Finite Group Databasebeta

← #7677056

Subgroups — #7677056

Order 512.

5696 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C214yesmaximal, complemented
2#59826C214yesmaximal, complemented
3#59677C214yesmaximal, complemented
4#59440C214yesmaximal, complemented
5#45373C214yesmaximal, complemented
6#45371C214yesmaximal, complemented
7#44977C214yesmaximal, complemented
8#44975C214yesmaximal, complemented
9#39549C214yesmaximal, complemented
10#37941C214yesmaximal, complemented
11#37890C214yesmaximal, complemented
12#36157C214yesmaximal, complemented
13#35557C212yesmaximal, complemented
14#35516C212yesmaximal, complemented
15#35223C211yesmaximal, characteristic, complemented
16#35223C211yesmaximal, characteristic, complemented
17#35159C211yesmaximal, characteristic, complemented
18#34737C212yesmaximal, complemented
19#34274C211yesmaximal, characteristic, complemented
20#34202C212yesmaximal, complemented
21#34178C211yesmaximal, characteristic, complemented
22C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
23C2×#2316C211yesmaximal, characteristic, complemented
24C2×#553C2214yes—
25C2×#537C2211yescharacteristic
26C2×#525C2212yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×#117C2212yes—
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2851C2214yes—
35#2847C2214yes—
36#2847C2214yes—
37#2802C2218yescomplemented
38#2800C2218yescomplemented
39#2786C2218yescomplemented
40#2780C2218yescomplemented
41#2779C2218yescomplemented
42#2772C2218yescomplemented
43#2750C2218yescomplemented
44#2747C2218yescomplemented
45#2739C2218yescomplemented
46#2725C2218yescomplemented
47#2701C2218yescomplemented
48#2691C2218yescomplemented
49#2646C2214yes—
50#2618C2214yes—
51#2618C2214yes—
52#2608C2218yescomplemented
53#2601C2218yescomplemented
54#2590C2218yescomplemented
55#2587C2218yescomplemented
56#2579C2218yescomplemented
57#2569C2218yescomplemented
58#2562C2214yes—
59#2559C2218yescomplemented
60#2535C2214yes—
61#2522C2218yescomplemented
62#2512C2214yescomplemented
63#2512C2214yescomplemented
64#2511C2214yescomplemented
65#2511C2214yescomplemented
66#2509C2214yescomplemented
67#2508C2214yescomplemented
68#2507C2214yescomplemented
69#2506C2214yescomplemented
70#2497C2214yescomplemented
71#2497C2214yescomplemented
72#2496C2214yescomplemented
73#2496C2214yescomplemented
74#2487C2214yes—
75#2487C2214yescomplemented
76#2486C2214yescomplemented
77#2485C2214yes—
78#2485C2214yescomplemented
79#2485C2214yescomplemented
80#2481C2218yes—
81#2481C2218yes—
82#2481C2218yescomplemented
83#2470C2218yescomplemented
84#2467C2218yes—
85#2466C2218yescomplemented
86#2457C2218yes—
87#2444C2218yes—
88#2444C2218yescomplemented
89#2423C2214yescomplemented
90#2422C2214yescomplemented
91#2421C2214yescomplemented
92#2420C2214yescomplemented
93#2419C2218yes—
94#2418C2218yes—
95#2417C2212yes—
96#2417C2212yes—
97#2417C2214yescomplemented
98#2417C2214yescomplemented
99#2417C2214yescomplemented
100#2417C2214yescomplemented
101#2416C2214yes—
102#2416C2212yes—
103#2416C2212yes—
104#2416C2214yescomplemented
105#2416C2214yescomplemented
106#2416C2214yescomplemented
107#2416C2214yescomplemented
108#2415C2212yes—
109#2415C2212yes—
110#2414C2214yes—
111#2414C2212yes—
112#2414C2212yes—
113#2413C2214yes—
114#2412C2214yes—
115#2411C2214yes—
116#2410C2214yes—
117#2392C2214yes—
118#2392C2214yes—
119#2364C2218yes—
120#2363C2214yescomplemented
121#2362C2214yescomplemented
122#2361C2214yescomplemented
123#2360C2214yescomplemented
124#2359C2218yes—
125#2358C2218yes—
126#2354C2214yescomplemented
127#2352C2214yes—
128#2352C2214yescomplemented
129#2352C2214yescomplemented
130D4×C4⋊C4C2214yes—
131D4×C4⋊C4C2214yes—
132D4×C4⋊C4C2214yes—
133D4×C4⋊C4C2214yes—
134D4×C4⋊C4C2214yescomplemented
135#2345C2214yescomplemented
136#2345C2214yescomplemented
137#2344C2214yescomplemented
138#2344C2214yescomplemented
139#2325C2214yes—
140#2324C2214yescomplemented
141#2323C2214yescomplemented
142#2317C2212yes—
143#2316C2214yes—
144#2316C2211yescharacteristic
145#2316C2211yescharacteristic
146#2316C2212yes—
147#2316C2211yescharacteristic
148#2316C2214yescomplemented
149#2316C2214yescomplemented
150#2313C2214yes—
151#2311C2212yes—
152#2311C2212yes—
153C4×C22⋊Q8C2214yescomplemented
154C4×#121C2214yes—
155C4×#121C2214yes—
156C4×#121C2214yes—
157C4×#121C2214yescomplemented
158#2297C2212yes—
159#2296C2212yes—
160C2×#389C2212yes—
161C2×#389C2214yescomplemented
162C2×#389C2214yescomplemented
163C2×#385C2212yes—
164C2×#385C2212yes—
165C2×#384C2211yescharacteristic
166#2280C2214yes—
167#2280C2212yes—
168C2×#380C2214yes—
169C2×#380C2211yescharacteristic
170C2×#380C2211yescharacteristic
171#2274C2212yes—
172C2×C4×C4⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C23×D4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177C24×C4C2312yes—
178C24×C4C2312yes—
179#553—416no—
180#537—28no—
181C2×#126C2318yes—
182C2×#126C2318yes—
183C2×#125C2314yes—
184#525—216no—
185#525—48no—
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2312yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#120C2314yes—
207C2×#120C2314yes—
208#520—48no—
209C2×C4×Q8C2314yes—
210C2×C4×D4—28no—
211C2×C4×D4—48no—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×#117—48no—
229C2×#117C2312yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2314yes—
233C2×#117C2314yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2314yes—
237C2×#117C2314yes—
238C2×#117C2314yes—
239C22×C4⋊C4—28no—
240C22×C4⋊C4—28no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2311yescharacteristic
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266C22×C42C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#399C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#397C2314yes—
283#397C2314yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2314yes—
293#396C2314yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2314yes—
299#394C2314yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2314yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#394C2318yes—
309#392C2314yes—
310#392C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#390C2314yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C2312yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#389C2318yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2318yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2318yes—
384#386C2318yes—
385#386C2314yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#386C2318yes—
392#386C2314yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2314yes—
407#384C2314yes—
408#384C2314yes—
409#384C2314yes—
410#382C2314yes—
411#382C2314yes—
412#381C2314yes—
413#381C2318yes—
414#381C2318yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2318yes—
430#380C2318yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2312yes—
435#380C2312yes—
436#380C2312yes—
437#380C2312yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#379C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2318yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C2×#95C2318yes—
463C2×#95C2312yes—
464C2×#95C2312yes—
465C2×#95C2312yes—
466C25C2411yescharacteristic
467C25C2411yescharacteristic
468C2×#41—28no—
469C2×#41—28no—
470C2×#41—28no—
471C22×Q8C2412yes—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4C2411yescharacteristic
476C22×D4C2411yescharacteristic
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2412yes—
480C22×D4C2411yescharacteristic
481C22×D4C2411yescharacteristic
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C23×C4—24no—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—24no—
491C23×C4—28no—
492C23×C4—28no—
493C23×C4—44no—
494C23×C4—44no—
495C23×C4—82no—
496C23×C4—82no—
497C23×C4#4118yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2418yes—
517C23×C4C2412yes—
518C23×C4C2411yescharacteristic
519#126—416no—
520#126—88no—
521#125—48no—
522#123—216no—
523#123—416no—
524#123—48no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—44no—
529C22⋊Q8—44no—
530#121—216no—
531#121—216no—
532#121—28no—
533#121—28no—
534#121—216no—
535#121—216no—
536#121—44no—
537#121—44no—
538#121—48no—
539#121—48no—
540#121—84no—
541#121—84no—
542#120—216no—
543#120—48no—
544C4×Q8—48no—
545C4×D4—216no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—216no—
551C4×D4—216no—
552C4×D4—48no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—48no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4—416no—
560C4×D4—416no—
561#117—28no—
562#117—28no—
563#117—28no—
564#117—48no—
565#117—48no—
566#117—48no—
567#117—44no—
568#117—44no—
569#117—48no—
570#117—84no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—216no—
578C2×C4⋊C4—216no—
579C2×C4⋊C4—216no—
580C2×C4⋊C4—216no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—48no—
585C2×C4⋊C4—48no—
586C2×C4⋊C4—84no—
587C2×C4⋊C4—82no—
588C2×C4⋊C4#4118yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—48no—
631C2×C22⋊C4—44no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C42—24no—
669C2×C42—48no—
670C2×C42—44no—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2418yes—
680C2×C42C2418yes—
681C2×C42C2418yes—
682C2×C42C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711C24—22no—
712C24—22no—
713C24—22no—
714C24—22no—
715C24—22no—
716C24—22no—
717C24—22no—
718C24—22no—
719C24—22no—
720C24—41no—
721C24—41no—
722C24—41no—
723C24—41no—
724C24C2×#4114yes—
725C24C2514yes—
726C24C2511yescharacteristic
727C24C2511yescharacteristic
728C24C2511yescharacteristic
729C24C2511yescharacteristic
730C24C2511yescharacteristic
731#41—432no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×D4—232no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—28no—
756C2×D4—22no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4H(5,𝔽2)14yes—
768C2×D42−1+414yes—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—232no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—42no—
804C22×C4—41no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—42no—
808C22×C4—41no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—44no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—416no—
827C22×C4—816no—
828C22×C4—816no—
829C22×C4C2×#4114yes—
830C22×C4C2×#4118yes—
831C22×C4C2×#4118yes—
832C22×C4C2×#4118yes—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4H(5,𝔽2)14yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C4⋊C4—216no—
854C4⋊C4—216no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4C2×#41116yes—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—28no—
931C42—28no—
932C42—28no—
933C42—44no—
934C42—44no—
935C42—44no—
936C42—48no—
937C42—48no—
938C42—48no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—28no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—28no—
967C23—28no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—44no—
976C23—44no—
977C23—44no—
978C23—44no—
979C23—44no—
980C23—44no—
981C23—44no—
982C23—44no—
983C23—44no—
984C23—44no—
985C23—44no—
986C23C22×#4112yes—
987C23C22×#4112yes—
988C23C22×#4112yes—
989C23C22×#4112yes—
990C23C2×H(5,𝔽2)12yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2×H(5,𝔽2)12yes—
993C23C2×2−1+412yes—
994C23C2×2−1+412yes—
995C23C2611yescharacteristic
996Q8—48no—
997D4—28no—
998D4—28no—
999D4—28no—
1000D4—28no—
1001D4—416no—
1002D4—416no—
1003D4—48no—
1004D4—88no—
1005D4—88no—
1006D4—88no—
1007D4—88no—
1008C2×C4—28no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—24no—
1017C2×C4—28no—
1018C2×C4—216no—
1019C2×C4—216no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—48no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—416no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—84no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4—84no—
1070C2×C4—84no—
1071C2×C4—168no—
1072C2×C4#553116yescomplemented
1073C2×C4C22×#4114yes—
1074C2×C4C22×#4118yes—
1075C2×C4C22×#4114yes—
1076C2×C4C22×#4114yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)14yes—
1079C2×C4C2×2−1+412yes—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—416no—
1102C22—416no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22—44no—
1119C22—44no—
1120C22—44no—
1121C22—44no—
1122C22C2×#55314yes—
1123C22#349214yes—
1124C22C23×#4111yescharacteristic
1125C22C23×#4111yescharacteristic
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×2−1+411yescharacteristic
1129C22H(7,𝔽2)11yescharacteristic
1130C222−1+611yescharacteristic
1131C4—28no—
1132C4—22no—
1133C4—22no—
1134C4—24no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—42no—
1146C4—44no—
1147C4C2×#55318yes—
1148C2—24no—
1149C2—24no—
1150C2—42no—
1151C2—42no—
1152C2—42no—
1153C2—84no—
1154C2C22×#55311yescharacteristic
1155C2C2×#349211yescharacteristic
1156C2#6285611yescharacteristic
1157C2#6291411yescharacteristic
1158C2#6294411yescharacteristic
1159C2#6298311yescharacteristic
1160C2#6299811yescharacteristic
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. #59856C2semidirect
2. #59826C2semidirect
3. #59677C2semidirect
4. #59440C2semidirect
5. #45373C2semidirect
6. #45371C2semidirect
7. #44977C2semidirect
8. #44975C2semidirect
9. #39549C2semidirect
10. #37941C2semidirect
11. #37890C2semidirect
12. #36157C2semidirect
13. #35557C2semidirect
14. #35516C2semidirect
15. #35223C2semidirect
16. #35223C2semidirect
17. #35159C2semidirect
18. #34737C2semidirect
19. #34274C2semidirect
20. #34202C2semidirect
21. #34178C2semidirect
22. C2×D4×C4⋊C4C2semidirect
23. C2×#2316C2semidirect
37. #2802C22semidirect
38. #2800C22semidirect
39. #2786C22semidirect
40. #2780C22semidirect
41. #2779C22semidirect
42. #2772C22semidirect
43. #2750C22semidirect
44. #2747C22semidirect
45. #2739C22semidirect
46. #2725C22semidirect
47. #2701C22semidirect
48. #2691C22semidirect
52. #2608C22semidirect
53. #2601C22semidirect
54. #2590C22semidirect
55. #2587C22semidirect
56. #2579C22semidirect
57. #2569C22semidirect
59. #2559C22semidirect
61. #2522C22semidirect
62. #2512C22semidirect
63. #2512C22semidirect
64. #2511C22semidirect
65. #2511C22semidirect
66. #2509C22semidirect
67. #2508C22semidirect
68. #2507C22semidirect
69. #2506C22semidirect
70. #2497C22semidirect
71. #2497C22semidirect
72. #2496C22semidirect
73. #2496C22semidirect
75. #2487C22semidirect
76. #2486C22semidirect
78. #2485C22semidirect
79. #2485C22semidirect
82. #2481C22semidirect
83. #2470C22semidirect
85. #2466C22semidirect
88. #2444C22semidirect
89. #2423C22semidirect
90. #2422C22semidirect
91. #2421C22semidirect
92. #2420C22semidirect
97. #2417C22semidirect
98. #2417C22semidirect
99. #2417C22semidirect
100. #2417C22semidirect
104. #2416C22semidirect
105. #2416C22semidirect
106. #2416C22semidirect
107. #2416C22semidirect
120. #2363C22semidirect
121. #2362C22semidirect
122. #2361C22semidirect
123. #2360C22semidirect
126. #2354C22semidirect
128. #2352C22semidirect
129. #2352C22semidirect
134. D4×C4⋊C4C22semidirect
135. #2345C22semidirect
136. #2345C22semidirect
137. #2344C22semidirect
138. #2344C22semidirect
140. #2324C22semidirect
141. #2323C22semidirect
148. #2316C22semidirect
149. #2316C22semidirect
153. C4×C22⋊Q8C22semidirect
157. C4×#121C22semidirect
161. C2×#389C22semidirect
162. C2×#389C22semidirect
1072. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
#598562
#598262
#596772
#594402
#453732
#453712
#449772
#449752
#395492
#379412
#378902
#361572
#355572
#355162
#352232
#351592
#347372
#342742
#342022
#341782
C2×D4×C4⋊C42
C2×#23162