Finite Group Databasebeta

← #7646146

Subgroups — #7646146

Order 512.

5380 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42752C214yesmaximal, complemented
2#42726C214yesmaximal, complemented
3#42608C214yesmaximal, complemented
4#42541C214yesmaximal, complemented
5#40198C214yesmaximal, complemented
6#40092C214yesmaximal, complemented
7#39664C214yesmaximal, complemented
8#39246C214yesmaximal, complemented
9#37465C214yesmaximal, complemented
10#36761C214yesmaximal, complemented
11#36727C214yesmaximal, complemented
12#35518C212yesmaximal, complemented
13#35517C212yesmaximal, complemented
14#35255C212yesmaximal, complemented
15#35223C211yesmaximal, characteristic, complemented
16#35223C211yesmaximal, characteristic, complemented
17#35166C211yesmaximal, characteristic, complemented
18#35159C211yesmaximal, characteristic, complemented
19#35081C214yesmaximal, complemented
20#34743C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2345C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#537C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#537C2212yes—
27C2×#532C2212yes—
28C2×#525C2212yes—
29C2×#525C2212yes—
30C2×#520C2212yes—
31C2×C4×#41C2212yes—
32C23×C4⋊C4C2211yescharacteristic
33#2856C2214yes—
34#2855C2214yescomplemented
35#2854C2214yescomplemented
36#2851C2214yes—
37#2847C2214yes—
38#2847C2214yes—
39#2836C2218yescomplemented
40#2829C2218yescomplemented
41#2800C2218yescomplemented
42#2791C2218yescomplemented
43#2786C2218yescomplemented
44#2780C2218yescomplemented
45#2761C2218yescomplemented
46#2748C2218yes—
47#2748C2218yes—
48#2741C2218yes—
49#2741C2218yes—
50#2740C2218yescomplemented
51#2709C2218yescomplemented
52#2707C2218yescomplemented
53#2703C2218yes—
54#2703C2218yes—
55#2671C2218yes—
56#2671C2218yes—
57#2667C2218yescomplemented
58#2656C2214yes—
59#2654C2218yescomplemented
60#2648C2218yes—
61#2648C2218yes—
62#2648C2218yescomplemented
63#2646C2214yes—
64#2630C2218yescomplemented
65#2625C2214yescomplemented
66#2624C2214yescomplemented
67#2618C2214yes—
68#2618C2214yes—
69#2542C2214yescomplemented
70#2541C2214yescomplemented
71#2540C2214yescomplemented
72#2540C2214yescomplemented
73#2538C2214yes—
74#2537C2214yes—
75#2536C2214yes—
76#2535C2214yes—
77#2522C2218yescomplemented
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2507C2214yescomplemented
81#2506C2214yescomplemented
82#2497C2214yes—
83#2497C2214yes—
84#2490C2214yes—
85#2490C2214yes—
86#2487C2214yescomplemented
87#2486C2214yescomplemented
88#2485C2214yescomplemented
89#2485C2214yescomplemented
90#2457C2218yescomplemented
91#2448C2214yescomplemented
92#2447C2214yescomplemented
93#2446C2214yescomplemented
94#2445C2214yescomplemented
95#2444C2218yes—
96#2444C2218yes—
97#2443C2218yes—
98#2443C2218yes—
99#2429C2212yes—
100#2429C2212yes—
101#2428C2214yes—
102#2428C2214yes—
103#2428C2212yes—
104#2428C2212yes—
105#2427C2212yes—
106#2427C2212yes—
107#2426C2212yes—
108#2426C2212yes—
109#2425C2214yes—
110#2425C2218yes—
111#2425C2214yes—
112#2424C2214yes—
113#2424C2218yes—
114#2424C2214yes—
115#2423C2214yescomplemented
116#2422C2214yescomplemented
117#2421C2214yescomplemented
118#2420C2214yes—
119#2420C2214yes—
120#2420C2214yescomplemented
121#2417C2214yes—
122#2417C2214yes—
123#2417C2214yes—
124#2417C2214yes—
125#2417C2214yes—
126#2416C2214yes—
127#2416C2214yes—
128#2416C2214yes—
129#2416C2214yes—
130#2416C2214yes—
131#2415C2214yes—
132#2414C2214yes—
133#2392C2214yes—
134#2392C2214yes—
135#2363C2214yescomplemented
136#2362C2214yescomplemented
137#2361C2214yescomplemented
138#2360C2214yescomplemented
139#2345C2214yes—
140#2345C2214yes—
141#2345C2214yes—
142#2345C2214yes—
143#2333C2218yes—
144#2333C2218yes—
145#2325C2214yes—
146#2325C2214yes—
147#2324C2214yescomplemented
148#2323C2214yescomplemented
149#2317C2212yes—
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2311C2212yes—
153#2311C2212yes—
154#2311C2212yes—
155C4×C22⋊Q8C2214yescomplemented
156C4×#121C2214yes—
157C4×#121C2214yes—
158C4×#121C2214yes—
159C4×#121C2214yes—
160C4×#121C2214yescomplemented
161#2297C2212yes—
162#2296C2212yes—
163C2×#389C2211yescharacteristic
164C2×#389C2211yescharacteristic
165C2×#387C2212yes—
166C2×#387C2212yes—
167C2×#380C2212yes—
168C2×#380C2211yescharacteristic
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×C4×C22⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C22×#41C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177#537—28no—
178#537—28no—
179#537—48no—
180#532—48no—
181C2×C4⋊Q8C2312yes—
182C2×#127C2312yes—
183C2×#127C2314yes—
184C2×#125C2314yes—
185C2×#124C2312yes—
186C2×#124C2312yes—
187#525—48no—
188#525—48no—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2312yes—
214C2×#121C2312yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#120C2314yes—
222C2×#120C2314yes—
223#520—48no—
224C4×#41—48no—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C22×C4⋊C4—28no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2314yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#399C2318yes—
270#399C2318yes—
271#399C2318yes—
272#399C2318yes—
273#398C2318yes—
274#398C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#397C2314yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2314yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#394C2314yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#392C2318yes—
317#392C2318yes—
318#392C2314yes—
319#392C2314yes—
320#392C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#390C2318yes—
333#390C2318yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2314yes—
392#386C2318yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#384C2314yes—
414#384C2314yes—
415#382C2314yes—
416#382C2314yes—
417#381C2318yes—
418#381C2318yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2318yes—
434#380C2318yes—
435#380C2318yes—
436#380C2314yes—
437#380C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C2×#95C2312yes—
459C2×#95C2312yes—
460C2×#95C2311yescharacteristic
461C2×#95C2311yescharacteristic
462C2×#95C2312yes—
463C2×#95C2312yes—
464C2×#95C2312yes—
465C25C2411yescharacteristic
466C2×#41—28no—
467C2×#41—28no—
468C2×#41—28no—
469C2×#41—28no—
470C2×#41—28no—
471C2×#41—28no—
472C22×Q8C2412yes—
473C22×Q8C2412yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2412yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2418yes—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—28no—
491C23×C4—82no—
492C23×C4—82no—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2412yes—
502C23×C4C2411yescharacteristic
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2418yes—
509C23×C4C2414yes—
510C23×C4C2412yes—
511C23×C4C2411yescharacteristic
512C4⋊Q8—44no—
513#127—44no—
514#127—84no—
515#125—84no—
516#124—44no—
517#124—44no—
518#123—48no—
519#123—48no—
520#123—88no—
521#123—88no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—44no—
525C22⋊Q8—44no—
526C22⋊Q8—44no—
527C22⋊Q8—44no—
528C22⋊Q8—48no—
529C22⋊Q8—48no—
530#121—216no—
531#121—216no—
532#121—216no—
533#121—216no—
534#121—216no—
535#121—48no—
536#121—416no—
537#121—44no—
538#121—44no—
539#121—44no—
540#121—44no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—416no—
546#121—84no—
547#121—84no—
548#121—84no—
549#121—84no—
550#120—48no—
551#120—48no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—48no—
555C4×D4—44no—
556C4×D4—44no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—48no—
561C4×D4—48no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—416no—
567C4×D4—84no—
568C4×D4—84no—
569#117—28no—
570#117—28no—
571#117—48no—
572#117—48no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—216no—
578C2×C4⋊C4—216no—
579C2×C4⋊C4—48no—
580C2×C4⋊C4—82no—
581C2×C4⋊C4—82no—
582C2×C4⋊C4#4118yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—44no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2411yescharacteristic
623C2×C22⋊C4C2411yescharacteristic
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2411yescharacteristic
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—48no—
661C2×C42—82no—
662C2×C42—82no—
663C2×C42C2414yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2418yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676#95C2412yes—
677#95C2412yes—
678#95C2414yes—
679#95C2414yes—
680#95C2412yes—
681#95C2414yes—
682#95C2412yes—
683#95C2414yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—41no—
711C24—41no—
712C24C2514yes—
713C24C2514yes—
714C24C2511yescharacteristic
715C24C2511yescharacteristic
716C24C2511yescharacteristic
717#41—432no—
718#41—432no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C22×C4—24no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4—42no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—416no—
818C22×C4—816no—
819C22×C4C2×#4118yes—
820C22×C4C2×#4114yes—
821C22×C4H(5,𝔽2)14yes—
822C22×C4H(5,𝔽2)14yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C4⋊C4—216no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4C2×#41116yes—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—22no—
877C22⋊C4—24no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—28no—
884C22⋊C4—42no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C42−1+414yes—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—28no—
918C42—28no—
919C42—44no—
920C42—44no—
921C42—44no—
922C42—44no—
923C42—44no—
924C42—44no—
925C42—48no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—28no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23C22×#4112yes—
964C23C2×H(5,𝔽2)12yes—
965C23C2×H(5,𝔽2)12yes—
966C23C2×2−1+412yes—
967C23#58512yes—
968C23C2611yescharacteristic
969Q8—48no—
970Q8—48no—
971D4—416no—
972D4—416no—
973D4—48no—
974D4—48no—
975D4—88no—
976D4—88no—
977D4—88no—
978D4—88no—
979D4—88no—
980D4—88no—
981D4—88no—
982D4—88no—
983D4—168no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—48no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—48no—
1036C2×C4—44no—
1037C2×C4—48no—
1038C2×C4—48no—
1039C2×C4—416no—
1040C2×C4—416no—
1041C2×C4—88no—
1042C2×C4—88no—
1043C2×C4—88no—
1044C2×C4—82no—
1045C2×C4—84no—
1046C2×C4—82no—
1047C2×C4—84no—
1048C2×C4—88no—
1049C2×C4—168no—
1050C2×C4#540116yes—
1051C2×C4C22×#4118yes—
1052C2×C4C22×#4114yes—
1053C2×C4C2×H(5,𝔽2)14yes—
1054C2×C4C2×H(5,𝔽2)14yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—416no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22—41no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22C2×#54014yes—
1093C22C23×#4111yescharacteristic
1094C22C22×H(5,𝔽2)11yescharacteristic
1095C22C22×H(5,𝔽2)11yescharacteristic
1096C22C22×2−1+411yescharacteristic
1097C22C2×#58511yescharacteristic
1098C22H(7,𝔽2)11yescharacteristic
1099C22H(7,𝔽2)11yescharacteristic
1100C4—28no—
1101C4—22no—
1102C4—22no—
1103C4—44no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—41no—
1108C4—41no—
1109C4—44no—
1110C4—44no—
1111C4—42no—
1112C4—44no—
1113C4—44no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4C2×#54018yes—
1118C2—24no—
1119C2—42no—
1120C2—42no—
1121C2—84no—
1122C2—84no—
1123C2C22×#54011yescharacteristic
1124C2#6278811yescharacteristic
1125C2#6284611yescharacteristic
1126C2#6294411yescharacteristic
1127C2#6294411yescharacteristic
1128C2#6295711yescharacteristic
1129C2#6295711yescharacteristic
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. #42752C2semidirect
2. #42726C2semidirect
3. #42608C2semidirect
4. #42541C2semidirect
5. #40198C2semidirect
6. #40092C2semidirect
7. #39664C2semidirect
8. #39246C2semidirect
9. #37465C2semidirect
10. #36761C2semidirect
11. #36727C2semidirect
12. #35518C2semidirect
13. #35517C2semidirect
14. #35255C2semidirect
15. #35223C2semidirect
16. #35223C2semidirect
17. #35166C2semidirect
18. #35159C2semidirect
19. #35081C2semidirect
20. #34743C2semidirect
21. #34274C2semidirect
22. C2×#2345C2semidirect
23. C4×#537C2semidirect
34. #2855C22semidirect
35. #2854C22semidirect
39. #2836C22semidirect
40. #2829C22semidirect
41. #2800C22semidirect
42. #2791C22semidirect
43. #2786C22semidirect
44. #2780C22semidirect
45. #2761C22semidirect
50. #2740C22semidirect
51. #2709C22semidirect
52. #2707C22semidirect
57. #2667C22semidirect
59. #2654C22semidirect
62. #2648C22semidirect
64. #2630C22semidirect
65. #2625C22semidirect
66. #2624C22semidirect
69. #2542C22semidirect
70. #2541C22semidirect
71. #2540C22semidirect
72. #2540C22semidirect
77. #2522C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2507C22semidirect
81. #2506C22semidirect
86. #2487C22semidirect
87. #2486C22semidirect
88. #2485C22semidirect
89. #2485C22semidirect
90. #2457C22semidirect
91. #2448C22semidirect
92. #2447C22semidirect
93. #2446C22semidirect
94. #2445C22semidirect
115. #2423C22semidirect
116. #2422C22semidirect
117. #2421C22semidirect
120. #2420C22semidirect
135. #2363C22semidirect
136. #2362C22semidirect
137. #2361C22semidirect
138. #2360C22semidirect
147. #2324C22semidirect
148. #2323C22semidirect
155. C4×C22⋊Q8C22semidirect
160. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#427522
#427262
#426082
#425412
#401982
#400922
#396642
#392462
#374652
#367612
#367272
#355182
#355172
#352552
#352232
#351662
#351592
#350812
#347432
#342742
C2×#23452
C4×#5372