Finite Group Databasebeta

← #8429567

Subgroups — #8429567

Order 512.

5826 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59816C211yesmaximal, characteristic, complemented
2#59808C214yesmaximal, complemented
3#59313C211yesmaximal, characteristic, complemented
4#59233C211yesmaximal, characteristic, complemented
5#58267C214yesmaximal, complemented
6#56317C214yesmaximal, complemented
7#53103C214yesmaximal, complemented
8#53101C214yesmaximal, complemented
9#52696C214yesmaximal, complemented
10#42478C214yesmaximal, complemented
11#42474C214yesmaximal, complemented
12#41986C214yesmaximal, complemented
13#39046C214yesmaximal, complemented
14#39006C214yesmaximal, complemented
15#38975C212yesmaximal, complemented
16#38910C212yesmaximal, complemented
17#37629C211yesmaximal, characteristic, complemented
18#37620C211yesmaximal, characteristic, complemented
19#37492C214yesmaximal, complemented
20#36258C212yesmaximal, complemented
21#36182C211yesmaximal, characteristic, complemented
22#34976C211yesmaximal, characteristic, complemented
23#34727C212yesmaximal, complemented
24C2×#553C2212yescomplemented
25C2×#547C2214yescomplemented
26C2×#546C2214yescomplemented
27C2×#546C2214yescomplemented
28C2×D42C2214yes—
29C2×D42C2212yes—
30C2×#529C2212yescomplemented
31C2×C4×#41C2212yescomplemented
32#2859C2211yescharacteristic, complemented
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2854C2214yescomplemented
36#2830C2218yescomplemented
37#2830C2214yescomplemented
38#2829C2218yescomplemented
39#2829C2218yescomplemented
40#2823C2214yescomplemented
41#2816C2218yescomplemented
42#2815C2214yescomplemented
43#2814C2214yescomplemented
44#2812C2218yescomplemented
45#2785C2214yescomplemented
46#2768C2218yescomplemented
47#2761C2218yescomplemented
48#2761C2218yescomplemented
49#2752C2218yescomplemented
50#2735C2218yescomplemented
51#2707C2218yescomplemented
52#2706C2218yescomplemented
53#2706C2218yescomplemented
54#2701C2218yescomplemented
55#2697C2218yescomplemented
56#2685C2218yescomplemented
57#2682C2218yescomplemented
58#2681C2218yescomplemented
59#2680C2214yescomplemented
60#2679C2214yes—
61#2678C2218yescomplemented
62#2678C2218yescomplemented
63#2678C2218yescomplemented
64#2678C2218yescomplemented
65#2662C2214yescomplemented
66#2651C2218yescomplemented
67#2644C2214yescomplemented
68#2644C2214yescomplemented
69#2640C2214yescomplemented
70#2638C2214yescomplemented
71#2629C2214yescomplemented
72#2626C2218yescomplemented
73#2624C2214yescomplemented
74#2622C2218yescomplemented
75#2620C2214yescomplemented
76#2618C2214yescomplemented
77#2615C2214yescomplemented
78#2613C2214yescomplemented
79#2610C2214yescomplemented
80#2609C2214yescomplemented
81#2603C2214yescomplemented
82#2582C2211yescharacteristic, complemented
83#2566C2212yescomplemented
84#2563C2214yescomplemented
85#2551C2211yescharacteristic, complemented
86#2548C2212yes—
87#2540C2214yescomplemented
88#2538C2212yescomplemented
89#2538C2212yescomplemented
90#2537C2214yes—
91#2537C2211yescharacteristic
92#2537C2211yescharacteristic
93#2534C2218yescomplemented
94#2531C2218yescomplemented
95#2512C2214yescomplemented
96#2507C2214yescomplemented
97#2504C2212yescomplemented
98#2500C2212yescomplemented
99#2491C2214yescomplemented
100#2490C2214yescomplemented
101#2486C2214yescomplemented
102#2486C2214yescomplemented
103#2485C2214yescomplemented
104#2485C2214yescomplemented
105#2480C2218yescomplemented
106#2479C2214yescomplemented
107#2472C2218yescomplemented
108#2471C2214yescomplemented
109#2467C2214yescomplemented
110#2464C2218yescomplemented
111#2456C2214yescomplemented
112#2454C2212yescomplemented
113#2452C2214yescomplemented
114#2448C2212yescomplemented
115#2447C2214yescomplemented
116#2445C2214yes—
117#2441C2212yescomplemented
118#2440C2214yescomplemented
119#2435C2214yescomplemented
120#2431C2212yes—
121#2428C2212yes—
122#2426C2214yescomplemented
123#2424C2218yescomplemented
124#2423C2212yescomplemented
125#2422C2214yescomplemented
126#2422C2214yescomplemented
127#2417C2214yescomplemented
128#2417C2214yescomplemented
129#2416C2214yescomplemented
130#2416C2214yescomplemented
131#2416C2214yescomplemented
132#2415C2214yescomplemented
133#2414C2214yescomplemented
134#2414C2214yescomplemented
135#2414C2214yescomplemented
136#2414C2212yescomplemented
137#2411C2218yescomplemented
138#2408C2214yes—
139#2408C2214yes—
140#2408C2214yes—
141#2408C2214yescomplemented
142#2408C2214yescomplemented
143#2408C2214yescomplemented
144#2407C2214yescomplemented
145#2407C2212yescomplemented
146#2406C2214yescomplemented
147#2405C2218yescomplemented
148#2404C2218yescomplemented
149#2397C2214yescomplemented
150#2392C2214yescomplemented
151#2392C2214yescomplemented
152#2361C2214yescomplemented
153#2354C2212yescomplemented
154D4×C4⋊C4C2212yescomplemented
155#2346C2214yescomplemented
156D4×C22⋊C4C2214yescomplemented
157#2319C2214yescomplemented
158#2319C2214yescomplemented
159#2309C2214yescomplemented
160C4×#127C2212yes—
161C4×#127C2211yescharacteristic
162C4×C22⋊Q8C2214yescomplemented
163C4×#121C2214yescomplemented
164C4×#121C2212yescomplemented
165C4×#121C2214yescomplemented
166C4×#121C2212yescomplemented
167#2295C2212yescomplemented
168C2×#390C2214yescomplemented
169#2290C2214yescomplemented
170#2285C2211yescharacteristic, complemented
171C2×#384C2211yescharacteristic, complemented
172C42×D4C2211yescharacteristic, complemented
173C22×#41C2312yes—
174C22×#41C2314yes—
175C23×D4C2314yes—
176C23×D4C2314yes—
177C23×D4C2314yes—
178#553—48no—
179#547—416no—
180#546—416no—
181#546—416no—
182D42—48no—
183D42—416no—
184C2×C4⋊Q8C2314yes—
185C2×#127C2311yescharacteristic
186C2×#127C2312yes—
187#529—48no—
188C2×#126C2314yes—
189C2×#126C2314yes—
190C2×#125C2312yes—
191C2×#125C2312yes—
192C2×#124C2314yes—
193C2×#124C2312yes—
194C2×#124C2314yes—
195C2×#123C2318yes—
196C2×#123C2314yes—
197C2×#123C2314yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2312yes—
214C2×#121C2312yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2312yes—
221C2×#121C2312yes—
222C2×#120C2318yes—
223C2×#120C2318yes—
224C2×#120C2318yes—
225C2×#120C2318yes—
226C2×#120C2318yes—
227C4×#41—48no—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C22⋊C4C2318yes—
256C22×C22⋊C4C2318yes—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2314yes—
260#399C2314yes—
261#399C2318yes—
262#399C2314yes—
263#399C2314yes—
264#399C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2314yes—
270#398C2314yes—
271#398C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2314yes—
294#396C2314yes—
295#395C2314yes—
296#395C2314yes—
297#394C2314yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2314yes—
305#394C2318yes—
306#394C2314yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2314yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#393C2314yes—
320#393C2318yes—
321#393C2318yes—
322#393C2314yes—
323#392C2314yes—
324#392C2318yes—
325#392C2314yes—
326#392C2314yes—
327#392C2314yes—
328#392C2314yes—
329#392C2314yes—
330#392C2318yes—
331#392C2314yes—
332#392C2314yes—
333#392C2314yes—
334#392C2318yes—
335#391C2314yes—
336#391C2312yes—
337#391C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2318yes—
345#390C2312yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2318yes—
350#390C2318yes—
351#390C2312yes—
352#390C2312yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2318yes—
361#390C2314yes—
362#390C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2314yes—
373#389C2312yes—
374#389C2314yes—
375#389C2312yes—
376#388C2314yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#385C2318yes—
411#385C2314yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#384C2311yescharacteristic
418#384C2312yes—
419#384C2312yes—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2314yes—
423#382C2318yes—
424#382C2312yes—
425#382C2312yes—
426#381C2318yes—
427#381C2314yes—
428#381C2314yes—
429#380C2312yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2318yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2312yes—
441#380C2314yes—
442#379C2318yes—
443#379C2318yes—
444#379C2318yes—
445#379C2318yes—
446#379C2318yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2314yes—
462#376C2314yes—
463C43C2311yescharacteristic
464C25C2418yes—
465C2×#41—28no—
466C2×#41—48no—
467C2×#41—416no—
468C2×#41—44no—
469C2×#41—44no—
470C22×Q8C2412yes—
471C22×Q8C2414yes—
472C22×D4—216no—
473C22×D4—48no—
474C22×D4—48no—
475C22×D4—48no—
476C22×D4—48no—
477C22×D4—48no—
478C22×D4—48no—
479C22×D4—416no—
480C22×D4C2412yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2412yes—
486C22×D4C2411yescharacteristic
487C22×D4C2414yes—
488C22×D4C2412yes—
489C22×D4C2414yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2414yes—
496C22×D4C2418yes—
497C23×C4C2412yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2418yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C4⋊Q8—48no—
509#127—28no—
510#127—24no—
511#126—48no—
512#126—48no—
513#125—44no—
514#125—44no—
515#124—48no—
516#124—44no—
517#124—48no—
518#123—416no—
519#123—416no—
520#123—48no—
521#123—48no—
522#123—416no—
523#123—416no—
524C22⋊Q8—416no—
525C22⋊Q8—48no—
526C22⋊Q8—48no—
527C22⋊Q8—44no—
528C22⋊Q8—48no—
529#121—216no—
530#121—28no—
531#121—216no—
532#121—44no—
533#121—416no—
534#121—44no—
535#121—48no—
536#121—44no—
537#121—48no—
538#121—48no—
539#121—48no—
540#121—48no—
541#121—48no—
542#121—416no—
543#121—48no—
544#121—44no—
545#120—416no—
546#120—416no—
547#120—416no—
548#120—416no—
549#120—416no—
550C4×Q8—28no—
551C4×Q8—44no—
552C4×D4—216no—
553C4×D4—216no—
554C4×D4—24no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—44no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—44no—
561C4×D4—48no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—44no—
568C4×D4—48no—
569#117—48no—
570#117—44no—
571#117—48no—
572#117—48no—
573#117—44no—
574C2×C4⋊C4—48no—
575C2×C4⋊C4—48no—
576C2×C4⋊C4—44no—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C22⋊C4—416no—
611C2×C22⋊C4—416no—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2411yescharacteristic
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2411yescharacteristic
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—48no—
660C2×C42C2411yescharacteristic
661C2×C42C2412yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2411yescharacteristic
670C2×C42C2414yes—
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2414yes—
691#95C2418yes—
692#95C2414yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700C24—216no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24C2514yes—
708C24C2514yes—
709C24C2511yescharacteristic
710C24C2514yes—
711C24C2511yescharacteristic
712#41—432no—
713#41—832no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8—44no—
718C2×Q8—48no—
719C2×D4—22no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—216no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—832no—
765C2×D4—832no—
766C2×D4—832no—
767C2×D4H(5,𝔽2)18yes—
768C22×C4—28no—
769C22×C4—22no—
770C22×C4—216no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—22no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—24no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—44no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—44no—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2512yes—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—22no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—42no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—42no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C22⋊C4—216no—
851C22⋊C4—216no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—22no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4H(5,𝔽2)14yes—
895C42—24no—
896C42—22no—
897C42—24no—
898C42—22no—
899C42—28no—
900C42—28no—
901C42—28no—
902C42—22no—
903C42—24no—
904C42—24no—
905C42—44no—
906C42—44no—
907C42—41no—
908C42—48no—
909C42H(5,𝔽2)14yes—
910C23—24no—
911C23—21no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—24no—
919C23—21no—
920C23—21no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—21no—
925C23—24no—
926C23—28no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—22no—
932C23—28no—
933C23—24no—
934C23—24no—
935C23—21no—
936C23—24no—
937C23—816no—
938C23—816no—
939C23—816no—
940C23—816no—
941C23—816no—
942C23—168no—
943C23—168no—
944C23C2×H(5,𝔽2)18yes—
945C23C2×H(5,𝔽2)12yes—
946C23C2611yescharacteristic
947Q8—48no—
948Q8—88no—
949D4—216no—
950D4—416no—
951D4—416no—
952D4—416no—
953D4—44no—
954D4—416no—
955D4—48no—
956D4—416no—
957D4—84no—
958D4—88no—
959D4—88no—
960D4—88no—
961D4—816no—
962D4—88no—
963D4—88no—
964D4—816no—
965D4—164no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—416no—
1012C2×C4—48no—
1013C2×C4—416no—
1014C2×C4—416no—
1015C2×C4—48no—
1016C2×C4—88no—
1017C2×C4—88no—
1018C2×C4—88no—
1019C2×C4—816no—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×H(5,𝔽2)12yes—
1022C2×C4C2×H(5,𝔽2)12yes—
1023C2×C4C2×H(5,𝔽2)14yes—
1024C2×C4C2×H(5,𝔽2)14yes—
1025C2×C4#58514yes—
1026C22—22no—
1027C22—28no—
1028C22—22no—
1029C22—22no—
1030C22—28no—
1031C22—28no—
1032C22—44no—
1033C22—44no—
1034C22—42no—
1035C22—44no—
1036C22—42no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—41no—
1041C22—41no—
1042C22—44no—
1043C22—44no—
1044C22—41no—
1045C22—44no—
1046C22—44no—
1047C22—42no—
1048C22—44no—
1049C22—44no—
1050C22—48no—
1051C22—42no—
1052C22—44no—
1053C22—48no—
1054C22—44no—
1055C22—1632no—
1056C22C22×H(5,𝔽2)11yescharacteristic
1057C22C22×H(5,𝔽2)12yes—
1058C22C22×H(5,𝔽2)11yescharacteristic
1059C22C2×#58512yes—
1060C222−1+611yescharacteristic
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4—41no—
1068C4—44no—
1069C4—41no—
1070C4—44no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4#354218yes—
1079C2—42no—
1080C2—48no—
1081C2—81no—
1082C2—84no—
1083C2—84no—
1084C2C2×#354212yes—
1085C2#6275911yescharacteristic
1086C2#6291411yescharacteristic
1087C2#6292112yes—
1088C2#6301111yescharacteristic
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. #59816C2semidirect
2. #59808C2semidirect
3. #59313C2semidirect
4. #59233C2semidirect
5. #58267C2semidirect
6. #56317C2semidirect
7. #53103C2semidirect
8. #53101C2semidirect
9. #52696C2semidirect
10. #42478C2semidirect
11. #42474C2semidirect
12. #41986C2semidirect
13. #39046C2semidirect
14. #39006C2semidirect
15. #38975C2semidirect
16. #38910C2semidirect
17. #37629C2semidirect
18. #37620C2semidirect
19. #37492C2semidirect
20. #36258C2semidirect
21. #36182C2semidirect
22. #34976C2semidirect
23. #34727C2semidirect
24. C2×#553C22semidirect
25. C2×#547C22semidirect
26. C2×#546C22semidirect
27. C2×#546C22semidirect
30. C2×#529C22semidirect
31. C2×C4×#41C22semidirect
32. #2859C22semidirect
35. #2854C22semidirect
36. #2830C22semidirect
37. #2830C22semidirect
38. #2829C22semidirect
39. #2829C22semidirect
40. #2823C22semidirect
41. #2816C22semidirect
42. #2815C22semidirect
43. #2814C22semidirect
44. #2812C22semidirect
45. #2785C22semidirect
46. #2768C22semidirect
47. #2761C22semidirect
48. #2761C22semidirect
49. #2752C22semidirect
50. #2735C22semidirect
51. #2707C22semidirect
52. #2706C22semidirect
53. #2706C22semidirect
54. #2701C22semidirect
55. #2697C22semidirect
56. #2685C22semidirect
57. #2682C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
61. #2678C22semidirect
62. #2678C22semidirect
63. #2678C22semidirect
64. #2678C22semidirect
65. #2662C22semidirect
66. #2651C22semidirect
67. #2644C22semidirect
68. #2644C22semidirect
69. #2640C22semidirect
70. #2638C22semidirect
71. #2629C22semidirect
72. #2626C22semidirect
73. #2624C22semidirect
74. #2622C22semidirect
75. #2620C22semidirect
76. #2618C22semidirect
77. #2615C22semidirect
78. #2613C22semidirect
79. #2610C22semidirect
80. #2609C22semidirect
81. #2603C22semidirect
82. #2582C22semidirect
83. #2566C22semidirect
84. #2563C22semidirect
85. #2551C22semidirect
87. #2540C22semidirect
88. #2538C22semidirect
89. #2538C22semidirect
93. #2534C22semidirect
94. #2531C22semidirect
95. #2512C22semidirect
96. #2507C22semidirect
97. #2504C22semidirect
98. #2500C22semidirect
99. #2491C22semidirect
100. #2490C22semidirect
101. #2486C22semidirect
102. #2486C22semidirect
103. #2485C22semidirect
104. #2485C22semidirect
105. #2480C22semidirect
106. #2479C22semidirect
107. #2472C22semidirect
108. #2471C22semidirect
109. #2467C22semidirect
110. #2464C22semidirect
111. #2456C22semidirect
112. #2454C22semidirect
113. #2452C22semidirect
114. #2448C22semidirect
115. #2447C22semidirect
117. #2441C22semidirect
118. #2440C22semidirect
119. #2435C22semidirect
122. #2426C22semidirect
123. #2424C22semidirect
124. #2423C22semidirect
125. #2422C22semidirect
126. #2422C22semidirect
127. #2417C22semidirect
128. #2417C22semidirect
129. #2416C22semidirect
130. #2416C22semidirect
131. #2416C22semidirect
132. #2415C22semidirect
133. #2414C22semidirect
134. #2414C22semidirect
135. #2414C22semidirect
136. #2414C22semidirect
137. #2411C22semidirect
141. #2408C22semidirect
142. #2408C22semidirect
143. #2408C22semidirect
144. #2407C22semidirect
145. #2407C22semidirect
146. #2406C22semidirect
147. #2405C22semidirect
148. #2404C22semidirect
149. #2397C22semidirect
150. #2392C22semidirect
151. #2392C22semidirect
152. #2361C22semidirect
153. #2354C22semidirect
154. D4×C4⋊C4C22semidirect
155. #2346C22semidirect
156. D4×C22⋊C4C22semidirect
157. #2319C22semidirect
158. #2319C22semidirect
159. #2309C22semidirect
162. C4×C22⋊Q8C22semidirect
163. C4×#121C22semidirect
164. C4×#121C22semidirect
165. C4×#121C22semidirect
166. C4×#121C22semidirect
167. #2295C22semidirect
168. C2×#390C22semidirect
169. #2290C22semidirect
170. #2285C22semidirect
171. C2×#384C22semidirect
172. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598162
#598082
#593132
#592332
#582672
#563172
#531032
#531012
#526962
#424782
#424742
#419862
#390462
#390062
#389752
#389102
#376292
#376202
#374922
#362582
#361822
#349762
#347272