Finite Group Databasebeta

← #8932559

Subgroups — #8932559

Order 512.

5236 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#47809C213yesmaximal, complemented
2#47752C213yesmaximal, complemented
3#47694C216yesmaximal, complemented
4#47675C216yesmaximal, complemented
5#47645C216yesmaximal, complemented
6#47563C211yesmaximal, characteristic, complemented
7#46591C216yesmaximal, complemented
8#46586C216yesmaximal, complemented
9#46458C213yesmaximal, complemented
10#46432C212yesmaximal, complemented
11#35573C216yesmaximal, complemented
12#35515C213yesmaximal, complemented
13#35445C213yesmaximal, complemented
14#35419C213yesmaximal, complemented
15#35361C216yesmaximal, complemented
16C2×#542C2216yescomplemented
17C2×#538C2216yescomplemented
18C2×#533C2213yescomplemented
19C2×#518C2213yes—
20#2840C2211yescharacteristic
21#2837C2216yescomplemented
22#2823C2213yescomplemented
23#2819C2213yescomplemented
24#2812C2211yescharacteristic
25#2804C2216yescomplemented
26#2792C2213yescomplemented
27#2788C2216yescomplemented
28#2785C2211yescharacteristic, complemented
29#2782C2213yescomplemented
30#2777C2216yescomplemented
31#2775C2216yescomplemented
32#2757C2216yescomplemented
33#2756C2216yescomplemented
34#2735C2213yescomplemented
35#2730C2216yescomplemented
36#2729C2216yescomplemented
37#2727C2216yescomplemented
38#2718C2216yescomplemented
39#2715C2216yescomplemented
40#2714C2216yescomplemented
41#2710C2216yescomplemented
42#2710C2216yescomplemented
43#2697C2216yescomplemented
44#2693C2216yescomplemented
45#2692C2216yescomplemented
46#2691C2216yescomplemented
47#2682C2216yescomplemented
48#2681C2216yescomplemented
49#2680C2213yescomplemented
50#2676C2216yescomplemented
51#2675C2212yescomplemented
52#2674C2216yescomplemented
53#2672C2216yescomplemented
54#2670C2213yes—
55#2670C2216yes—
56#2670C2213yes—
57#2670C2213yescomplemented
58#2612C2213yescomplemented
59#2610C2216yes—
60#2610C2213yes—
61#2610C2213yes—
62#2610C2216yescomplemented
63#2606C2213yescomplemented
64#2606C2213yescomplemented
65#2604C2216yescomplemented
66#2604C2216yescomplemented
67#2603C2216yes—
68#2602C2216yes—
69#2601C2216yescomplemented
70#2601C2216yescomplemented
71#2599C2213yescomplemented
72#2598C2213yescomplemented
73#2597C2216yescomplemented
74#2596C2216yescomplemented
75#2592C2213yescomplemented
76#2589C2216yescomplemented
77#2580C2216yescomplemented
78#2580C2216yescomplemented
79#2558C2216yescomplemented
80#2558C2216yescomplemented
81#2556C2216yescomplemented
82#2556C2216yescomplemented
83#2551C2213yescomplemented
84#2545C2216yescomplemented
85#2545C2216yescomplemented
86#2540C2216yes—
87#2540C2213yescomplemented
88#2539C2216yescomplemented
89#2538C2216yescomplemented
90#2538C2216yescomplemented
91#2492C2216yescomplemented
92#2491C2216yescomplemented
93#2479C2216yescomplemented
94#2479C2216yescomplemented
95#2478C2216yescomplemented
96#2472C2216yescomplemented
97#2471C2216yescomplemented
98#2467C2216yes—
99#2464C2216yes—
100#2461C2216yes—
101#2461C2216yescomplemented
102#2456C2216yes—
103#2456C2216yescomplemented
104#2455C2216yescomplemented
105#2454C2216yescomplemented
106#2454C2216yescomplemented
107#2452C2216yescomplemented
108#2452C2216yescomplemented
109#2452C2216yescomplemented
110#2450C2216yescomplemented
111#2449C2216yescomplemented
112#2443C2216yescomplemented
113#2437C2216yes—
114#2437C2213yes—
115#2437C2216yescomplemented
116#2437C2216yescomplemented
117#2429C2216yescomplemented
118#2426C2216yescomplemented
119#2425C2216yescomplemented
120#2424C2216yescomplemented
121#2424C2216yescomplemented
122#2418C2216yescomplemented
123#2414C2216yes—
124#2411C2216yescomplemented
125#2410C2216yes—
126#2403C2213yes—
127#2337C2213yescomplemented
128#2337C2213yescomplemented
129#2335C2216yescomplemented
130#2334C2216yescomplemented
131#2326C2216yescomplemented
132#2323C2216yescomplemented
133#2321C2216yes—
134#2321C2216yescomplemented
135#2317C2213yescomplemented
136#2316C2213yescomplemented
137#2309C2213yes—
138C4×#121C2216yescomplemented
139#2296C2213yescomplemented
140C2×#390C2213yes—
141#2290C2216yescomplemented
142#2276C2213yescomplemented
143#2275C2211yescharacteristic, complemented
144C23×D4C2313yes—
145#542—424no—
146#538—424no—
147#533—412no—
148C2×C4⋊Q8C2316yes—
149C2×C4⋊Q8C2316yes—
150C2×#126C2316yes—
151C2×#126C2316yes—
152C2×#126C2316yes—
153C2×#125C2316yes—
154C2×#124C2316yes—
155C2×#124C2313yes—
156C2×#124C2313yes—
157C2×#124C2316yes—
158C2×#124C2316yes—
159C2×#124C2316yes—
160C2×#123C2316yes—
161C2×#123C2316yes—
162C2×#123C2316yes—
163C2×#123C2316yes—
164C2×#123C2316yes—
165C2×C22⋊Q8C2316yes—
166C2×C22⋊Q8C2316yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2316yes—
172C2×#121C2316yes—
173C2×#121C2316yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C2316yes—
177C2×#120C2312yes—
178C2×#120C2316yes—
179C2×#120C2316yes—
180C2×#120C2316yes—
181#518—412no—
182C2×C4×Q8C2316yes—
183C2×C4×Q8C2316yes—
184C2×C4×Q8C2313yes—
185C2×C4×D4C2316yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C2316yes—
188C2×C4×D4C2316yes—
189C2×C4×D4C2316yes—
190C2×C4×D4C2313yes—
191C2×C4×D4C2316yes—
192C2×#117C2313yes—
193C2×#117C2313yes—
194C2×#117C2313yes—
195C2×#117C2313yes—
196C2×#117C2316yes—
197C22×C4⋊C4C2313yes—
198C22×C22⋊C4C2316yes—
199C22×C22⋊C4C2316yes—
200C22×C22⋊C4C2316yes—
201C22×C42C2313yes—
202#400C2316yes—
203#400C2316yes—
204#400C2313yes—
205#400C2316yes—
206#399C2313yes—
207#399C2316yes—
208#399C2316yes—
209#399C2316yes—
210#399C2316yes—
211#399C2316yes—
212#399C2316yes—
213#398C2313yes—
214#398C2316yes—
215#398C2316yes—
216#398C2316yes—
217#398C2316yes—
218#398C2316yes—
219#397C2316yes—
220#397C2316yes—
221#397C2316yes—
222#397C2313yes—
223#397C2316yes—
224#397C2316yes—
225#396C2316yes—
226#396C2316yes—
227#396C2316yes—
228#396C2316yes—
229#396C2316yes—
230#396C2316yes—
231#396C2316yes—
232#396C2316yes—
233#396C2316yes—
234#396C2316yes—
235#396C2312yes—
236#396C2312yes—
237#396C2316yes—
238#396C2316yes—
239#395C2313yes—
240#395C2316yes—
241#395C2311yescharacteristic
242#395C2313yes—
243#395C2316yes—
244#394C2313yes—
245#394C2313yes—
246#394C2316yes—
247#394C2316yes—
248#394C2313yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2316yes—
254#394C2316yes—
255#394C2316yes—
256#394C2316yes—
257#394C2316yes—
258#393C2316yes—
259#393C2316yes—
260#393C2313yes—
261#393C2316yes—
262#393C2316yes—
263#393C2313yes—
264#393C2316yes—
265#393C2313yes—
266#393C2312yes—
267#392C2316yes—
268#392C2316yes—
269#392C2313yes—
270#392C2313yes—
271#392C2313yes—
272#392C2316yes—
273#392C2316yes—
274#392C2316yes—
275#392C2312yes—
276#392C2316yes—
277#391C2316yes—
278#391C2316yes—
279#391C2316yes—
280#391C2316yes—
281#390C2316yes—
282#390C2316yes—
283#390C2316yes—
284#390C2316yes—
285#390C2316yes—
286#390C2316yes—
287#390C2316yes—
288#390C2316yes—
289#390C2316yes—
290#390C2316yes—
291#390C2316yes—
292#390C2316yes—
293#390C2316yes—
294#390C2316yes—
295#390C2316yes—
296#389C2316yes—
297#389C2316yes—
298#389C2316yes—
299#389C2316yes—
300#389C2316yes—
301#389C2316yes—
302#389C2316yes—
303#389C2316yes—
304#389C2316yes—
305#389C2316yes—
306#389C2316yes—
307#389C2316yes—
308#389C2316yes—
309#388C2316yes—
310#388C2316yes—
311#388C2316yes—
312#388C2316yes—
313#388C2316yes—
314#388C2316yes—
315#388C2316yes—
316#388C2316yes—
317#388C2316yes—
318#388C2316yes—
319#388C2316yes—
320#388C2316yes—
321#388C2316yes—
322#388C2316yes—
323#388C2316yes—
324#388C2316yes—
325#388C2316yes—
326#388C2316yes—
327#388C2316yes—
328#388C2316yes—
329#388C2316yes—
330#388C2316yes—
331#388C2316yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C2316yes—
336#387C2316yes—
337#387C2316yes—
338#387C2316yes—
339#387C2316yes—
340#387C2316yes—
341#387C2316yes—
342#387C2316yes—
343#387C2316yes—
344#387C2316yes—
345#386C2316yes—
346#386C2316yes—
347#386C2316yes—
348#386C2316yes—
349#386C2316yes—
350#386C2316yes—
351#386C2316yes—
352#386C2316yes—
353#386C2316yes—
354#386C2316yes—
355#386C2316yes—
356#386C2316yes—
357#386C2316yes—
358#385C2316yes—
359#385C2316yes—
360#385C2316yes—
361#385C2316yes—
362#385C2316yes—
363#385C2316yes—
364#385C2316yes—
365#385C2316yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2316yes—
373#385C2316yes—
374#385C2316yes—
375#384C2313yes—
376#384C2313yes—
377#383C2313yes—
378#383C2313yes—
379#382C2313yes—
380#382C2313yes—
381#380C2316yes—
382#380C2316yes—
383#380C2316yes—
384#380C2316yes—
385#380C2316yes—
386#379C2311yescharacteristic
387#379C2313yes—
388#379C2313yes—
389#379C2313yes—
390#379C2316yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2316yes—
393C4×C4⋊C4C2313yes—
394C4×C4⋊C4C2316yes—
395C4×C4⋊C4C2313yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C2316yes—
402C4×C22⋊C4C2316yes—
403#376C2316yes—
404#376C2313yes—
405#376C2311yescharacteristic
406C2×#95C2312yes—
407C25C2413yes—
408C25C2411yescharacteristic
409C22×Q8C2413yes—
410C22×Q8C2416yes—
411C22×Q8C2413yes—
412C22×Q8C2411yescharacteristic
413C22×D4—212no—
414C22×D4—46no—
415C22×D4—46no—
416C22×D4C2416yes—
417C22×D4C2416yes—
418C22×D4C2416yes—
419C22×D4C2416yes—
420C22×D4C2411yescharacteristic
421C22×D4C2413yes—
422C22×D4C2416yes—
423C22×D4C2413yes—
424C22×D4C2416yes—
425C23×C4C2413yes—
426C23×C4C2416yes—
427C23×C4C2416yes—
428C23×C4C2416yes—
429C23×C4C2416yes—
430C23×C4C2416yes—
431C4⋊Q8—412no—
432C4⋊Q8—412no—
433#126—224no—
434#126—412no—
435#126—412no—
436#125—412no—
437#124—224no—
438#124—46no—
439#124—46no—
440#124—412no—
441#124—412no—
442#124—412no—
443#123—412no—
444#123—412no—
445#123—412no—
446#123—412no—
447#123—412no—
448C22⋊Q8—412no—
449C22⋊Q8—412no—
450C22⋊Q8—412no—
451C22⋊Q8—412no—
452C22⋊Q8—412no—
453C22⋊Q8—412no—
454C22⋊Q8—412no—
455#121—412no—
456#121—412no—
457#121—412no—
458#121—412no—
459#121—412no—
460#120—28no—
461#120—412no—
462#120—412no—
463#120—412no—
464C4×Q8—224no—
465C4×Q8—412no—
466C4×Q8—46no—
467C4×D4—224no—
468C4×D4—46no—
469C4×D4—412no—
470C4×D4—412no—
471C4×D4—412no—
472C4×D4—412no—
473C4×D4—412no—
474#117—212no—
475#117—46no—
476#117—46no—
477#117—412no—
478#117—46no—
479C2×C4⋊C4—46no—
480C2×C4⋊C4C2416yes—
481C2×C4⋊C4C2416yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2413yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2413yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C22⋊C4—412no—
509C2×C22⋊C4—412no—
510C2×C22⋊C4—412no—
511C2×C22⋊C4C2416yes—
512C2×C22⋊C4C2416yes—
513C2×C22⋊C4C2416yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C2416yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C2413yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2416yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2413yes—
535C2×C22⋊C4C2416yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2416yes—
548C2×C42—46no—
549C2×C42C2413yes—
550C2×C42C2416yes—
551C2×C42C2413yes—
552C2×C42C2416yes—
553C2×C42C2413yes—
554C2×C42C2413yes—
555C2×C42C2413yes—
556C2×C42C2416yes—
557C2×C42C2416yes—
558C2×C42C2416yes—
559C2×C42C2413yes—
560C2×C42C2413yes—
561C2×C42C2413yes—
562#95C2411yescharacteristic
563#95C2416yes—
564#95C2413yes—
565#95C2413yes—
566#95C2416yes—
567#95C2416yes—
568#95C2416yes—
569#95C2416yes—
570#95C2413yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2413yes—
580#95C2416yes—
581#95C2413yes—
582#95C2416yes—
583#95C2416yes—
584#95C2416yes—
585#95C2413yes—
586#95C2413yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2412yes—
591C24—26no—
592C24—43no—
593C24—43no—
594C24—43no—
595C24—43no—
596C24—46no—
597C24—46no—
598C242−1+414yes—
599C24C2516yes—
600C24C2512yes—
601C24C2513yes—
602C2×Q8—212no—
603C2×Q8—212no—
604C2×Q8—43no—
605C2×Q8—46no—
606C2×Q8—46no—
607C2×Q8—46no—
608C2×Q8—43no—
609C2×Q8—43no—
610C2×D4—212no—
611C2×D4—212no—
612C2×D4—212no—
613C2×D4—212no—
614C2×D4—212no—
615C2×D4—212no—
616C2×D4—46no—
617C2×D4—43no—
618C2×D4—46no—
619C2×D4—448no—
620C2×D4—46no—
621C2×D4—46no—
622C2×D4—46no—
623C2×D4—46no—
624C2×D4—46no—
625C2×D4—46no—
626C2×D4—46no—
627C2×D4—46no—
628C2×D4—46no—
629C2×D4—46no—
630C2×D4—46no—
631C2×D4—46no—
632C2×D4—43no—
633C2×D4—43no—
634C22×C4—26no—
635C22×C4—26no—
636C22×C4—26no—
637C22×C4—212no—
638C22×C4—212no—
639C22×C4—46no—
640C22×C4—46no—
641C22×C4—46no—
642C22×C4—46no—
643C22×C4—46no—
644C22×C4—46no—
645C22×C4—46no—
646C22×C4—46no—
647C22×C4—46no—
648C22×C4—46no—
649C22×C4—46no—
650C22×C4—46no—
651C22×C4—46no—
652C22×C4C2513yes—
653C22×C4C2516yes—
654C22×C4C2511yescharacteristic
655C22×C4C2513yes—
656C22×C4C2516yes—
657C22×C4C2516yes—
658C22×C4C2516yes—
659C22×C4C2516yes—
660C22×C4C2513yes—
661C22×C4C2513yes—
662C22×C4C2516yes—
663C22×C4C2513yes—
664C4⋊C4—212no—
665C4⋊C4—212no—
666C4⋊C4—212no—
667C4⋊C4—212no—
668C4⋊C4—212no—
669C4⋊C4—212no—
670C4⋊C4—212no—
671C4⋊C4—212no—
672C4⋊C4—212no—
673C4⋊C4—212no—
674C4⋊C4—43no—
675C4⋊C4—43no—
676C4⋊C4—43no—
677C4⋊C4—43no—
678C4⋊C4—46no—
679C4⋊C4—46no—
680C4⋊C4—43no—
681C4⋊C4—46no—
682C4⋊C4—43no—
683C4⋊C4—46no—
684C4⋊C4—46no—
685C4⋊C4—46no—
686C4⋊C4—46no—
687C4⋊C4—46no—
688C4⋊C4—46no—
689C4⋊C4—46no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C22⋊C4—212no—
693C22⋊C4—212no—
694C22⋊C4—212no—
695C22⋊C4—212no—
696C22⋊C4—212no—
697C22⋊C4—212no—
698C22⋊C4—212no—
699C22⋊C4—212no—
700C22⋊C4—212no—
701C22⋊C4—212no—
702C22⋊C4—212no—
703C22⋊C4—212no—
704C22⋊C4—212no—
705C22⋊C4—212no—
706C22⋊C4—46no—
707C22⋊C4—46no—
708C22⋊C4—46no—
709C22⋊C4—46no—
710C22⋊C4—46no—
711C22⋊C4—43no—
712C22⋊C4—43no—
713C22⋊C4—43no—
714C22⋊C4—43no—
715C22⋊C4—46no—
716C22⋊C4—46no—
717C22⋊C4—46no—
718C22⋊C4—46no—
719C22⋊C4—46no—
720C22⋊C4—46no—
721C22⋊C4—46no—
722C22⋊C4—46no—
723C22⋊C4—46no—
724C22⋊C4—46no—
725C22⋊C4—46no—
726C22⋊C4—46no—
727C22⋊C4—46no—
728C22⋊C4—46no—
729C42—212no—
730C42—26no—
731C42—212no—
732C42—26no—
733C42—26no—
734C42—43no—
735C42—43no—
736C42—43no—
737C42—43no—
738C42—46no—
739C42—46no—
740C42—46no—
741C42H(5,𝔽2)112yes—
742C23—23no—
743C23—26no—
744C23—23no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—26no—
750C23—22no—
751C23—26no—
752C23—26no—
753C23—26no—
754C23—26no—
755C23—26no—
756C23—412no—
757C23—412no—
758C23—812no—
759C23—163no—
760C23—166no—
761C23—163no—
762C23—161no—
763C23—163no—
764C23C2×2−1+416yes—
765C23C2611yescharacteristic
766Q8—412no—
767Q8—812no—
768Q8—163no—
769Q8—161no—
770D4—424no—
771D4—424no—
772D4—44no—
773D4—812no—
774D4—812no—
775D4—166no—
776D4—163no—
777D4—166no—
778D4—163no—
779C2×C4—224no—
780C2×C4—26no—
781C2×C4—23no—
782C2×C4—23no—
783C2×C4—23no—
784C2×C4—26no—
785C2×C4—23no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—26no—
789C2×C4—26no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—26no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—23no—
799C2×C4—23no—
800C2×C4—23no—
801C2×C4—23no—
802C2×C4—26no—
803C2×C4—26no—
804C2×C4—26no—
805C2×C4—26no—
806C2×C4—26no—
807C2×C4—26no—
808C2×C4—812no—
809C2×C4—812no—
810C2×C4—166no—
811C2×C4—166no—
812C2×C4—166no—
813C2×C4C2×H(5,𝔽2)16yes—
814C2×C4C2×H(5,𝔽2)112yes—
815C2×C4#58516yes—
816C22—26no—
817C22—212no—
818C22—46no—
819C22—43no—
820C22—43no—
821C22—46no—
822C22—46no—
823C22—46no—
824C22—46no—
825C22—46no—
826C22—46no—
827C22—46no—
828C22—46no—
829C22—42no—
830C22—46no—
831C22—164no—
832C22—1612no—
833C22C22×H(5,𝔽2)13yes—
834C22C22×2−1+411yescharacteristic
835C22C2×#58513yes—
836C4—26no—
837C4—26no—
838C4—212no—
839C4—46no—
840C4—46no—
841C4—46no—
842C4—43no—
843C4—46no—
844C4—46no—
845C4—43no—
846C4—41no—
847C4—43no—
848C2—46no—
849C2—82no—
850C2—86no—
851C2#6281913yes—
852C2#6283413yes—
853C2#6284111yescharacteristic
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. #47809C2semidirect
2. #47752C2semidirect
3. #47694C2semidirect
4. #47675C2semidirect
5. #47645C2semidirect
6. #47563C2semidirect
7. #46591C2semidirect
8. #46586C2semidirect
9. #46458C2semidirect
10. #46432C2semidirect
11. #35573C2semidirect
12. #35515C2semidirect
13. #35445C2semidirect
14. #35419C2semidirect
15. #35361C2semidirect
16. C2×#542C22semidirect
17. C2×#538C22semidirect
18. C2×#533C22semidirect
21. #2837C22semidirect
22. #2823C22semidirect
23. #2819C22semidirect
25. #2804C22semidirect
26. #2792C22semidirect
27. #2788C22semidirect
28. #2785C22semidirect
29. #2782C22semidirect
30. #2777C22semidirect
31. #2775C22semidirect
32. #2757C22semidirect
33. #2756C22semidirect
34. #2735C22semidirect
35. #2730C22semidirect
36. #2729C22semidirect
37. #2727C22semidirect
38. #2718C22semidirect
39. #2715C22semidirect
40. #2714C22semidirect
41. #2710C22semidirect
42. #2710C22semidirect
43. #2697C22semidirect
44. #2693C22semidirect
45. #2692C22semidirect
46. #2691C22semidirect
47. #2682C22semidirect
48. #2681C22semidirect
49. #2680C22semidirect
50. #2676C22semidirect
51. #2675C22semidirect
52. #2674C22semidirect
53. #2672C22semidirect
57. #2670C22semidirect
58. #2612C22semidirect
62. #2610C22semidirect
63. #2606C22semidirect
64. #2606C22semidirect
65. #2604C22semidirect
66. #2604C22semidirect
69. #2601C22semidirect
70. #2601C22semidirect
71. #2599C22semidirect
72. #2598C22semidirect
73. #2597C22semidirect
74. #2596C22semidirect
75. #2592C22semidirect
76. #2589C22semidirect
77. #2580C22semidirect
78. #2580C22semidirect
79. #2558C22semidirect
80. #2558C22semidirect
81. #2556C22semidirect
82. #2556C22semidirect
83. #2551C22semidirect
84. #2545C22semidirect
85. #2545C22semidirect
87. #2540C22semidirect
88. #2539C22semidirect
89. #2538C22semidirect
90. #2538C22semidirect
91. #2492C22semidirect
92. #2491C22semidirect
93. #2479C22semidirect
94. #2479C22semidirect
95. #2478C22semidirect
96. #2472C22semidirect
97. #2471C22semidirect
101. #2461C22semidirect
103. #2456C22semidirect
104. #2455C22semidirect
105. #2454C22semidirect
106. #2454C22semidirect
107. #2452C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
110. #2450C22semidirect
111. #2449C22semidirect
112. #2443C22semidirect
115. #2437C22semidirect
116. #2437C22semidirect
117. #2429C22semidirect
118. #2426C22semidirect
119. #2425C22semidirect
120. #2424C22semidirect
121. #2424C22semidirect
122. #2418C22semidirect
124. #2411C22semidirect
127. #2337C22semidirect
128. #2337C22semidirect
129. #2335C22semidirect
130. #2334C22semidirect
131. #2326C22semidirect
132. #2323C22semidirect
134. #2321C22semidirect
135. #2317C22semidirect
136. #2316C22semidirect
138. C4×#121C22semidirect
139. #2296C22semidirect
141. #2290C22semidirect
142. #2276C22semidirect
143. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#478092
#477522
#476942
#476752
#476452
#475632
#465912
#465862
#464582
#464322
#355732
#355152
#354452
#354192
#353612