Finite Group Databasebeta

← #7644212

Subgroups — #7644212

Order 512.

4756 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42899C214yesmaximal, complemented
2#42897C214yesmaximal, complemented
3#42873C214yesmaximal, complemented
4#42868C214yesmaximal, complemented
5#42841C214yesmaximal, complemented
6#42837C214yesmaximal, complemented
7#42833C214yesmaximal, complemented
8#42830C214yesmaximal, complemented
9#37506C218yesmaximal, complemented
10#36792C218yesmaximal, complemented
11#35679C211yesmaximal, characteristic, complemented
12#35677C211yesmaximal, characteristic
13#35673C211yesmaximal, characteristic, complemented
14#35668C211yesmaximal, characteristic, complemented
15#35558C211yesmaximal, characteristic, complemented
16#35555C211yesmaximal, characteristic, complemented
17#35532C211yesmaximal, characteristic, complemented
18#35531C211yesmaximal, characteristic
19#35174C211yesmaximal, characteristic, complemented
20#35152C211yesmaximal, characteristic
21#34639C211yesmaximal, characteristic, complemented
22#34638C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34249C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35#2849C2214yes—
36#2848C2214yes—
37#2838C2218yescomplemented
38#2837C2218yescomplemented
39#2837C2218yescomplemented
40#2836C2218yescomplemented
41#2807C2218yescomplemented
42#2796C2218yescomplemented
43#2790C2218yescomplemented
44#2787C2218yescomplemented
45#2782C2218yescomplemented
46#2781C2218yescomplemented
47#2771C2218yescomplemented
48#2765C2218yescomplemented
49#2744C2218yescomplemented
50#2732C2218yescomplemented
51#2724C2218yescomplemented
52#2720C2218yescomplemented
53#2718C2218yescomplemented
54#2694C2218yescomplemented
55#2689C2218yescomplemented
56#2680C2218yescomplemented
57#2664C2218yescomplemented
58#2663C2218yescomplemented
59#2654C2218yescomplemented
60#2654C2218yescomplemented
61#2651C2218yescomplemented
62#2651C2218yescomplemented
63#2650C2218yescomplemented
64#2649C2218yescomplemented
65#2647C2212yescomplemented
66#2647C2212yescomplemented
67#2647C2212yescomplemented
68#2647C2212yescomplemented
69#2646C2214yes—
70#2646C2214yes—
71#2645C2212yescomplemented
72#2645C2212yescomplemented
73#2644C2212yescomplemented
74#2644C2212yescomplemented
75#2643C2214yes—
76#2643C2214yes—
77#2626C2214yes—
78#2622C2214yes—
79#2596C2218yescomplemented
80#2594C2218yescomplemented
81#2570C2214yescomplemented
82#2568C2212yescomplemented
83#2567C2212yescomplemented
84#2567C2212yescomplemented
85#2566C2212yescomplemented
86#2565C2212yescomplemented
87#2565C2212yescomplemented
88#2565C2212yescomplemented
89#2560C2218yescomplemented
90#2558C2218yescomplemented
91#2552C2214yescomplemented
92#2548C2212yes—
93#2548C2212yes—
94#2545C2212yes—
95#2545C2212yes—
96#2542C2212yescomplemented
97#2513C2214yes—
98#2513C2214yes—
99#2512C2214yes—
100#2512C2214yes—
101#2507C2214yescomplemented
102#2506C2214yescomplemented
103#2504C2212yes—
104#2501C2212yes—
105#2500C2212yes—
106#2500C2212yes—
107#2498C2218yes—
108#2482C2218yes—
109#2480C2218yes—
110#2473C2218yes—
111#2454C2214yes—
112#2454C2214yes—
113#2453C2214yescomplemented
114#2452C2214yes—
115#2452C2214yes—
116#2451C2214yescomplemented
117#2449C2218yes—
118#2448C2214yes—
119#2448C2214yes—
120#2448C2214yes—
121#2448C2214yes—
122#2448C2214yes—
123#2448C2214yescomplemented
124#2447C2214yes—
125#2446C2214yescomplemented
126#2445C2214yes—
127#2445C2214yes—
128#2441C2214yescomplemented
129#2440C2214yescomplemented
130#2438C2218yes—
131#2426C2214yes—
132#2426C2214yes—
133#2423C2214yescomplemented
134#2422C2214yes—
135#2421C2214yescomplemented
136#2420C2214yes—
137#2418C2218yes—
138#2411C2218yes—
139#2402C2214yescomplemented
140#2402C2214yescomplemented
141#2401C2214yescomplemented
142#2401C2214yescomplemented
143#2367C2214yescomplemented
144#2365C2214yescomplemented
145#2362C2214yescomplemented
146#2360C2214yescomplemented
147#2351C2214yescomplemented
148#2351C2214yescomplemented
149Q8×C4⋊C4C2214yescomplemented
150Q8×C4⋊C4C2214yescomplemented
151#2326C2214yes—
152#2326C2214yes—
153#2326C2214yes—
154#2326C2214yes—
155#2322C2214yes—
156#2317C2211yescharacteristic
157#2317C2214yes—
158#2317C2211yescharacteristic
159#2317C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166C4×#123C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2214yes—
178C2×#391C2211yescharacteristic
179C2×#390C2211yescharacteristic
180C2×#388C2214yes—
181C2×#385C2214yes—
182#2285C2211yescharacteristic
183#2285C2211yescharacteristic
184C2×#384C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#544—44no—
192#536—28no—
193#535—44no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2312yes—
198C2×#126C2318yes—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2318yes—
202C2×#124—28no—
203C2×#124C2314yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#123C2314yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#120C2314yes—
218#520—44no—
219#519—28no—
220#519—44no—
221C2×C4×Q8—44no—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4—44no—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2314yes—
251C22×C22⋊C4C2314yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2314yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#401C2314yes—
259#401C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#399C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2314yes—
321#395C2318yes—
322#395C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2318yes—
330#391C2318yes—
331#391C2312yes—
332#391C2311yescharacteristic
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2311yescharacteristic
339#391C2314yes—
340#391C2312yes—
341#391C2312yes—
342#390C2318yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2311yescharacteristic
352#390C2312yes—
353#390C2314yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2311yescharacteristic
359#390C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
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#388C2318yes—
405#388C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2312yes—
418#386C2318yes—
419#386C2312yes—
420#386C2314yes—
421#386C2314yes—
422#385C2318yes—
423#385C2312yes—
424#385C2312yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2312yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2312yes—
438#385C2312yes—
439#385C2312yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#384C2311yescharacteristic
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2314yes—
451#384C2318yes—
452#384C2312yes—
453#384C2312yes—
454#382C2311yescharacteristic
455#382C2312yes—
456#382C2312yes—
457#382C2311yescharacteristic
458#382C2312yes—
459#382C2318yes—
460#382C2312yes—
461#381C2314yes—
462#381C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2318yes—
466#380C2314yes—
467#380C2314yes—
468#379C2314yes—
469#379C2314yes—
470#379C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
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×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494#376C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2312yes—
498C2×#95C2312yes—
499C2×#95C2312yes—
500C2×#95C2314yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8#4118yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2414yes—
512C22×D4—24no—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2411yescharacteristic
519C22×D4C2414yes—
520C22×D4C2414yes—
521C23×C4—44no—
522C23×C4—84no—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2411yescharacteristic
529C23×C4C2412yes—
530C23×C4C2411yescharacteristic
531C23×C4C2414yes—
532C23×C4C2418yes—
533C23×C4C2411yescharacteristic
534C4⋊Q8—28no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537#127—44no—
538#126—88no—
539#125—44no—
540#125—44no—
541#125—88no—
542#124—216no—
543#124—28no—
544#124—28no—
545#124—28no—
546#124—44no—
547#123—216no—
548#123—88no—
549#123—88no—
550C22⋊Q8—216no—
551C22⋊Q8—48no—
552C22⋊Q8—88no—
553C22⋊Q8—88no—
554#121—44no—
555#121—44no—
556#120—48no—
557C4×Q8—216no—
558C4×Q8—216no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×Q8—44no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—44no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—44no—
569C4×D4—48no—
570#117—216no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—48no—
579#117—44no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—84no—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C22⋊C4—216no—
633C2×C22⋊C4—44no—
634C2×C22⋊C4—84no—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—24no—
667C2×C42—44no—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688C2×C42C2418yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731C24—24no—
732C24—24no—
733C24—24no—
734C24—44no—
735C24—44no—
736C24C2514yes—
737C24C2512yes—
738C24C2511yescharacteristic
739#41—416no—
740C2×Q8—232no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—22no—
748C2×Q8—44no—
749C2×Q8—48no—
750C2×Q8C2×#4118yes—
751C2×Q8C2×#4118yes—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—22no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—22no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—416no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—816no—
794C22×C4C2×#4118yes—
795C22×C4C2×#4114yes—
796C22×C4H(5,𝔽2)14yes—
797C22×C42−1+414yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C4⋊C4—216no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—216no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—216no—
875C22⋊C4—216no—
876C22⋊C4—216no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C42—22no—
897C42—22no—
898C42—24no—
899C42—216no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—48no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—48no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—24no—
921C23—24no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—28no—
927C23—24no—
928C23—28no—
929C23—416no—
930C23—48no—
931C23—84no—
932C23—88no—
933C23—84no—
934C23C22×#4112yes—
935C23C2×H(5,𝔽2)12yes—
936C23C2×2−1+412yes—
937C23C2611yescharacteristic
938Q8—216no—
939Q8—216no—
940Q8—44no—
941Q8—164no—
942D4—48no—
943D4—48no—
944D4—48no—
945D4—44no—
946D4—164no—
947D4—164no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—216no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—28no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—48no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4—816no—
1008C2×C4—164no—
1009C2×C4#539116yes—
1010C2×C4C22×#4118yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4C2×2−1+412yes—
1017C22—24no—
1018C22—22no—
1019C22—24no—
1020C22—22no—
1021C22—44no—
1022C22—48no—
1023C22—44no—
1024C22—42no—
1025C22—44no—
1026C22—48no—
1027C22—42no—
1028C22—44no—
1029C22—42no—
1030C22—44no—
1031C22—816no—
1032C22C2×#53914yes—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22H(7,𝔽2)12yes—
1037C222−1+612yes—
1038C4—28no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—44no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4C2×#53914yes—
1059C4C2×#53914yes—
1060C2—24no—
1061C2—82no—
1062C2—84no—
1063C2C22×#53911yescharacteristic
1064C2#6285112yes—
1065C2#6287611yescharacteristic
1066C2#6287912yes—
1067C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42899C2semidirect
2. #42897C2semidirect
3. #42873C2semidirect
4. #42868C2semidirect
5. #42841C2semidirect
6. #42837C2semidirect
7. #42833C2semidirect
8. #42830C2semidirect
9. #37506C2semidirect
10. #36792C2semidirect
11. #35679C2semidirect
13. #35673C2semidirect
14. #35668C2semidirect
15. #35558C2semidirect
16. #35555C2semidirect
17. #35532C2semidirect
19. #35174C2semidirect
21. #34639C2semidirect
22. #34638C2semidirect
23. #34266C2semidirect
24. #34249C2semidirect
25. C2×#2326C2semidirect
37. #2838C22semidirect
38. #2837C22semidirect
39. #2837C22semidirect
40. #2836C22semidirect
41. #2807C22semidirect
42. #2796C22semidirect
43. #2790C22semidirect
44. #2787C22semidirect
45. #2782C22semidirect
46. #2781C22semidirect
47. #2771C22semidirect
48. #2765C22semidirect
49. #2744C22semidirect
50. #2732C22semidirect
51. #2724C22semidirect
52. #2720C22semidirect
53. #2718C22semidirect
54. #2694C22semidirect
55. #2689C22semidirect
56. #2680C22semidirect
57. #2664C22semidirect
58. #2663C22semidirect
59. #2654C22semidirect
60. #2654C22semidirect
61. #2651C22semidirect
62. #2651C22semidirect
63. #2650C22semidirect
64. #2649C22semidirect
65. #2647C22semidirect
66. #2647C22semidirect
67. #2647C22semidirect
68. #2647C22semidirect
71. #2645C22semidirect
72. #2645C22semidirect
73. #2644C22semidirect
74. #2644C22semidirect
79. #2596C22semidirect
80. #2594C22semidirect
81. #2570C22semidirect
82. #2568C22semidirect
83. #2567C22semidirect
84. #2567C22semidirect
85. #2566C22semidirect
86. #2565C22semidirect
87. #2565C22semidirect
88. #2565C22semidirect
89. #2560C22semidirect
90. #2558C22semidirect
91. #2552C22semidirect
96. #2542C22semidirect
101. #2507C22semidirect
102. #2506C22semidirect
113. #2453C22semidirect
116. #2451C22semidirect
123. #2448C22semidirect
125. #2446C22semidirect
128. #2441C22semidirect
129. #2440C22semidirect
133. #2423C22semidirect
135. #2421C22semidirect
139. #2402C22semidirect
140. #2402C22semidirect
141. #2401C22semidirect
142. #2401C22semidirect
143. #2367C22semidirect
144. #2365C22semidirect
145. #2362C22semidirect
146. #2360C22semidirect
147. #2351C22semidirect
148. #2351C22semidirect
149. Q8×C4⋊C4C22semidirect
150. Q8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#428992
#428972
#428732
#428682
#428412
#428372
#428332
#428302
#375062
#367922
#356792
#356772
#356732
#356682
#355582
#355552
#355322
#355312
#351742
#351522
#346392
#346382
#342662
#342492
C2×#23262