Finite Group Databasebeta

← #7658008

Subgroups — #7658008

Order 512.

5410 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42589C214yesmaximal, complemented
2#42580C214yesmaximal, complemented
3#40806C218yesmaximal, complemented
4#40796C218yesmaximal, complemented
5#39736C212yesmaximal, complemented
6#39506C211yesmaximal, characteristic, complemented
7#39386C211yesmaximal, characteristic, complemented
8#37898C212yesmaximal, complemented
9#37700C212yesmaximal, complemented
10#37670C214yesmaximal, complemented
11#37625C212yesmaximal, complemented
12#37498C214yesmaximal, complemented
13#36192C211yesmaximal, characteristic, complemented
14#36128C211yesmaximal, characteristic, complemented
15#36101C212yesmaximal, complemented
16#35882C214yesmaximal, complemented
17#35865C214yesmaximal, complemented
18#35278C211yesmaximal, characteristic, complemented
19#35261C212yesmaximal, complemented
20#34633C212yesmaximal, complemented
21#34629C211yesmaximal, characteristic, complemented
22#34330C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C2×#550C2212yes—
25C2×#540C2212yes—
26C2×#540C2212yescomplemented
27C2×#532C2212yescomplemented
28C2×#525C2214yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2867C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2856C2212yes—
34#2856C2212yescomplemented
35#2851C2212yescomplemented
36#2847C2214yes—
37#2829C2218yescomplemented
38#2826C2218yescomplemented
39#2825C2218yes—
40#2783C2218yescomplemented
41#2761C2218yescomplemented
42#2708C2218yescomplemented
43#2706C2218yescomplemented
44#2703C2218yes—
45#2693C2218yescomplemented
46#2691C2218yes—
47#2691C2218yescomplemented
48#2688C2218yes—
49#2678C2218yes—
50#2673C2218yescomplemented
51#2668C2218yes—
52#2655C2214yescomplemented
53#2652C2214yes—
54#2649C2218yescomplemented
55#2648C2218yescomplemented
56#2647C2211yescharacteristic, complemented
57#2645C2212yescomplemented
58#2644C2214yescomplemented
59#2642C2211yescharacteristic, complemented
60#2641C2214yes—
61#2641C2212yescomplemented
62#2636C2218yescomplemented
63#2635C2218yes—
64#2630C2218yescomplemented
65#2629C2211yescharacteristic
66#2625C2212yes—
67#2624C2214yescomplemented
68#2621C2211yescharacteristic
69#2621C2212yescomplemented
70#2620C2214yes—
71#2620C2214yescomplemented
72#2619C2212yes—
73#2619C2212yescomplemented
74#2618C2218yescomplemented
75#2617C2218yes—
76#2597C2218yescomplemented
77#2576C2218yescomplemented
78#2566C2214yescomplemented
79#2559C2218yescomplemented
80#2554C2218yescomplemented
81#2552C2212yescomplemented
82#2548C2212yescomplemented
83#2541C2212yes—
84#2541C2214yes—
85#2541C2214yes—
86#2538C2212yes—
87#2522C2218yescomplemented
88#2513C2214yes—
89#2512C2214yescomplemented
90#2512C2214yescomplemented
91#2508C2214yescomplemented
92#2490C2214yes—
93#2489C2214yescomplemented
94#2476C2218yescomplemented
95#2471C2218yes—
96#2457C2218yescomplemented
97#2456C2218yes—
98#2454C2214yes—
99#2454C2214yescomplemented
100#2447C2214yescomplemented
101#2445C2214yes—
102#2445C2214yes—
103#2445C2214yescomplemented
104#2445C2214yescomplemented
105#2445C2214yescomplemented
106#2444C2218yes—
107#2444C2218yescomplemented
108#2443C2218yescomplemented
109#2441C2214yescomplemented
110#2433C2214yes—
111#2431C2214yescomplemented
112#2428C2214yes—
113#2428C2214yes—
114#2428C2218yescomplemented
115#2428C2214yescomplemented
116#2427C2214yescomplemented
117#2425C2218yescomplemented
118#2424C2218yes—
119#2424C2218yes—
120#2422C2214yescomplemented
121#2420C2218yes—
122#2420C2214yes—
123#2419C2218yescomplemented
124#2414C2214yes—
125#2407C2214yes—
126#2402C2214yescomplemented
127#2401C2214yes—
128#2392C2218yes—
129#2392C2218yescomplemented
130#2370C2214yescomplemented
131#2366C2214yes—
132#2366C2214yes—
133#2366C2214yescomplemented
134#2366C2212yescomplemented
135#2364C2218yescomplemented
136#2363C2214yescomplemented
137#2361C2214yes—
138#2357C2214yescomplemented
139#2355C2212yescomplemented
140#2354C2212yes—
141#2354C2212yes—
142#2352C2214yes—
143D4×C4⋊C4C2212yes—
144#2344C2212yes—
145#2342C2214yes—
146#2339C2214yescomplemented
147D4×C22⋊C4C2212yes—
148#2333C2218yescomplemented
149#2328C2214yes—
150#2328C2212yescomplemented
151#2324C2214yes—
152#2314C2212yescomplemented
153C4×C4⋊Q8C2211yescharacteristic, complemented
154C4×#127C2212yescomplemented
155C4×#125C2211yescharacteristic, complemented
156C4×C22⋊Q8C2212yes—
157C4×#121C2214yescomplemented
158#2297C2214yescomplemented
159#2295C2212yescomplemented
160#2293C2211yescharacteristic
161#2293C2211yescharacteristic
162#2290C2212yes—
163#2290C2212yes—
164#2285C2211yescharacteristic
165#2285C2212yescomplemented
166#2280C2212yes—
167#2275C2214yescomplemented
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C22×#41C2314yes—
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174#550—216no—
175#540—48no—
176#540—48no—
177#532—48no—
178C2×C4⋊Q8C2311yescharacteristic
179C2×#127C2312yes—
180C2×#127C2314yes—
181C2×#127C2312yes—
182C2×#127C2314yes—
183C2×#127C2312yes—
184C2×#127C2314yes—
185C2×#127C2314yes—
186C2×#126C2318yes—
187C2×#125C2311yescharacteristic
188C2×#125C2314yes—
189C2×#125C2312yes—
190C2×#124C2314yes—
191#525—416no—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2318yes—
204C2×#121C2314yes—
205C2×#121C2318yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#120C2318yes—
211C2×#120C2318yes—
212C2×C4×Q8C2312yes—
213C2×C4×D4—28no—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2311yescharacteristic
232C2×#117—48no—
233C2×#117C2312yes—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2312yes—
237C2×#117C2314yes—
238C2×#117C2314yes—
239C2×#117C2314yes—
240C2×#117C2312yes—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2314yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C42C2312yes—
246C22×C42C2311yescharacteristic
247C22×C42C2312yes—
248#401C2314yes—
249#400C2314yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#399C2318yes—
258#399C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2318yes—
262#398C2314yes—
263#398C2314yes—
264#398C2314yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2312yes—
312#391C2312yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2318yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2312yes—
325#390C2312yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#390C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2318yes—
345#389C2312yes—
346#388C2318yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2314yes—
361#387C2314yes—
362#387C2318yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2314yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2314yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2314yes—
395#385C2314yes—
396#384C2312yes—
397#384C2311yescharacteristic
398#384C2312yes—
399#384C2314yes—
400#382C2311yescharacteristic
401#382C2314yes—
402#382C2312yes—
403#382C2318yes—
404#382C2312yes—
405#381C2318yes—
406#381C2318yes—
407#381C2314yes—
408#380C2314yes—
409#380C2312yes—
410#380C2314yes—
411#380C2312yes—
412#380C2312yes—
413#380C2314yes—
414#380C2314yes—
415#380C2318yes—
416#380C2318yes—
417#379C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2318yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2312yes—
447#376C2314yes—
448#376C2311yescharacteristic
449#376C2311yescharacteristic
450C2×#95C2318yes—
451C43C2311yescharacteristic
452C43C2311yescharacteristic
453C25C2412yes—
454C2×#41—216no—
455C2×#41—48no—
456C2×#41—48no—
457C22×Q8C2412yes—
458C22×D4—24no—
459C22×D4—44no—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2411yescharacteristic
463C22×D4C2411yescharacteristic
464C22×D4C2412yes—
465C22×D4C2418yes—
466C22×D4C2418yes—
467C22×D4C2418yes—
468C22×D4C2414yes—
469C22×D4C2418yes—
470C22×D4C2418yes—
471C22×D4C2418yes—
472C22×D4C2418yes—
473C23×C4—28no—
474C23×C4—28no—
475C23×C4—44no—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2418yes—
486C23×C4C2414yes—
487C23×C4C2418yes—
488C23×C4C2418yes—
489C4⋊Q8—24no—
490#127—216no—
491#127—28no—
492#127—28no—
493#127—48no—
494#127—48no—
495#127—44no—
496#127—84no—
497#126—88no—
498#125—24no—
499#125—48no—
500#125—44no—
501#124—48no—
502#123—416no—
503#123—416no—
504#123—416no—
505#123—88no—
506C22⋊Q8—28no—
507C22⋊Q8—48no—
508#121—216no—
509#121—216no—
510#121—232no—
511#121—416no—
512#121—416no—
513#121—48no—
514#121—48no—
515#121—416no—
516#121—48no—
517#121—88no—
518#121—88no—
519#121—84no—
520#120—416no—
521#120—88no—
522C4×Q8—28no—
523C4×D4—24no—
524C4×D4—28no—
525C4×D4—24no—
526C4×D4—216no—
527C4×D4—28no—
528C4×D4—24no—
529C4×D4—44no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—44no—
533C4×D4—416no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—416no—
537C4×D4—416no—
538C4×D4—84no—
539C4×D4—88no—
540C4×D4#4118yes—
541#117—24no—
542#117—24no—
543#117—28no—
544#117—44no—
545#117—44no—
546#117—48no—
547#117—48no—
548#117—48no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—48no—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—28no—
583C2×C22⋊C4—48no—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2412yes—
619C2×C42—24no—
620C2×C42—28no—
621C2×C42—44no—
622C2×C42C2411yescharacteristic
623C2×C42C2412yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2412yes—
635C2×C42C2414yes—
636C2×C42C2418yes—
637C2×C42C2412yes—
638C2×C42C2418yes—
639C2×C42C2412yes—
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2414yes—
654#95C2412yes—
655#95C2412yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2418yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2418yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675C24—24no—
676C24—24no—
677C24—42no—
678C24—44no—
679C24—44no—
680C24C2512yes—
681C24C2518yes—
682C24C2512yes—
683C24C2511yescharacteristic
684#41—832no—
685C2×Q8—24no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×D4—24no—
689C2×D4—216no—
690C2×D4—216no—
691C2×D4—216no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—216no—
699C2×D4—24no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—416no—
724C2×D4C2×#4114yes—
725C22×C4—22no—
726C22×C4—24no—
727C22×C4—22no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—22no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—22no—
741C22×C4—216no—
742C22×C4—28no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—432no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—48no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4C2×#4118yes—
762C22×C4H(5,𝔽2)14yes—
763C22×C4C2511yescharacteristic
764C22×C4C2512yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2511yescharacteristic
773C22×C4C2518yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2512yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C4⋊C4—24no—
783C4⋊C4—22no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—48no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4C2×#4114yes—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—28no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—216no—
819C22⋊C4—24no—
820C22⋊C4—28no—
821C22⋊C4—216no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—44no—
847C22⋊C4C2×#4118yes—
848C42—22no—
849C42—22no—
850C42—22no—
851C42—28no—
852C42—28no—
853C42—24no—
854C42—22no—
855C42—24no—
856C42—22no—
857C42—22no—
858C42—24no—
859C42—28no—
860C42—24no—
861C42—44no—
862C42—48no—
863C42—42no—
864C42—48no—
865C42—42no—
866C42C2×#4114yes—
867C42H(5,𝔽2)14yes—
868C23—21no—
869C23—21no—
870C23—22no—
871C23—22no—
872C23—24no—
873C23—22no—
874C23—24no—
875C23—22no—
876C23—22no—
877C23—28no—
878C23—22no—
879C23—28no—
880C23—22no—
881C23—28no—
882C23—28no—
883C23—28no—
884C23—24no—
885C23—24no—
886C23—28no—
887C23—28no—
888C23—48no—
889C23—48no—
890C23—84no—
891C23—88no—
892C23—88no—
893C23C22×#4114yes—
894C23C2×H(5,𝔽2)12yes—
895C23C2611yescharacteristic
896Q8—48no—
897D4—28no—
898D4—48no—
899D4—416no—
900D4—44no—
901D4—416no—
902D4—88no—
903D4—816no—
904D4—816no—
905D4—816no—
906D4—816no—
907D4—816no—
908D4—168no—
909D4—168no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—28no—
918C2×C4—216no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—28no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—44no—
960C2×C4—48no—
961C2×C4—82no—
962C2×C4—88no—
963C2×C4—816no—
964C2×C4—88no—
965C2×C4—168no—
966C2×C4—168no—
967C2×C4C22×#4112yes—
968C2×C4C22×#4114yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C2×H(5,𝔽2)14yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4C2×H(5,𝔽2)12yes—
974C2×C4C2×H(5,𝔽2)12yes—
975C2×C4#58514yes—
976C22—22no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—41no—
982C22—41no—
983C22—44no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—48no—
988C22—48no—
989C22—42no—
990C22—42no—
991C22—48no—
992C22—48no—
993C22—48no—
994C22—44no—
995C22—48no—
996C22—48no—
997C22—44no—
998C22—816no—
999C22C23×#4111yescharacteristic
1000C22C22×H(5,𝔽2)11yescharacteristic
1001C22C22×H(5,𝔽2)11yescharacteristic
1002C22C2×#58512yes—
1003C22H(7,𝔽2)12yes—
1004C4—22no—
1005C4—24no—
1006C4—22no—
1007C4—24no—
1008C4—42no—
1009C4—44no—
1010C4—41no—
1011C4—44no—
1012C4—41no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—42no—
1017C4—44no—
1018C4—48no—
1019C4—44no—
1020C4—42no—
1021C4#345514yes—
1022C4#351914yes—
1023C2—44no—
1024C2—42no—
1025C2—88no—
1026C2—82no—
1027C2C2×#345511yescharacteristic
1028C2C2×#351911yescharacteristic
1029C2#6285811yescharacteristic
1030C2#6295512yes—
1031C2#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. #42589C2semidirect
2. #42580C2semidirect
3. #40806C2semidirect
4. #40796C2semidirect
5. #39736C2semidirect
6. #39506C2semidirect
7. #39386C2semidirect
8. #37898C2semidirect
9. #37700C2semidirect
10. #37670C2semidirect
11. #37625C2semidirect
12. #37498C2semidirect
13. #36192C2semidirect
14. #36128C2semidirect
15. #36101C2semidirect
16. #35882C2semidirect
17. #35865C2semidirect
18. #35278C2semidirect
19. #35261C2semidirect
20. #34633C2semidirect
21. #34629C2semidirect
22. #34330C2semidirect
23. D4×#117C2semidirect
26. C2×#540C22semidirect
27. C2×#532C22semidirect
31. #2867C22semidirect
32. #2859C22semidirect
34. #2856C22semidirect
35. #2851C22semidirect
37. #2829C22semidirect
38. #2826C22semidirect
40. #2783C22semidirect
41. #2761C22semidirect
42. #2708C22semidirect
43. #2706C22semidirect
45. #2693C22semidirect
47. #2691C22semidirect
50. #2673C22semidirect
52. #2655C22semidirect
54. #2649C22semidirect
55. #2648C22semidirect
56. #2647C22semidirect
57. #2645C22semidirect
58. #2644C22semidirect
59. #2642C22semidirect
61. #2641C22semidirect
62. #2636C22semidirect
64. #2630C22semidirect
67. #2624C22semidirect
69. #2621C22semidirect
71. #2620C22semidirect
73. #2619C22semidirect
74. #2618C22semidirect
76. #2597C22semidirect
77. #2576C22semidirect
78. #2566C22semidirect
79. #2559C22semidirect
80. #2554C22semidirect
81. #2552C22semidirect
82. #2548C22semidirect
87. #2522C22semidirect
89. #2512C22semidirect
90. #2512C22semidirect
91. #2508C22semidirect
93. #2489C22semidirect
94. #2476C22semidirect
96. #2457C22semidirect
99. #2454C22semidirect
100. #2447C22semidirect
103. #2445C22semidirect
104. #2445C22semidirect
105. #2445C22semidirect
107. #2444C22semidirect
108. #2443C22semidirect
109. #2441C22semidirect
111. #2431C22semidirect
114. #2428C22semidirect
115. #2428C22semidirect
116. #2427C22semidirect
117. #2425C22semidirect
120. #2422C22semidirect
123. #2419C22semidirect
126. #2402C22semidirect
129. #2392C22semidirect
130. #2370C22semidirect
133. #2366C22semidirect
134. #2366C22semidirect
135. #2364C22semidirect
136. #2363C22semidirect
138. #2357C22semidirect
139. #2355C22semidirect
146. #2339C22semidirect
148. #2333C22semidirect
150. #2328C22semidirect
152. #2314C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#127C22semidirect
155. C4×#125C22semidirect
157. C4×#121C22semidirect
158. #2297C22semidirect
159. #2295C22semidirect
165. #2285C22semidirect
167. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#425892
#425802
#408062
#407962
#397362
#395062
#393862
#378982
#377002
#376702
#376252
#374982
#361922
#361282
#361012
#358822
#358652
#352782
#352612
#346332
#346292
#343302
D4×#1172