Finite Group Databasebeta

← #7715040

Subgroups — #7715040

Order 512.

5570 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51755C218yesmaximal, complemented
2#51549C218yesmaximal, complemented
3#46455C214yesmaximal, complemented
4#46452C214yesmaximal, complemented
5#46389C212yesmaximal, complemented
6#46386C212yesmaximal, complemented
7#46385C212yesmaximal, complemented
8#46385C212yesmaximal, complemented
9#39563C214yesmaximal, complemented
10#39562C214yesmaximal, complemented
11#39439C214yesmaximal, complemented
12#39438C214yesmaximal, complemented
13#37480C211yesmaximal, characteristic, complemented
14#37451C211yesmaximal, characteristic, complemented
15#37282C214yesmaximal, complemented
16#35305C211yesmaximal, characteristic, complemented
17#35260C214yesmaximal, complemented
18#35250C211yesmaximal, characteristic
19#34370C211yesmaximal, characteristic, complemented
20#34363C211yesmaximal, characteristic, complemented
21#34044C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C2×#542C2214yescomplemented
24C2×#536C2212yescomplemented
25C2×#535C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#117C2212yescomplemented
29#2857C2214yescomplemented
30#2850C2214yescomplemented
31#2848C2212yescomplemented
32#2848C2212yescomplemented
33#2847C2212yes—
34#2847C2212yes—
35#2842C2212yes—
36#2840C2212yes—
37#2816C2214yes—
38#2799C2218yescomplemented
39#2798C2218yescomplemented
40#2786C2218yescomplemented
41#2784C2218yescomplemented
42#2779C2218yescomplemented
43#2751C2218yescomplemented
44#2751C2218yescomplemented
45#2750C2218yescomplemented
46#2750C2218yescomplemented
47#2743C2218yescomplemented
48#2730C2218yescomplemented
49#2716C2218yescomplemented
50#2715C2218yescomplemented
51#2712C2218yescomplemented
52#2709C2218yescomplemented
53#2705C2218yescomplemented
54#2700C2218yescomplemented
55#2696C2218yescomplemented
56#2696C2218yescomplemented
57#2693C2218yescomplemented
58#2685C2218yescomplemented
59#2685C2218yescomplemented
60#2684C2218yescomplemented
61#2684C2218yescomplemented
62#2665C2214yescomplemented
63#2665C2214yescomplemented
64#2628C2214yescomplemented
65#2626C2214yescomplemented
66#2625C2214yescomplemented
67#2624C2214yescomplemented
68#2620C2214yes—
69#2618C2214yescomplemented
70#2616C2214yes—
71#2615C2214yes—
72#2607C2218yescomplemented
73#2607C2214yescomplemented
74#2601C2218yescomplemented
75#2588C2218yescomplemented
76#2560C2218yescomplemented
77#2557C2218yescomplemented
78#2557C2218yescomplemented
79#2557C2218yescomplemented
80#2554C2218yescomplemented
81#2544C2218yescomplemented
82#2534C2218yescomplemented
83#2521C2218yescomplemented
84#2502C2212yescomplemented
85#2501C2212yescomplemented
86#2497C2214yescomplemented
87#2496C2214yescomplemented
88#2492C2218yescomplemented
89#2492C2214yescomplemented
90#2491C2214yescomplemented
91#2481C2218yescomplemented
92#2479C2218yescomplemented
93#2477C2218yescomplemented
94#2477C2218yescomplemented
95#2474C2218yescomplemented
96#2472C2218yescomplemented
97#2472C2218yescomplemented
98#2470C2218yescomplemented
99#2467C2218yescomplemented
100#2457C2218yescomplemented
101#2449C2218yescomplemented
102#2439C2214yescomplemented
103#2439C2214yescomplemented
104#2436C2212yes—
105#2436C2212yescomplemented
106#2435C2212yescomplemented
107#2435C2212yescomplemented
108#2434C2212yescomplemented
109#2433C2212yes—
110#2432C2214yes—
111#2431C2214yes—
112#2427C2214yescomplemented
113#2426C2214yescomplemented
114#2421C2214yescomplemented
115#2420C2214yescomplemented
116#2418C2218yescomplemented
117#2406C2214yescomplemented
118#2405C2212yes—
119#2405C2212yes—
120#2405C2212yes—
121#2405C2212yes—
122#2404C2214yes—
123#2403C2212yes—
124#2403C2212yes—
125#2378C2214yescomplemented
126#2377C2214yescomplemented
127#2363C2214yescomplemented
128#2362C2214yescomplemented
129#2345C2214yescomplemented
130#2345C2212yescomplemented
131#2344C2212yescomplemented
132#2342C2214yescomplemented
133Q8×C22⋊C4C2212yescomplemented
134D4×C22⋊C4C2212yescomplemented
135#2333C2214yes—
136#2332C2214yescomplemented
137#2324C2214yes—
138#2323C2214yescomplemented
139#2314C2214yescomplemented
140#2312C2212yes—
141#2312C2212yes—
142#2311C2214yes—
143#2311C2212yes—
144#2311C2214yescomplemented
145#2311C2212yescomplemented
146#2310C2212yescomplemented
147#2309C2211yescharacteristic
148#2309C2212yes—
149#2309C2211yescharacteristic
150#2308C2211yescharacteristic
151#2308C2212yes—
152#2308C2211yescharacteristic
153#2308C2212yescomplemented
154C4×C22⋊Q8C2214yescomplemented
155C4×#121C2214yescomplemented
156#2297C2214yes—
157#2297C2214yescomplemented
158#2280C2211yescharacteristic
159#2280C2211yescharacteristic
160#2280C2211yescharacteristic
161#2280C2211yescharacteristic
162#2280C2212yescomplemented
163C22×#41—28no—
164C22×#41—48no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C23×Q8C2311yescharacteristic
170C23×Q8C2311yescharacteristic
171C23×D4C2311yescharacteristic
172C23×D4C2311yescharacteristic
173C23×D4C2311yescharacteristic
174C23×D4C2311yescharacteristic
175C23×D4C2312yes—
176C24×C4C2311yescharacteristic
177C24×C4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179#542—416no—
180#536—48no—
181#535—48no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#127C2314yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#124C2318yes—
191C2×#124C2318yes—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2318yes—
195C2×#123C2314yes—
196C2×#123C2314yes—
197C2×C22⋊Q8—28no—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×#121—28no—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#120C2314yes—
214C2×#120C2314yes—
215C2×#120C2314yes—
216C2×#120C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2318yes—
220C2×#117—48no—
221C2×#117C2314yes—
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2314yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2314yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2314yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2314yes—
239C22×C42C2314yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#399C2318yes—
247#399C2318yes—
248#399C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2318yes—
265#395C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#393C2318yes—
279#393C2318yes—
280#393C2318yes—
281#393C2318yes—
282#393C2318yes—
283#393C2318yes—
284#393C2318yes—
285#392C2318yes—
286#392C2318yes—
287#392C2318yes—
288#391C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2314yes—
300#391C2318yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2318yes—
307#390C2318yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2318yes—
312#389C2314yes—
313#389C2318yes—
314#389C2314yes—
315#389C2318yes—
316#389C2314yes—
317#389C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
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#386C2314yes—
347#386C2314yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2314yes—
355#386C2314yes—
356#386C2314yes—
357#386C2314yes—
358#386C2314yes—
359#386C2314yes—
360#386C2318yes—
361#386C2314yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#385C2318yes—
376#385C2318yes—
377#385C2314yes—
378#385C2314yes—
379#385C2318yes—
380#384C2314yes—
381#382C2314yes—
382#381C2312yes—
383#381C2312yes—
384#381C2312yes—
385#381C2314yes—
386#381C2312yes—
387#381C2318yes—
388#381C2312yes—
389#381C2312yes—
390#380C2312yes—
391#380C2312yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2312yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2318yes—
407#380C2318yes—
408#379C2311yescharacteristic
409#379C2311yescharacteristic
410#379C2311yescharacteristic
411#379C2312yes—
412#379C2311yescharacteristic
413#379C2312yes—
414#379C2312yes—
415#379C2314yes—
416#379C2312yes—
417#379C2314yes—
418#379C2314yes—
419#379C2314yes—
420#379C2314yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C25C2411yescharacteristic
441C25C2412yes—
442C25C2411yescharacteristic
443C25C2411yescharacteristic
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—44no—
453C2×#41—44no—
454C2×#41—44no—
455C2×#41—44no—
456C2×#41—464no—
457C22×Q8—24no—
458C22×Q8—24no—
459C22×Q8—44no—
460C22×Q8—44no—
461C22×Q8C2412yes—
462C22×Q8C2412yes—
463C22×Q8C2412yes—
464C22×Q8C2412yes—
465C22×Q8C2418yes—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—28no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—44no—
474C22×D4—44no—
475C22×D4—84no—
476C22×D4C2412yes—
477C22×D4C2412yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2412yes—
483C22×D4C2418yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2412yes—
487C22×D4C2418yes—
488C23×C4—24no—
489C23×C4—28no—
490C23×C4—24no—
491C23×C4—44no—
492C23×C4—44no—
493C23×C4#4118yes—
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2411yescharacteristic
505C23×C4C2412yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2418yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C4⋊Q8—48no—
513C4⋊Q8—48no—
514#127—48no—
515#126—416no—
516#126—88no—
517#124—48no—
518#124—48no—
519#124—416no—
520#124—48no—
521#124—88no—
522#123—48no—
523#123—416no—
524#123—48no—
525#123—84no—
526#123—84no—
527C22⋊Q8—28no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—216no—
532C22⋊Q8—416no—
533C22⋊Q8—48no—
534C22⋊Q8—88no—
535#121—28no—
536#121—28no—
537#121—28no—
538#121—28no—
539#121—216no—
540#121—48no—
541#120—48no—
542#120—48no—
543#120—84no—
544#120—84no—
545C4×Q8—48no—
546C4×D4—48no—
547C4×D4—88no—
548#117—216no—
549#117—44no—
550#117—44no—
551#117—48no—
552#117—44no—
553#117—44no—
554#117—44no—
555#117—44no—
556#117—84no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—28no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C22⋊C4—28no—
584C2×C22⋊C4—28no—
585C2×C22⋊C4—44no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—84no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C42—48no—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640C2×C42C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669C24—22no—
670C24—24no—
671C24—24no—
672C24—22no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—44no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—42no—
682C24—44no—
683C24—44no—
684C24C2×#4114yes—
685C24C2514yes—
686C24C2512yes—
687C24C2511yescharacteristic
688C24C2511yescharacteristic
689C24C2511yescharacteristic
690C24C2512yes—
691#41—432no—
692#41—432no—
693#41—432no—
694#41—432no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—24no—
698C2×Q8—24no—
699C2×Q8—28no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—42no—
703C2×Q8—42no—
704C2×Q8—44no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—48no—
708C2×Q8—416no—
709C2×Q8—88no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—416no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—416no—
746C2×D4—416no—
747C2×D4—88no—
748C2×D4—816no—
749C22×C4—232no—
750C22×C4—22no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—416no—
769C22×C4—44no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—416no—
788C22×C4C2×#4114yes—
789C22×C4C2×#4114yes—
790C22×C4C2×#4114yes—
791C22×C4C2×#4114yes—
792C22×C4C2×#4114yes—
793C22×C4C2×#4114yes—
794C22×C4H(5,𝔽2)18yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2518yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—216no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—216no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—216no—
840C22⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—42no—
848C22⋊C4—44no—
849C22⋊C4—48no—
850C22⋊C4—42no—
851C22⋊C4—44no—
852C22⋊C4—42no—
853C22⋊C4—44no—
854C22⋊C4—42no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—42no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—48no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C42—28no—
876C42—28no—
877C42—44no—
878C42—44no—
879C42—44no—
880C42—44no—
881C42—48no—
882C42—48no—
883C42—48no—
884C23—28no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—24no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—24no—
899C23—22no—
900C23—28no—
901C23—22no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—28no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—48no—
913C23—82no—
914C23—82no—
915C23—82no—
916C23—82no—
917C23—88no—
918C23—84no—
919C23—84no—
920C23—88no—
921C23—88no—
922C23—168no—
923C23C22×#4112yes—
924C23C22×#4112yes—
925C23C22×#4112yes—
926C23C2×H(5,𝔽2)14yes—
927C23C2611yescharacteristic
928Q8—48no—
929Q8—48no—
930Q8—48no—
931Q8—84no—
932Q8—168no—
933D4—48no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—48no—
939D4—48no—
940D4—84no—
941D4—816no—
942D4—88no—
943D4—88no—
944D4—168no—
945C2×C4—28no—
946C2×C4—216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—28no—
953C2×C4—216no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—88no—
994C2×C4—88no—
995C2×C4—168no—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C2×H(5,𝔽2)14yes—
1001C2×C4C2×H(5,𝔽2)14yes—
1002C22—22no—
1003C22—24no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—28no—
1013C22—42no—
1014C22—42no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—44no—
1025C22—48no—
1026C22—44no—
1027C22—48no—
1028C22—44no—
1029C22—88no—
1030C22—88no—
1031C22—88no—
1032C22—168no—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)12yes—
1035C22H(7,𝔽2)12yes—
1036C222−1+612yes—
1037C4—22no—
1038C4—24no—
1039C4—22no—
1040C4—22no—
1041C4—42no—
1042C4—44no—
1043C4—44no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—48no—
1050C4—48no—
1051C4#349014yes—
1052C2—44no—
1053C2—42no—
1054C2—42no—
1055C2—42no—
1056C2—82no—
1057C2—84no—
1058C2C2×#349011yescharacteristic
1059C2#6285511yescharacteristic
1060C2#6286011yescharacteristic
1061C2#6287814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35250C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51755C2semidirect
2. #51549C2semidirect
3. #46455C2semidirect
4. #46452C2semidirect
5. #46389C2semidirect
6. #46386C2semidirect
7. #46385C2semidirect
8. #46385C2semidirect
9. #39563C2semidirect
10. #39562C2semidirect
11. #39439C2semidirect
12. #39438C2semidirect
13. #37480C2semidirect
14. #37451C2semidirect
15. #37282C2semidirect
16. #35305C2semidirect
17. #35260C2semidirect
19. #34370C2semidirect
20. #34363C2semidirect
21. #34044C2semidirect
23. C2×#542C22semidirect
24. C2×#536C22semidirect
28. C22×#117C22semidirect
29. #2857C22semidirect
30. #2850C22semidirect
31. #2848C22semidirect
32. #2848C22semidirect
38. #2799C22semidirect
39. #2798C22semidirect
40. #2786C22semidirect
41. #2784C22semidirect
42. #2779C22semidirect
43. #2751C22semidirect
44. #2751C22semidirect
45. #2750C22semidirect
46. #2750C22semidirect
47. #2743C22semidirect
48. #2730C22semidirect
49. #2716C22semidirect
50. #2715C22semidirect
51. #2712C22semidirect
52. #2709C22semidirect
53. #2705C22semidirect
54. #2700C22semidirect
55. #2696C22semidirect
56. #2696C22semidirect
57. #2693C22semidirect
58. #2685C22semidirect
59. #2685C22semidirect
60. #2684C22semidirect
61. #2684C22semidirect
62. #2665C22semidirect
63. #2665C22semidirect
64. #2628C22semidirect
65. #2626C22semidirect
66. #2625C22semidirect
67. #2624C22semidirect
69. #2618C22semidirect
72. #2607C22semidirect
73. #2607C22semidirect
74. #2601C22semidirect
75. #2588C22semidirect
76. #2560C22semidirect
77. #2557C22semidirect
78. #2557C22semidirect
79. #2557C22semidirect
80. #2554C22semidirect
81. #2544C22semidirect
82. #2534C22semidirect
83. #2521C22semidirect
84. #2502C22semidirect
85. #2501C22semidirect
86. #2497C22semidirect
87. #2496C22semidirect
88. #2492C22semidirect
89. #2492C22semidirect
90. #2491C22semidirect
91. #2481C22semidirect
92. #2479C22semidirect
93. #2477C22semidirect
94. #2477C22semidirect
95. #2474C22semidirect
96. #2472C22semidirect
97. #2472C22semidirect
98. #2470C22semidirect
99. #2467C22semidirect
100. #2457C22semidirect
101. #2449C22semidirect
102. #2439C22semidirect
103. #2439C22semidirect
105. #2436C22semidirect
106. #2435C22semidirect
107. #2435C22semidirect
108. #2434C22semidirect
112. #2427C22semidirect
113. #2426C22semidirect
114. #2421C22semidirect
115. #2420C22semidirect
116. #2418C22semidirect
117. #2406C22semidirect
125. #2378C22semidirect
126. #2377C22semidirect
127. #2363C22semidirect
128. #2362C22semidirect
129. #2345C22semidirect
130. #2345C22semidirect
131. #2344C22semidirect
132. #2342C22semidirect
133. Q8×C22⋊C4C22semidirect
134. D4×C22⋊C4C22semidirect
136. #2332C22semidirect
138. #2323C22semidirect
139. #2314C22semidirect
144. #2311C22semidirect
145. #2311C22semidirect
146. #2310C22semidirect
153. #2308C22semidirect
154. C4×C22⋊Q8C22semidirect
155. C4×#121C22semidirect
157. #2297C22semidirect
162. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#517552
#515492
#464552
#464522
#463892
#463862
#463852
#395632
#395622
#394392
#394382
#374802
#374512
#372822
#353052
#352602
#352502
#343702
#343632
#340442