Finite Group Databasebeta

← #7674188

Subgroups — #7674188

Order 512.

5162 conjugacy classes of subgroups.

The subgroup lattice has 1119 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45294C214yesmaximal, complemented
2#45285C214yesmaximal, complemented
3#45028C214yesmaximal, complemented
4#45000C214yesmaximal, complemented
5#39287C214yesmaximal, complemented
6#39281C214yesmaximal, complemented
7#39147C214yesmaximal, complemented
8#39143C214yesmaximal, complemented
9#39049C218yesmaximal, complemented
10#38126C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35677C211yesmaximal, characteristic, complemented
13#35555C211yesmaximal, characteristic, complemented
14#35530C211yesmaximal, characteristic, complemented
15#35266C211yesmaximal, characteristic, complemented
16#35256C211yesmaximal, characteristic
17#35153C211yesmaximal, characteristic, complemented
18#35152C211yesmaximal, characteristic, complemented
19#34639C211yesmaximal, characteristic, complemented
20#34276C211yesmaximal, characteristic, complemented
21#34268C211yesmaximal, characteristic, complemented
22#34265C211yesmaximal, characteristic, complemented
23#34249C211yesmaximal, characteristic, complemented
24C2×#2326C211yesmaximal, characteristic, complemented
25#34056C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2860C2214yes—
39#2856C2212yes—
40#2854C2214yes—
41#2850C2212yes—
42#2849C2214yes—
43#2803C2218yescomplemented
44#2801C2218yescomplemented
45#2800C2218yescomplemented
46#2790C2218yescomplemented
47#2783C2218yescomplemented
48#2780C2218yescomplemented
49#2779C2218yescomplemented
50#2765C2218yescomplemented
51#2761C2218yescomplemented
52#2757C2218yescomplemented
53#2757C2218yescomplemented
54#2753C2218yescomplemented
55#2725C2218yescomplemented
56#2718C2218yescomplemented
57#2701C2218yescomplemented
58#2701C2218yescomplemented
59#2645C2212yescomplemented
60#2645C2212yescomplemented
61#2644C2214yes—
62#2644C2212yescomplemented
63#2644C2212yescomplemented
64#2643C2214yes—
65#2643C2214yes—
66#2622C2214yes—
67#2620C2212yes—
68#2619C2212yes—
69#2618C2214yes—
70#2602C2218yescomplemented
71#2597C2218yescomplemented
72#2594C2218yescomplemented
73#2593C2218yescomplemented
74#2587C2218yescomplemented
75#2576C2218yescomplemented
76#2570C2214yescomplemented
77#2566C2218yescomplemented
78#2558C2218yescomplemented
79#2554C2218yescomplemented
80#2552C2214yescomplemented
81#2548C2214yes—
82#2548C2212yes—
83#2548C2212yes—
84#2545C2214yes—
85#2545C2212yes—
86#2545C2212yes—
87#2525C2218yescomplemented
88#2516C2218yescomplemented
89#2515C2218yescomplemented
90#2513C2214yes—
91#2513C2218yescomplemented
92#2512C2214yes—
93#2507C2214yescomplemented
94#2506C2214yescomplemented
95#2502C2212yescomplemented
96#2501C2212yescomplemented
97#2500C2212yescomplemented
98#2499C2212yescomplemented
99#2490C2218yescomplemented
100#2480C2218yes—
101#2473C2218yes—
102#2466C2218yescomplemented
103#2447C2214yes—
104#2445C2214yes—
105#2443C2218yes—
106#2429C2214yescomplemented
107#2429C2214yescomplemented
108#2428C2214yes—
109#2426C2214yes—
110#2426C2214yes—
111#2426C2214yes—
112#2426C2214yes—
113#2426C2214yes—
114#2426C2214yescomplemented
115#2426C2214yescomplemented
116#2424C2218yes—
117#2423C2214yescomplemented
118#2422C2214yes—
119#2422C2214yescomplemented
120#2422C2218yescomplemented
121#2420C2214yes—
122#2411C2218yes—
123#2411C2218yes—
124#2401C2214yescomplemented
125#2401C2214yescomplemented
126#2367C2214yes—
127#2367C2214yescomplemented
128#2366C2214yes—
129#2365C2214yescomplemented
130#2363C2214yes—
131#2362C2214yescomplemented
132#2361C2214yes—
133#2360C2214yescomplemented
134#2359C2218yes—
135#2359C2218yes—
136#2351C2214yescomplemented
137#2351C2214yescomplemented
138Q8×C4⋊C4C2214yescomplemented
139Q8×C4⋊C4C2214yescomplemented
140#2327C2212yescomplemented
141#2326C2214yes—
142#2326C2214yes—
143#2326C2214yes—
144#2326C2214yes—
145#2326C2212yescomplemented
146#2323C2214yescomplemented
147#2321C2214yes—
148#2320C2212yescomplemented
149#2320C2212yescomplemented
150#2319C2212yescomplemented
151#2319C2212yescomplemented
152#2318C2214yes—
153#2318C2214yes—
154#2317C2211yescharacteristic
155#2317C2214yes—
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2316C2211yescharacteristic
159#2311C2211yescharacteristic
160#2309C2211yescharacteristic
161#2309C2211yescharacteristic
162C4×C4⋊Q8C2212yescomplemented
163C4×#124C2212yescomplemented
164C4×C22⋊Q8C2214yescomplemented
165C4×#120C2214yes—
166#2298C2214yescomplemented
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2214yes—
178C2×#391C2211yescharacteristic
179C2×#390C2211yescharacteristic
180C2×#388C2214yes—
181C2×#385C2214yes—
182C2×#384C2211yescharacteristic
183#2283C2214yescomplemented
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#537—44no—
193#536—28no—
194#536—28no—
195#535—28no—
196#535—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×#127C2312yes—
200C2×#127C2312yes—
201C2×#126C2318yes—
202C2×#125C2318yes—
203C2×#124—28no—
204C2×#124C2314yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×#121C2314yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2318yes—
226C2×#120C2314yes—
227C2×#120C2314yes—
228#520—44no—
229#519—28no—
230#519—44no—
231C4×#41—28no—
232C2×C4×Q8—44no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×D4—44no—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2314yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274#401C2314yes—
275#401C2314yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#399C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2314yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2314yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#392C2318yes—
322#391C2311yescharacteristic
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2312yes—
329#391C2314yes—
330#391C2311yescharacteristic
331#391C2312yes—
332#391C2312yes—
333#390C2314yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2318yes—
339#390C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2318yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2311yescharacteristic
349#390C2318yes—
350#390C2318yes—
351#390C2318yes—
352#390C2311yescharacteristic
353#390C2312yes—
354#390C2312yes—
355#390C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2312yes—
374#389C2318yes—
375#389C2312yes—
376#389C2318yes—
377#389C2312yes—
378#389C2312yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#386C2314yes—
416#386C2312yes—
417#386C2312yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2312yes—
422#386C2318yes—
423#386C2314yes—
424#386C2312yes—
425#386C2318yes—
426#386C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2312yes—
432#385C2312yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#385C2312yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#385C2312yes—
445#385C2314yes—
446#384C2312yes—
447#384C2318yes—
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#383C2314yes—
454#383C2314yes—
455#382C2314yes—
456#382C2312yes—
457#382C2312yes—
458#382C2318yes—
459#382C2312yes—
460#382C2314yes—
461#381C2314yes—
462#381C2314yes—
463#381C2318yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#379C2314yes—
469#379C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495#376C2312yes—
496#376C2312yes—
497#376C2312yes—
498#376C2312yes—
499#376C2312yes—
500C2×#95C2312yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8#4118yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2411yescharacteristic
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×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2412yes—
541C23×C4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2418yes—
545C23×C4C2411yescharacteristic
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548#127—28no—
549#127—44no—
550#126—88no—
551#125—88no—
552#124—216no—
553#124—28no—
554#124—28no—
555#124—28no—
556#124—28no—
557#124—28no—
558#124—44no—
559#123—216no—
560#123—216no—
561#123—88no—
562#123—88no—
563C22⋊Q8—216no—
564C22⋊Q8—216no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567#121—216no—
568#121—44no—
569#121—44no—
570#121—44no—
571#121—44no—
572#121—48no—
573#121—88no—
574#120—216no—
575#120—48no—
576C4×Q8—28no—
577C4×Q8—216no—
578C4×Q8—216no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×D4—28no—
587C4×D4—216no—
588C4×D4—48no—
589C4×D4—48no—
590C4×D4—44no—
591C4×D4—48no—
592C4×D4—88no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—216no—
599#117—28no—
600#117—48no—
601#117—44no—
602#117#4118yes—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—84no—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C22⋊C4—216no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—84no—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C42—24no—
684C2×C42—24no—
685C2×C42—24no—
686C2×C42—28no—
687C2×C42—44no—
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2418yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749C24—24no—
750C24—24no—
751C24—24no—
752C24—44no—
753C24—44no—
754C24C2514yes—
755C24C2512yes—
756C24C2512yes—
757C24C2511yescharacteristic
758#41—416no—
759#41—416no—
760C2×Q8—232no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8C2×#4118yes—
772C2×Q8C2×#4118yes—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—22no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—216no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4—48no—
800C2×D4—416no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—816no—
832C22×C4C2×#4118yes—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4H(5,𝔽2)14yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—28no—
858C4⋊C4—216no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—216no—
863C4⋊C4—216no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4C2×#4118yes—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—216no—
904C22⋊C4—216no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4C2×#4118yes—
929C42—22no—
930C42—22no—
931C42—24no—
932C42—28no—
933C42—22no—
934C42—22no—
935C42—24no—
936C42—216no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—48no—
945C42—44no—
946C42—44no—
947C42—44no—
948C42—44no—
949C42—48no—
950C42—44no—
951C42C2×#4118yes—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—28no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—28no—
969C23—416no—
970C23—48no—
971C23—84no—
972C23—88no—
973C23—84no—
974C23C22×#4112yes—
975C23C22×#4112yes—
976C23C2×H(5,𝔽2)12yes—
977C23C2611yescharacteristic
978Q8—216no—
979Q8—216no—
980Q8—44no—
981Q8—44no—
982D4—48no—
983D4—48no—
984D4—48no—
985D4—48no—
986D4—44no—
987D4—44no—
988D4—816no—
989D4—164no—
990D4—164no—
991D4—164no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—216no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—28no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—48no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—88no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—816no—
1052C2×C4—164no—
1053C2×C4#553116yes—
1054C2×C4C22×#4118yes—
1055C2×C4C22×#4118yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C22—24no—
1063C22—24no—
1064C22—22no—
1065C22—22no—
1066C22—44no—
1067C22—44no—
1068C22—48no—
1069C22—44no—
1070C22—44no—
1071C22—48no—
1072C22—44no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—44no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—44no—
1081C22—816no—
1082C22C2×#55314yes—
1083C22C23×#4111yescharacteristic
1084C22C23×#4111yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22H(7,𝔽2)12yes—
1087C222−1+612yes—
1088C4—28no—
1089C4—28no—
1090C4—44no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—44no—
1099C4—44no—
1100C4—42no—
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4C2×#55314yes—
1108C4C2×#55314yes—
1109C2—24no—
1110C2—82no—
1111C2—82no—
1112C2—84no—
1113C2C22×#55311yescharacteristic
1114C2#6285112yes—
1115C2#6285712yes—
1116C2#6287611yescharacteristic
1117C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35256C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45294C2semidirect
2. #45285C2semidirect
3. #45028C2semidirect
4. #45000C2semidirect
5. #39287C2semidirect
6. #39281C2semidirect
7. #39147C2semidirect
8. #39143C2semidirect
9. #39049C2semidirect
10. #38126C2semidirect
11. #35677C2semidirect
12. #35677C2semidirect
13. #35555C2semidirect
14. #35530C2semidirect
15. #35266C2semidirect
17. #35153C2semidirect
18. #35152C2semidirect
19. #34639C2semidirect
20. #34276C2semidirect
21. #34268C2semidirect
22. #34265C2semidirect
23. #34249C2semidirect
24. C2×#2326C2semidirect
25. #34056C2semidirect
43. #2803C22semidirect
44. #2801C22semidirect
45. #2800C22semidirect
46. #2790C22semidirect
47. #2783C22semidirect
48. #2780C22semidirect
49. #2779C22semidirect
50. #2765C22semidirect
51. #2761C22semidirect
52. #2757C22semidirect
53. #2757C22semidirect
54. #2753C22semidirect
55. #2725C22semidirect
56. #2718C22semidirect
57. #2701C22semidirect
58. #2701C22semidirect
59. #2645C22semidirect
60. #2645C22semidirect
62. #2644C22semidirect
63. #2644C22semidirect
70. #2602C22semidirect
71. #2597C22semidirect
72. #2594C22semidirect
73. #2593C22semidirect
74. #2587C22semidirect
75. #2576C22semidirect
76. #2570C22semidirect
77. #2566C22semidirect
78. #2558C22semidirect
79. #2554C22semidirect
80. #2552C22semidirect
87. #2525C22semidirect
88. #2516C22semidirect
89. #2515C22semidirect
91. #2513C22semidirect
93. #2507C22semidirect
94. #2506C22semidirect
95. #2502C22semidirect
96. #2501C22semidirect
97. #2500C22semidirect
98. #2499C22semidirect
99. #2490C22semidirect
102. #2466C22semidirect
106. #2429C22semidirect
107. #2429C22semidirect
114. #2426C22semidirect
115. #2426C22semidirect
117. #2423C22semidirect
119. #2422C22semidirect
120. #2422C22semidirect
124. #2401C22semidirect
125. #2401C22semidirect
127. #2367C22semidirect
129. #2365C22semidirect
131. #2362C22semidirect
133. #2360C22semidirect
136. #2351C22semidirect
137. #2351C22semidirect
138. Q8×C4⋊C4C22semidirect
139. Q8×C4⋊C4C22semidirect
140. #2327C22semidirect
145. #2326C22semidirect
146. #2323C22semidirect
148. #2320C22semidirect
149. #2320C22semidirect
150. #2319C22semidirect
151. #2319C22semidirect
162. C4×C4⋊Q8C22semidirect
163. C4×#124C22semidirect
164. C4×C22⋊Q8C22semidirect
166. #2298C22semidirect
183. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#452942
#452852
#450282
#450002
#392872
#392812
#391472
#391432
#390492
#381262
#356772
#355552
#355302
#352662
#352562
#351532
#351522
#346392
#342762
#342682
#342652
#342492
C2×#23262
#340562