Finite Group Databasebeta

← #7673907

Subgroups — #7673907

Order 512.

5200 conjugacy classes of subgroups.

The subgroup lattice has 1129 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45156C214yesmaximal, complemented
2#45155C214yesmaximal, complemented
3#44970C214yesmaximal, complemented
4#44969C214yesmaximal, complemented
5#39255C218yesmaximal, complemented
6#39253C218yesmaximal, complemented
7#37945C214yesmaximal, complemented
8#37944C214yesmaximal, complemented
9#37899C214yesmaximal, complemented
10#37892C214yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35621C211yesmaximal, characteristic, complemented
13#35558C211yesmaximal, characteristic, complemented
14#35533C211yesmaximal, characteristic
15#35327C211yesmaximal, characteristic, complemented
16#35327C211yesmaximal, characteristic, complemented
17#35182C211yesmaximal, characteristic, complemented
18#35152C211yesmaximal, characteristic, complemented
19#34638C211yesmaximal, characteristic, complemented
20#34266C211yesmaximal, characteristic, complemented
21#34265C211yesmaximal, characteristic, complemented
22#34188C211yesmaximal, characteristic, complemented
23#34183C211yesmaximal, characteristic, complemented
24#34070C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2853C2214yes—
39#2850C2214yes—
40#2850C2212yes—
41#2850C2212yes—
42#2849C2214yes—
43#2795C2218yescomplemented
44#2793C2218yescomplemented
45#2790C2218yescomplemented
46#2786C2218yescomplemented
47#2783C2218yescomplemented
48#2782C2218yescomplemented
49#2781C2218yescomplemented
50#2780C2218yescomplemented
51#2779C2218yescomplemented
52#2778C2218yescomplemented
53#2778C2218yescomplemented
54#2765C2218yescomplemented
55#2756C2218yescomplemented
56#2750C2218yescomplemented
57#2718C2218yescomplemented
58#2708C2218yescomplemented
59#2647C2212yescomplemented
60#2647C2212yescomplemented
61#2647C2212yescomplemented
62#2647C2212yescomplemented
63#2646C2214yes—
64#2646C2214yes—
65#2623C2214yes—
66#2622C2214yes—
67#2620C2212yes—
68#2620C2212yes—
69#2620C2214yes—
70#2601C2218yescomplemented
71#2598C2218yescomplemented
72#2595C2218yescomplemented
73#2595C2218yescomplemented
74#2594C2218yescomplemented
75#2593C2218yescomplemented
76#2591C2218yescomplemented
77#2587C2218yescomplemented
78#2579C2218yescomplemented
79#2573C2218yescomplemented
80#2548C2212yes—
81#2547C2212yescomplemented
82#2546C2212yescomplemented
83#2545C2214yes—
84#2545C2212yes—
85#2545C2214yes—
86#2545C2212yescomplemented
87#2544C2212yes—
88#2544C2214yes—
89#2544C2214yes—
90#2544C2212yescomplemented
91#2541C2212yes—
92#2534C2218yes—
93#2534C2218yes—
94#2525C2218yescomplemented
95#2514C2214yescomplemented
96#2514C2214yescomplemented
97#2513C2214yes—
98#2513C2214yes—
99#2512C2214yes—
100#2512C2214yes—
101#2511C2214yescomplemented
102#2511C2214yescomplemented
103#2493C2218yes—
104#2481C2218yescomplemented
105#2480C2218yes—
106#2476C2218yescomplemented
107#2470C2218yescomplemented
108#2468C2218yescomplemented
109#2448C2214yescomplemented
110#2447C2214yes—
111#2446C2214yescomplemented
112#2445C2214yes—
113#2443C2218yescomplemented
114#2425C2218yes—
115#2424C2218yes—
116#2423C2214yescomplemented
117#2422C2214yes—
118#2421C2214yescomplemented
119#2420C2214yes—
120#2417C2214yescomplemented
121#2416C2214yes—
122#2415C2214yescomplemented
123#2414C2214yes—
124#2402C2214yescomplemented
125#2402C2214yescomplemented
126#2367C2214yes—
127#2367C2214yescomplemented
128#2366C2214yes—
129#2365C2214yescomplemented
130#2363C2214yes—
131#2362C2214yescomplemented
132#2361C2214yes—
133#2360C2214yescomplemented
134#2355C2214yescomplemented
135#2354C2214yescomplemented
136#2352C2218yes—
137Q8×C4⋊C4C2214yescomplemented
138D4×C4⋊C4C2218yes—
139D4×C4⋊C4C2214yescomplemented
140#2328C2212yescomplemented
141#2327C2212yescomplemented
142#2326C2214yes—
143#2326C2214yes—
144#2326C2214yes—
145#2326C2214yes—
146#2326C2212yescomplemented
147#2326C2212yescomplemented
148#2325C2214yes—
149#2325C2214yes—
150#2322C2214yes—
151#2321C2214yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yescomplemented
155#2317C2212yescomplemented
156#2314C2214yescomplemented
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×#123C2214yes—
164C4×#120C2214yes—
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171C2×#391C2211yescharacteristic
172C2×#390C2211yescharacteristic
173#2290C2214yescomplemented
174#2290C2214yescomplemented
175C2×#388C2214yes—
176C2×#385C2214yes—
177#2285C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180#2285C2212yescomplemented
181#2285C2214yescomplemented
182C2×#384C2211yescharacteristic
183C2×#384C2212yescomplemented
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#536—28no—
193#536—44no—
194#535—28no—
195#535—44no—
196#532—28no—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2311yescharacteristic
201C2×#127C2312yes—
202C2×#127C2312yes—
203C2×#126C2318yes—
204C2×#124—28no—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#124C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2318yes—
225C2×#120C2314yes—
226C2×#120C2314yes—
227#520—44no—
228#520—44no—
229C4×#41—28no—
230C4×#41—28no—
231C2×C4×Q8—44no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4—44no—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2318yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2318yes—
268C22×C4⋊C4C2314yes—
269C22×C22⋊C4C2314yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2314yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278#401C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2318yes—
291#399C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#392C2318yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2318yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2312yes—
407#386C2318yes—
408#386C2312yes—
409#386C2318yes—
410#386C2318yes—
411#386C2312yes—
412#386C2312yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2312yes—
429#385C2312yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2312yes—
441#385C2312yes—
442#385C2314yes—
443#385C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2314yes—
449#384C2312yes—
450#384C2318yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#383C2318yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2312yes—
461#382C2318yes—
462#381C2314yes—
463#381C2314yes—
464#381C2318yes—
465#380C2314yes—
466#380C2314yes—
467#380C2318yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2314yes—
472#380C2318yes—
473#379C2314yes—
474#379C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497#376C2312yes—
498#376C2312yes—
499#376C2312yes—
500#376C2312yes—
501C2×#95C2312yes—
502C2×#95C2312yes—
503C2×#95C2314yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41#4118yes—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C22×D4C2412yes—
526C22×D4C2411yescharacteristic
527C22×D4C2418yes—
528C22×D4C2414yes—
529C22×D4C2414yes—
530C22×D4C2414yes—
531C23×C4—44no—
532C23×C4—84no—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2412yes—
540C23×C4C2414yes—
541C23×C4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2418yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—44no—
551#127—24no—
552#127—28no—
553#127—44no—
554#126—88no—
555#124—24no—
556#124—28no—
557#124—24no—
558#124—28no—
559#124—28no—
560#124—28no—
561#124—216no—
562#124—44no—
563#124—44no—
564#123—216no—
565#123—48no—
566#123—88no—
567C22⋊Q8—216no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570#121—216no—
571#121—216no—
572#121—44no—
573#121—44no—
574#121—88no—
575#120—216no—
576#120—48no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×D4—216no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—48no—
589C4×D4—48no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—88no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—28no—
602#117—28no—
603#117—44no—
604#117—44no—
605#117—88no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—84no—
612C2×C4⋊C4—88no—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C22⋊C4—216no—
653C2×C22⋊C4—44no—
654C2×C22⋊C4—84no—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—28no—
691C2×C42—28no—
692C2×C42—44no—
693C2×C42#4118yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2418yes—
711C2×C42C2418yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753C24—24no—
754C24—24no—
755C24—24no—
756C24—44no—
757C24—44no—
758C24C2514yes—
759C24C2512yes—
760C24C2512yes—
761C24C2511yescharacteristic
762#41—232no—
763#41—416no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—416no—
776C2×Q8C2×#4114yes—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—28no—
783C2×D4—216no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—416no—
804C2×D4C2×#4118yes—
805C2×D4C2×#4114yes—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—42no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—42no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—816no—
841C22×C4C2×#4118yes—
842C22×C4C2×#4118yes—
843C22×C4C2×#4114yes—
844C22×C4C2×#4114yes—
845C22×C4H(5,𝔽2)14yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—216no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—28no—
943C42—28no—
944C42—22no—
945C42—22no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—48no—
953C42—44no—
954C42—44no—
955C42—48no—
956C42—48no—
957C42C2×#4114yes—
958C42C2×#4114yes—
959C42C2×#4118yes—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—28no—
974C23—28no—
975C23—24no—
976C23—416no—
977C23—48no—
978C23—84no—
979C23—88no—
980C23—84no—
981C23C22×#4114yes—
982C23C22×#4112yes—
983C23C22×#4112yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2611yescharacteristic
986Q8—28no—
987Q8—48no—
988Q8—48no—
989Q8—44no—
990D4—216no—
991D4—28no—
992D4—48no—
993D4—48no—
994D4—48no—
995D4—44no—
996D4—88no—
997D4—816no—
998D4—164no—
999D4—164no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—216no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—48no—
1050C2×C4—416no—
1051C2×C4—416no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—84no—
1059C2×C4—816no—
1060C2×C4—164no—
1061C2×C4—164no—
1062C2×C4#553116yes—
1063C2×C4C22×#4114yes—
1064C2×C4C22×#4114yes—
1065C2×C4C22×#4114yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C22—24no—
1073C22—24no—
1074C22—22no—
1075C22—22no—
1076C22—28no—
1077C22—24no—
1078C22—44no—
1079C22—42no—
1080C22—42no—
1081C22—44no—
1082C22—48no—
1083C22—44no—
1084C22—48no—
1085C22—44no—
1086C22—42no—
1087C22—42no—
1088C22—44no—
1089C22—42no—
1090C22—44no—
1091C22—816no—
1092C22C2×#55314yes—
1093C22C23×#4111yescharacteristic
1094C22C23×#4111yescharacteristic
1095C22C22×H(5,𝔽2)11yescharacteristic
1096C22H(7,𝔽2)12yes—
1097C222−1+612yes—
1098C4—24no—
1099C4—24no—
1100C4—24no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—42no—
1105C4—42no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—44no—
1117C4C2×#55314yes—
1118C4C2×#55314yes—
1119C2—24no—
1120C2—44no—
1121C2—82no—
1122C2—84no—
1123C2C22×#55311yescharacteristic
1124C2#6284512yes—
1125C2#6285712yes—
1126C2#6287611yescharacteristic
1127C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #45156C2semidirect
2. #45155C2semidirect
3. #44970C2semidirect
4. #44969C2semidirect
5. #39255C2semidirect
6. #39253C2semidirect
7. #37945C2semidirect
8. #37944C2semidirect
9. #37899C2semidirect
10. #37892C2semidirect
11. #35630C2semidirect
12. #35621C2semidirect
13. #35558C2semidirect
15. #35327C2semidirect
16. #35327C2semidirect
17. #35182C2semidirect
18. #35152C2semidirect
19. #34638C2semidirect
20. #34266C2semidirect
21. #34265C2semidirect
22. #34188C2semidirect
23. #34183C2semidirect
24. #34070C2semidirect
25. C2×#2326C2semidirect
43. #2795C22semidirect
44. #2793C22semidirect
45. #2790C22semidirect
46. #2786C22semidirect
47. #2783C22semidirect
48. #2782C22semidirect
49. #2781C22semidirect
50. #2780C22semidirect
51. #2779C22semidirect
52. #2778C22semidirect
53. #2778C22semidirect
54. #2765C22semidirect
55. #2756C22semidirect
56. #2750C22semidirect
57. #2718C22semidirect
58. #2708C22semidirect
59. #2647C22semidirect
60. #2647C22semidirect
61. #2647C22semidirect
62. #2647C22semidirect
70. #2601C22semidirect
71. #2598C22semidirect
72. #2595C22semidirect
73. #2595C22semidirect
74. #2594C22semidirect
75. #2593C22semidirect
76. #2591C22semidirect
77. #2587C22semidirect
78. #2579C22semidirect
79. #2573C22semidirect
81. #2547C22semidirect
82. #2546C22semidirect
86. #2545C22semidirect
90. #2544C22semidirect
94. #2525C22semidirect
95. #2514C22semidirect
96. #2514C22semidirect
101. #2511C22semidirect
102. #2511C22semidirect
104. #2481C22semidirect
106. #2476C22semidirect
107. #2470C22semidirect
108. #2468C22semidirect
109. #2448C22semidirect
111. #2446C22semidirect
113. #2443C22semidirect
116. #2423C22semidirect
118. #2421C22semidirect
120. #2417C22semidirect
122. #2415C22semidirect
124. #2402C22semidirect
125. #2402C22semidirect
127. #2367C22semidirect
129. #2365C22semidirect
131. #2362C22semidirect
133. #2360C22semidirect
134. #2355C22semidirect
135. #2354C22semidirect
137. Q8×C4⋊C4C22semidirect
139. D4×C4⋊C4C22semidirect
140. #2328C22semidirect
141. #2327C22semidirect
146. #2326C22semidirect
147. #2326C22semidirect
154. #2317C22semidirect
155. #2317C22semidirect
156. #2314C22semidirect
173. #2290C22semidirect
174. #2290C22semidirect
180. #2285C22semidirect
181. #2285C22semidirect
183. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#451562
#451552
#449702
#449692
#392552
#392532
#379452
#379442
#378992
#378922
#356302
#356212
#355582
#355332
#353272
#351822
#351522
#346382
#342662
#342652
#341882
#341832
#340702
C2×#23262