Finite Group Databasebeta

← #7715516

Subgroups — #7715516

Order 512.

4782 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51224C214yesmaximal, complemented
2#50914C214yesmaximal, complemented
3#48876C218yesmaximal, complemented
4#47710C218yesmaximal, complemented
5#47223C214yesmaximal, complemented
6#46854C214yesmaximal, complemented
7#39811C214yesmaximal, complemented
8#39418C214yesmaximal, complemented
9#37773C214yesmaximal, complemented
10#37749C214yesmaximal, complemented
11#37615C211yesmaximal, characteristic, complemented
12#37559C211yesmaximal, characteristic
13#37432C212yesmaximal, complemented
14#37395C212yesmaximal, complemented
15#35344C211yesmaximal, characteristic, complemented
16#35331C212yesmaximal, complemented
17#35322C212yesmaximal, complemented
18#35317C211yesmaximal, characteristic, complemented
19#34402C211yesmaximal, characteristic, complemented
20#34371C211yesmaximal, characteristic, complemented
21#34081C211yesmaximal, characteristic, complemented
22C2×#542C2214yes—
23C2×#536C2214yes—
24C2×#533C2214yes—
25C2×#532C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#529C2211yescharacteristic
28#2868C2211yescharacteristic
29#2868C2211yescharacteristic
30#2864C2212yes—
31#2862C2212yes—
32#2862C2214yes—
33#2858C2211yescharacteristic
34#2858C2211yescharacteristic
35#2850C2214yes—
36#2821C2214yes—
37#2816C2212yes—
38#2815C2212yes—
39#2798C2218yes—
40#2797C2218yes—
41#2793C2218yes—
42#2793C2218yes—
43#2791C2218yes—
44#2791C2218yes—
45#2786C2218yes—
46#2773C2218yes—
47#2754C2218yes—
48#2754C2218yes—
49#2752C2218yes—
50#2740C2218yes—
51#2732C2218yes—
52#2730C2218yes—
53#2721C2218yes—
54#2706C2218yes—
55#2700C2218yes—
56#2698C2218yes—
57#2696C2218yes—
58#2694C2218yes—
59#2694C2218yes—
60#2692C2218yes—
61#2690C2218yes—
62#2687C2218yes—
63#2661C2214yes—
64#2660C2212yes—
65#2658C2214yes—
66#2640C2214yes—
67#2640C2212yes—
68#2633C2212yes—
69#2631C2212yes—
70#2628C2214yes—
71#2623C2214yes—
72#2621C2212yes—
73#2621C2212yes—
74#2621C2212yes—
75#2621C2214yes—
76#2619C2212yes—
77#2607C2214yes—
78#2607C2218yes—
79#2607C2214yes—
80#2605C2214yes—
81#2605C2214yes—
82#2603C2214yes—
83#2592C2212yes—
84#2589C2218yes—
85#2575C2218yes—
86#2568C2212yes—
87#2565C2218yes—
88#2565C2218yes—
89#2560C2218yes—
90#2560C2218yes—
91#2557C2218yes—
92#2557C2218yes—
93#2557C2218yes—
94#2553C2218yes—
95#2549C2218yes—
96#2542C2214yes—
97#2542C2214yes—
98#2542C2212yes—
99#2540C2212yes—
100#2517C2218yes—
101#2504C2212yes—
102#2502C2212yes—
103#2501C2214yes—
104#2501C2214yes—
105#2499C2218yes—
106#2499C2218yes—
107#2488C2218yes—
108#2479C2218yes—
109#2477C2218yes—
110#2471C2218yes—
111#2471C2218yes—
112#2465C2218yes—
113#2458C2218yes—
114#2448C2214yes—
115#2448C2218yes—
116#2447C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2429C2214yes—
120#2429C2214yes—
121#2427C2214yes—
122#2426C2214yes—
123#2423C2218yes—
124#2409C2214yes—
125#2407C2214yes—
126#2381C2214yes—
127#2377C2214yes—
128#2367C2214yes—
129#2365C2214yes—
130#2353C2214yes—
131#2345C2214yes—
132#2341C2212yes—
133Q8×C22⋊C4C2212yes—
134Q8×C22⋊C4C2212yes—
135#2339C2212yes—
136#2337C2212yes—
137#2336C2212yes—
138#2335C2214yes—
139#2334C2214yes—
140#2333C2214yes—
141#2333C2212yes—
142#2332C2212yes—
143#2331C2214yes—
144#2331C2214yes—
145#2328C2212yes—
146#2327C2212yes—
147#2327C2212yes—
148#2327C2212yes—
149#2327C2214yes—
150#2318C2214yes—
151#2313C2214yes—
152C4×#124C2214yes—
153#2298C2212yes—
154#2295C2212yes—
155#2293C2212yes—
156#2290C2212yes—
157#2290C2212yes—
158#2283C2211yescharacteristic
159#2283C2211yescharacteristic
160#2283C2211yescharacteristic
161C4×#117C2212yes—
162C4×#117C2211yescharacteristic
163C22×#41C2312yes—
164C23×Q8C2312yes—
165#542—416no—
166#536—416no—
167#533—416no—
168#532—28no—
169C2×C4⋊Q8—28no—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2314yes—
179C2×#127C2311yescharacteristic
180#529—28no—
181C2×#126C2312yes—
182C2×#126C2318yes—
183C2×#125C2311yescharacteristic
184C2×#125C2318yes—
185C2×#124C2312yes—
186C2×#124C2311yescharacteristic
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2318yes—
190C2×#123C2312yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2311yescharacteristic
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×#121C2312yes—
203C2×#121C2311yescharacteristic
204C2×#121C2312yes—
205C2×#121C2314yes—
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2318yes—
208C2×C4×Q8C2314yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2314yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2318yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#399C2314yes—
229#399C2318yes—
230#399C2318yes—
231#399C2318yes—
232#399C2318yes—
233#399C2318yes—
234#399C2318yes—
235#399C2318yes—
236#398C2314yes—
237#398C2314yes—
238#398C2314yes—
239#398C2314yes—
240#398C2314yes—
241#398C2314yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2314yes—
251#397C2314yes—
252#397C2314yes—
253#397C2314yes—
254#397C2314yes—
255#397C2314yes—
256#397C2314yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#395C2318yes—
267#395C2318yes—
268#394C2314yes—
269#394C2314yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#393C2318yes—
274#393C2318yes—
275#393C2314yes—
276#393C2318yes—
277#393C2318yes—
278#392C2314yes—
279#392C2314yes—
280#392C2314yes—
281#392C2318yes—
282#391C2318yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2318yes—
294#391C2318yes—
295#391C2318yes—
296#391C2318yes—
297#391C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2318yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2318yes—
307#390C2314yes—
308#390C2318yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2318yes—
327#388C2318yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2314yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2314yes—
352#387C2314yes—
353#387C2318yes—
354#387C2314yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2314yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#384C2314yes—
377#384C2314yes—
378#384C2314yes—
379#384C2314yes—
380#384C2314yes—
381#383C2312yes—
382#383C2312yes—
383#383C2312yes—
384#382C2318yes—
385#382C2318yes—
386#382C2314yes—
387#382C2312yes—
388#382C2312yes—
389#382C2312yes—
390#382C2314yes—
391#381C2312yes—
392#381C2312yes—
393#381C2314yes—
394#381C2318yes—
395#381C2312yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#380C2312yes—
401#380C2312yes—
402#380C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2311yescharacteristic
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429#376C2312yes—
430#376C2312yes—
431#376C2312yes—
432#376C2312yes—
433#376C2312yes—
434C2×#95C2314yes—
435C43C2311yescharacteristic
436C43C2311yescharacteristic
437C43C2312yes—
438C2×#41—28no—
439C2×#41—48no—
440C22×Q8—28no—
441C22×Q8—48no—
442C22×Q8C2412yes—
443C22×Q8C2412yes—
444C22×Q8C2412yes—
445C22×Q8C2418yes—
446C22×Q8C2411yescharacteristic
447C22×Q8C2414yes—
448C22×D4C2412yes—
449C22×D4C2412yes—
450C22×D4C2411yescharacteristic
451C22×D4C2412yes—
452C22×D4C2412yes—
453C22×D4C2414yes—
454C22×D4C2418yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2414yes—
458C23×C4C2414yes—
459C23×C4C2414yes—
460C23×C4C2418yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C4⋊Q8—24no—
464C4⋊Q8—24no—
465C4⋊Q8—28no—
466C4⋊Q8—28no—
467C4⋊Q8—28no—
468C4⋊Q8—24no—
469C4⋊Q8—216no—
470C4⋊Q8—216no—
471C4⋊Q8—48no—
472#127—24no—
473#126—28no—
474#126—416no—
475#125—24no—
476#125—416no—
477#124—24no—
478#124—28no—
479#124—216no—
480#124—48no—
481#124—416no—
482#123—28no—
483#123—416no—
484#123—416no—
485#123—416no—
486C22⋊Q8—24no—
487C22⋊Q8—416no—
488C22⋊Q8—416no—
489C22⋊Q8—416no—
490C22⋊Q8—48no—
491C22⋊Q8—48no—
492C22⋊Q8—416no—
493C22⋊Q8—48no—
494#121—24no—
495#121—28no—
496#121—28no—
497#121—48no—
498C4×Q8—24no—
499C4×Q8—48no—
500C4×Q8—48no—
501C4×Q8—416no—
502C4×Q8—48no—
503C4×D4—28no—
504C4×D4—24no—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—48no—
508#117—28no—
509#117—28no—
510#117—28no—
511#117—416no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C42—28no—
577C2×C42#4118yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2414yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2418yes—
586C2×C42C2412yes—
587C2×C42C2412yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2412yes—
599#95C2412yes—
600#95C2414yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2412yes—
612#95C2414yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636C24C2512yes—
637C24C2514yes—
638C24C2511yescharacteristic
639#41—816no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—22no—
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—28no—
647C2×Q8—28no—
648C2×Q8—216no—
649C2×Q8—48no—
650C2×Q8—42no—
651C2×Q8—48no—
652C2×Q8—48no—
653C2×Q8—816no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—28no—
661C2×D4—48no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C22×C4—24no—
670C22×C4—28no—
671C22×C4—24no—
672C22×C4—28no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—28no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—48no—
681C22×C4—48no—
682C22×C4—48no—
683C22×C4—48no—
684C22×C4—48no—
685C22×C4C2×#4114yes—
686C22×C4C2×#4114yes—
687C22×C4C2×#4114yes—
688C22×C4C2512yes—
689C22×C4C2512yes—
690C22×C4C2514yes—
691C22×C4C2518yes—
692C22×C4C2518yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2511yescharacteristic
700C22×C4C2511yescharacteristic
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C22×C4C2514yes—
705C22×C4C2511yescharacteristic
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—22no—
717C4⋊C4—24no—
718C4⋊C4—22no—
719C4⋊C4—24no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—216no—
723C4⋊C4—216no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—216no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—48no—
757C22⋊C4—42no—
758C22⋊C4—48no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C42—24no—
769C42—24no—
770C42—28no—
771C42—24no—
772C42—24no—
773C42—44no—
774C42—42no—
775C42—42no—
776C42—42no—
777C42—42no—
778C42—44no—
779C42—44no—
780C42—44no—
781C42—48no—
782C42—48no—
783C42—48no—
784C42C2×#4114yes—
785C42C2×#4114yes—
786C42C2×#4114yes—
787C42C2×#4114yes—
788C42H(5,𝔽2)18yes—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—22no—
795C23—28no—
796C23—22no—
797C23—24no—
798C23—28no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23C22×#4112yes—
803C23C2611yescharacteristic
804Q8—48no—
805Q8—48no—
806Q8—48no—
807Q8—82no—
808Q8—816no—
809Q8—88no—
810D4—48no—
811D4—84no—
812D4—84no—
813D4—82no—
814D4—84no—
815D4—88no—
816D4—168no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—416no—
856C2×C4—48no—
857C2×C4—88no—
858C2×C4—88no—
859C2×C4—168no—
860C2×C4C22×#4112yes—
861C2×C4C22×#4112yes—
862C2×C4C22×#4112yes—
863C2×C4C22×#4112yes—
864C2×C4C22×#4112yes—
865C2×C4C22×#4112yes—
866C2×C4C2×H(5,𝔽2)18yes—
867C2×C4C2×H(5,𝔽2)14yes—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—42no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—48no—
880C22—44no—
881C22—48no—
882C22C23×#4111yescharacteristic
883C22C22×H(5,𝔽2)12yes—
884C222−1+612yes—
885C222−1+612yes—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—28no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4—42no—
897C4—42no—
898C4—44no—
899C4—44no—
900C4—44no—
901C4—48no—
902C4—48no—
903C4#350814yes—
904C2—42no—
905C2—82no—
906C2—84no—
907C2C2×#350811yescharacteristic
908C2#6286011yescharacteristic
909C2#6286011yescharacteristic
910C2#6288714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37559C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #51224C2semidirect
2. #50914C2semidirect
3. #48876C2semidirect
4. #47710C2semidirect
5. #47223C2semidirect
6. #46854C2semidirect
7. #39811C2semidirect
8. #39418C2semidirect
9. #37773C2semidirect
10. #37749C2semidirect
11. #37615C2semidirect
13. #37432C2semidirect
14. #37395C2semidirect
15. #35344C2semidirect
16. #35331C2semidirect
17. #35322C2semidirect
18. #35317C2semidirect
19. #34402C2semidirect
20. #34371C2semidirect
21. #34081C2semidirect

Maximal subgroups

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

subgroupindex
#512242
#509142
#488762
#477102
#472232
#468542
#398112
#394182
#377732
#377492
#376152
#375592
#374322
#373952
#353442
#353312
#353222
#353172
#344022
#343712
#340812