Finite Group Databasebeta

← #7720532

Subgroups — #7720532

Order 512.

5882 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51056C218yesmaximal, complemented
2#51040C214yesmaximal, complemented
3#50658C214yesmaximal, complemented
4#45070C212yesmaximal, complemented
5#45041C212yesmaximal, complemented
6#44963C212yesmaximal, complemented
7#44959C214yesmaximal, complemented
8#44931C212yesmaximal, complemented
9#44876C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39770C212yesmaximal, complemented
12#37751C214yesmaximal, complemented
13#37748C214yesmaximal, complemented
14#37290C214yesmaximal, complemented
15#36128C212yesmaximal, complemented
16#36115C212yesmaximal, complemented
17#35303C214yesmaximal, complemented
18#35274C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic, complemented
20#35190C211yesmaximal, characteristic, complemented
21#34625C211yesmaximal, characteristic, complemented
22#34393C211yesmaximal, characteristic, complemented
23#34364C211yesmaximal, characteristic, complemented
24#34123C211yesmaximal, characteristic, complemented
25C2×#550C2214yescomplemented
26C2×#535C2212yes—
27C2×#535C2214yes—
28C2×#532C2211yescharacteristic
29C2×#532C2214yescomplemented
30C22×#127C2211yescharacteristic
31C2×#529C2214yescomplemented
32C2×C4×#41C2211yescharacteristic
33#2867C2212yes—
34#2858C2212yes—
35#2856C2214yes—
36#2856C2214yescomplemented
37#2850C2214yescomplemented
38#2850C2214yescomplemented
39#2796C2218yescomplemented
40#2756C2218yescomplemented
41#2753C2218yescomplemented
42#2751C2218yescomplemented
43#2749C2218yescomplemented
44#2709C2218yescomplemented
45#2709C2218yescomplemented
46#2706C2218yescomplemented
47#2703C2218yescomplemented
48#2699C2218yescomplemented
49#2691C2218yescomplemented
50#2688C2218yescomplemented
51#2688C2218yescomplemented
52#2686C2218yescomplemented
53#2685C2218yes—
54#2684C2218yes—
55#2678C2218yes—
56#2671C2218yescomplemented
57#2671C2218yescomplemented
58#2668C2218yes—
59#2667C2212yes—
60#2666C2214yescomplemented
61#2665C2212yes—
62#2660C2212yescomplemented
63#2657C2212yes—
64#2657C2212yes—
65#2647C2212yescomplemented
66#2641C2214yescomplemented
67#2640C2214yescomplemented
68#2635C2214yes—
69#2629C2212yes—
70#2628C2212yes—
71#2619C2214yes—
72#2610C2218yescomplemented
73#2610C2218yescomplemented
74#2603C2218yescomplemented
75#2603C2218yescomplemented
76#2598C2214yescomplemented
77#2592C2214yescomplemented
78#2580C2214yescomplemented
79#2568C2211yescharacteristic, complemented
80#2548C2212yes—
81#2548C2212yes—
82#2548C2214yescomplemented
83#2548C2211yescharacteristic, complemented
84#2544C2214yescomplemented
85#2544C2214yescomplemented
86#2543C2218yescomplemented
87#2543C2218yescomplemented
88#2542C2211yescharacteristic, complemented
89#2541C2212yes—
90#2541C2212yes—
91#2541C2214yes—
92#2541C2212yes—
93#2541C2212yes—
94#2541C2211yescharacteristic, complemented
95#2541C2214yescomplemented
96#2513C2214yescomplemented
97#2512C2214yescomplemented
98#2500C2212yes—
99#2476C2218yescomplemented
100#2471C2218yescomplemented
101#2467C2218yescomplemented
102#2464C2218yescomplemented
103#2448C2214yescomplemented
104#2447C2214yescomplemented
105#2447C2214yescomplemented
106#2445C2214yescomplemented
107#2445C2214yescomplemented
108#2445C2214yescomplemented
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2444C2218yescomplemented
112#2433C2214yes—
113#2433C2212yes—
114#2433C2212yes—
115#2431C2212yes—
116#2431C2218yescomplemented
117#2430C2218yescomplemented
118#2430C2218yescomplemented
119#2430C2218yescomplemented
120#2428C2218yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2427C2214yescomplemented
124#2426C2214yescomplemented
125#2424C2218yes—
126#2418C2218yes—
127#2411C2218yes—
128#2408C2214yes—
129#2408C2212yes—
130#2408C2212yes—
131#2407C2214yes—
132#2404C2218yes—
133#2402C2212yescomplemented
134#2399C2212yescomplemented
135#2396C2214yes—
136#2380C2214yes—
137#2377C2214yes—
138#2366C2212yes—
139#2366C2212yes—
140#2366C2214yescomplemented
141#2366C2214yescomplemented
142#2366C2212yescomplemented
143#2365C2212yescomplemented
144#2357C2212yescomplemented
145#2356C2211yescharacteristic, complemented
146#2356C2211yescharacteristic, complemented
147#2354C2214yescomplemented
148#2353C2212yes—
149#2353C2212yes—
150#2349C2212yescomplemented
151#2349C2211yescharacteristic, complemented
152#2349C2211yescharacteristic, complemented
153#2346C2212yes—
154#2343C2214yescomplemented
155#2341C2212yes—
156#2339C2212yes—
157#2339C2212yes—
158D4×C22⋊C4C2214yes—
159D4×C22⋊C4C2214yes—
160#2328C2212yes—
161#2328C2212yes—
162#2328C2214yes—
163#2328C2214yescomplemented
164#2328C2212yescomplemented
165#2326C2212yescomplemented
166#2326C2214yescomplemented
167#2326C2214yescomplemented
168#2324C2214yes—
169#2318C2214yescomplemented
170#2309C2212yes—
171#2308C2214yes—
172C4×C4⋊Q8C2212yescomplemented
173C4×#125C2212yescomplemented
174#2295C2212yescomplemented
175#2290C2214yes—
176#2285C2211yescharacteristic
177#2283C2211yescharacteristic
178#2283C2211yescharacteristic
179#2283C2212yescomplemented
180C42×D4C2212yescomplemented
181C4×#117C2211yescharacteristic
182C2×#376C2212yescomplemented
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C22×#41C2318yes—
186C23×D4C2312yes—
187C23×D4C2312yes—
188C23×D4C2312yes—
189#550—416no—
190#535—416no—
191#535—48no—
192#532—28no—
193#532—416no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×#127—28no—
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2314yes—
200C2×#127C2312yes—
201C2×#127C2312yes—
202C2×#127C2311yescharacteristic
203C2×#127C2312yes—
204C2×#127C2314yes—
205C2×#127C2314yes—
206C2×#127C2314yes—
207C2×#127C2314yes—
208C2×#127C2314yes—
209C2×#127C2314yes—
210#529—416no—
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2312yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#124C2318yes—
219C2×#123C2318yes—
220C2×#123C2318yes—
221C2×#123C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×#121C2318yes—
237C2×#120C2314yes—
238C2×#120C2318yes—
239C2×#120C2314yes—
240C2×#120C2318yes—
241C4×#41—28no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2318yes—
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2318yes—
267C22×C22⋊C4C2318yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270C22×C42C2311yescharacteristic
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#399C2318yes—
276#399C2314yes—
277#399C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C2314yes—
291#396C2314yes—
292#396C2318yes—
293#395C2314yes—
294#395C2314yes—
295#395C2314yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2314yes—
316#392C2314yes—
317#392C2314yes—
318#392C2318yes—
319#392C2314yes—
320#392C2314yes—
321#392C2318yes—
322#392C2314yes—
323#392C2318yes—
324#392C2314yes—
325#392C2318yes—
326#392C2314yes—
327#392C2318yes—
328#392C2318yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#390C2314yes—
336#390C2318yes—
337#390C2314yes—
338#390C2318yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#390C2318yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2318yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#387C2314yes—
381#387C2314yes—
382#387C2318yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#383C2312yes—
425#383C2312yes—
426#383C2312yes—
427#383C2312yes—
428#382C2312yes—
429#382C2312yes—
430#382C2312yes—
431#382C2312yes—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2314yes—
435#381C2312yes—
436#381C2312yes—
437#381C2314yes—
438#381C2314yes—
439#381C2318yes—
440#380C2314yes—
441#380C2312yes—
442#380C2312yes—
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2312yes—
446#380C2312yes—
447#380C2318yes—
448#380C2312yes—
449#379C2318yes—
450#379C2314yes—
451#379C2314yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2314yes—
476#376C2312yes—
477#376C2312yes—
478#376C2314yes—
479#376C2314yes—
480#376C2312yes—
481#376C2312yes—
482#376C2311yescharacteristic
483#376C2311yescharacteristic
484C2×#95C2314yes—
485C2×#95C2314yes—
486C2×#95C2312yes—
487C2×#95C2312yes—
488C43C2312yes—
489C25C2414yes—
490C2×#41—24no—
491C2×#41—24no—
492C2×#41—28no—
493C2×#41—416no—
494C2×#41—42no—
495C2×#41—416no—
496C2×#41—48no—
497C2×#41—88no—
498C22×Q8C2412yes—
499C22×Q8C2411yescharacteristic
500C22×Q8C2414yes—
501C22×D4—28no—
502C22×D4—28no—
503C22×D4—28no—
504C22×D4—48no—
505C22×D4—44no—
506C22×D4—44no—
507C22×D4—84no—
508C22×D4C2412yes—
509C22×D4C2414yes—
510C22×D4C2412yes—
511C22×D4C2414yes—
512C22×D4C2412yes—
513C22×D4C2411yescharacteristic
514C22×D4C2418yes—
515C22×D4C2418yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2418yes—
519C22×D4C2418yes—
520C22×D4C2418yes—
521C22×D4C2414yes—
522C22×D4C2414yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2418yes—
526C22×D4C2418yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2414yes—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2414yes—
533C23×C4C2414yes—
534C23×C4C2412yes—
535C23×C4C2418yes—
536C23×C4C2418yes—
537C23×C4C2418yes—
538C23×C4C2411yescharacteristic
539C4⋊Q8—24no—
540C4⋊Q8—28no—
541#127—216no—
542#127—28no—
543#127—28no—
544#127—28no—
545#127—28no—
546#127—28no—
547#127—24no—
548#127—216no—
549#127—48no—
550#127—48no—
551#127—48no—
552#127—84no—
553#127—84no—
554#126—416no—
555#125—28no—
556#124—28no—
557#124—216no—
558#124—44no—
559#124—416no—
560#124—48no—
561#124—48no—
562#123—416no—
563#123—88no—
564#123—88no—
565C22⋊Q8—48no—
566#121—28no—
567#121—28no—
568#121—416no—
569#121—416no—
570#121—416no—
571#121—416no—
572#121—48no—
573#121—48no—
574#121—48no—
575#121—416no—
576#121—416no—
577#121—416no—
578#121—88no—
579#121—88no—
580#120—416no—
581#120—416no—
582#120—48no—
583#120—48no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—48no—
596C4×D4—44no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—416no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4—416no—
604#117—24no—
605#117—28no—
606#117—28no—
607#117—44no—
608#117—416no—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C22⋊C4—88no—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C42—28no—
676C2×C42—216no—
677C2×C42#4118yescomplemented
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2418yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698#95C2411yescharacteristic
699#95C2412yes—
700#95C2411yescharacteristic
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2412yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2411yescharacteristic
712#95C2411yescharacteristic
713#95C2412yes—
714#95C2414yes—
715#95C2414yes—
716#95C2412yes—
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736C24—28no—
737C24—48no—
738C24—48no—
739C24—44no—
740C24—44no—
741C24C2518yes—
742C24C2514yes—
743C24C2511yescharacteristic
744C24C2512yes—
745#41—416no—
746#41—816no—
747#41—864no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—22no—
752C2×Q8—28no—
753C2×Q8—22no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—28no—
759C2×D4—216no—
760C2×D4—216no—
761C2×D4—216no—
762C2×D4—22no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—24no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—24no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—216no—
778C2×D4—216no—
779C2×D4—22no—
780C2×D4—28no—
781C2×D4—24no—
782C2×D4—42no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—48no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—48no—
806C2×D4—48no—
807C2×D4—816no—
808C2×D4—816no—
809C2×D4—816no—
810C2×D4H(5,𝔽2)14yes—
811C22×C4—24no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4C2×#4114yes—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—28no—
931C42—28no—
932C42—28no—
933C42—24no—
934C42—28no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—48no—
940C42—42no—
941C42—42no—
942C42C2×#4114yes—
943C42C2×#4114yes—
944C42C2×#4114yes—
945C42C2×#4114yes—
946C42H(5,𝔽2)18yes—
947C23—22no—
948C23—22no—
949C23—21no—
950C23—24no—
951C23—22no—
952C23—21no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—28no—
957C23—28no—
958C23—28no—
959C23—28no—
960C23—24no—
961C23—28no—
962C23—24no—
963C23—28no—
964C23—28no—
965C23—28no—
966C23—28no—
967C23—416no—
968C23—88no—
969C23—88no—
970C23—168no—
971C23—168no—
972C23C22×#4112yes—
973C23C2×H(5,𝔽2)14yes—
974C23C2611yescharacteristic
975Q8—416no—
976Q8—44no—
977Q8—48no—
978D4—28no—
979D4—48no—
980D4—48no—
981D4—416no—
982D4—416no—
983D4—48no—
984D4—84no—
985D4—816no—
986D4—88no—
987D4—88no—
988D4—88no—
989D4—88no—
990D4—816no—
991D4—816no—
992D4—88no—
993D4—816no—
994D4—816no—
995D4—168no—
996D4—168no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—44no—
1042C2×C4—48no—
1043C2×C4—416no—
1044C2×C4—48no—
1045C2×C4—84no—
1046C2×C4—88no—
1047C2×C4—88no—
1048C2×C4—816no—
1049C2×C4—816no—
1050C2×C4—816no—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C2×H(5,𝔽2)14yes—
1058C2×C4C2×H(5,𝔽2)14yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)14yes—
1061C2×C4#58512yes—
1062C22—22no—
1063C22—24no—
1064C22—22no—
1065C22—22no—
1066C22—28no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—44no—
1071C22—42no—
1072C22—48no—
1073C22—44no—
1074C22—44no—
1075C22—48no—
1076C22—48no—
1077C22—44no—
1078C22—48no—
1079C22—48no—
1080C22—48no—
1081C22—48no—
1082C22—48no—
1083C22—48no—
1084C22—1616no—
1085C22C23×#4111yescharacteristic
1086C22C22×H(5,𝔽2)11yescharacteristic
1087C22C22×H(5,𝔽2)12yes—
1088C22C2×#58511yescharacteristic
1089C22H(7,𝔽2)12yes—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—22no—
1094C4—24no—
1095C4—24no—
1096C4—42no—
1097C4—42no—
1098C4—44no—
1099C4—42no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4#349414yes—
1109C4#350814yes—
1110C2—44no—
1111C2—42no—
1112C2—84no—
1113C2—88no—
1114C2C2×#349411yescharacteristic
1115C2C2×#350811yescharacteristic
1116C2#6285511yescharacteristic
1117C2#6291212yes—
1118C2#6295512yes—
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. #51056C2semidirect
2. #51040C2semidirect
3. #50658C2semidirect
4. #45070C2semidirect
5. #45041C2semidirect
6. #44963C2semidirect
7. #44959C2semidirect
8. #44931C2semidirect
9. #44876C2semidirect
10. #39771C2semidirect
11. #39770C2semidirect
12. #37751C2semidirect
13. #37748C2semidirect
14. #37290C2semidirect
15. #36128C2semidirect
16. #36115C2semidirect
17. #35303C2semidirect
18. #35274C2semidirect
19. #35272C2semidirect
20. #35190C2semidirect
21. #34625C2semidirect
22. #34393C2semidirect
23. #34364C2semidirect
24. #34123C2semidirect
25. C2×#550C22semidirect
29. C2×#532C22semidirect
31. C2×#529C22semidirect
36. #2856C22semidirect
37. #2850C22semidirect
38. #2850C22semidirect
39. #2796C22semidirect
40. #2756C22semidirect
41. #2753C22semidirect
42. #2751C22semidirect
43. #2749C22semidirect
44. #2709C22semidirect
45. #2709C22semidirect
46. #2706C22semidirect
47. #2703C22semidirect
48. #2699C22semidirect
49. #2691C22semidirect
50. #2688C22semidirect
51. #2688C22semidirect
52. #2686C22semidirect
56. #2671C22semidirect
57. #2671C22semidirect
60. #2666C22semidirect
62. #2660C22semidirect
65. #2647C22semidirect
66. #2641C22semidirect
67. #2640C22semidirect
72. #2610C22semidirect
73. #2610C22semidirect
74. #2603C22semidirect
75. #2603C22semidirect
76. #2598C22semidirect
77. #2592C22semidirect
78. #2580C22semidirect
79. #2568C22semidirect
82. #2548C22semidirect
83. #2548C22semidirect
84. #2544C22semidirect
85. #2544C22semidirect
86. #2543C22semidirect
87. #2543C22semidirect
88. #2542C22semidirect
94. #2541C22semidirect
95. #2541C22semidirect
96. #2513C22semidirect
97. #2512C22semidirect
99. #2476C22semidirect
100. #2471C22semidirect
101. #2467C22semidirect
102. #2464C22semidirect
103. #2448C22semidirect
104. #2447C22semidirect
105. #2447C22semidirect
106. #2445C22semidirect
107. #2445C22semidirect
108. #2445C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
111. #2444C22semidirect
116. #2431C22semidirect
117. #2430C22semidirect
118. #2430C22semidirect
119. #2430C22semidirect
120. #2428C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
133. #2402C22semidirect
134. #2399C22semidirect
140. #2366C22semidirect
141. #2366C22semidirect
142. #2366C22semidirect
143. #2365C22semidirect
144. #2357C22semidirect
145. #2356C22semidirect
146. #2356C22semidirect
147. #2354C22semidirect
150. #2349C22semidirect
151. #2349C22semidirect
152. #2349C22semidirect
154. #2343C22semidirect
163. #2328C22semidirect
164. #2328C22semidirect
165. #2326C22semidirect
166. #2326C22semidirect
167. #2326C22semidirect
169. #2318C22semidirect
172. C4×C4⋊Q8C22semidirect
173. C4×#125C22semidirect
174. #2295C22semidirect
179. #2283C22semidirect
180. C42×D4C22semidirect
182. C2×#376C22semidirect
677. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#510562
#510402
#506582
#450702
#450412
#449632
#449592
#449312
#448762
#397712
#397702
#377512
#377482
#372902
#361282
#361152
#353032
#352742
#352722
#351902
#346252
#343932
#343642
#341232