Finite Group Databasebeta

← #7987070

Subgroups — #7987070

Order 512.

4183 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59653C212yesmaximal
3#59434C212yesmaximal
4#59242C212yesmaximal, complemented
5#49094C218yesmaximal, complemented
6#46117C214yesmaximal, complemented
7#45414C214yesmaximal, complemented
8#45183C214yesmaximal, complemented
9#42902C214yesmaximal
10#42717C214yesmaximal, complemented
11#39762C212yesmaximal, complemented
12#39225C214yesmaximal, complemented
13#38978C212yesmaximal
14#38978C212yesmaximal
15#38943C212yesmaximal, complemented
16#36584C212yesmaximal, complemented
17#36563C211yesmaximal, characteristic, complemented
18#36563C211yesmaximal, characteristic, complemented
19#36450C212yesmaximal, complemented
20#36194C211yesmaximal, characteristic
21#35202C212yesmaximal, complemented
22#35187C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic
25#34488C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#556C2211yescharacteristic
29#2868C2211yescharacteristic
30#2864C2214yes—
31#2863C2214yes—
32#2859C2214yes—
33#2859C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2838C2218yes—
37#2798C2218yes—
38#2787C2218yes—
39#2777C2218yes—
40#2777C2218yes—
41#2777C2218yes—
42#2776C2218yes—
43#2776C2218yes—
44#2775C2218yes—
45#2774C2218yes—
46#2772C2218yes—
47#2772C2218yes—
48#2769C2218yes—
49#2762C2218yes—
50#2758C2218yes—
51#2744C2218yes—
52#2726C2214yes—
53#2725C2218yes—
54#2667C2218yes—
55#2655C2218yes—
56#2650C2218yes—
57#2644C2214yes—
58#2642C2214yes—
59#2606C2218yes—
60#2594C2218yes—
61#2585C2214yes—
62#2582C2212yes—
63#2582C2212yes—
64#2582C2212yes—
65#2582C2211yescharacteristic
66#2577C2218yes—
67#2573C2214yes—
68#2571C2214yes—
69#2571C2214yes—
70#2571C2212yes—
71#2571C2211yescharacteristic
72#2568C2211yescharacteristic
73#2568C2211yescharacteristic
74#2567C2212yes—
75#2567C2212yes—
76#2563C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2212yes—
80#2552C2211yescharacteristic
81#2550C2214yes—
82#2550C2214yes—
83#2547C2211yescharacteristic
84#2546C2211yescharacteristic
85#2546C2212yes—
86#2545C2214yes—
87#2538C2212yes—
88#2538C2211yescharacteristic
89#2528C2218yes—
90#2524C2218yes—
91#2524C2218yes—
92#2519C2218yes—
93#2514C2214yes—
94#2514C2214yes—
95#2514C2218yes—
96#2514C2214yes—
97#2514C2214yes—
98#2514C2214yes—
99#2514C2212yes—
100#2511C2212yes—
101#2509C2212yes—
102#2509C2214yes—
103#2509C2214yes—
104#2509C2214yes—
105#2509C2218yes—
106#2509C2218yes—
107#2508C2214yes—
108#2507C2214yes—
109#2507C2214yes—
110#2506C2214yes—
111#2499C2214yes—
112#2499C2214yes—
113#2497C2214yes—
114#2497C2214yes—
115#2495C2214yes—
116#2495C2214yes—
117#2494C2214yes—
118#2494C2212yes—
119#2492C2214yes—
120#2489C2214yes—
121#2489C2214yes—
122#2489C2214yes—
123#2453C2212yes—
124#2453C2214yes—
125#2451C2214yes—
126#2451C2214yes—
127#2448C2214yes—
128#2448C2214yes—
129#2447C2212yes—
130#2446C2214yes—
131#2446C2214yes—
132#2446C2212yes—
133#2441C2214yes—
134#2441C2214yes—
135#2441C2214yes—
136#2441C2214yes—
137#2439C2214yes—
138#2429C2214yes—
139#2421C2212yes—
140#2402C2214yes—
141#2401C2214yes—
142#2382C2218yes—
143#2373C2214yes—
144#2370C2214yes—
145#2369C2212yes—
146#2369C2212yes—
147#2369C2212yes—
148#2367C2212yes—
149#2365C2212yes—
150#2365C2214yes—
151#2365C2211yescharacteristic
152#2362C2214yes—
153#2362C2212yes—
154#2356C2212yes—
155#2355C2212yes—
156#2355C2211yescharacteristic
157#2355C2212yes—
158#2355C2212yes—
159#2355C2214yes—
160#2354C2212yes—
161#2354C2211yescharacteristic
162#2351C2214yes—
163#2351C2214yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167#2347C2214yes—
168#2347C2212yes—
169#2336C2218yes—
170#2330C2214yes—
171#2330C2214yes—
172#2327C2214yes—
173#2320C2214yes—
174#2320C2214yes—
175#2320C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#125C2212yes—
183C4×#125C2214yes—
184C4×#126C2214yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—216no—
200#556—28no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126C2314yes—
210C2×#125C2314yes—
211C2×#125C2318yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2312yes—
239C2×#117C2314yes—
240C2×#117C2312yes—
241C22×C42C2312yes—
242#401C2318yes—
243#401C2318yes—
244#401C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#399C2318yes—
264#399C2318yes—
265#398C2318yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#396C2314yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#395C2318yes—
292#393C2318yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2312yes—
297#391C2312yes—
298#391C2312yes—
299#391C2312yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2318yes—
316#391C2318yes—
317#391C2318yes—
318#390C2314yes—
319#390C2312yes—
320#390C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2312yes—
325#389C2314yes—
326#389C2314yes—
327#389C2312yes—
328#389C2314yes—
329#389C2312yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2314yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2312yes—
342#389C2318yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2318yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#385C2314yes—
421#385C2314yes—
422#384C2312yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2314yes—
429#384C2314yes—
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#383C2314yes—
434#383C2314yes—
435#383C2318yes—
436#383C2318yes—
437#383C2318yes—
438#383C2318yes—
439#382C2312yes—
440#382C2314yes—
441#382C2312yes—
442#382C2312yes—
443#382C2314yes—
444#382C2314yes—
445#382C2318yes—
446#382C2312yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#382C2314yes—
451#382C2312yes—
452#381C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2314yes—
516#376C2314yes—
517C43C2314yes—
518C43C2312yes—
519C43C2311yescharacteristic
520C43C2312yes—
521C22×Q8C2412yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×D4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C4⋊Q8—216no—
532C4⋊Q8—24no—
533C4⋊Q8—24no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8#4118yes—
539#126—216no—
540#125—232no—
541#125—216no—
542#125—44no—
543#125—48no—
544#125—48no—
545#124—28no—
546#124—44no—
547C22⋊Q8—28no—
548C22⋊Q8—44no—
549C22⋊Q8—48no—
550C4×Q8—28no—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—24no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—44no—
561C4×Q8—48no—
562C4×Q8—48no—
563C4×Q8—42no—
564C4×Q8—42no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—42no—
568#117—28no—
569#117—44no—
570#117—48no—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C42—28no—
645C2×C42C2414yes—
646C2×C42C2411yescharacteristic
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2414yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2418yes—
670C2×C42C2418yes—
671C2×C42C2411yescharacteristic
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#95C2412yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2412yes—
705#95C2414yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734C24C2512yes—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—22no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×Q8C2×#4118yes—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2511yescharacteristic
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2518yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—24no—
793C4⋊C4—28no—
794C4⋊C4—216no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—216no—
799C4⋊C4—24no—
800C4⋊C4—216no—
801C4⋊C4—22no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—22no—
819C4⋊C4—28no—
820C4⋊C4—22no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—42no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4C2×#4118yes—
849C4⋊C4C2×#4118yes—
850C22⋊C4—28no—
851C22⋊C4—24no—
852C22⋊C4—28no—
853C22⋊C4—24no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—42no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C42—28no—
864C42—24no—
865C42—216no—
866C42—28no—
867C42—28no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—22no—
876C42—24no—
877C42—24no—
878C42—22no—
879C42—22no—
880C42—24no—
881C42—24no—
882C42—41no—
883C42—42no—
884C42—42no—
885C42—44no—
886C42—48no—
887C42—44no—
888C42—42no—
889C42—42no—
890C42—48no—
891C42—44no—
892C42—48no—
893C42C2×#4114yes—
894C422−1+414yes—
895C422−1+414yes—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23C2611yescharacteristic
904Q8—216no—
905Q8—48no—
906Q8—48no—
907Q8—44no—
908Q8—44no—
909Q8—164no—
910D4—44no—
911C2×C4—24no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—28no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—48no—
974C2×C4—48no—
975C2×C4—84no—
976C2×C4C22×#4118yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C2×2−1+412yes—
981C2×C4C2×2−1+412yes—
982C2×C4C2×2−1+412yes—
983C2×C4C2×2−1+412yes—
984C2×C4C2×2−1+412yes—
985C2×C4C2×2−1+412yes—
986C2×C4#58512yes—
987C2×C4#58512yes—
988C2×C4#58512yes—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22C23×#4111yescharacteristic
997C22C22×2−1+411yescharacteristic
998C22C22×2−1+411yescharacteristic
999C22C2×#58511yescharacteristic
1000C22C2×#58511yescharacteristic
1001C22C2×#58511yescharacteristic
1002C222−1+611yescharacteristic
1003C4—22no—
1004C4—28no—
1005C4—22no—
1006C4—22no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—42no—
1014C4—42no—
1015C4—48no—
1016C4—41no—
1017C4—42no—
1018C4—44no—
1019C4—42no—
1020C4—42no—
1021C4—44no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4#351514yes—
1026C4#351814yes—
1027C4#355514yes—
1028C2—82no—
1029C2C2×#355511yescharacteristic
1030C2C2×#351511yescharacteristic
1031C2C2×#351811yescharacteristic
1032C2#6295611yescharacteristic
1033C2#6295911yescharacteristic
1034C2#6300711yescharacteristic
1035C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
4. #59242C2semidirect
5. #49094C2semidirect
6. #46117C2semidirect
7. #45414C2semidirect
8. #45183C2semidirect
10. #42717C2semidirect
11. #39762C2semidirect
12. #39225C2semidirect
15. #38943C2semidirect
16. #36584C2semidirect
17. #36563C2semidirect
18. #36563C2semidirect
19. #36450C2semidirect
21. #35202C2semidirect
22. #35187C2semidirect
23. #34951C2semidirect
25. #34488C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596532
#594342
#592422
#490942
#461172
#454142
#451832
#429022
#427172
#397622
#392252
#389782
#389432
#365842
#365632
#364502
#361942
#352022
#351872
#349512
#349452
#344882
C4×#5562