Finite Group Databasebeta

← #7986695

Subgroups — #7986695

Order 512.

4673 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C212yesmaximal, complemented
2#59821C211yesmaximal, characteristic, complemented
3#59646C212yesmaximal
4#59052C212yesmaximal, complemented
5#49090C218yesmaximal, complemented
6#46078C214yesmaximal, complemented
7#45021C214yesmaximal, complemented
8#44978C214yesmaximal, complemented
9#42873C214yesmaximal, complemented
10#42714C214yesmaximal, complemented
11#39251C214yesmaximal, complemented
12#39192C212yesmaximal, complemented
13#38978C212yesmaximal, complemented
14#38975C212yesmaximal, complemented
15#38921C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36559C211yesmaximal, characteristic, complemented
18Q8×#125C212yesmaximal, complemented
19#36459C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35201C212yesmaximal, complemented
22#35186C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic
25#34481C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#554C2212yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2861C2214yes—
34#2860C2214yes—
35#2859C2212yes—
36#2859C2212yes—
37#2859C2214yes—
38#2857C2212yes—
39#2837C2218yes—
40#2803C2218yes—
41#2796C2218yes—
42#2793C2218yes—
43#2777C2218yes—
44#2777C2218yes—
45#2772C2218yes—
46#2772C2218yes—
47#2770C2218yes—
48#2761C2218yes—
49#2732C2218yes—
50#2727C2214yes—
51#2727C2218yes—
52#2725C2218yes—
53#2718C2218yes—
54#2707C2218yes—
55#2698C2218yes—
56#2680C2218yes—
57#2663C2218yes—
58#2651C2218yes—
59#2651C2218yes—
60#2644C2214yes—
61#2625C2214yes—
62#2604C2218yes—
63#2602C2218yes—
64#2585C2214yes—
65#2582C2211yescharacteristic
66#2582C2212yes—
67#2568C2211yescharacteristic
68#2567C2212yes—
69#2566C2214yes—
70#2563C2212yes—
71#2560C2218yes—
72#2554C2214yes—
73#2552C2214yes—
74#2552C2212yes—
75#2552C2214yes—
76#2552C2211yescharacteristic
77#2552C2211yescharacteristic
78#2552C2212yes—
79#2550C2214yes—
80#2548C2211yescharacteristic
81#2548C2212yes—
82#2548C2214yes—
83#2546C2211yescharacteristic
84#2542C2212yes—
85#2542C2212yes—
86#2542C2214yes—
87#2541C2211yescharacteristic
88#2538C2212yes—
89#2538C2212yes—
90#2538C2212yes—
91#2538C2211yescharacteristic
92#2538C2212yes—
93#2532C2218yes—
94#2515C2218yes—
95#2513C2214yes—
96#2512C2214yes—
97#2512C2218yes—
98#2512C2214yes—
99#2512C2212yes—
100#2511C2212yes—
101#2509C2214yes—
102#2509C2212yes—
103#2507C2214yes—
104#2507C2214yes—
105#2507C2218yes—
106#2507C2214yes—
107#2507C2218yes—
108#2500C2214yes—
109#2499C2214yes—
110#2496C2214yes—
111#2495C2214yes—
112#2490C2214yes—
113#2490C2212yes—
114#2489C2214yes—
115#2486C2214yes—
116#2485C2214yes—
117#2468C2218yes—
118#2454C2214yes—
119#2453C2212yes—
120#2452C2214yes—
121#2452C2214yes—
122#2451C2214yes—
123#2448C2214yes—
124#2448C2214yes—
125#2448C2214yes—
126#2447C2214yes—
127#2446C2212yes—
128#2445C2214yes—
129#2445C2212yes—
130#2441C2214yes—
131#2441C2214yes—
132#2429C2214yes—
133#2429C2214yes—
134#2426C2212yes—
135#2423C2214yes—
136#2423C2218yes—
137#2422C2214yes—
138#2417C2214yes—
139#2415C2214yes—
140#2415C2214yes—
141#2415C2214yes—
142#2415C2214yes—
143#2402C2214yes—
144#2392C2214yes—
145#2383C2218yes—
146#2373C2214yes—
147#2369C2212yes—
148#2367C2212yes—
149#2367C2214yes—
150#2365C2212yes—
151#2365C2211yescharacteristic
152#2363C2214yes—
153#2362C2212yes—
154#2360C2214yes—
155#2356C2212yes—
156#2355C2211yescharacteristic
157#2355C2212yes—
158#2354C2212yes—
159#2354C2212yes—
160#2354C2211yescharacteristic
161#2354C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2214yes—
165Q8×C4⋊C4C2214yes—
166Q8×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169#2347C2214yes—
170#2347C2212yes—
171#2334C2218yes—
172#2326C2214yes—
173#2323C2214yes—
174#2323C2214yes—
175#2320C2214yes—
176#2319C2214yes—
177#2317C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×#127C2212yes—
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#125C2214yes—
186C4×#125C2212yes—
187C4×#126C2214yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#556—28no—
200#556—216no—
201#554—48no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#127C2312yes—
211#529—48no—
212C2×#126C2314yes—
213C2×#126C2318yes—
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#123C2314yes—
225C2×#123C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C42C2312yes—
269#400C2314yes—
270#400C2314yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#398C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2314yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2314yes—
317#394C2314yes—
318#393C2318yes—
319#392C2314yes—
320#391C2318yes—
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#390C2318yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2314yes—
352#390C2318yes—
353#390C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2312yes—
381#389C2314yes—
382#389C2318yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2318yes—
392#389C2318yes—
393#389C2318yes—
394#389C2312yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2318yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2318yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2318yes—
434#387C2314yes—
435#387C2318yes—
436#386C2314yes—
437#386C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2312yes—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2318yes—
454#384C2314yes—
455#384C2314yes—
456#384C2312yes—
457#384C2318yes—
458#383C2314yes—
459#383C2318yes—
460#382C2314yes—
461#382C2312yes—
462#382C2318yes—
463#382C2314yes—
464#382C2312yes—
465#381C2318yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2314yes—
473#380C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518#376C2314yes—
519#376C2314yes—
520C43C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×D4C2412yes—
530C22×D4C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C23×C4C2414yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2418yes—
540C4⋊Q8—24no—
541C4⋊Q8—28no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—82no—
545C4⋊Q8#4118yes—
546#127—24no—
547#127—44no—
548#126—216no—
549#126—232no—
550#126—48no—
551#126—88no—
552#125—28no—
553#125—44no—
554#125—48no—
555#125—48no—
556#125—84no—
557#124—216no—
558#124—28no—
559#124—44no—
560#123—48no—
561#123—88no—
562C22⋊Q8—216no—
563C22⋊Q8—28no—
564C22⋊Q8—416no—
565C22⋊Q8—48no—
566C22⋊Q8—44no—
567C22⋊Q8—48no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—84no—
571#121—28no—
572#121—44no—
573C4×Q8—216no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—28no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—24no—
580C4×Q8—28no—
581C4×Q8—24no—
582C4×Q8—42no—
583C4×Q8—44no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×D4—28no—
588C4×D4—24no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—48no—
592C4×D4—42no—
593C4×D4—48no—
594C4×D4—44no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—84no—
598#117—216no—
599#117—28no—
600#117—48no—
601#117—44no—
602#117—48no—
603C2×C4⋊C4—48no—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C42—28no—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2418yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761C24C2514yes—
762C24C2512yes—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8C2×#4118yes—
778C2×D4—22no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—22no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—28no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C22×C4—28no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2511yescharacteristic
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2518yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—216no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—22no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—28no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—42no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—42no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—42no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4C2×#4118yes—
891C4⋊C4C2×#4118yes—
892C4⋊C42−1+414yes—
893C22⋊C4—28no—
894C22⋊C4—216no—
895C22⋊C4—24no—
896C22⋊C4—28no—
897C22⋊C4—216no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—24no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—42no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C42—28no—
921C42—216no—
922C42—24no—
923C42—28no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—22no—
930C42—24no—
931C42—28no—
932C42—24no—
933C42—24no—
934C42—22no—
935C42—24no—
936C42—24no—
937C42—22no—
938C42—24no—
939C42—44no—
940C42—48no—
941C42—42no—
942C42—48no—
943C42—42no—
944C42—44no—
945C42—42no—
946C42—44no—
947C42—41no—
948C42C2×#4114yes—
949C42H(5,𝔽2)14yes—
950C422−1+414yes—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23C2611yescharacteristic
966Q8—216no—
967Q8—44no—
968Q8—48no—
969Q8—44no—
970Q8—88no—
971D4—48no—
972D4—44no—
973D4—48no—
974D4—48no—
975D4—88no—
976D4—88no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—24no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—48no—
1036C2×C4—416no—
1037C2×C4—48no—
1038C2×C4—84no—
1039C2×C4—168no—
1040C2×C4C22×#4118yes—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4112yes—
1043C2×C4C22×#4112yes—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×2−1+414yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4#58512yes—
1053C2×C4#58512yes—
1054C22—44no—
1055C22—42no—
1056C22—42no—
1057C22—44no—
1058C22—42no—
1059C22—44no—
1060C22—42no—
1061C22—44no—
1062C22—44no—
1063C22—42no—
1064C22—44no—
1065C22—42no—
1066C22—42no—
1067C22—44no—
1068C22C23×#4111yescharacteristic
1069C22C22×H(5,𝔽2)11yescharacteristic
1070C22C22×2−1+411yescharacteristic
1071C22C22×2−1+411yescharacteristic
1072C22C2×#58511yescharacteristic
1073C22C2×#58511yescharacteristic
1074C22H(7,𝔽2)11yescharacteristic
1075C4—22no—
1076C4—24no—
1077C4—28no—
1078C4—22no—
1079C4—22no—
1080C4—42no—
1081C4—44no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—41no—
1086C4—42no—
1087C4—44no—
1088C4—42no—
1089C4—44no—
1090C4—42no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—48no—
1095C4—42no—
1096C4#351514yes—
1097C4#351714yes—
1098C4#355014yes—
1099C2—82no—
1100C2—84no—
1101C2C2×#355011yescharacteristic
1102C2C2×#351511yescharacteristic
1103C2C2×#351711yescharacteristic
1104C2#6292611yescharacteristic
1105C2#6295511yescharacteristic
1106C2#6299911yescharacteristic
1107C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59821C2semidirect
4. #59052C2semidirect
5. #49090C2semidirect
6. #46078C2semidirect
7. #45021C2semidirect
8. #44978C2semidirect
9. #42873C2semidirect
10. #42714C2semidirect
11. #39251C2semidirect
12. #39192C2semidirect
13. #38978C2semidirect
14. #38975C2semidirect
15. #38921C2semidirect
16. #36563C2semidirect
17. #36559C2semidirect
18. Q8×#125C2semidirect
19. #36459C2semidirect
20. #36134C2semidirect
21. #35201C2semidirect
22. #35186C2semidirect
23. #34951C2semidirect
25. #34481C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#596462
#590522
#490902
#460782
#450212
#449782
#428732
#427142
#392512
#391922
#389782
#389752
#389212
#365632
#365592
Q8×#1252
#364592
#361342
#352012
#351862
#349512
#349342
#344812
C4×#5562