Finite Group Databasebeta

← #7987579

Subgroups — #7987579

Order 512.

8281 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3549C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59659C211yesmaximal, characteristic, complemented
4#59095C214yesmaximal, complemented
5#59084C211yesmaximal, characteristic, complemented
6#59056C211yesmaximal, characteristic, complemented
7#51896C214yesmaximal, complemented
8#51783C214yesmaximal, complemented
9#46225C214yesmaximal, complemented
10#44927C214yesmaximal, complemented
11#44886C214yesmaximal, complemented
12#42971C214yesmaximal, complemented
13#42963C214yesmaximal, complemented
14#39361C212yesmaximal, complemented
15#39341C212yesmaximal, complemented
16#37782C214yesmaximal, complemented
17#37681C214yesmaximal, complemented
18#36258C212yesmaximal, complemented
19#36231C214yesmaximal, complemented
20#36128C211yesmaximal, characteristic, complemented
21#35256C214yesmaximal, complemented
22#34715C212yesmaximal, complemented
23#34485C211yesmaximal, characteristic, complemented
24#3549—216no—
25C2×H(3,𝔽4)C2214yes—
26#3483—216no—
27C2×Q82C2211yescharacteristic, complemented
28C2×#555C2211yescharacteristic
29C2×#555C2214yes—
30C2×#555C2211yescharacteristic
31C2×#555C2214yescomplemented
32C2×#555C2214yescomplemented
33C2×#550C2214yescomplemented
34C2×#550C2212yescomplemented
35C2×#550C2212yescomplemented
36C2×#546C2214yescomplemented
37C2×#546C2214yescomplemented
38C2×D42C2214yes—
39C2×D42C2212yes—
40C2×#537C2214yescomplemented
41C2×#535C2214yes—
42C2×#535C2214yes—
43C2×#535C2214yes—
44C2×#535C2214yescomplemented
45C2×#532C2211yescharacteristic
46C2×#532C2212yes—
47C2×#532C2211yescharacteristic, complemented
48C2×#532C2214yescomplemented
49C2×#532C2214yescomplemented
50C2×C4×#41C2214yescomplemented
51C2×C4×#41C2212yescomplemented
52#2867C2211yescharacteristic
53#2856C2211yescharacteristic
54#2856C2211yescharacteristic, complemented
55#2856C2214yescomplemented
56#2854C2214yescomplemented
57#2850C2218yescomplemented
58#2819C2218yescomplemented
59#2733C2214yescomplemented
60#2731C2214yescomplemented
61#2731C2214yescomplemented
62#2712C2218yescomplemented
63#2678C2218yescomplemented
64#2676C2218yescomplemented
65#2676C2218yescomplemented
66#2676C2218yescomplemented
67#2675C2218yescomplemented
68#2675C2218yescomplemented
69#2673C2218yescomplemented
70#2670C2218yescomplemented
71#2670C2218yescomplemented
72#2669C2218yescomplemented
73#2669C2218yescomplemented
74#2669C2218yescomplemented
75#2669C2218yescomplemented
76#2669C2218yescomplemented
77#2657C2214yescomplemented
78#2620C2214yescomplemented
79#2620C2218yescomplemented
80#2619C2214yescomplemented
81#2619C2218yescomplemented
82#2615C2214yescomplemented
83#2610C2218yescomplemented
84#2609C2218yescomplemented
85#2548C2212yes—
86#2548C2212yescomplemented
87#2545C2214yescomplemented
88#2541C2214yes—
89#2541C2214yescomplemented
90#2541C2214yescomplemented
91#2541C2214yescomplemented
92#2541C2212yescomplemented
93#2538C2212yescomplemented
94#2491C2214yescomplemented
95#2491C2214yescomplemented
96#2476C2214yescomplemented
97#2474C2214yescomplemented
98#2464C2218yescomplemented
99#2461C2218yescomplemented
100#2459C2218yescomplemented
101#2459C2214yescomplemented
102#2456C2214yescomplemented
103#2456C2218yescomplemented
104#2452C2214yescomplemented
105#2452C2214yescomplemented
106#2451C2212yescomplemented
107#2445C2212yes—
108#2439C2214yescomplemented
109#2439C2212yescomplemented
110#2433C2214yescomplemented
111#2433C2214yescomplemented
112#2433C2214yescomplemented
113#2433C2214yescomplemented
114#2432C2214yescomplemented
115#2431C2212yes—
116#2431C2212yescomplemented
117#2431C2212yescomplemented
118#2431C2214yescomplemented
119#2431C2214yescomplemented
120#2431C2214yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2428C2214yescomplemented
124#2428C2214yescomplemented
125#2428C2214yescomplemented
126#2428C2214yescomplemented
127#2428C2214yescomplemented
128#2426C2214yescomplemented
129#2426C2214yescomplemented
130#2426C2214yescomplemented
131#2426C2212yescomplemented
132#2424C2218yescomplemented
133#2424C2218yescomplemented
134#2424C2218yescomplemented
135#2424C2218yescomplemented
136#2424C2218yescomplemented
137#2424C2218yescomplemented
138#2420C2212yescomplemented
139#2416C2214yescomplemented
140#2416C2214yescomplemented
141#2414C2214yescomplemented
142#2414C2212yescomplemented
143#2414C2214yescomplemented
144#2411C2218yescomplemented
145#2410C2218yescomplemented
146#2408C2214yescomplemented
147#2407C2212yescomplemented
148#2407C2214yescomplemented
149#2404C2218yescomplemented
150#2392C2214yescomplemented
151#2388C2214yescomplemented
152#2379C2214yescomplemented
153#2369C2211yescharacteristic, complemented
154#2367C2214yescomplemented
155#2366C2214yescomplemented
156#2363C2214yescomplemented
157#2362C2214yescomplemented
158#2361C2214yescomplemented
159D4×C4⋊C4C2212yescomplemented
160#2346C2214yescomplemented
161D4×C22⋊C4C2214yescomplemented
162#2326C2214yescomplemented
163#2324C2214yescomplemented
164#2317C2214yescomplemented
165C4×C4⋊Q8C2211yescharacteristic, complemented
166C4×#124C2212yescomplemented
167C4×C22⋊Q8C2212yescomplemented
168C4×#123C2214yescomplemented
169C4×#121C2212yescomplemented
170#2297C2214yescomplemented
171#2293C2212yescomplemented
172C2×#390C2214yescomplemented
173#2290C2214yescomplemented
174C42×D4C2211yescharacteristic, complemented
175C22×#41C2314yes—
176C22×#41C2312yes—
177C22×#41C2314yes—
178C22×#41C2314yes—
179C22×#41C2312yes—
180C22×#41C2312yes—
181C23×D4C2314yes—
182C23×D4C2314yes—
183C23×D4C2314yes—
184H(3,𝔽4)—232no—
185Q82—28no—
186#555—28no—
187#555—232no—
188#555—232no—
189#555—232no—
190#555D4116yescomplemented
191#550—232no—
192#550—216no—
193#550—48no—
194#546—416no—
195#546—416no—
196D42—232no—
197D42—216no—
198#537—416no—
199#535—232no—
200#535—232no—
201#535—232no—
202#535—416no—
203#532—28no—
204#532—28no—
205#532—232no—
206#532—232no—
207#532—216no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2314yes—
215C2×#127C2314yes—
216C2×#127C2314yes—
217C2×#127C2312yes—
218C2×#127C2314yes—
219C2×#127C2314yes—
220C2×#127C2314yes—
221C2×#127C2312yes—
222C2×#127C2314yes—
223C2×#127C2314yes—
224C2×#127C2312yes—
225C2×#127C2314yes—
226C2×#124C2314yes—
227C2×#124C2318yes—
228C2×#124C2314yes—
229C2×#124C2318yes—
230C2×#124C2314yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#123C2314yes—
240C2×#123C2318yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2318yes—
257C2×#121C2314yes—
258C2×#121C2318yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2318yes—
263C2×#121C2318yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2318yes—
271C2×#121C2318yes—
272C2×#121C2318yes—
273C2×#121C2314yes—
274C2×#121C2318yes—
275C2×#121C2314yes—
276C2×#120C2318yes—
277C2×#120C2318yes—
278C2×#120C2318yes—
279C2×#120C2318yes—
280C2×#120C2318yes—
281C2×#120C2318yes—
282C2×#120C2318yes—
283C2×#120C2318yes—
284C2×#120C2318yes—
285C4×#41—216no—
286C4×#41—232no—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2318yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2318yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×#117C2314yes—
309C2×#117C2318yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C22⋊C4C2318yes—
317C22×C22⋊C4C2318yes—
318C22×C42C2314yes—
319C22×C42C2314yes—
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322#398C2314yes—
323#397C2314yes—
324#396C2318yes—
325#396C2318yes—
326#396C2314yes—
327#396C2314yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#395C2314yes—
332#394C2314yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2314yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2318yes—
348#394C2318yes—
349#393C2314yes—
350#393C2318yes—
351#393C2318yes—
352#393C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2314yes—
366#392C2314yes—
367#392C2314yes—
368#392C2314yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#392C2318yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2314yes—
378#391C2314yes—
379#391C2312yes—
380#390C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2318yes—
385#390C2314yes—
386#390C2312yes—
387#390C2314yes—
388#390C2314yes—
389#390C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2318yes—
393#390C2318yes—
394#390C2312yes—
395#390C2314yes—
396#390C2314yes—
397#390C2318yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2314yes—
402#390C2312yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#388C2318yes—
412#388C2314yes—
413#388C2318yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#387C2314yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#386C2318yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2314yes—
453#385C2314yes—
454#384C2311yescharacteristic
455#384C2314yes—
456#382C2318yes—
457#382C2312yes—
458#381C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#379C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2314yes—
483C43C2311yescharacteristic
484C25C2418yes—
485C2×#41—28no—
486C2×#41—28no—
487C2×#41—216no—
488C2×#41—28no—
489C2×#41—28no—
490C2×#41—216no—
491C2×#41—216no—
492C2×#41—216no—
493C2×#41—48no—
494C2×#41—48no—
495C2×#41—44no—
496C2×#41—44no—
497C2×#41—48no—
498C2×#41—48no—
499C2×#41—44no—
500C2×#41—82no—
501C2×#41—84no—
502C2×#41—82no—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2414yes—
506C22×Q8C2412yes—
507C22×D4—216no—
508C22×D4—216no—
509C22×D4—216no—
510C22×D4—48no—
511C22×D4—48no—
512C22×D4—48no—
513C22×D4—48no—
514C22×D4—48no—
515C22×D4—84no—
516C22×D4C2414yes—
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2414yes—
520C22×D4C2418yes—
521C22×D4C2414yes—
522C22×D4C2412yes—
523C22×D4C2411yescharacteristic
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2412yes—
527C22×D4C2418yes—
528C22×D4C2418yes—
529C22×D4C2414yes—
530C22×D4C2414yes—
531C22×D4C2418yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C22×D4C2412yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2418yes—
539C22×D4C2414yes—
540C22×D4C2418yes—
541C22×D4C2418yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2418yes—
551C23×C4C2414yes—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2414yes—
555C23×C4C2418yes—
556C4⋊Q8—216no—
557C4⋊Q8—28no—
558C4⋊Q8—216no—
559C4⋊Q8C2×D418yes—
560#127—28no—
561#127—216no—
562#127—216no—
563#127—216no—
564#127—24no—
565#127—24no—
566#127—216no—
567#127—48no—
568#127—48no—
569#127—48no—
570#127—48no—
571#127—44no—
572#127—84no—
573#127—82no—
574#124—28no—
575#124—28no—
576#124—216no—
577#124—28no—
578#124—216no—
579#124—232no—
580#124—216no—
581#124—232no—
582#124—216no—
583#124—232no—
584#124—48no—
585#124—84no—
586#124C2×D4132yes—
587#123—216no—
588#123—416no—
589C22⋊Q8—28no—
590C22⋊Q8—216no—
591C22⋊Q8—416no—
592C22⋊Q8—48no—
593#121—28no—
594#121—232no—
595#121—216no—
596#121—216no—
597#121—28no—
598#121—216no—
599#121—216no—
600#121—216no—
601#121—216no—
602#121—216no—
603#121—232no—
604#121—232no—
605#121—232no—
606#121—416no—
607#121—416no—
608#121—416no—
609#121—48no—
610#121—44no—
611#121—48no—
612#121—44no—
613#121—48no—
614#121—416no—
615#121—416no—
616#121—416no—
617#121—416no—
618#121—44no—
619#121—48no—
620#121—48no—
621#121—48no—
622#121—48no—
623#121C2×D4132yes—
624#120—232no—
625#120—232no—
626#120—232no—
627#120—232no—
628#120—416no—
629#120—416no—
630#120—416no—
631#120—416no—
632#120—88no—
633C4×Q8—28no—
634C4×Q8—216no—
635C4×Q8—28no—
636C4×Q8—44no—
637C4×D4—28no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—216no—
641C4×D4—216no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—24no—
645C4×D4—216no—
646C4×D4—232no—
647C4×D4—232no—
648C4×D4—28no—
649C4×D4—48no—
650C4×D4—48no—
651C4×D4—44no—
652C4×D4—48no—
653C4×D4C2×D4116yes—
654#117—28no—
655#117—216no—
656#117—216no—
657#117—232no—
658#117—216no—
659#117—48no—
660#117C2×D4132yes—
661C2×C4⋊C4—48no—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C22⋊C4—416no—
686C2×C22⋊C4—416no—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2411yescharacteristic
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C42—216no—
731C2×C42—24no—
732C2×C42—216no—
733C2×C42—24no—
734C2×C42C2411yescharacteristic
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2412yes—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2411yescharacteristic
746C2×C42C2412yes—
747C2×C42C2411yescharacteristic
748C2×C42C2414yes—
749C2×C42C2411yescharacteristic
750C2×C42C2414yes—
751C2×C42C2411yescharacteristic
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2412yes—
756#95C2414yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772C24—216no—
773C24—48no—
774C24—48no—
775C24—48no—
776C24—48no—
777C24—48no—
778C24—48no—
779C24C2514yes—
780C24C2514yes—
781C24C2511yescharacteristic
782C24C2514yes—
783C24C2511yescharacteristic
784C24C2514yes—
785#41—464no—
786#41—432no—
787#41—832no—
788#41—832no—
789#41—816no—
790#41—816no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—28no—
794C2×Q8—24no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8C22×D418yes—
802C2×Q8H(5,𝔽2)18yes—
803C2×D4—28no—
804C2×D4—216no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—216no—
808C2×D4—28no—
809C2×D4—216no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—216no—
815C2×D4—28no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—216no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—24no—
828C2×D4—28no—
829C2×D4—24no—
830C2×D4—28no—
831C2×D4—24no—
832C2×D4—28no—
833C2×D4—44no—
834C2×D4—42no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—48no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—48no—
847C2×D4—44no—
848C2×D4—42no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—48no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—48no—
869C2×D4—48no—
870C2×D4—48no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—48no—
879C2×D4—48no—
880C2×D4—832no—
881C2×D4—832no—
882C2×D4—832no—
883C2×D4C22×D418yes—
884C2×D4C22×D4116yes—
885C22×C4—28no—
886C22×C4—28no—
887C22×C4—28no—
888C22×C4—28no—
889C22×C4—216no—
890C22×C4—24no—
891C22×C4—28no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—28no—
898C22×C4—28no—
899C22×C4—28no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—28no—
905C22×C4—216no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—28no—
910C22×C4—44no—
911C22×C4—48no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—44no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4C22×D4116yes—
921C22×C4C2512yes—
922C22×C4C2514yes—
923C22×C4C2512yes—
924C22×C4C2514yes—
925C22×C4C2511yescharacteristic
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2514yes—
931C22×C4C2511yescharacteristic
932C22×C4C2514yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2514yes—
937C22×C4C2512yes—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—216no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—216no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—48no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—42no—
957C4⋊C4—44no—
958C4⋊C4C22×D418yes—
959C4⋊C4C22×D4116yes—
960C4⋊C4H(5,𝔽2)14yes—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—216no—
964C22⋊C4—28no—
965C22⋊C4—216no—
966C22⋊C4—216no—
967C22⋊C4—216no—
968C22⋊C4—28no—
969C22⋊C4—216no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—216no—
974C22⋊C4—216no—
975C22⋊C4—28no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—216no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—44no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—48no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4C22×D4116yes—
1003C22⋊C4C22×D4132yes—
1004C42—28no—
1005C42—24no—
1006C42—22no—
1007C42—28no—
1008C42—24no—
1009C42—28no—
1010C42—28no—
1011C42—22no—
1012C42—28no—
1013C42—24no—
1014C42—28no—
1015C42—28no—
1016C42—22no—
1017C42—24no—
1018C42—44no—
1019C42—41no—
1020C42C22×D414yes—
1021C42C22×D4116yes—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—21no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—21no—
1033C23—24no—
1034C23—24no—
1035C23—28no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—21no—
1040C23—21no—
1041C23—24no—
1042C23—22no—
1043C23—28no—
1044C23—22no—
1045C23—22no—
1046C23—28no—
1047C23—24no—
1048C23—24no—
1049C23—28no—
1050C23—21no—
1051C23—24no—
1052C23—24no—
1053C23—21no—
1054C23—24no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—168no—
1061C23—168no—
1062C23C23×D418yes—
1063C23C2611yescharacteristic
1064Q8—216no—
1065Q8—48no—
1066Q8—88no—
1067Q8—88no—
1068D4—216no—
1069D4—416no—
1070D4—416no—
1071D4—432no—
1072D4—416no—
1073D4—44no—
1074D4—416no—
1075D4—48no—
1076D4—416no—
1077D4—88no—
1078D4—88no—
1079D4—816no—
1080D4—88no—
1081D4—88no—
1082D4—84no—
1083D4—84no—
1084D4—88no—
1085D4—816no—
1086D4—816no—
1087D4—88no—
1088D4—88no—
1089D4—88no—
1090D4—164no—
1091D4—164no—
1092D4—168no—
1093D4—164no—
1094D4—168no—
1095D4—168no—
1096C2×C4—21no—
1097C2×C4—24no—
1098C2×C4—21no—
1099C2×C4—24no—
1100C2×C4—21no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—232no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—28no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—416no—
1136C2×C4—432no—
1137C2×C4—416no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—416no—
1143C2×C4—48no—
1144C2×C4—48no—
1145C2×C4—168no—
1146C2×C4C23×D418yes—
1147C2×C4C23×D418yes—
1148C2×C4C23×D412yes—
1149C2×C4C23×D414yes—
1150C2×C4C2×H(5,𝔽2)12yes—
1151C2×C4C2×H(5,𝔽2)18yes—
1152C2×C4C2×H(5,𝔽2)12yes—
1153C2×C4C2×H(5,𝔽2)12yes—
1154C2×C4C2×H(5,𝔽2)14yes—
1155C2×C4#58514yes—
1156C22—28no—
1157C22—28no—
1158C22—28no—
1159C22—44no—
1160C22—44no—
1161C22—44no—
1162C22—44no—
1163C22—41no—
1164C22—41no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—41no—
1169C22—41no—
1170C22—44no—
1171C22—44no—
1172C22—44no—
1173C22—41no—
1174C22—41no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—48no—
1179C22—42no—
1180C22—42no—
1181C22—44no—
1182C22—44no—
1183C22—48no—
1184C22—42no—
1185C22—44no—
1186C22—48no—
1187C22—44no—
1188C22—48no—
1189C22—42no—
1190C22—1632no—
1191C22C24×D411yescharacteristic
1192C22C22×H(5,𝔽2)11yescharacteristic
1193C22C22×H(5,𝔽2)12yes—
1194C22C2×#58512yes—
1195C22H(7,𝔽2)11yescharacteristic
1196C4—22no—
1197C4—22no—
1198C4—28no—
1199C4—22no—
1200C4—22no—
1201C4—28no—
1202C4—28no—
1203C4—44no—
1204C4—44no—
1205C4—44no—
1206C4—41no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—44no—
1211C4—42no—
1212C4#348818yes—
1213C2—48no—
1214C2—81no—
1215C2—81no—
1216C2—84no—
1217C2—84no—
1218C2—84no—
1219C2#6275911yescharacteristic
1220C2C2×#348812yes—
1221C2#6292312yes—
1222C2D4×H(5,𝔽2)11yescharacteristic
1223C2#6304011yescharacteristic
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. C2×#3549C2semidirect
2. C2×#3483C2semidirect
3. #59659C2semidirect
4. #59095C2semidirect
5. #59084C2semidirect
6. #59056C2semidirect
7. #51896C2semidirect
8. #51783C2semidirect
9. #46225C2semidirect
10. #44927C2semidirect
11. #44886C2semidirect
12. #42971C2semidirect
13. #42963C2semidirect
14. #39361C2semidirect
15. #39341C2semidirect
16. #37782C2semidirect
17. #37681C2semidirect
18. #36258C2semidirect
19. #36231C2semidirect
20. #36128C2semidirect
21. #35256C2semidirect
22. #34715C2semidirect
23. #34485C2semidirect
27. C2×Q82C22semidirect
31. C2×#555C22semidirect
32. C2×#555C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
35. C2×#550C22semidirect
36. C2×#546C22semidirect
37. C2×#546C22semidirect
40. C2×#537C22semidirect
44. C2×#535C22semidirect
47. C2×#532C22semidirect
48. C2×#532C22semidirect
49. C2×#532C22semidirect
50. C2×C4×#41C22semidirect
51. C2×C4×#41C22semidirect
54. #2856C22semidirect
55. #2856C22semidirect
56. #2854C22semidirect
57. #2850C22semidirect
58. #2819C22semidirect
59. #2733C22semidirect
60. #2731C22semidirect
61. #2731C22semidirect
62. #2712C22semidirect
63. #2678C22semidirect
64. #2676C22semidirect
65. #2676C22semidirect
66. #2676C22semidirect
67. #2675C22semidirect
68. #2675C22semidirect
69. #2673C22semidirect
70. #2670C22semidirect
71. #2670C22semidirect
72. #2669C22semidirect
73. #2669C22semidirect
74. #2669C22semidirect
75. #2669C22semidirect
76. #2669C22semidirect
77. #2657C22semidirect
78. #2620C22semidirect
79. #2620C22semidirect
80. #2619C22semidirect
81. #2619C22semidirect
82. #2615C22semidirect
83. #2610C22semidirect
84. #2609C22semidirect
86. #2548C22semidirect
87. #2545C22semidirect
89. #2541C22semidirect
90. #2541C22semidirect
91. #2541C22semidirect
92. #2541C22semidirect
93. #2538C22semidirect
94. #2491C22semidirect
95. #2491C22semidirect
96. #2476C22semidirect
97. #2474C22semidirect
98. #2464C22semidirect
99. #2461C22semidirect
100. #2459C22semidirect
101. #2459C22semidirect
102. #2456C22semidirect
103. #2456C22semidirect
104. #2452C22semidirect
105. #2452C22semidirect
106. #2451C22semidirect
108. #2439C22semidirect
109. #2439C22semidirect
110. #2433C22semidirect
111. #2433C22semidirect
112. #2433C22semidirect
113. #2433C22semidirect
114. #2432C22semidirect
116. #2431C22semidirect
117. #2431C22semidirect
118. #2431C22semidirect
119. #2431C22semidirect
120. #2431C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2428C22semidirect
128. #2426C22semidirect
129. #2426C22semidirect
130. #2426C22semidirect
131. #2426C22semidirect
132. #2424C22semidirect
133. #2424C22semidirect
134. #2424C22semidirect
135. #2424C22semidirect
136. #2424C22semidirect
137. #2424C22semidirect
138. #2420C22semidirect
139. #2416C22semidirect
140. #2416C22semidirect
141. #2414C22semidirect
142. #2414C22semidirect
143. #2414C22semidirect
144. #2411C22semidirect
145. #2410C22semidirect
146. #2408C22semidirect
147. #2407C22semidirect
148. #2407C22semidirect
149. #2404C22semidirect
150. #2392C22semidirect
151. #2388C22semidirect
152. #2379C22semidirect
153. #2369C22semidirect
154. #2367C22semidirect
155. #2366C22semidirect
156. #2363C22semidirect
157. #2362C22semidirect
158. #2361C22semidirect
159. D4×C4⋊C4C22semidirect
160. #2346C22semidirect
161. D4×C22⋊C4C22semidirect
162. #2326C22semidirect
163. #2324C22semidirect
164. #2317C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#124C22semidirect
167. C4×C22⋊Q8C22semidirect
168. C4×#123C22semidirect
169. C4×#121C22semidirect
170. #2297C22semidirect
171. #2293C22semidirect
172. C2×#390C22semidirect
173. #2290C22semidirect
174. C42×D4C22semidirect
190. #555D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35492
C2×#34832
#596592
#590952
#590842
#590562
#518962
#517832
#462252
#449272
#448862
#429712
#429632
#393612
#393412
#377822
#376812
#362582
#362312
#361282
#352562
#347152
#344852