Finite Group Databasebeta

← #7674189

Subgroups — #7674189

Order 512.

5528 conjugacy classes of subgroups.

The subgroup lattice has 1135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45292C214yesmaximal, complemented
2#45283C214yesmaximal, complemented
3#45026C214yesmaximal, complemented
4#44998C214yesmaximal, complemented
5#39037C218yesmaximal, complemented
6#38255C214yesmaximal, complemented
7#38249C214yesmaximal, complemented
8#38114C218yesmaximal, complemented
9#38061C214yesmaximal, complemented
10#38055C214yesmaximal, complemented
11#35679C211yesmaximal, characteristic, complemented
12#35676C211yesmaximal, characteristic
13#35557C211yesmaximal, characteristic, complemented
14#35532C211yesmaximal, characteristic, complemented
15#35264C211yesmaximal, characteristic, complemented
16#35254C211yesmaximal, characteristic, complemented
17#35154C211yesmaximal, characteristic, complemented
18#35152C211yesmaximal, characteristic, complemented
19#34639C211yesmaximal, characteristic, complemented
20#34265C211yesmaximal, characteristic, complemented
21#34259C211yesmaximal, characteristic, complemented
22#34257C211yesmaximal, characteristic, complemented
23#34254C211yesmaximal, characteristic, complemented
24C2×#2326C211yesmaximal, characteristic, complemented
25#34056C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#2861C2212yes—
37#2858C2212yes—
38#2855C2214yes—
39#2854C2214yes—
40#2849C2214yes—
41#2798C2218yescomplemented
42#2798C2218yescomplemented
43#2797C2218yescomplemented
44#2764C2218yescomplemented
45#2763C2218yescomplemented
46#2759C2218yescomplemented
47#2754C2218yescomplemented
48#2752C2218yescomplemented
49#2749C2218yescomplemented
50#2748C2218yescomplemented
51#2746C2218yescomplemented
52#2743C2218yescomplemented
53#2730C2218yescomplemented
54#2717C2218yescomplemented
55#2706C2218yescomplemented
56#2705C2218yescomplemented
57#2645C2212yescomplemented
58#2645C2212yescomplemented
59#2644C2212yescomplemented
60#2644C2212yescomplemented
61#2643C2214yes—
62#2643C2214yes—
63#2641C2212yes—
64#2640C2212yes—
65#2627C2214yes—
66#2624C2214yes—
67#2622C2214yes—
68#2603C2218yescomplemented
69#2589C2218yescomplemented
70#2578C2218yescomplemented
71#2567C2212yescomplemented
72#2566C2212yescomplemented
73#2565C2212yescomplemented
74#2564C2218yescomplemented
75#2553C2218yescomplemented
76#2542C2212yescomplemented
77#2531C2218yescomplemented
78#2527C2218yescomplemented
79#2526C2218yescomplemented
80#2521C2218yescomplemented
81#2518C2218yescomplemented
82#2518C2218yescomplemented
83#2516C2218yescomplemented
84#2512C2214yescomplemented
85#2511C2214yescomplemented
86#2510C2218yescomplemented
87#2497C2214yescomplemented
88#2496C2214yescomplemented
89#2491C2214yes—
90#2490C2214yes—
91#2488C2218yescomplemented
92#2482C2218yes—
93#2481C2218yes—
94#2472C2218yes—
95#2461C2218yescomplemented
96#2453C2214yescomplemented
97#2453C2214yescomplemented
98#2451C2214yescomplemented
99#2451C2214yescomplemented
100#2449C2218yes—
101#2448C2214yes—
102#2448C2214yes—
103#2448C2214yes—
104#2448C2214yes—
105#2448C2214yes—
106#2447C2214yes—
107#2445C2214yes—
108#2445C2214yes—
109#2441C2214yescomplemented
110#2440C2214yescomplemented
111#2436C2214yes—
112#2436C2212yes—
113#2436C2212yes—
114#2431C2214yes—
115#2431C2212yes—
116#2431C2212yes—
117#2422C2214yes—
118#2420C2214yes—
119#2419C2218yescomplemented
120#2418C2218yes—
121#2404C2218yes—
122#2401C2214yescomplemented
123#2401C2214yescomplemented
124#2367C2214yes—
125#2366C2214yes—
126#2363C2214yes—
127#2361C2214yes—
128#2356C2214yescomplemented
129#2355C2214yescomplemented
130#2343C2218yes—
131#2341C2214yescomplemented
132#2341C2214yescomplemented
133Q8×C22⋊C4C2214yescomplemented
134Q8×C22⋊C4C2214yescomplemented
135Q8×C22⋊C4C2214yescomplemented
136#2339C2218yes—
137#2339C2214yescomplemented
138#2326C2214yes—
139#2326C2214yes—
140#2326C2214yes—
141#2326C2214yes—
142#2321C2214yes—
143#2320C2212yescomplemented
144#2320C2212yescomplemented
145#2320C2214yescomplemented
146#2319C2212yescomplemented
147#2319C2212yescomplemented
148#2318C2214yes—
149#2318C2214yes—
150#2317C2211yescharacteristic
151#2316C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2214yes—
154#2311C2211yescharacteristic
155#2311C2211yescharacteristic
156#2311C2212yescomplemented
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2310C2212yescomplemented
160#2309C2211yescharacteristic
161#2309C2211yescharacteristic
162C4×#120C2214yes—
163#2298C2214yescomplemented
164#2297C2211yescharacteristic
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2214yes—
170#2297C2212yescomplemented
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2295C2214yescomplemented
177C2×#391C2211yescharacteristic
178C2×#391C2212yescomplemented
179C2×#390C2211yescharacteristic
180C2×#388C2214yes—
181C2×#385C2214yes—
182C2×#384C2211yescharacteristic
183#2283C2214yescomplemented
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—28no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2314yes—
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2311yescharacteristic
195C23×Q8C2312yes—
196C23×Q8C2312yes—
197C23×Q8C2311yescharacteristic
198C23×D4C2311yescharacteristic
199C24×C4C2312yes—
200#544—44no—
201#535—28no—
202#535—44no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#124—28no—
211C2×#124C2314yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2318yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2318yes—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#120C2314yes—
225C2×#120C2314yes—
226#520—44no—
227#519—28no—
228C4×#41—28no—
229C2×C4×Q8—44no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×D4—44no—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2312yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2314yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266#401C2314yes—
267#401C2314yes—
268#400C2314yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#399C2318yes—
278#399C2318yes—
279#399C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#397C2314yes—
285#397C2318yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2314yes—
292#397C2314yes—
293#397C2314yes—
294#397C2314yes—
295#397C2318yes—
296#397C2318yes—
297#396C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#392C2318yes—
313#392C2318yes—
314#391C2311yescharacteristic
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2311yescharacteristic
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2312yes—
328#391C2311yescharacteristic
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2312yes—
334#391C2318yes—
335#391C2318yes—
336#391C2311yescharacteristic
337#391C2312yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2311yescharacteristic
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2318yes—
348#390C2311yescharacteristic
349#390C2312yes—
350#390C2311yescharacteristic
351#390C2318yes—
352#390C2312yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2318yes—
357#390C2318yes—
358#390C2311yescharacteristic
359#390C2312yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2318yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
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#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2312yes—
410#386C2312yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#386C2312yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2312yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2312yes—
432#385C2312yes—
433#385C2314yes—
434#385C2312yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2318yes—
440#385C2312yes—
441#385C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2314yes—
446#383C2314yes—
447#383C2314yes—
448#383C2318yes—
449#382C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2318yes—
453#381C2314yes—
454#381C2314yes—
455#381C2318yes—
456#381C2314yes—
457#381C2314yes—
458#381C2318yes—
459#380C2314yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2318yes—
466#380C2314yes—
467#380C2314yes—
468#379C2314yes—
469#379C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493#376C2312yes—
494#376C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2312yes—
498#376C2318yes—
499C2×#95C2318yes—
500C2×#95C2312yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2412yes—
5052−1+4—464no—
506C2×#41—28no—
507C2×#41—28no—
508C2×#41—216no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—28no—
512C2×#41—216no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—48no—
518C2×#41—44no—
519C2×#41—44no—
520C2×#41#4118yes—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—28no—
524C22×Q8—24no—
525C22×Q8—28no—
526C22×Q8—24no—
527C22×Q8—44no—
528C22×Q8—44no—
529C22×Q8#4118yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2414yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2418yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C23×C4—44no—
550C23×C4—84no—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2414yes—
563C23×C4C2414yes—
564C23×C4C2418yes—
565C23×C4C2411yescharacteristic
566C4⋊Q8—44no—
567C4⋊Q8—44no—
568#127—28no—
569#127—44no—
570#126—88no—
571#125—44no—
572#125—44no—
573#124—216no—
574#124—28no—
575#124—28no—
576#124—28no—
577#124—44no—
578#124—88no—
579#123—88no—
580#123—88no—
581C22⋊Q8—48no—
582C22⋊Q8—88no—
583#121—216no—
584#121—44no—
585#121—44no—
586#120—216no—
587#120—48no—
588C4×Q8—28no—
589C4×Q8—216no—
590C4×Q8—216no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×Q8—44no—
594C4×D4—216no—
595C4×D4—28no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—44no—
599C4×D4—48no—
600C4×D4—88no—
601#117—28no—
602#117—24no—
603#117—216no—
604#117—24no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—44no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—84no—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C42—28no—
685C2×C42—24no—
686C2×C42—24no—
687C2×C42—24no—
688C2×C42—44no—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2418yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752C24—24no—
753C24—24no—
754C24—24no—
755C24—44no—
756C24—44no—
757C24C2514yes—
758C24C2512yes—
759C24C2512yes—
760C24C2511yescharacteristic
761#41—232no—
762#41—464no—
763#41—432no—
764#41—432no—
765#41—416no—
766C2×Q8—232no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—28no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—48no—
781C2×Q8—432no—
782C2×Q8—432no—
783C2×Q8C2×#4114yes—
784C2×Q8C2×#4118yes—
785C2×Q8C2×#4118yes—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—28no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—216no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—28no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—44no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—416no—
813C2×D4C2×#4118yes—
814C2×D4C2×#4114yes—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—28no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—816no—
851C22×C4C2×#4118yes—
852C22×C4C2×#4118yes—
853C22×C4C2×#4114yes—
854C22×C4C2×#4114yes—
855C22×C4H(5,𝔽2)14yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—216no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
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—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—28no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—216no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C42—22no—
944C42—22no—
945C42—24no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—22no—
950C42—22no—
951C42—216no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—48no—
960C42—44no—
961C42—44no—
962C42—48no—
963C42—44no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—28no—
978C23—24no—
979C23—28no—
980C23—416no—
981C23—48no—
982C23—84no—
983C23—88no—
984C23—84no—
985C23C22×#4114yes—
986C23C22×#4112yes—
987C23C22×#4112yes—
988C23C2×H(5,𝔽2)12yes—
989C23C2611yescharacteristic
990Q8—216no—
991Q8—216no—
992Q8—28no—
993Q8—416no—
994Q8—44no—
995Q8—164no—
996D4—216no—
997D4—28no—
998D4—416no—
999D4—48no—
1000D4—48no—
1001D4—48no—
1002D4—44no—
1003D4—816no—
1004D4—164no—
1005D4—164no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—216no—
1011C2×C4—216no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—48no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—84no—
1064C2×C4—88no—
1065C2×C4—84no—
1066C2×C4—84no—
1067C2×C4—816no—
1068C2×C4—164no—
1069C2×C4#551116yes—
1070C2×C4C22×#4118yes—
1071C2×C4C22×#4114yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C22—24no—
1079C22—24no—
1080C22—22no—
1081C22—22no—
1082C22—28no—
1083C22—24no—
1084C22—44no—
1085C22—42no—
1086C22—42no—
1087C22—44no—
1088C22—48no—
1089C22—48no—
1090C22—44no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—44no—
1095C22—42no—
1096C22—44no—
1097C22—816no—
1098C22C2×#55114yes—
1099C22C23×#4111yescharacteristic
1100C22C23×#4111yescharacteristic
1101C22C22×H(5,𝔽2)11yescharacteristic
1102C22H(7,𝔽2)12yes—
1103C222−1+612yes—
1104C4—24no—
1105C4—28no—
1106C4—44no—
1107C4—44no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—44no—
1112C4—42no—
1113C4—44no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4C2×#55114yes—
1124C4C2×#55114yes—
1125C2—24no—
1126C2—44no—
1127C2—82no—
1128C2—84no—
1129C2C22×#55111yescharacteristic
1130C2#6285112yes—
1131C2#6285712yes—
1132C2#6287611yescharacteristic
1133C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45292C2semidirect
2. #45283C2semidirect
3. #45026C2semidirect
4. #44998C2semidirect
5. #39037C2semidirect
6. #38255C2semidirect
7. #38249C2semidirect
8. #38114C2semidirect
9. #38061C2semidirect
10. #38055C2semidirect
11. #35679C2semidirect
13. #35557C2semidirect
14. #35532C2semidirect
15. #35264C2semidirect
16. #35254C2semidirect
17. #35154C2semidirect
18. #35152C2semidirect
19. #34639C2semidirect
20. #34265C2semidirect
21. #34259C2semidirect
22. #34257C2semidirect
23. #34254C2semidirect
24. C2×#2326C2semidirect
25. #34056C2semidirect
41. #2798C22semidirect
42. #2798C22semidirect
43. #2797C22semidirect
44. #2764C22semidirect
45. #2763C22semidirect
46. #2759C22semidirect
47. #2754C22semidirect
48. #2752C22semidirect
49. #2749C22semidirect
50. #2748C22semidirect
51. #2746C22semidirect
52. #2743C22semidirect
53. #2730C22semidirect
54. #2717C22semidirect
55. #2706C22semidirect
56. #2705C22semidirect
57. #2645C22semidirect
58. #2645C22semidirect
59. #2644C22semidirect
60. #2644C22semidirect
68. #2603C22semidirect
69. #2589C22semidirect
70. #2578C22semidirect
71. #2567C22semidirect
72. #2566C22semidirect
73. #2565C22semidirect
74. #2564C22semidirect
75. #2553C22semidirect
76. #2542C22semidirect
77. #2531C22semidirect
78. #2527C22semidirect
79. #2526C22semidirect
80. #2521C22semidirect
81. #2518C22semidirect
82. #2518C22semidirect
83. #2516C22semidirect
84. #2512C22semidirect
85. #2511C22semidirect
86. #2510C22semidirect
87. #2497C22semidirect
88. #2496C22semidirect
91. #2488C22semidirect
95. #2461C22semidirect
96. #2453C22semidirect
97. #2453C22semidirect
98. #2451C22semidirect
99. #2451C22semidirect
109. #2441C22semidirect
110. #2440C22semidirect
119. #2419C22semidirect
122. #2401C22semidirect
123. #2401C22semidirect
128. #2356C22semidirect
129. #2355C22semidirect
131. #2341C22semidirect
132. #2341C22semidirect
133. Q8×C22⋊C4C22semidirect
134. Q8×C22⋊C4C22semidirect
135. Q8×C22⋊C4C22semidirect
137. #2339C22semidirect
143. #2320C22semidirect
144. #2320C22semidirect
145. #2320C22semidirect
146. #2319C22semidirect
147. #2319C22semidirect
156. #2311C22semidirect
159. #2310C22semidirect
163. #2298C22semidirect
170. #2297C22semidirect
176. #2295C22semidirect
178. C2×#391C22semidirect
183. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#452922
#452832
#450262
#449982
#390372
#382552
#382492
#381142
#380612
#380552
#356792
#356762
#355572
#355322
#352642
#352542
#351542
#351522
#346392
#342652
#342592
#342572
#342542
C2×#23262
#340562