Finite Group Databasebeta

← #8424428

Subgroups — #8424428

Order 512.

6836 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59816C211yesmaximal, characteristic, complemented
2#59303C211yesmaximal, characteristic, complemented
3#59220C211yesmaximal, characteristic, complemented
4#58997C214yesmaximal, complemented
5#55043C214yesmaximal, complemented
6#54926C214yesmaximal, complemented
7#53102C214yesmaximal, complemented
8#52957C214yesmaximal, complemented
9#52410C214yesmaximal, complemented
10#42606C214yesmaximal, complemented
11#42420C214yesmaximal, complemented
12#40594C214yesmaximal, complemented
13#39342C212yesmaximal, complemented
14#39191C212yesmaximal, complemented
15#38938C214yesmaximal, complemented
16#37650C214yesmaximal, complemented
17#37639C211yesmaximal, characteristic, complemented
18#37626C211yesmaximal, characteristic, complemented
19#37439C214yesmaximal, complemented
20#36182C211yesmaximal, characteristic, complemented
21D4×#121C212yesmaximal, complemented
22C2×#2537C211yesmaximal, characteristic, complemented
23#34681C212yesmaximal, complemented
24C2×#553C2212yescomplemented
25C2×D42C2214yescomplemented
26C2×D42C2214yescomplemented
27C2×D42C2214yescomplemented
28C2×D42C2212yescomplemented
29C2×#535C2214yescomplemented
30C2×#532C2212yescomplemented
31C2×#525C2214yescomplemented
32C22×#121C2214yescomplemented
33C22×#121C2214yescomplemented
34C22×C4×D4C2212yescomplemented
35#2859C2211yescharacteristic, complemented
36#2856C2211yescharacteristic
37#2856C2211yescharacteristic, complemented
38#2847C2214yescomplemented
39#2828C2218yescomplemented
40#2828C2214yescomplemented
41#2824C2218yescomplemented
42#2819C2214yescomplemented
43#2818C2214yescomplemented
44#2813C2218yescomplemented
45#2813C2218yescomplemented
46#2813C2214yescomplemented
47#2812C2218yescomplemented
48#2795C2214yescomplemented
49#2784C2218yescomplemented
50#2782C2214yescomplemented
51#2781C2218yescomplemented
52#2756C2218yescomplemented
53#2753C2218yescomplemented
54#2711C2218yescomplemented
55#2686C2218yescomplemented
56#2685C2218yescomplemented
57#2684C2218yescomplemented
58#2679C2214yescomplemented
59#2678C2218yescomplemented
60#2676C2218yescomplemented
61#2675C2218yescomplemented
62#2673C2218yescomplemented
63#2673C2218yescomplemented
64#2670C2218yescomplemented
65#2669C2218yescomplemented
66#2669C2218yescomplemented
67#2669C2218yescomplemented
68#2656C2214yescomplemented
69#2639C2218yescomplemented
70#2636C2214yescomplemented
71#2635C2214yescomplemented
72#2626C2218yescomplemented
73#2624C2214yescomplemented
74#2624C2214yescomplemented
75#2619C2214yescomplemented
76#2619C2214yescomplemented
77#2617C2218yescomplemented
78#2615C2214yescomplemented
79#2615C2214yescomplemented
80#2615C2214yescomplemented
81#2613C2214yescomplemented
82#2598C2214yescomplemented
83#2591C2214yescomplemented
84#2571C2211yescharacteristic, complemented
85#2566C2212yescomplemented
86#2563C2214yescomplemented
87#2541C2214yescomplemented
88#2541C2214yescomplemented
89#2541C2212yescomplemented
90#2537C2211yescharacteristic
91#2537C2214yescomplemented
92#2537C2212yescomplemented
93#2537C2211yescharacteristic, complemented
94#2537C2211yescharacteristic, complemented
95#2537C2212yescomplemented
96#2537C2214yescomplemented
97#2537C2214yescomplemented
98#2537C2214yescomplemented
99#2535C2214yescomplemented
100#2512C2214yescomplemented
101#2504C2212yescomplemented
102#2500C2212yescomplemented
103#2500C2214yescomplemented
104#2497C2214yescomplemented
105#2497C2214yescomplemented
106#2495C2214yescomplemented
107#2491C2214yescomplemented
108#2487C2214yescomplemented
109#2487C2214yescomplemented
110#2485C2214yescomplemented
111#2472C2218yescomplemented
112#2472C2214yescomplemented
113#2464C2214yescomplemented
114#2461C2214yescomplemented
115#2452C2212yescomplemented
116#2445C2212yescomplemented
117#2440C2212yescomplemented
118#2433C2212yes—
119#2433C2214yescomplemented
120#2433C2214yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2428C2214yescomplemented
124#2428C2212yescomplemented
125#2424C2218yescomplemented
126#2424C2218yescomplemented
127#2424C2218yescomplemented
128#2424C2214yescomplemented
129#2422C2214yescomplemented
130#2422C2212yescomplemented
131#2420C2214yescomplemented
132#2416C2214yescomplemented
133#2416C2214yescomplemented
134#2416C2214yescomplemented
135#2416C2212yescomplemented
136#2416C2214yescomplemented
137#2416C2214yescomplemented
138#2414C2214yescomplemented
139#2414C2214yescomplemented
140#2410C2218yescomplemented
141#2410C2218yescomplemented
142#2410C2218yescomplemented
143#2410C2218yescomplemented
144#2408C2214yescomplemented
145#2408C2212yescomplemented
146#2408C2214yescomplemented
147#2408C2214yescomplemented
148#2408C2214yescomplemented
149#2408C2214yescomplemented
150#2408C2214yescomplemented
151#2403C2218yescomplemented
152#2392C2214yescomplemented
153#2388C2214yescomplemented
154C2×#394C2214yescomplemented
155#2361C2214yescomplemented
156#2361C2214yescomplemented
157#2354C2212yescomplemented
158#2352C2214yescomplemented
159D4×C4⋊C4C2212yescomplemented
160D4×C22⋊C4C2214yescomplemented
161#2324C2214yescomplemented
162#2318C2214yescomplemented
163C4×#127C2212yescomplemented
164C4×#127C2211yescharacteristic, complemented
165C4×#121C2212yescomplemented
166C4×#121C2212yescomplemented
167C4×#120C2214yescomplemented
168#2293C2212yescomplemented
169#2285C2211yescharacteristic, complemented
170C2×#384C2211yescharacteristic, complemented
171C2×#380C2214yescomplemented
172C42×D4C2211yescharacteristic, complemented
173C22×#41C2314yes—
174C23×D4C2312yes—
175C23×D4C2314yes—
176C23×D4C2314yes—
177C23×D4C2314yes—
178C23×D4C2318yes—
179C23×D4C2314yes—
180C24×C4C2314yes—
181#553—48no—
182D42—48no—
183D42—416no—
184D42—416no—
185D42—416no—
186#535—416no—
187#532—48no—
188C2×C4⋊Q8C2312yes—
189C2×#127C2311yescharacteristic
190C2×#127C2312yes—
191C2×#127C2314yes—
192C2×#127C2314yes—
193C2×#127C2318yes—
194C2×#127C2312yes—
195C2×#126C2314yes—
196C2×#125C2312yes—
197C2×#124C2314yes—
198C2×#124C2318yes—
199#525—416no—
200C2×#123C2314yes—
201C2×#123C2314yes—
202C2×#123C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×#121—416no—
206C2×#121—416no—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2312yes—
216C2×#121C2314yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2318yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×#121C2318yes—
239C2×#120C2314yes—
240C2×#120C2318yes—
241C2×#120C2318yes—
242C2×#120C2318yes—
243C2×#120C2314yes—
244C2×#120C2318yes—
245C2×#120C2318yes—
246C2×#120C2314yes—
247C2×#120C2318yes—
248C2×#120C2318yes—
249C2×#120C2318yes—
250C2×C4×D4—48no—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×#117C2314yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2318yes—
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2318yes—
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#400C2318yes—
286#399C2314yes—
287#399C2314yes—
288#399C2318yes—
289#398C2314yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#396C2318yes—
296#396C2314yes—
297#396C2318yes—
298#396C2318yes—
299#396C2314yes—
300#396C2318yes—
301#395C2314yes—
302#394C2314yes—
303#394C2314yes—
304#394C2314yes—
305#394C2318yes—
306#394C2314yes—
307#394C2314yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2314yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#393C2318yes—
332#393C2318yes—
333#393C2314yes—
334#393C2318yes—
335#392C2318yes—
336#392C2314yes—
337#392C2314yes—
338#392C2318yes—
339#392C2318yes—
340#392C2318yes—
341#392C2318yes—
342#392C2318yes—
343#392C2318yes—
344#392C2318yes—
345#392C2314yes—
346#392C2314yes—
347#392C2314yes—
348#392C2318yes—
349#392C2314yes—
350#392C2318yes—
351#392C2318yes—
352#392C2314yes—
353#392C2314yes—
354#392C2314yes—
355#392C2314yes—
356#392C2318yes—
357#390C2312yes—
358#390C2312yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2314yes—
363#390C2318yes—
364#390C2312yes—
365#390C2312yes—
366#390C2318yes—
367#390C2318yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#387C2318yes—
397#387C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2314yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2314yes—
427#383C2314yes—
428#382C2314yes—
429#382C2312yes—
430#382C2314yes—
431#382C2312yes—
432#381C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2312yes—
439#380C2314yes—
440#380C2314yes—
441#380C2312yes—
442#380C2314yes—
443#380C2314yes—
444#380C2318yes—
445#380C2314yes—
446#380C2314yes—
447#380C2318yes—
448#379C2318yes—
449#379C2318yes—
450#379C2318yes—
451#379C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C2×#95C2314yes—
466C43C2311yescharacteristic
467C25C2414yes—
468C25C2418yes—
469C2×#41—48no—
470C2×#41—48no—
471C2×#41—48no—
472C22×Q8C2414yes—
473C22×D4—28no—
474C22×D4—216no—
475C22×D4—28no—
476C22×D4—44no—
477C22×D4—48no—
478C22×D4—48no—
479C22×D4—48no—
480C22×D4—48no—
481C22×D4—48no—
482C22×D4—48no—
483C22×D4—48no—
484C22×D4—416no—
485C22×D4—416no—
486C22×D4—416no—
487C22×D4—416no—
488C22×D4—416no—
489C22×D4C2411yescharacteristic
490C22×D4C2412yes—
491C22×D4C2414yes—
492C22×D4C2414yes—
493C22×D4C2412yes—
494C22×D4C2414yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2412yes—
499C22×D4C2414yes—
500C22×D4C2412yes—
501C22×D4C2414yes—
502C22×D4C2414yes—
503C22×D4C2418yes—
504C22×D4C2418yes—
505C22×D4C2418yes—
506C22×D4C2414yes—
507C22×D4C2414yes—
508C22×D4C2418yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C22×D4C2418yes—
512C22×D4C2418yes—
513C22×D4C2414yes—
514C22×D4C2414yes—
515C23×C4—216no—
516C23×C4—48no—
517C23×C4—48no—
518C23×C4C2414yes—
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2412yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2418yes—
531C4⋊Q8—44no—
532#127—28no—
533#127—24no—
534#127—44no—
535#127—48no—
536#127—48no—
537#127—416no—
538#126—48no—
539#125—44no—
540#124—48no—
541#124—416no—
542#123—48no—
543#123—48no—
544#123—48no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547#121—216no—
548#121—216no—
549#121—28no—
550#121—28no—
551#121—216no—
552#121—416no—
553#121—48no—
554#121—48no—
555#121—48no—
556#121—44no—
557#121—416no—
558#121—416no—
559#121—416no—
560#121—416no—
561#121—416no—
562#121—48no—
563#121—48no—
564#121—48no—
565#121—48no—
566#121—44no—
567#121—44no—
568#121—48no—
569#121—48no—
570#121—48no—
571#121—48no—
572#121—48no—
573#121—48no—
574#121—416no—
575#121—48no—
576#121—48no—
577#121—48no—
578#121—44no—
579#120—216no—
580#120—416no—
581#120—416no—
582#120—416no—
583#120—48no—
584#120—48no—
585#120—416no—
586#120—416no—
587#120—416no—
588#120—416no—
589#120—416no—
590C4×D4—28no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—24no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—44no—
609#117—48no—
610#117—44no—
611#117—48no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C22⋊C4—48no—
644C2×C22⋊C4—416no—
645C2×C22⋊C4—416no—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2411yescharacteristic
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2411yescharacteristic
693C2×C42—24no—
694C2×C42—24no—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2418yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728C24—28no—
729C24—28no—
730C24—28no—
731C24—28no—
732C24—216no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24—48no—
737C24—48no—
738C24—48no—
739C24—48no—
740C24—48no—
741C24—48no—
742C24C2514yes—
743C24C2514yes—
744C24C2514yes—
745C24C2511yescharacteristic
746C24C2514yes—
747C24C2511yescharacteristic
748#41—832no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×D4—24no—
753C2×D4—28no—
754C2×D4—22no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—216no—
758C2×D4—216no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—216no—
765C2×D4—216no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—24no—
774C2×D4—28no—
775C2×D4—24no—
776C2×D4—28no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—28no—
780C2×D4—24no—
781C2×D4—432no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—42no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—48no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—42no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—44no—
823C2×D4—48no—
824C2×D4—832no—
825C2×D4—832no—
826C2×D4—832no—
827C2×D4—864no—
828C2×D4—832no—
829C2×D4H(5,𝔽2)18yes—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—22no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—22no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—24no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—832no—
867C22×C4H(5,𝔽2)18yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2511yescharacteristic
878C22×C4C2514yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2512yes—
884C22×C4C2512yes—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—42no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—28no—
915C22⋊C4—24no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—216no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—24no—
925C22⋊C4—22no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4H(5,𝔽2)14yes—
959C42—22no—
960C42—24no—
961C42—24no—
962C42—22no—
963C42—24no—
964C42—28no—
965C42—28no—
966C42—22no—
967C42—24no—
968C42—41no—
969C42—48no—
970C42H(5,𝔽2)14yes—
971C23—21no—
972C23—22no—
973C23—21no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—21no—
981C23—24no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—28no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—28no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—21no—
998C23—24no—
999C23—22no—
1000C23—24no—
1001C23—24no—
1002C23—21no—
1003C23—24no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—88no—
1009C23—88no—
1010C23—88no—
1011C23—816no—
1012C23—816no—
1013C23—816no—
1014C23—816no—
1015C23—816no—
1016C23—168no—
1017C23—168no—
1018C23C2×H(5,𝔽2)18yes—
1019C23C2×H(5,𝔽2)14yes—
1020C23C2×H(5,𝔽2)12yes—
1021C23C2611yescharacteristic
1022Q8—88no—
1023D4—216no—
1024D4—416no—
1025D4—416no—
1026D4—416no—
1027D4—44no—
1028D4—416no—
1029D4—416no—
1030D4—48no—
1031D4—48no—
1032D4—416no—
1033D4—84no—
1034D4—88no—
1035D4—88no—
1036D4—88no—
1037D4—816no—
1038D4—816no—
1039D4—816no—
1040D4—88no—
1041D4—88no—
1042D4—816no—
1043D4—816no—
1044D4—88no—
1045D4—88no—
1046D4—88no—
1047D4—164no—
1048D4—168no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—216no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—21no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—24no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—416no—
1092C2×C4—416no—
1093C2×C4—416no—
1094C2×C4—48no—
1095C2×C4—88no—
1096C2×C4—88no—
1097C2×C4—88no—
1098C2×C4—88no—
1099C2×C4—88no—
1100C2×C4—816no—
1101C2×C4C2×H(5,𝔽2)12yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)14yes—
1105C2×C4C2×H(5,𝔽2)14yes—
1106C2×C4C2×H(5,𝔽2)14yes—
1107C2×C4C2×H(5,𝔽2)14yes—
1108C22—24no—
1109C22—22no—
1110C22—22no—
1111C22—24no—
1112C22—28no—
1113C22—28no—
1114C22—28no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22—44no—
1119C22—44no—
1120C22—42no—
1121C22—44no—
1122C22—44no—
1123C22—48no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—41no—
1129C22—44no—
1130C22—44no—
1131C22—41no—
1132C22—44no—
1133C22—41no—
1134C22—42no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—48no—
1141C22—44no—
1142C22—44no—
1143C22—832no—
1144C22—1632no—
1145C22#354914yes—
1146C22C22×H(5,𝔽2)11yescharacteristic
1147C22C22×H(5,𝔽2)12yes—
1148C22C22×H(5,𝔽2)12yes—
1149C22C22×H(5,𝔽2)11yescharacteristic
1150C222−1+611yescharacteristic
1151C4—24no—
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—41no—
1164C4—41no—
1165C4—42no—
1166C4—44no—
1167C4#353718yes—
1168C2—24no—
1169C2—48no—
1170C2—81no—
1171C2—84no—
1172C2—84no—
1173C2—84no—
1174C2C2×#353712yes—
1175C2C2×#354911yescharacteristic
1176C2#6291411yescharacteristic
1177C2#6291412yes—
1178C2#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. #59303C2semidirect
3. #59220C2semidirect
4. #58997C2semidirect
5. #55043C2semidirect
6. #54926C2semidirect
7. #53102C2semidirect
8. #52957C2semidirect
9. #52410C2semidirect
10. #42606C2semidirect
11. #42420C2semidirect
12. #40594C2semidirect
13. #39342C2semidirect
14. #39191C2semidirect
15. #38938C2semidirect
16. #37650C2semidirect
17. #37639C2semidirect
18. #37626C2semidirect
19. #37439C2semidirect
20. #36182C2semidirect
21. D4×#121C2semidirect
22. C2×#2537C2semidirect
23. #34681C2semidirect
24. C2×#553C22semidirect
25. C2×D42C22semidirect
26. C2×D42C22semidirect
27. C2×D42C22semidirect
28. C2×D42C22semidirect
29. C2×#535C22semidirect
30. C2×#532C22semidirect
31. C2×#525C22semidirect
32. C22×#121C22semidirect
33. C22×#121C22semidirect
34. C22×C4×D4C22semidirect
35. #2859C22semidirect
37. #2856C22semidirect
38. #2847C22semidirect
39. #2828C22semidirect
40. #2828C22semidirect
41. #2824C22semidirect
42. #2819C22semidirect
43. #2818C22semidirect
44. #2813C22semidirect
45. #2813C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2795C22semidirect
49. #2784C22semidirect
50. #2782C22semidirect
51. #2781C22semidirect
52. #2756C22semidirect
53. #2753C22semidirect
54. #2711C22semidirect
55. #2686C22semidirect
56. #2685C22semidirect
57. #2684C22semidirect
58. #2679C22semidirect
59. #2678C22semidirect
60. #2676C22semidirect
61. #2675C22semidirect
62. #2673C22semidirect
63. #2673C22semidirect
64. #2670C22semidirect
65. #2669C22semidirect
66. #2669C22semidirect
67. #2669C22semidirect
68. #2656C22semidirect
69. #2639C22semidirect
70. #2636C22semidirect
71. #2635C22semidirect
72. #2626C22semidirect
73. #2624C22semidirect
74. #2624C22semidirect
75. #2619C22semidirect
76. #2619C22semidirect
77. #2617C22semidirect
78. #2615C22semidirect
79. #2615C22semidirect
80. #2615C22semidirect
81. #2613C22semidirect
82. #2598C22semidirect
83. #2591C22semidirect
84. #2571C22semidirect
85. #2566C22semidirect
86. #2563C22semidirect
87. #2541C22semidirect
88. #2541C22semidirect
89. #2541C22semidirect
91. #2537C22semidirect
92. #2537C22semidirect
93. #2537C22semidirect
94. #2537C22semidirect
95. #2537C22semidirect
96. #2537C22semidirect
97. #2537C22semidirect
98. #2537C22semidirect
99. #2535C22semidirect
100. #2512C22semidirect
101. #2504C22semidirect
102. #2500C22semidirect
103. #2500C22semidirect
104. #2497C22semidirect
105. #2497C22semidirect
106. #2495C22semidirect
107. #2491C22semidirect
108. #2487C22semidirect
109. #2487C22semidirect
110. #2485C22semidirect
111. #2472C22semidirect
112. #2472C22semidirect
113. #2464C22semidirect
114. #2461C22semidirect
115. #2452C22semidirect
116. #2445C22semidirect
117. #2440C22semidirect
119. #2433C22semidirect
120. #2433C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2424C22semidirect
126. #2424C22semidirect
127. #2424C22semidirect
128. #2424C22semidirect
129. #2422C22semidirect
130. #2422C22semidirect
131. #2420C22semidirect
132. #2416C22semidirect
133. #2416C22semidirect
134. #2416C22semidirect
135. #2416C22semidirect
136. #2416C22semidirect
137. #2416C22semidirect
138. #2414C22semidirect
139. #2414C22semidirect
140. #2410C22semidirect
141. #2410C22semidirect
142. #2410C22semidirect
143. #2410C22semidirect
144. #2408C22semidirect
145. #2408C22semidirect
146. #2408C22semidirect
147. #2408C22semidirect
148. #2408C22semidirect
149. #2408C22semidirect
150. #2408C22semidirect
151. #2403C22semidirect
152. #2392C22semidirect
153. #2388C22semidirect
154. C2×#394C22semidirect
155. #2361C22semidirect
156. #2361C22semidirect
157. #2354C22semidirect
158. #2352C22semidirect
159. D4×C4⋊C4C22semidirect
160. D4×C22⋊C4C22semidirect
161. #2324C22semidirect
162. #2318C22semidirect
163. C4×#127C22semidirect
164. C4×#127C22semidirect
165. C4×#121C22semidirect
166. C4×#121C22semidirect
167. C4×#120C22semidirect
168. #2293C22semidirect
169. #2285C22semidirect
170. C2×#384C22semidirect
171. C2×#380C22semidirect
172. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598162
#593032
#592202
#589972
#550432
#549262
#531022
#529572
#524102
#426062
#424202
#405942
#393422
#391912
#389382
#376502
#376392
#376262
#374392
#361822
D4×#1212
C2×#25372
#346812