirect
128. #2467C22semidirect
131. #2459C22semidirect
133. #2456C22semidirect
135. #2431C22semidirect
136. #2430C22semidirect
138. #2428C22semidirect
139. #2428C22semidirect
140. #2424C22semidirect
141. #2420C22semidirect
143. #2396C22semidirect
144. #2392C22semidirect
146. #2363C22semidirect
147. #2363C22semidirect
149. #2353C22semidirect
150. #2343C22semidirect
151. #2343C22semidirect
152. C4×#126C22semidirect
153. C4×#124C22semidirect
154. C4×#124C22semidirect
155. C4×#123C22semidirect
156. C4×#121C22semidirect
158. #2297C22semidirect
159. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#600452
#596202
#595372
#589892
#586212
#548522
#534932
#529162
#527122
#523252
#423032
#419452
#405012
#394572
#394432
#376112
#375132
#364122
#349622