Finite Group Databasebeta

← #7673908

Subgroups — #7673908

Order 512.

5154 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45168C214yesmaximal, complemented
2#45167C214yesmaximal, complemented
3#44986C214yesmaximal, complemented
4#44985C214yesmaximal, complemented
5#39809C214yesmaximal, complemented
6#39808C214yesmaximal, complemented
7#39771C214yesmaximal, complemented
8#39765C214yesmaximal, complemented
9#39267C218yesmaximal, complemented
10#39265C218yesmaximal, complemented
11#35628C211yesmaximal, characteristic, complemented
12#35619C211yesmaximal, characteristic, complemented
13#35556C211yesmaximal, characteristic, complemented
14#35531C211yesmaximal, characteristic, complemented
15#35338C211yesmaximal, characteristic, complemented
16#35329C211yesmaximal, characteristic
17#35182C211yesmaximal, characteristic, complemented
18#35152C211yesmaximal, characteristic, complemented
19#34637C211yesmaximal, characteristic, complemented
20#34266C211yesmaximal, characteristic, complemented
21#34265C211yesmaximal, characteristic, complemented
22#34214C211yesmaximal, characteristic, complemented
23#34207C211yesmaximal, characteristic, complemented
24#34074C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2861C2214yes—
39#2858C2212yes—
40#2858C2212yes—
41#2853C2214yes—
42#2849C2214yes—
43#2808C2218yescomplemented
44#2808C2218yescomplemented
45#2807C2218yescomplemented
46#2804C2218yescomplemented
47#2803C2218yescomplemented
48#2803C2218yescomplemented
49#2798C2218yescomplemented
50#2797C2218yescomplemented
51#2796C2218yescomplemented
52#2796C2218yescomplemented
53#2773C2218yescomplemented
54#2771C2218yescomplemented
55#2751C2218yescomplemented
56#2751C2218yescomplemented
57#2724C2218yescomplemented
58#2710C2218yescomplemented
59#2658C2212yes—
60#2657C2212yes—
61#2642C2212yescomplemented
62#2641C2212yescomplemented
63#2640C2214yes—
64#2640C2212yescomplemented
65#2640C2212yescomplemented
66#2639C2214yes—
67#2639C2214yes—
68#2623C2214yes—
69#2622C2214yes—
70#2602C2218yescomplemented
71#2600C2218yescomplemented
72#2597C2218yescomplemented
73#2597C2218yescomplemented
74#2596C2218yescomplemented
75#2596C2218yescomplemented
76#2592C2214yes—
77#2592C2214yes—
78#2592C2214yes—
79#2592C2214yescomplemented
80#2592C2218yescomplemented
81#2589C2218yescomplemented
82#2580C2218yescomplemented
83#2575C2218yescomplemented
84#2568C2214yescomplemented
85#2561C2218yes—
86#2548C2214yes—
87#2540C2214yes—
88#2540C2214yes—
89#2539C2218yes—
90#2513C2218yescomplemented
91#2504C2212yes—
92#2503C2212yescomplemented
93#2502C2212yescomplemented
94#2501C2212yes—
95#2500C2212yes—
96#2500C2212yes—
97#2499C2212yescomplemented
98#2499C2212yescomplemented
99#2492C2214yescomplemented
100#2491C2214yes—
101#2490C2214yes—
102#2489C2214yescomplemented
103#2488C2218yes—
104#2472C2218yes—
105#2459C2218yescomplemented
106#2458C2218yescomplemented
107#2458C2218yescomplemented
108#2455C2218yescomplemented
109#2448C2214yes—
110#2448C2214yescomplemented
111#2447C2214yes—
112#2447C2214yescomplemented
113#2447C2218yescomplemented
114#2446C2214yescomplemented
115#2446C2214yescomplemented
116#2445C2214yes—
117#2445C2214yes—
118#2423C2214yescomplemented
119#2422C2214yes—
120#2421C2214yescomplemented
121#2420C2214yes—
122#2419C2218yes—
123#2418C2218yes—
124#2398C2214yescomplemented
125#2398C2214yescomplemented
126#2367C2214yes—
127#2367C2214yescomplemented
128#2366C2214yes—
129#2365C2214yescomplemented
130#2363C2214yes—
131#2362C2214yescomplemented
132#2361C2218yes—
133#2361C2214yes—
134#2360C2218yes—
135#2360C2214yescomplemented
136#2355C2214yescomplemented
137#2354C2214yescomplemented
138Q8×C4⋊C4C2214yescomplemented
139D4×C4⋊C4C2214yescomplemented
140#2331C2212yescomplemented
141#2331C2212yescomplemented
142#2330C2212yescomplemented
143#2330C2212yescomplemented
144#2330C2214yescomplemented
145#2329C2214yes—
146#2329C2214yes—
147#2326C2214yes—
148#2326C2214yes—
149#2326C2214yes—
150#2326C2214yes—
151#2326C2212yescomplemented
152#2326C2212yescomplemented
153#2322C2214yes—
154#2321C2214yes—
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×C4⋊Q8C2214yescomplemented
164C4×C4⋊Q8C2212yescomplemented
165C4×#127C2212yescomplemented
166C4×#123C2214yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2295C2214yescomplemented
175#2295C2214yescomplemented
176C2×#391C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#388C2214yes—
179C2×#385C2214yes—
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
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#533—28no—
197#533—28no—
198#532—28no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×#127C2311yescharacteristic
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124—28no—
210C2×#124C2314yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2318yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#120C2314yes—
234C2×#120C2314yes—
235#520—44no—
236#520—44no—
237C2×C4×Q8—44no—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2318yes—
245C2×C4×D4—44no—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2318yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C22⋊C4C2314yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2314yes—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2314yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2314yes—
307#394C2318yes—
308#394C2314yes—
309#394C2318yes—
310#394C2314yes—
311#394C2314yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2314yes—
317#393C2318yes—
318#393C2314yes—
319#393C2318yes—
320#393C2314yes—
321#393C2314yes—
322#392C2318yes—
323#392C2318yes—
324#391C2312yes—
325#391C2312yes—
326#391C2318yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2318yes—
360#390C2318yes—
361#390C2318yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2318yes—
379#389C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
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#387C2314yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#386C2314yes—
419#386C2314yes—
420#386C2312yes—
421#386C2318yes—
422#386C2312yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2312yes—
427#386C2312yes—
428#386C2314yes—
429#386C2314yes—
430#385C2314yes—
431#385C2314yes—
432#385C2318yes—
433#385C2312yes—
434#385C2312yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2312yes—
444#385C2312yes—
445#385C2318yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#384C2314yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#382C2318yes—
454#382C2312yes—
455#382C2312yes—
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#381C2314yes—
459#381C2314yes—
460#381C2318yes—
461#381C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#379C2314yes—
466#379C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2312yes—
494#376C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2312yes—
498#376C2312yes—
499C2×#95C2312yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C43C2312yes—
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—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2414yes—
519C22×Q8C2414yes—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2414yes—
530C22×D4C2418yes—
531C22×D4C2414yes—
532C22×D4C2414yes—
533C23×C4—44no—
534C23×C4—84no—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2411yescharacteristic
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2418yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—44no—
553#127—24no—
554#127—28no—
555#127—44no—
556#125—28no—
557#125—28no—
558#124—216no—
559#124—28no—
560#124—28no—
561#124—24no—
562#124—24no—
563#124—28no—
564#124—28no—
565#124—44no—
566#124—44no—
567#124—88no—
568#123—216no—
569#123—48no—
570#123—88no—
571#123—88no—
572C22⋊Q8—216no—
573C22⋊Q8—216no—
574C22⋊Q8—216no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577#121—216no—
578#121—216no—
579#121—44no—
580#121—44no—
581#120—216no—
582#120—48no—
583C4×Q8—216no—
584C4×Q8—216no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—88no—
590C4×D4—216no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4—44no—
594C4×D4—44no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—88no—
598C4×D4—88no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—44no—
605#117—44no—
606#117#4118yes—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—84no—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C22⋊C4—216no—
649C2×C22⋊C4—44no—
650C2×C22⋊C4—84no—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C42—24no—
687C2×C42—24no—
688C2×C42—44no—
689C2×C42#4118yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2418yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751C24—24no—
752C24—24no—
753C24—24no—
754C24—44no—
755C24—44no—
756C24C2514yes—
757C24C2512yes—
758C24C2512yes—
759C24C2511yescharacteristic
760#41—416no—
761#41—416no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—28no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—416no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—28no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—216no—
797C2×D4—24no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—48no—
808C2×D4—48no—
809C2×D4—416no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—816no—
840C22×C4C2×#4118yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4114yes—
843C22×C4H(5,𝔽2)14yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—216no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4C2×#4118yes—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—216no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—216no—
910C22⋊C4—216no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4C2×#4118yes—
935C42—24no—
936C42—22no—
937C42—22no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—48no—
946C42—44no—
947C42—44no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—48no—
952C42—44no—
953C42—48no—
954C42C2×#4118yes—
955C42C2×#4114yes—
956C42C2×#4114yes—
957C42C2×#4118yes—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—28no—
972C23—24no—
973C23—24no—
974C23—28no—
975C23—416no—
976C23—48no—
977C23—84no—
978C23—88no—
979C23—84no—
980C23C22×#4112yes—
981C23C22×#4112yes—
982C23C2×H(5,𝔽2)12yes—
983C23C2611yescharacteristic
984Q8—416no—
985Q8—48no—
986Q8—48no—
987Q8—44no—
988Q8—44no—
989Q8—88no—
990D4—416no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—48no—
995D4—44no—
996D4—44no—
997D4—816no—
998D4—164no—
999D4—164no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—48no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—84no—
1057C2×C4—816no—
1058C2×C4—164no—
1059C2×C4—164no—
1060C2×C4#559116yes—
1061C2×C4C22×#4114yes—
1062C2×C4C22×#4114yes—
1063C2×C4C22×#4118yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C22—24no—
1071C22—24no—
1072C22—22no—
1073C22—22no—
1074C22—44no—
1075C22—44no—
1076C22—48no—
1077C22—44no—
1078C22—48no—
1079C22—44no—
1080C22—44no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—44no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—44no—
1089C22—816no—
1090C22C2×#55914yes—
1091C22C23×#4111yescharacteristic
1092C22C23×#4111yescharacteristic
1093C22C22×H(5,𝔽2)11yescharacteristic
1094C22H(7,𝔽2)12yes—
1095C222−1+612yes—
1096C4—24no—
1097C4—24no—
1098C4—28no—
1099C4—44no—
1100C4—44no—
1101C4—42no—
1102C4—42no—
1103C4—44no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4C2×#55914yes—
1116C4C2×#55914yes—
1117C2—24no—
1118C2—82no—
1119C2—82no—
1120C2—84no—
1121C2C22×#55911yescharacteristic
1122C2#6284512yes—
1123C2#6285712yes—
1124C2#6287611yescharacteristic
1125C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35329C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45168C2semidirect
2. #45167C2semidirect
3. #44986C2semidirect
4. #44985C2semidirect
5. #39809C2semidirect
6. #39808C2semidirect
7. #39771C2semidirect
8. #39765C2semidirect
9. #39267C2semidirect
10. #39265C2semidirect
11. #35628C2semidirect
12. #35619C2semidirect
13. #35556C2semidirect
14. #35531C2semidirect
15. #35338C2semidirect
17. #35182C2semidirect
18. #35152C2semidirect
19. #34637C2semidirect
20. #34266C2semidirect
21. #34265C2semidirect
22. #34214C2semidirect
23. #34207C2semidirect
24. #34074C2semidirect
25. C2×#2326C2semidirect
43. #2808C22semidirect
44. #2808C22semidirect
45. #2807C22semidirect
46. #2804C22semidirect
47. #2803C22semidirect
48. #2803C22semidirect
49. #2798C22semidirect
50. #2797C22semidirect
51. #2796C22semidirect
52. #2796C22semidirect
53. #2773C22semidirect
54. #2771C22semidirect
55. #2751C22semidirect
56. #2751C22semidirect
57. #2724C22semidirect
58. #2710C22semidirect
61. #2642C22semidirect
62. #2641C22semidirect
64. #2640C22semidirect
65. #2640C22semidirect
70. #2602C22semidirect
71. #2600C22semidirect
72. #2597C22semidirect
73. #2597C22semidirect
74. #2596C22semidirect
75. #2596C22semidirect
79. #2592C22semidirect
80. #2592C22semidirect
81. #2589C22semidirect
82. #2580C22semidirect
83. #2575C22semidirect
84. #2568C22semidirect
90. #2513C22semidirect
92. #2503C22semidirect
93. #2502C22semidirect
97. #2499C22semidirect
98. #2499C22semidirect
99. #2492C22semidirect
102. #2489C22semidirect
105. #2459C22semidirect
106. #2458C22semidirect
107. #2458C22semidirect
108. #2455C22semidirect
110. #2448C22semidirect
112. #2447C22semidirect
113. #2447C22semidirect
114. #2446C22semidirect
115. #2446C22semidirect
118. #2423C22semidirect
120. #2421C22semidirect
124. #2398C22semidirect
125. #2398C22semidirect
127. #2367C22semidirect
129. #2365C22semidirect
131. #2362C22semidirect
135. #2360C22semidirect
136. #2355C22semidirect
137. #2354C22semidirect
138. Q8×C4⋊C4C22semidirect
139. D4×C4⋊C4C22semidirect
140. #2331C22semidirect
141. #2331C22semidirect
142. #2330C22semidirect
143. #2330C22semidirect
144. #2330C22semidirect
151. #2326C22semidirect
152. #2326C22semidirect
163. C4×C4⋊Q8C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×#127C22semidirect
174. #2295C22semidirect
175. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#451682
#451672
#449862
#449852
#398092
#398082
#397712
#397652
#392672
#392652
#356282
#356192
#355562
#355312
#353382
#353292
#351822
#351522
#346372
#342662
#342652
#342142
#342072
#340742
C2×#23262