Finite Group Databasebeta

← #7804428

Subgroups — #7804428

Order 512.

5873 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#60033C213yesmaximal, complemented
2#60029C213yesmaximal, complemented
3#59977C216yesmaximal, complemented
4#59975C213yesmaximal, complemented
5#59173C216yesmaximal, complemented
6#59001C213yesmaximal, complemented
7#47563C211yesmaximal, characteristic, complemented
8#47018C211yesmaximal, characteristic, complemented
9#46458C213yesmaximal, complemented
10#46414C213yesmaximal, complemented
11#41289C213yesmaximal, complemented
12#41261C216yesmaximal, complemented
13#41234C213yesmaximal, complemented
14#37528C211yesmaximal, characteristic, complemented
15#35866C216yesmaximal, complemented
16#35844C213yesmaximal, complemented
17#35740C213yesmaximal, complemented
18#34655C213yesmaximal, complemented
19#34265C213yesmaximal, complemented
20C2×#559C2213yescomplemented
21C2×#548C2213yescomplemented
22C2×#535C2213yes—
23C2×#525C2216yescomplemented
24C2×#520C2213yescomplemented
25C22×C4×D4C2213yes—
26#2840C2211yescharacteristic
27#2828C2216yescomplemented
28#2825C2212yescomplemented
29#2812C2213yes—
30#2784C2216yescomplemented
31#2763C2213yescomplemented
32#2757C2216yescomplemented
33#2756C2216yescomplemented
34#2742C2213yescomplemented
35#2735C2213yescomplemented
36#2714C2216yescomplemented
37#2712C2213yes—
38#2697C2216yescomplemented
39#2691C2216yescomplemented
40#2678C2216yescomplemented
41#2675C2213yes—
42#2673C2216yes—
43#2670C2213yes—
44#2670C2216yes—
45#2670C2213yes—
46#2670C2213yescomplemented
47#2670C2216yescomplemented
48#2669C2216yescomplemented
49#2669C2216yescomplemented
50#2662C2216yescomplemented
51#2653C2216yescomplemented
52#2651C2216yescomplemented
53#2638C2213yescomplemented
54#2632C2213yescomplemented
55#2631C2213yescomplemented
56#2631C2213yescomplemented
57#2619C2213yescomplemented
58#2618C2213yescomplemented
59#2610C2213yes—
60#2610C2216yes—
61#2610C2213yes—
62#2610C2213yescomplemented
63#2602C2216yescomplemented
64#2602C2216yescomplemented
65#2601C2216yescomplemented
66#2599C2213yescomplemented
67#2598C2213yescomplemented
68#2598C2213yescomplemented
69#2597C2216yescomplemented
70#2594C2216yescomplemented
71#2587C2216yescomplemented
72#2586C2216yescomplemented
73#2583C2213yescomplemented
74#2580C2213yescomplemented
75#2559C2216yescomplemented
76#2557C2216yescomplemented
77#2555C2216yes—
78#2555C2216yescomplemented
79#2554C2216yescomplemented
80#2543C2213yes—
81#2541C2213yes—
82#2532C2216yescomplemented
83#2525C2216yescomplemented
84#2523C2213yescomplemented
85#2518C2216yescomplemented
86#2476C2216yescomplemented
87#2474C2216yescomplemented
88#2474C2216yescomplemented
89#2474C2216yescomplemented
90#2474C2216yescomplemented
91#2465C2216yescomplemented
92#2465C2216yescomplemented
93#2463C2213yes—
94#2463C2213yescomplemented
95#2461C2216yescomplemented
96#2461C2216yescomplemented
97#2461C2216yescomplemented
98#2459C2216yescomplemented
99#2459C2216yescomplemented
100#2456C2216yes—
101#2456C2216yescomplemented
102#2456C2216yescomplemented
103#2456C2216yescomplemented
104#2456C2216yescomplemented
105#2455C2213yes—
106#2449C2216yescomplemented
107#2448C2216yescomplemented
108#2443C2216yescomplemented
109#2443C2216yescomplemented
110#2437C2213yes—
111#2431C2216yescomplemented
112#2431C2216yescomplemented
113#2430C2216yescomplemented
114#2426C2216yescomplemented
115#2424C2216yescomplemented
116#2418C2216yescomplemented
117#2414C2216yescomplemented
118#2410C2216yes—
119#2409C2213yescomplemented
120#2406C2213yescomplemented
121#2403C2213yes—
122#2399C2213yescomplemented
123#2397C2213yes—
124#2397C2211yescharacteristic, complemented
125#2396C2213yescomplemented
126#2392C2216yes—
127#2388C2213yes—
128C2×#395C2211yescharacteristic, complemented
129#2374C2216yescomplemented
130#2373C2216yescomplemented
131#2367C2216yescomplemented
132#2367C2216yescomplemented
133#2367C2216yescomplemented
134#2366C2216yescomplemented
135#2366C2216yescomplemented
136#2363C2216yescomplemented
137#2363C2216yescomplemented
138#2362C2216yescomplemented
139#2361C2216yescomplemented
140#2361C2216yescomplemented
141#2361C2216yescomplemented
142#2359C2216yescomplemented
143#2356C2213yescomplemented
144#2353C2213yescomplemented
145#2321C2213yes—
146#2321C2213yes—
147#2321C2213yescomplemented
148#2321C2213yescomplemented
149#2309C2213yes—
150C4×#121C2216yescomplemented
151C4×#120C2213yes—
152C4×#120C2211yescharacteristic
153C4×#120C2213yescomplemented
154C4×#120C2216yescomplemented
155C4×#120C2213yescomplemented
156#2297C2213yescomplemented
157#2296C2213yescomplemented
158#2290C2216yescomplemented
159#2274C2213yescomplemented
160C22×#41C2313yes—
161C22×#41C2313yes—
162C23×Q8C2311yescharacteristic
163C23×D4C2313yes—
164C24×C4C2311yescharacteristic
165C24×C4C2313yes—
166#559—412no—
167#548—412no—
168#535—224no—
169C2×#127C2316yes—
170C2×#127C2313yes—
171C2×#126C2316yes—
172C2×#124C2316yes—
173C2×#124C2316yes—
174C2×#124C2313yes—
175C2×#124C2313yes—
176C2×#124C2313yes—
177C2×#124C2316yes—
178C2×#124C2316yes—
179#525—424no—
180C2×#123C2316yes—
181C2×#123C2316yes—
182C2×#123C2316yes—
183C2×#123C2316yes—
184C2×C22⋊Q8C2316yes—
185C2×C22⋊Q8C2313yes—
186C2×C22⋊Q8C2316yes—
187C2×#121C2316yes—
188C2×#121C2316yes—
189C2×#121C2316yes—
190C2×#121C2313yes—
191C2×#121C2316yes—
192C2×#121C2316yes—
193C2×#121C2316yes—
194C2×#121C2316yes—
195C2×#120C2313yes—
196C2×#120C2313yes—
197C2×#120C2313yes—
198C2×#120C2316yes—
199C2×#120C2316yes—
200C2×#120C2316yes—
201C2×#120C2311yescharacteristic
202#520—412no—
203C2×C4×Q8C2313yes—
204C2×C4×Q8C2313yes—
205C2×C4×Q8C2313yes—
206C2×C4×Q8C2313yes—
207C2×C4×D4—412no—
208C2×C4×D4C2313yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2313yes—
211C2×C4×D4C2313yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2313yes—
214C2×C4×D4C2313yes—
215C2×C4×D4C2313yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2316yes—
224C2×C4×D4C2316yes—
225C2×#117C2313yes—
226C2×#117C2313yes—
227C2×#117C2313yes—
228C2×#117C2313yes—
229C2×#117C2316yes—
230C2×#117C2313yes—
231C22×C4⋊C4C2313yes—
232C22×C4⋊C4C2313yes—
233C22×C4⋊C4C2313yes—
234C22×C22⋊C4C2313yes—
235C22×C22⋊C4C2313yes—
236C22×C42C2313yes—
237#401C2312yes—
238#400C2316yes—
239#400C2313yes—
240#399C2311yescharacteristic
241#399C2313yes—
242#399C2316yes—
243#399C2313yes—
244#398C2313yes—
245#398C2313yes—
246#398C2316yes—
247#398C2316yes—
248#398C2313yes—
249#397C2316yes—
250#397C2316yes—
251#397C2316yes—
252#397C2316yes—
253#397C2316yes—
254#397C2316yes—
255#397C2313yes—
256#396C2312yes—
257#396C2316yes—
258#396C2316yes—
259#396C2316yes—
260#396C2316yes—
261#396C2316yes—
262#396C2316yes—
263#395C2311yescharacteristic
264#395C2313yes—
265#395C2313yes—
266#395C2316yes—
267#395C2316yes—
268#395C2313yes—
269#395C2311yescharacteristic
270#395C2313yes—
271#395C2313yes—
272#394C2316yes—
273#394C2313yes—
274#394C2316yes—
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2313yes—
279#394C2313yes—
280#394C2316yes—
281#394C2313yes—
282#394C2313yes—
283#394C2316yes—
284#394C2316yes—
285#394C2316yes—
286#394C2316yes—
287#394C2316yes—
288#394C2316yes—
289#393C2313yes—
290#393C2313yes—
291#393C2313yes—
292#393C2316yes—
293#393C2313yes—
294#393C2313yes—
295#393C2316yes—
296#392C2316yes—
297#392C2312yes—
298#392C2313yes—
299#392C2316yes—
300#392C2316yes—
301#392C2316yes—
302#392C2313yes—
303#392C2313yes—
304#392C2313yes—
305#392C2316yes—
306#392C2313yes—
307#392C2313yes—
308#392C2311yescharacteristic
309#392C2316yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#392C2316yes—
314#392C2316yes—
315#391C2316yes—
316#391C2316yes—
317#391C2316yes—
318#391C2316yes—
319#390C2316yes—
320#390C2316yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
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#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
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#387C2316yes—
368#387C2316yes—
369#387C2316yes—
370#387C2316yes—
371#387C2316yes—
372#387C2316yes—
373#387C2316yes—
374#387C2316yes—
375#387C2316yes—
376#387C2316yes—
377#386C2316yes—
378#386C2313yes—
379#386C2313yes—
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#386C2313yes—
394#386C2316yes—
395#386C2316yes—
396#386C2316yes—
397#386C2316yes—
398#386C2316yes—
399#386C2313yes—
400#385C2313yes—
401#385C2313yes—
402#385C2316yes—
403#385C2316yes—
404#385C2316yes—
405#385C2316yes—
406#385C2316yes—
407#385C2316yes—
408#385C2316yes—
409#385C2316yes—
410#385C2313yes—
411#385C2316yes—
412#385C2316yes—
413#385C2316yes—
414#385C2313yes—
415#383C2313yes—
416#383C2313yes—
417#383C2313yes—
418#382C2313yes—
419#381C2313yes—
420#380C2313yes—
421#380C2316yes—
422#379C2311yescharacteristic
423#379C2313yes—
424#379C2313yes—
425#379C2313yes—
426#379C2316yes—
427C4×C4⋊C4C2316yes—
428C4×C4⋊C4C2316yes—
429C4×C4⋊C4C2316yes—
430C4×C4⋊C4C2316yes—
431C4×C4⋊C4C2316yes—
432C4×C4⋊C4C2316yes—
433C4×C4⋊C4C2316yes—
434C4×C4⋊C4C2313yes—
435C4×C4⋊C4C2316yes—
436C4×C22⋊C4C2313yes—
437C4×C22⋊C4C2313yes—
438C4×C22⋊C4C2313yes—
439C4×C22⋊C4C2313yes—
440C4×C22⋊C4C2313yes—
441C4×C22⋊C4C2316yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2316yes—
444C4×C22⋊C4C2316yes—
445C4×C22⋊C4C2316yes—
446C4×C22⋊C4C2316yes—
447C4×C22⋊C4C2316yes—
448C4×C22⋊C4C2316yes—
449#376C2313yes—
450#376C2311yescharacteristic
451#376C2313yes—
452C2×#95C2313yes—
453C25C2413yes—
454C25C2411yescharacteristic
455C2×#41—212no—
456C2×#41—46no—
457C2×#41—46no—
458C2×#41—46no—
459C2×#41—412no—
460C22×Q8—46no—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×Q8C2413yes—
464C22×Q8C2411yescharacteristic
465C22×D4—212no—
466C22×D4—46no—
467C22×D4—46no—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C2413yes—
478C22×D4C2416yes—
479C22×D4C2413yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C23×C4—46no—
483C23×C4—46no—
484C23×C4—412no—
485C23×C4C2413yes—
486C23×C4C2413yes—
487C23×C4C2413yes—
488C23×C4C2416yes—
489C23×C4C2413yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2413yes—
493C23×C4C2413yes—
494C23×C4C2416yes—
495C23×C4C2413yes—
496C23×C4C2411yescharacteristic
497C23×C4C2413yes—
498#127—224no—
499#127—46no—
500#126—412no—
501#124—224no—
502#124—412no—
503#124—46no—
504#124—46no—
505#124—46no—
506#124—412no—
507#124—412no—
508#123—224no—
509#123—412no—
510#123—412no—
511#123—412no—
512C22⋊Q8—224no—
513C22⋊Q8—412no—
514C22⋊Q8—46no—
515#121—224no—
516#121—224no—
517#121—412no—
518#121—412no—
519#121—46no—
520#121—412no—
521#121—412no—
522#121—412no—
523#120—212no—
524#120—212no—
525#120—212no—
526#120—412no—
527#120—412no—
528#120—412no—
529#120#4118yescomplemented
530C4×Q8—212no—
531C4×Q8—46no—
532C4×Q8—46no—
533C4×Q8—46no—
534C4×D4—224no—
535C4×D4—212no—
536C4×D4—412no—
537C4×D4—46no—
538C4×D4—412no—
539C4×D4—46no—
540C4×D4—46no—
541C4×D4—46no—
542C4×D4—46no—
543C4×D4—412no—
544C4×D4—412no—
545C4×D4—46no—
546C4×D4—46no—
547C4×D4—412no—
548C4×D4—412no—
549C4×D4—412no—
550C4×D4—412no—
551#117—212no—
552#117—46no—
553#117—46no—
554#117—46no—
555#117—46no—
556#117—412no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4—46no—
559C2×C4⋊C4—46no—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C22⋊C4—46no—
585C2×C22⋊C4—46no—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2413yes—
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⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2413yes—
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×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2413yes—
627C2×C42—46no—
628C2×C42C2416yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2416yes—
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2416yes—
639C2×C42C2416yes—
640C2×C42C2416yes—
641#95C2413yes—
642#95C2416yes—
643#95C2413yes—
644#95C2413yes—
645#95C2416yes—
646#95C2413yes—
647#95C2411yescharacteristic
648#95C2413yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2413yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2413yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2412yes—
669#95C2416yes—
670C24—26no—
671C24—43no—
672C24—43no—
673C24—43no—
674C24—43no—
675C24—46no—
676C24—46no—
677C24C2×#4114yes—
678C24C2516yes—
679C24C2513yes—
680C24C2513yes—
681C24C2511yescharacteristic
682#41—448no—
683#41—824no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—212no—
687C2×Q8—43no—
688C2×Q8—43no—
689C2×Q8—43no—
690C2×Q8—43no—
691C2×Q8—46no—
692C2×Q8—88no—
693C2×D4—26no—
694C2×D4—212no—
695C2×D4—212no—
696C2×D4—26no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—26no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—46no—
705C2×D4—43no—
706C2×D4—43no—
707C2×D4—46no—
708C2×D4—43no—
709C2×D4—43no—
710C2×D4—43no—
711C2×D4—448no—
712C2×D4—46no—
713C2×D4—46no—
714C2×D4—46no—
715C2×D4—46no—
716C2×D4—46no—
717C2×D4—43no—
718C2×D4—43no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—43no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4C2×#41112yes—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—212no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—212no—
748C22×C4—43no—
749C22×C4—43no—
750C22×C4—43no—
751C22×C4—46no—
752C22×C4—43no—
753C22×C4—46no—
754C22×C4—46no—
755C22×C4—46no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4—43no—
761C22×C4—43no—
762C22×C4—46no—
763C22×C4—88no—
764C22×C4—824no—
765C22×C4C2513yes—
766C22×C4C2513yes—
767C22×C4C2516yes—
768C22×C4C2516yes—
769C22×C4C2516yes—
770C22×C4C2513yes—
771C22×C4C2513yes—
772C22×C4C2511yescharacteristic
773C22×C4C2513yes—
774C22×C4C2511yescharacteristic
775C22×C4C2513yes—
776C22×C4C2513yes—
777C22×C4C2513yes—
778C22×C4C2513yes—
779C22×C4C2513yes—
780C4⋊C4—212no—
781C4⋊C4—26no—
782C4⋊C4—26no—
783C4⋊C4—26no—
784C4⋊C4—26no—
785C4⋊C4—26no—
786C4⋊C4—212no—
787C4⋊C4—212no—
788C4⋊C4—212no—
789C4⋊C4—212no—
790C4⋊C4—43no—
791C4⋊C4—43no—
792C4⋊C4—43no—
793C4⋊C4—46no—
794C4⋊C4—43no—
795C4⋊C4—46no—
796C4⋊C4—43no—
797C4⋊C4—46no—
798C4⋊C4—43no—
799C4⋊C4—46no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4H(5,𝔽2)112yes—
804C22⋊C4—26no—
805C22⋊C4—212no—
806C22⋊C4—212no—
807C22⋊C4—212no—
808C22⋊C4—212no—
809C22⋊C4—212no—
810C22⋊C4—26no—
811C22⋊C4—26no—
812C22⋊C4—212no—
813C22⋊C4—212no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—212no—
819C22⋊C4—212no—
820C22⋊C4—46no—
821C22⋊C4—46no—
822C22⋊C4—43no—
823C22⋊C4—43no—
824C22⋊C4—43no—
825C22⋊C4—43no—
826C22⋊C4—43no—
827C22⋊C4—43no—
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—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C22⋊C4—46no—
843C22⋊C4—46no—
844C22⋊C4C2×#41112yes—
845C42—212no—
846C42—212no—
847C42—26no—
848C42—26no—
849C42—26no—
850C42—26no—
851C42—212no—
852C42—46no—
853C42—46no—
854C42—43no—
855C42—43no—
856C42—46no—
857C42—46no—
858C23—26no—
859C23—23no—
860C23—23no—
861C23—23no—
862C23—23no—
863C23—26no—
864C23—26no—
865C23—23no—
866C23—26no—
867C23—26no—
868C23—23no—
869C23—26no—
870C23—26no—
871C23—26no—
872C23—26no—
873C23—26no—
874C23—26no—
875C23—23no—
876C23—412no—
877C23—412no—
878C23—812no—
879C23—82no—
880C23—86no—
881C23—86no—
882C23—86no—
883C23—812no—
884C23C22×#4116yes—
885C23C22×#4112yes—
886C23C2611yescharacteristic
887Q8—412no—
888Q8—412no—
889Q8—86no—
890Q8—82no—
891D4—412no—
892D4—424no—
893D4—424no—
894D4—412no—
895D4—412no—
896D4—812no—
897D4—812no—
898D4—812no—
899D4—812no—
900D4—812no—
901D4—86no—
902D4—86no—
903D4—812no—
904D4—86no—
905C2×C4—224no—
906C2×C4—23no—
907C2×C4—23no—
908C2×C4—23no—
909C2×C4—26no—
910C2×C4—23no—
911C2×C4—26no—
912C2×C4—23no—
913C2×C4—23no—
914C2×C4—26no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—23no—
918C2×C4—26no—
919C2×C4—23no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—26no—
923C2×C4—26no—
924C2×C4—26no—
925C2×C4—23no—
926C2×C4—23no—
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—412no—
937C2×C4—424no—
938C2×C4—412no—
939C2×C4—412no—
940C2×C4—86no—
941C2×C4—812no—
942C2×C4—86no—
943C2×C4—86no—
944C2×C4—86no—
945C2×C4—86no—
946C2×C4—161no—
947C2×C4—163no—
948C2×C4C22×#4116yes—
949C2×C4C2×H(5,𝔽2)16yes—
950C2×C4C2×H(5,𝔽2)16yes—
951C2×C4C2×H(5,𝔽2)16yes—
952C2×C4#58516yes—
953C22—26no—
954C22—26no—
955C22—212no—
956C22—43no—
957C22—41no—
958C22—43no—
959C22—43no—
960C22—46no—
961C22—46no—
962C22—43no—
963C22—46no—
964C22—46no—
965C22—46no—
966C22—46no—
967C22—43no—
968C22—43no—
969C22—46no—
970C22—46no—
971C22—46no—
972C22—46no—
973C22—88no—
974C22—824no—
975C22C23×#4111yescharacteristic
976C22C22×H(5,𝔽2)13yes—
977C22C2×#58513yes—
978C4—26no—
979C4—26no—
980C4—26no—
981C4—26no—
982C4—26no—
983C4—43no—
984C4—41no—
985C4—43no—
986C4—41no—
987C4—43no—
988C4—46no—
989C4—43no—
990C4—46no—
991C4—43no—
992C4—46no—
993C2—42no—
994C2—46no—
995C2—83no—
996C2—86no—
997C2#6277313yes—
998C2#6301111yescharacteristic
999C2#6302213yes—
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. #60033C2semidirect
2. #60029C2semidirect
3. #59977C2semidirect
4. #59975C2semidirect
5. #59173C2semidirect
6. #59001C2semidirect
7. #47563C2semidirect
8. #47018C2semidirect
9. #46458C2semidirect
10. #46414C2semidirect
11. #41289C2semidirect
12. #41261C2semidirect
13. #41234C2semidirect
14. #37528C2semidirect
15. #35866C2semidirect
16. #35844C2semidirect
17. #35740C2semidirect
18. #34655C2semidirect
19. #34265C2semidirect
20. C2×#559C22semidirect
21. C2×#548C22semidirect
23. C2×#525C22semidirect
24. C2×#520C22semidirect
27. #2828C22semidirect
28. #2825C22semidirect
30. #2784C22semidirect
31. #2763C22semidirect
32. #2757C22semidirect
33. #2756C22semidirect
34. #2742C22semidirect
35. #2735C22semidirect
36. #2714C22semidirect
38. #2697C22semidirect
39. #2691C22semidirect
40. #2678C22semidirect
46. #2670C22semidirect
47. #2670C22semidirect
48. #2669C22semidirect
49. #2669C22semidirect
50. #2662C22semidirect
51. #2653C22semidirect
52. #2651C22semidirect
53. #2638C22semidirect
54. #2632C22semidirect
55. #2631C22semidirect
56. #2631C22semidirect
57. #2619C22semidirect
58. #2618C22semidirect
62. #2610C22semidirect
63. #2602C22semidirect
64. #2602C22semidirect
65. #2601C22semidirect
66. #2599C22semidirect
67. #2598C22semidirect
68. #2598C22semidirect
69. #2597C22semidirect
70. #2594C22semidirect
71. #2587C22semidirect
72. #2586C22semidirect
73. #2583C22semidirect
74. #2580C22semidirect
75. #2559C22semidirect
76. #2557C22semidirect
78. #2555C22semidirect
79. #2554C22semidirect
82. #2532C22semidirect
83. #2525C22semidirect
84. #2523C22semidirect
85. #2518C22semidirect
86. #2476C22semidirect
87. #2474C22semidirect
88. #2474C22semidirect
89. #2474C22semidirect
90. #2474C22semidirect
91. #2465C22semidirect
92. #2465C22semidirect
94. #2463C22semidirect
95. #2461C22semidirect
96. #2461C22semidirect
97. #2461C22semidirect
98. #2459C22semidirect
99. #2459C22semidirect
101. #2456C22semidirect
102. #2456C22semidirect
103. #2456C22semidirect
104. #2456C22semidirect
106. #2449C22semidirect
107. #2448C22semidirect
108. #2443C22semidirect
109. #2443C22semidirect
111. #2431C22semidirect
112. #2431C22semidirect
113. #2430C22semidirect
114. #2426C22semidirect
115. #2424C22semidirect
116. #2418C22semidirect
117. #2414C22semidirect
119. #2409C22semidirect
120. #2406C22semidirect
122. #2399C22semidirect
124. #2397C22semidirect
125. #2396C22semidirect
128. C2×#395C22semidirect
129. #2374C22semidirect
130. #2373C22semidirect
131. #2367C22semidirect
132. #2367C22semidirect
133. #2367C22semidirect
134. #2366C22semidirect
135. #2366C22semidirect
136. #2363C22semidirect
137. #2363C22semidirect
138. #2362C22semidirect
139. #2361C22semidirect
140. #2361C22semidirect
141. #2361C22semidirect
142. #2359C22semidirect
143. #2356C22semidirect
144. #2353C22semidirect
147. #2321C22semidirect
148. #2321C22semidirect
150. C4×#121C22semidirect
153. C4×#120C22semidirect
154. C4×#120C22semidirect
155. C4×#120C22semidirect
156. #2297C22semidirect
157. #2296C22semidirect
158. #2290C22semidirect
159. #2274C22semidirect
529. #120#41semidirect

Maximal subgroups

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

subgroupindex
#600332
#600292
#599772
#599752
#591732
#590012
#475632
#470182
#464582
#464142
#412892
#412612
#412342
#375282
#358662
#358442
#357402
#346552
#342652