Finite Group Databasebeta

← #7720834

Subgroups — #7720834

Order 512.

4911 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51167C218yesmaximal, complemented
2#50854C218yesmaximal, complemented
3#45291C214yesmaximal, complemented
4#45289C214yesmaximal, complemented
5#45225C214yesmaximal, complemented
6#45101C214yesmaximal, complemented
7#39514C212yesmaximal, complemented
8#39513C211yesmaximal, characteristic, complemented
9#39507C211yesmaximal, characteristic, complemented
10#39500C212yesmaximal, complemented
11#39292C214yesmaximal, complemented
12#39124C212yesmaximal, complemented
13#37333C214yesmaximal, complemented
14#36565C211yesmaximal, characteristic, complemented
15Q8×#127C211yesmaximal, characteristic, complemented
16#36473C212yesmaximal, complemented
17#35287C212yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#35283C212yesmaximal, complemented
20#35170C212yesmaximal, complemented
21#34621C211yesmaximal, characteristic, complemented
22#34487C212yesmaximal, complemented
23#34151C211yesmaximal, characteristic, complemented
24C2×#556C2214yes—
25C2×D4×Q8C2212yes—
26C2×D4×Q8C2214yes—
27C2×#542C2214yes—
28C2×#529C2211yescharacteristic
29#2868C2211yescharacteristic
30#2868C2212yes—
31#2862C2212yes—
32#2860C2214yes—
33#2859C2211yescharacteristic
34#2857C2214yes—
35#2857C2212yes—
36#2854C2214yes—
37#2808C2218yes—
38#2803C2218yes—
39#2798C2218yes—
40#2793C2218yes—
41#2773C2218yes—
42#2754C2218yes—
43#2733C2218yes—
44#2730C2218yes—
45#2727C2218yes—
46#2723C2218yes—
47#2716C2218yes—
48#2716C2218yes—
49#2705C2218yes—
50#2702C2218yes—
51#2700C2218yes—
52#2700C2218yes—
53#2696C2218yes—
54#2692C2218yes—
55#2689C2218yes—
56#2687C2218yes—
57#2663C2218yes—
58#2651C2214yes—
59#2648C2214yes—
60#2647C2211yescharacteristic
61#2647C2212yes—
62#2644C2212yes—
63#2641C2211yescharacteristic
64#2629C2211yescharacteristic
65#2629C2212yes—
66#2629C2212yes—
67#2628C2214yes—
68#2624C2212yes—
69#2619C2211yescharacteristic
70#2619C2212yes—
71#2604C2218yes—
72#2596C2218yes—
73#2593C2218yes—
74#2586C2218yes—
75#2570C2218yes—
76#2563C2214yes—
77#2560C2218yes—
78#2554C2218yes—
79#2551C2212yes—
80#2550C2214yes—
81#2547C2212yes—
82#2545C2214yes—
83#2542C2214yes—
84#2542C2212yes—
85#2542C2214yes—
86#2542C2218yes—
87#2540C2214yes—
88#2537C2212yes—
89#2535C2214yes—
90#2521C2218yes—
91#2521C2218yes—
92#2512C2218yes—
93#2511C2218yes—
94#2507C2214yes—
95#2497C2214yes—
96#2497C2214yes—
97#2496C2214yes—
98#2496C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2492C2218yes—
102#2491C2214yes—
103#2491C2214yes—
104#2490C2214yes—
105#2489C2214yes—
106#2485C2214yes—
107#2468C2218yes—
108#2465C2218yes—
109#2459C2218yes—
110#2459C2218yes—
111#2457C2218yes—
112#2451C2218yes—
113#2451C2214yes—
114#2448C2218yes—
115#2446C2214yes—
116#2446C2214yes—
117#2436C2214yes—
118#2429C2214yes—
119#2427C2214yes—
120#2423C2218yes—
121#2415C2214yes—
122#2414C2214yes—
123#2409C2214yes—
124#2395C2214yes—
125#2392C2214yes—
126#2378C2218yes—
127#2374C2214yes—
128#2373C2214yes—
129#2370C2212yes—
130#2369C2214yes—
131#2369C2214yes—
132#2367C2212yes—
133#2365C2212yes—
134#2363C2212yes—
135#2362C2214yes—
136#2362C2212yes—
137#2362C2214yes—
138#2357C2214yes—
139#2355C2212yes—
140#2354C2212yes—
141Q8×C22⋊C4C2214yes—
142#2332C2218yes—
143#2331C2214yes—
144#2330C2212yes—
145#2324C2214yes—
146#2323C2214yes—
147#2323C2214yes—
148#2319C2214yes—
149#2314C2212yes—
150#2314C2212yes—
151#2314C2212yes—
152#2310C2214yes—
153C4×C4⋊Q8C2212yes—
154C4×C4⋊Q8C2214yes—
155C4×#127C2211yescharacteristic
156C4×#127C2212yes—
157C4×#125C2211yescharacteristic
158C4×#125C2212yes—
159C4×#121C2212yes—
160#2298C2212yes—
161#2295C2211yescharacteristic
162#2293C2212yes—
163#2293C2212yes—
164#2293C2211yescharacteristic
165#2290C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2211yescharacteristic
170C4×#117C2212yes—
171C23×Q8C2314yes—
172#556—416no—
173D4×Q8—216no—
174D4×Q8—416no—
175#542—416no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2318yes—
182C2×#127C2311yescharacteristic
183#529—28no—
184C2×#126C2312yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#126C2318yes—
188C2×#125C2311yescharacteristic
189C2×#125C2311yescharacteristic
190C2×#125C2312yes—
191C2×#124C2311yescharacteristic
192C2×#124C2314yes—
193C2×#124C2318yes—
194C2×#124C2318yes—
195C2×#123C2312yes—
196C2×#123C2318yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2311yescharacteristic
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2318yes—
206C2×#121C2311yescharacteristic
207C2×#121C2314yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2318yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2314yes—
223C2×#117C2312yes—
224C2×#117C2311yescharacteristic
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C2×#117C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2314yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#399C2314yes—
241#399C2318yes—
242#399C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2318yes—
249#397C2314yes—
250#397C2314yes—
251#397C2314yes—
252#397C2314yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2314yes—
259#396C2318yes—
260#396C2318yes—
261#396C2314yes—
262#396C2318yes—
263#395C2318yes—
264#395C2318yes—
265#395C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2314yes—
270#394C2314yes—
271#394C2314yes—
272#394C2314yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#393C2318yes—
277#393C2318yes—
278#393C2318yes—
279#393C2318yes—
280#393C2318yes—
281#392C2314yes—
282#392C2318yes—
283#392C2318yes—
284#391C2318yes—
285#391C2314yes—
286#391C2318yes—
287#391C2312yes—
288#391C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2318yes—
293#391C2318yes—
294#391C2318yes—
295#391C2318yes—
296#391C2318yes—
297#391C2314yes—
298#391C2318yes—
299#390C2318yes—
300#390C2318yes—
301#390C2314yes—
302#390C2312yes—
303#390C2314yes—
304#390C2318yes—
305#390C2312yes—
306#390C2314yes—
307#390C2312yes—
308#390C2318yes—
309#390C2312yes—
310#390C2312yes—
311#390C2314yes—
312#389C2314yes—
313#389C2312yes—
314#389C2312yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2312yes—
323#389C2318yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#388C2314yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2318yes—
353#388C2318yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#387C2318yes—
361#387C2314yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2314yes—
372#387C2318yes—
373#387C2314yes—
374#387C2318yes—
375#387C2314yes—
376#387C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2314yes—
380#386C2314yes—
381#386C2318yes—
382#386C2318yes—
383#385C2318yes—
384#385C2314yes—
385#384C2311yescharacteristic
386#384C2312yes—
387#384C2312yes—
388#384C2314yes—
389#384C2318yes—
390#384C2312yes—
391#384C2314yes—
392#382C2312yes—
393#382C2311yescharacteristic
394#382C2318yes—
395#382C2314yes—
396#381C2318yes—
397#381C2318yes—
398#380C2312yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2318yes—
404#380C2314yes—
405#380C2314yes—
406#380C2318yes—
407#380C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2312yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2312yes—
443#376C2312yes—
444#376C2311yescharacteristic
445#376C2312yes—
446#376C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2312yes—
449C43C2312yes—
450C43C2311yescharacteristic
451C22×Q8—216no—
452C22×Q8—48no—
453C22×Q8—48no—
454C22×Q8C2414yes—
455C22×Q8C2411yescharacteristic
456C22×Q8C2418yes—
457C22×Q8C2418yes—
458C22×D4C2411yescharacteristic
459C22×D4C2412yes—
460C22×D4C2414yes—
461C22×D4C2412yes—
462C22×D4C2414yes—
463C22×D4C2418yes—
464C23×C4C2411yescharacteristic
465C23×C4C2414yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2418yes—
469C23×C4C2414yes—
470C23×C4C2411yescharacteristic
471C4⋊Q8—216no—
472C4⋊Q8—28no—
473C4⋊Q8—216no—
474C4⋊Q8—48no—
475C4⋊Q8—416no—
476C4⋊Q8—48no—
477#127—24no—
478#126—28no—
479#126—416no—
480#126—416no—
481#126—416no—
482#125—24no—
483#125—24no—
484#125—44no—
485#124—24no—
486#124—48no—
487#124—416no—
488#124—416no—
489#123—28no—
490#123—416no—
491C22⋊Q8—24no—
492C22⋊Q8—216no—
493C22⋊Q8—232no—
494C22⋊Q8—216no—
495C22⋊Q8—216no—
496C22⋊Q8—416no—
497C22⋊Q8—416no—
498C22⋊Q8—416no—
499C22⋊Q8—48no—
500#121—24no—
501#121—48no—
502#121—44no—
503#121—48no—
504C4×Q8—28no—
505C4×Q8—48no—
506C4×Q8—416no—
507C4×Q8—48no—
508C4×Q8#4118yes—
509C4×D4—28no—
510C4×D4—24no—
511C4×D4—28no—
512C4×D4—28no—
513C4×D4—216no—
514C4×D4—416no—
515C4×D4—48no—
516C4×D4—48no—
517#117—28no—
518#117—28no—
519#117—28no—
520#117—24no—
521#117—42no—
522#117—48no—
523#117—48no—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2411yescharacteristic
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C42—24no—
595C2×C42—44no—
596C2×C42C2412yes—
597C2×C42C2411yescharacteristic
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2411yescharacteristic
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2418yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2414yes—
617C2×C42C2418yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621#95C2412yes—
622#95C2412yes—
623#95C2412yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2412yes—
628#95C2412yes—
629#95C2412yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24C2512yes—
657C24C2514yes—
658C24C2511yescharacteristic
659C2×Q8—28no—
660C2×Q8—216no—
661C2×Q8—24no—
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—216no—
665C2×Q8—48no—
666C2×Q8—48no—
667C2×Q8—48no—
668C2×Q8—48no—
669C2×Q8—832no—
670C2×Q8C2×#4114yes—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—28no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—22no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—216no—
700C22×C4—28no—
701C22×C4—44no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—42no—
705C22×C4—44no—
706C22×C4C2511yescharacteristic
707C22×C4C2511yescharacteristic
708C22×C4C2512yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2512yes—
713C22×C4C2514yes—
714C22×C4C2518yes—
715C22×C4C2512yes—
716C22×C4C2514yes—
717C22×C4C2518yes—
718C22×C4C2511yescharacteristic
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2511yescharacteristic
722C22×C4C2514yes—
723C22×C4C2512yes—
724C22×C4C2511yescharacteristic
725C22×C4C2511yescharacteristic
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—216no—
734C4⋊C4—24no—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—216no—
738C4⋊C4—216no—
739C4⋊C4—216no—
740C4⋊C4—28no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—42no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4C2×#4114yes—
762C4⋊C4C2×#4118yes—
763C4⋊C4H(5,𝔽2)18yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—216no—
774C22⋊C4—216no—
775C22⋊C4—24no—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4—42no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—48no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C42—22no—
797C42—22no—
798C42—22no—
799C42—28no—
800C42—24no—
801C42—28no—
802C42—28no—
803C42—24no—
804C42—24no—
805C42—22no—
806C42—22no—
807C42—24no—
808C42—22no—
809C42—44no—
810C42—44no—
811C42—48no—
812C42—42no—
813C42—42no—
814C42—44no—
815C42—48no—
816C42—48no—
817C42—48no—
818C42C2×#4114yes—
819C42C2×#4118yes—
820C422−1+414yes—
821C23—22no—
822C23—24no—
823C23—21no—
824C23—22no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—22no—
829C23—21no—
830C23—24no—
831C23—24no—
832C23—21no—
833C23—22no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23C2611yescharacteristic
839Q8—28no—
840Q8—416no—
841Q8—816no—
842Q8—816no—
843D4—416no—
844D4—44no—
845D4—48no—
846D4—84no—
847D4—88no—
848D4—168no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—28no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—44no—
894C2×C4—416no—
895C2×C4—44no—
896C2×C4—48no—
897C2×C4—82no—
898C2×C4—88no—
899C2×C4—816no—
900C2×C4C22×#4112yes—
901C2×C4C22×#4114yes—
902C2×C4C22×#4114yes—
903C2×C4C22×#4112yes—
904C2×C4C22×#4112yes—
905C2×C4C2×H(5,𝔽2)18yes—
906C2×C4C2×H(5,𝔽2)14yes—
907C2×C4C2×2−1+414yes—
908C2×C4C2×2−1+412yes—
909C2×C4#58512yes—
910C22—42no—
911C22—41no—
912C22—44no—
913C22—44no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—42no—
922C22—44no—
923C22—44no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22C23×#4111yescharacteristic
928C22C22×H(5,𝔽2)12yes—
929C22C22×2−1+411yescharacteristic
930C22C2×#58511yescharacteristic
931C222−1+612yes—
932C4—24no—
933C4—22no—
934C4—24no—
935C4—24no—
936C4—28no—
937C4—41no—
938C4—42no—
939C4—41no—
940C4—44no—
941C4—48no—
942C4—41no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4—42no—
947C4—42no—
948C4—44no—
949C4—48no—
950C4#350814yes—
951C4#351814yes—
952C2—81no—
953C2—82no—
954C2—84no—
955C2C2×#351811yescharacteristic
956C2C2×#350811yescharacteristic
957C2#6286111yescharacteristic
958C2#6291312yes—
959C2#6292112yes—
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. #51167C2semidirect
2. #50854C2semidirect
3. #45291C2semidirect
4. #45289C2semidirect
5. #45225C2semidirect
6. #45101C2semidirect
7. #39514C2semidirect
8. #39513C2semidirect
9. #39507C2semidirect
10. #39500C2semidirect
11. #39292C2semidirect
12. #39124C2semidirect
13. #37333C2semidirect
14. #36565C2semidirect
15. Q8×#127C2semidirect
16. #36473C2semidirect
17. #35287C2semidirect
18. #35284C2semidirect
19. #35283C2semidirect
20. #35170C2semidirect
21. #34621C2semidirect
22. #34487C2semidirect
23. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#511672
#508542
#452912
#452892
#452252
#451012
#395142
#395132
#395072
#395002
#392922
#391242
#373332
#365652
Q8×#1272
#364732
#352872
#352842
#352832
#351702
#346212
#344872
#341512