Finite Group Databasebeta

← #7720537

Subgroups — #7720537

Order 512.

5000 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51510C218yesmaximal, complemented
2#51041C214yesmaximal, complemented
3#50659C214yesmaximal, complemented
4#45365C214yesmaximal, complemented
5#45312C212yesmaximal, complemented
6#45299C212yesmaximal, complemented
7#45266C212yesmaximal, complemented
8#44963C212yesmaximal, complemented
9#44955C214yesmaximal, complemented
10#39202C212yesmaximal, complemented
11#39201C212yesmaximal, complemented
12#38206C214yesmaximal, complemented
13#38202C214yesmaximal, complemented
14#37292C214yesmaximal, complemented
15#36300C212yesmaximal, complemented
16#36271C212yesmaximal, complemented
17#35295C214yesmaximal, complemented
18#35285C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic
20#35200C211yesmaximal, characteristic, complemented
21#34625C211yesmaximal, characteristic, complemented
22#34394C211yesmaximal, characteristic, complemented
23#34364C211yesmaximal, characteristic, complemented
24#34125C211yesmaximal, characteristic, complemented
25C2×#556C2214yescomplemented
26C2×#535C2212yes—
27C2×#533C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30#2860C2214yescomplemented
31#2860C2214yescomplemented
32#2858C2212yes—
33#2858C2212yes—
34#2856C2214yes—
35#2851C2214yescomplemented
36#2797C2218yescomplemented
37#2761C2218yescomplemented
38#2757C2218yescomplemented
39#2757C2218yescomplemented
40#2756C2218yescomplemented
41#2753C2218yescomplemented
42#2752C2218yescomplemented
43#2737C2218yescomplemented
44#2736C2218yes—
45#2735C2218yes—
46#2723C2218yescomplemented
47#2723C2218yescomplemented
48#2712C2218yescomplemented
49#2710C2218yescomplemented
50#2701C2218yescomplemented
51#2691C2218yescomplemented
52#2686C2218yescomplemented
53#2685C2218yes—
54#2685C2218yes—
55#2672C2218yescomplemented
56#2667C2212yes—
57#2666C2214yescomplemented
58#2665C2212yes—
59#2660C2212yescomplemented
60#2647C2212yescomplemented
61#2641C2212yes—
62#2641C2212yes—
63#2638C2214yes—
64#2629C2212yes—
65#2628C2212yes—
66#2624C2214yescomplemented
67#2624C2214yescomplemented
68#2619C2214yes—
69#2610C2218yescomplemented
70#2601C2218yescomplemented
71#2599C2214yescomplemented
72#2597C2218yescomplemented
73#2597C2218yescomplemented
74#2592C2214yescomplemented
75#2580C2214yescomplemented
76#2567C2211yescharacteristic, complemented
77#2563C2211yescharacteristic, complemented
78#2560C2218yescomplemented
79#2559C2218yescomplemented
80#2559C2218yescomplemented
81#2554C2218yescomplemented
82#2548C2212yes—
83#2548C2214yes—
84#2548C2212yes—
85#2548C2212yes—
86#2548C2212yes—
87#2548C2214yescomplemented
88#2548C2214yescomplemented
89#2547C2211yescharacteristic, complemented
90#2546C2211yescharacteristic, complemented
91#2545C2214yescomplemented
92#2544C2214yescomplemented
93#2541C2212yes—
94#2541C2212yes—
95#2526C2218yescomplemented
96#2521C2218yescomplemented
97#2513C2214yescomplemented
98#2513C2214yescomplemented
99#2512C2214yescomplemented
100#2512C2214yescomplemented
101#2499C2212yes—
102#2491C2214yescomplemented
103#2490C2214yescomplemented
104#2485C2214yes—
105#2482C2218yes—
106#2480C2218yes—
107#2479C2218yescomplemented
108#2479C2218yescomplemented
109#2479C2218yescomplemented
110#2476C2218yescomplemented
111#2476C2218yescomplemented
112#2474C2218yescomplemented
113#2472C2218yes—
114#2454C2214yescomplemented
115#2452C2214yescomplemented
116#2448C2214yescomplemented
117#2448C2214yescomplemented
118#2447C2214yescomplemented
119#2445C2214yescomplemented
120#2435C2214yes—
121#2435C2212yes—
122#2435C2212yes—
123#2432C2212yes—
124#2422C2214yescomplemented
125#2420C2214yescomplemented
126#2411C2218yes—
127#2408C2212yes—
128#2408C2212yes—
129#2408C2214yes—
130#2402C2212yescomplemented
131#2399C2212yescomplemented
132#2396C2214yes—
133#2380C2214yes—
134#2378C2214yes—
135#2369C2212yescomplemented
136#2367C2214yescomplemented
137#2367C2214yescomplemented
138#2366C2212yes—
139#2366C2212yes—
140#2365C2212yescomplemented
141#2357C2212yes—
142#2357C2212yes—
143#2357C2211yescharacteristic, complemented
144#2357C2211yescharacteristic, complemented
145#2356C2212yescomplemented
146#2354C2214yescomplemented
147#2351C2212yescomplemented
148#2351C2211yescharacteristic, complemented
149#2351C2211yescharacteristic, complemented
150#2347C2212yes—
151#2347C2212yes—
152#2347C2214yescomplemented
153#2346C2212yes—
154#2341C2212yes—
155D4×C22⋊C4C2214yes—
156D4×C22⋊C4C2214yes—
157#2330C2214yescomplemented
158#2328C2212yes—
159#2328C2212yes—
160#2328C2214yes—
161#2327C2212yescomplemented
162#2326C2212yescomplemented
163#2324C2214yescomplemented
164#2324C2214yescomplemented
165#2323C2214yes—
166#2320C2214yescomplemented
167#2309C2212yes—
168#2309C2214yes—
169#2308C2214yes—
170C4×C4⋊Q8C2212yescomplemented
171C4×#125C2212yescomplemented
172#2293C2214yes—
173#2293C2212yescomplemented
174#2293C2214yescomplemented
175#2293C2214yescomplemented
176#2285C2211yescharacteristic
177#2283C2211yescharacteristic
178#2283C2211yescharacteristic
179#2283C2212yescomplemented
180C42×Q8C2212yescomplemented
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C22×#41C2311yescharacteristic
184C23×D4C2312yes—
185C23×D4C2312yes—
186C23×D4C2312yes—
187#556—416no—
188#535—48no—
189#533—28no—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2312yes—
194C2×#127—28no—
195C2×#127C2312yes—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2314yes—
200C2×#126C2318yes—
201C2×#126C2318yes—
202C2×#126C2318yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#124C2314yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#124C2314yes—
211C2×#124C2318yes—
212C2×#123C2318yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2318yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2318yes—
220C2×#120C2314yes—
221C2×#120C2314yes—
222C4×#41—28no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2318yes—
246C2×#117C2318yes—
247C22×C22⋊C4C2318yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#399C2318yes—
254#399C2318yes—
255#399C2314yes—
256#399C2318yes—
257#398C2314yes—
258#398C2314yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2314yes—
277#396C2314yes—
278#396C2318yes—
279#395C2314yes—
280#395C2314yes—
281#395C2314yes—
282#395C2314yes—
283#394C2318yes—
284#394C2314yes—
285#394C2318yes—
286#394C2318yes—
287#394C2314yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2314yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#393C2318yes—
302#393C2314yes—
303#393C2318yes—
304#393C2314yes—
305#392C2314yes—
306#392C2318yes—
307#392C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2318yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#390C2314yes—
315#390C2312yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2318yes—
325#390C2318yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#387C2318yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#383C2312yes—
414#383C2314yes—
415#383C2312yes—
416#383C2314yes—
417#382C2312yes—
418#382C2312yes—
419#382C2312yes—
420#382C2314yes—
421#382C2312yes—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2312yes—
425#382C2312yes—
426#381C2312yes—
427#381C2312yes—
428#381C2312yes—
429#381C2312yes—
430#381C2318yes—
431#380C2314yes—
432#380C2312yes—
433#380C2314yes—
434#380C2312yes—
435#380C2314yes—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2318yes—
439#380C2312yes—
440#379C2318yes—
441#379C2314yes—
442#379C2314yes—
443#379C2318yes—
444#379C2318yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2314yes—
479#376C2314yes—
480#376C2312yes—
481#376C2312yes—
482#376C2311yescharacteristic
483#376C2311yescharacteristic
484C43C2312yes—
485C43C2314yes—
486C25C2414yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—42no—
490C22×Q8C2412yes—
491C22×Q8C2411yescharacteristic
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×D4—28no—
495C22×D4—28no—
496C22×D4—28no—
497C22×D4—44no—
498C22×D4—48no—
499C22×D4—44no—
500C22×D4—84no—
501C22×D4C2414yes—
502C22×D4C2414yes—
503C22×D4C2411yescharacteristic
504C22×D4C2412yes—
505C22×D4C2414yes—
506C22×D4C2414yes—
507C22×D4C2414yes—
508C22×D4C2414yes—
509C22×D4C2418yes—
510C22×D4C2418yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2412yes—
516C23×C4C2418yes—
517C23×C4C2418yes—
518C23×C4C2411yescharacteristic
519C4⋊Q8—28no—
520C4⋊Q8—24no—
521C4⋊Q8—24no—
522C4⋊Q8—44no—
523#127—28no—
524#127—28no—
525#127—28no—
526#127—28no—
527#127—48no—
528#126—416no—
529#126—416no—
530#126—88no—
531#125—28no—
532#125—44no—
533#124—216no—
534#124—44no—
535#124—48no—
536#124—48no—
537#124—88no—
538#124—84no—
539#124—84no—
540#123—88no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—416no—
544#121—416no—
545#121—48no—
546#121—48no—
547#121—88no—
548#120—48no—
549#120—48no—
550C4×Q8—28no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—48no—
556C4×Q8—44no—
557C4×Q8—48no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566#117—24no—
567#117—28no—
568#117—28no—
569#117—48no—
570#117—44no—
571#117—44no—
572#117—416no—
573#117—88no—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C22⋊C4—88no—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C42—28no—
649C2×C42#4118yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#95C2412yes—
675#95C2412yes—
676#95C2411yescharacteristic
677#95C2412yes—
678#95C2411yescharacteristic
679#95C2414yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2411yescharacteristic
684#95C2411yescharacteristic
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2412yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2412yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2414yes—
703#95C2412yes—
704#95C2412yes—
705#95C2418yes—
706#95C2414yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712C24—28no—
713C24—48no—
714C24—44no—
715C24—48no—
716C24—44no—
717C24C2518yes—
718C24C2512yes—
719C24C2511yescharacteristic
720#41—416no—
721C2×Q8—22no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—22no—
726C2×Q8—24no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×Q8H(5,𝔽2)14yes—
732C2×D4—24no—
733C2×D4—22no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—22no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—816no—
761C2×D4—816no—
762C2×D4—816no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—216no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C22⋊C4—24no—
842C22⋊C4—28no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—42no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—48no—
891C42—44no—
892C42—48no—
893C42—44no—
894C42—42no—
895C42—42no—
896C42—44no—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C23—21no—
902C23—22no—
903C23—21no—
904C23—22no—
905C23—22no—
906C23—28no—
907C23—28no—
908C23—22no—
909C23—22no—
910C23—28no—
911C23—24no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—24no—
916C23—28no—
917C23—416no—
918C23—88no—
919C23—88no—
920C23—168no—
921C23—168no—
922C23C22×#4112yes—
923C23C2611yescharacteristic
924Q8—28no—
925Q8—48no—
926Q8—84no—
927Q8—88no—
928D4—48no—
929D4—416no—
930D4—44no—
931D4—416no—
932D4—88no—
933D4—88no—
934D4—88no—
935D4—88no—
936D4—168no—
937D4—168no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—44no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—84no—
990C2×C4—816no—
991C2×C4—816no—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C2×H(5,𝔽2)14yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4#58512yes—
1001C2×C4#58514yes—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—48no—
1009C22—42no—
1010C22—48no—
1011C22—42no—
1012C22—48no—
1013C22—48no—
1014C22—44no—
1015C22—48no—
1016C22—48no—
1017C22—44no—
1018C22—48no—
1019C22—1616no—
1020C22C23×#4111yescharacteristic
1021C22C22×H(5,𝔽2)11yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22C2×#58512yes—
1024C22H(7,𝔽2)12yes—
1025C4—22no—
1026C4—24no—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—44no—
1031C4—42no—
1032C4—42no—
1033C4—44no—
1034C4—42no—
1035C4—44no—
1036C4—44no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—44no—
1043C4—44no—
1044C4#349414yes—
1045C4#351014yes—
1046C2—42no—
1047C2—82no—
1048C2—88no—
1049C2C2×#349411yescharacteristic
1050C2C2×#351011yescharacteristic
1051C2#6285511yescharacteristic
1052C2#6292312yes—
1053C2#6296912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35272C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51510C2semidirect
2. #51041C2semidirect
3. #50659C2semidirect
4. #45365C2semidirect
5. #45312C2semidirect
6. #45299C2semidirect
7. #45266C2semidirect
8. #44963C2semidirect
9. #44955C2semidirect
10. #39202C2semidirect
11. #39201C2semidirect
12. #38206C2semidirect
13. #38202C2semidirect
14. #37292C2semidirect
15. #36300C2semidirect
16. #36271C2semidirect
17. #35295C2semidirect
18. #35285C2semidirect
20. #35200C2semidirect
21. #34625C2semidirect
22. #34394C2semidirect
23. #34364C2semidirect
24. #34125C2semidirect
25. C2×#556C22semidirect
30. #2860C22semidirect
31. #2860C22semidirect
35. #2851C22semidirect
36. #2797C22semidirect
37. #2761C22semidirect
38. #2757C22semidirect
39. #2757C22semidirect
40. #2756C22semidirect
41. #2753C22semidirect
42. #2752C22semidirect
43. #2737C22semidirect
46. #2723C22semidirect
47. #2723C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2701C22semidirect
51. #2691C22semidirect
52. #2686C22semidirect
55. #2672C22semidirect
57. #2666C22semidirect
59. #2660C22semidirect
60. #2647C22semidirect
66. #2624C22semidirect
67. #2624C22semidirect
69. #2610C22semidirect
70. #2601C22semidirect
71. #2599C22semidirect
72. #2597C22semidirect
73. #2597C22semidirect
74. #2592C22semidirect
75. #2580C22semidirect
76. #2567C22semidirect
77. #2563C22semidirect
78. #2560C22semidirect
79. #2559C22semidirect
80. #2559C22semidirect
81. #2554C22semidirect
87. #2548C22semidirect
88. #2548C22semidirect
89. #2547C22semidirect
90. #2546C22semidirect
91. #2545C22semidirect
92. #2544C22semidirect
95. #2526C22semidirect
96. #2521C22semidirect
97. #2513C22semidirect
98. #2513C22semidirect
99. #2512C22semidirect
100. #2512C22semidirect
102. #2491C22semidirect
103. #2490C22semidirect
107. #2479C22semidirect
108. #2479C22semidirect
109. #2479C22semidirect
110. #2476C22semidirect
111. #2476C22semidirect
112. #2474C22semidirect
114. #2454C22semidirect
115. #2452C22semidirect
116. #2448C22semidirect
117. #2448C22semidirect
118. #2447C22semidirect
119. #2445C22semidirect
124. #2422C22semidirect
125. #2420C22semidirect
130. #2402C22semidirect
131. #2399C22semidirect
135. #2369C22semidirect
136. #2367C22semidirect
137. #2367C22semidirect
140. #2365C22semidirect
143. #2357C22semidirect
144. #2357C22semidirect
145. #2356C22semidirect
146. #2354C22semidirect
147. #2351C22semidirect
148. #2351C22semidirect
149. #2351C22semidirect
152. #2347C22semidirect
157. #2330C22semidirect
161. #2327C22semidirect
162. #2326C22semidirect
163. #2324C22semidirect
164. #2324C22semidirect
166. #2320C22semidirect
170. C4×C4⋊Q8C22semidirect
171. C4×#125C22semidirect
173. #2293C22semidirect
174. #2293C22semidirect
175. #2293C22semidirect
179. #2283C22semidirect
180. C42×Q8C22semidirect
182. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#515102
#510412
#506592
#453652
#453122
#452992
#452662
#449632
#449552
#392022
#392012
#382062
#382022
#372922
#363002
#362712
#352952
#352852
#352722
#352002
#346252
#343942
#343642
#341252