Finite Group Databasebeta

← #7652151

Subgroups — #7652151

Order 512.

4814 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42772C214yesmaximal, complemented
2#42561C214yesmaximal, complemented
3#42513C214yesmaximal, complemented
4#42512C214yesmaximal, complemented
5#40847C218yesmaximal, complemented
6#40154C214yesmaximal, complemented
7#40000C214yesmaximal, complemented
8#39660C214yesmaximal, complemented
9#39633C214yesmaximal, complemented
10#38511C218yesmaximal, complemented
11#35662C211yesmaximal, characteristic, complemented
12#35661C211yesmaximal, characteristic
13#35644C211yesmaximal, characteristic, complemented
14#35619C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35312C211yesmaximal, characteristic, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35224C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21#34813C211yesmaximal, characteristic
22C2×#2502C211yesmaximal, characteristic, complemented
23#34254C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34200C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2868C2212yescomplemented
36#2862C2212yescomplemented
37#2861C2212yescomplemented
38#2859C2212yescomplemented
39#2848C2214yes—
40#2839C2218yescomplemented
41#2838C2218yescomplemented
42#2796C2218yes—
43#2790C2218yes—
44#2790C2218yescomplemented
45#2774C2218yescomplemented
46#2770C2218yes—
47#2767C2218yescomplemented
48#2766C2218yescomplemented
49#2764C2218yescomplemented
50#2763C2218yes—
51#2757C2218yes—
52#2755C2218yescomplemented
53#2729C2218yes—
54#2729C2218yescomplemented
55#2723C2218yes—
56#2715C2218yes—
57#2698C2218yescomplemented
58#2666C2218yescomplemented
59#2660C2212yescomplemented
60#2660C2212yescomplemented
61#2654C2218yescomplemented
62#2652C2218yes—
63#2647C2218yescomplemented
64#2642C2212yescomplemented
65#2640C2212yescomplemented
66#2638C2218yes—
67#2637C2218yescomplemented
68#2627C2214yes—
69#2582C2214yescomplemented
70#2581C2214yescomplemented
71#2567C2212yescomplemented
72#2566C2212yescomplemented
73#2565C2212yescomplemented
74#2561C2214yes—
75#2552C2214yescomplemented
76#2551C2214yescomplemented
77#2542C2212yescomplemented
78#2538C2214yes—
79#2536C2214yes—
80#2530C2218yes—
81#2529C2218yescomplemented
82#2512C2214yescomplemented
83#2511C2214yescomplemented
84#2503C2214yes—
85#2503C2212yescomplemented
86#2502C2214yes—
87#2502C2214yes—
88#2502C2214yes—
89#2502C2214yes—
90#2502C2212yescomplemented
91#2499C2212yescomplemented
92#2499C2212yescomplemented
93#2497C2212yes—
94#2497C2214yescomplemented
95#2496C2212yes—
96#2496C2214yescomplemented
97#2495C2212yes—
98#2494C2212yes—
99#2493C2214yes—
100#2492C2214yes—
101#2492C2214yes—
102#2492C2212yes—
103#2492C2214yescomplemented
104#2491C2212yes—
105#2490C2212yes—
106#2489C2214yes—
107#2489C2212yes—
108#2489C2214yes—
109#2489C2214yescomplemented
110#2488C2218yes—
111#2488C2214yes—
112#2481C2218yes—
113#2480C2214yes—
114#2472C2214yes—
115#2468C2218yes—
116#2465C2218yes—
117#2453C2214yescomplemented
118#2452C2218yes—
119#2451C2214yescomplemented
120#2451C2218yescomplemented
121#2449C2218yes—
122#2447C2214yescomplemented
123#2446C2214yescomplemented
124#2442C2214yes—
125#2442C2214yes—
126#2441C2214yescomplemented
127#2440C2214yes—
128#2440C2214yes—
129#2440C2218yes—
130#2440C2214yescomplemented
131#2438C2218yes—
132#2429C2214yes—
133#2426C2214yes—
134#2419C2218yes—
135#2413C2214yes—
136#2411C2214yes—
137#2401C2214yes—
138#2398C2214yes—
139C2×#398C2214yes—
140#2361C2214yes—
141#2360C2214yes—
142#2360C2218yes—
143#2356C2214yescomplemented
144#2355C2214yescomplemented
145#2355C2214yescomplemented
146#2352C2214yes—
147Q8×C4⋊C4C2214yescomplemented
148D4×C4⋊C4C2214yes—
149#2343C2218yes—
150#2334C2218yes—
151#2330C2214yescomplemented
152#2326C2218yes—
153#2322C2214yes—
154#2320C2214yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164C4×C4⋊Q8C2214yescomplemented
165C4×#126C2214yes—
166C4×#124C2214yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2295C2214yescomplemented
173C2×#391C2211yescharacteristic
174C2×#391C2211yescharacteristic
175C2×#385C2214yes—
176#2285C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#384C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2312yes—
191#544—44no—
192#544—44no—
193#536—44no—
194#533—28no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2318yes—
202C2×#126C2314yes—
203C2×#126C2318yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124C2314yes—
210C2×#124C2312yes—
211#525—28no—
212C2×#123C2312yes—
213C2×#123C2314yes—
214C2×C22⋊Q8—44no—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×#121C2312yes—
226C2×#120C2312yes—
227#520—44no—
228#519—28no—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2318yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—44no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#401C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2314yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2314yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2314yes—
314#393C2318yes—
315#393C2318yes—
316#393C2314yes—
317#393C2314yes—
318#391C2318yes—
319#391C2311yescharacteristic
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2311yescharacteristic
329#391C2312yes—
330#391C2314yes—
331#391C2318yes—
332#391C2312yes—
333#391C2318yes—
334#391C2314yes—
335#391C2312yes—
336#391C2318yes—
337#391C2312yes—
338#391C2314yes—
339#391C2312yes—
340#390C2311yescharacteristic
341#390C2312yes—
342#390C2312yes—
343#390C2318yes—
344#390C2311yescharacteristic
345#390C2312yes—
346#390C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2312yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#386C2314yes—
399#386C2314yes—
400#386C2318yes—
401#386C2314yes—
402#386C2314yes—
403#385C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#384C2312yes—
420#384C2312yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#384C2312yes—
425#384C2318yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2314yes—
429#384C2311yescharacteristic
430#384C2312yes—
431#384C2314yes—
432#383C2314yes—
433#383C2318yes—
434#382C2312yes—
435#382C2312yes—
436#382C2312yes—
437#382C2312yes—
438#382C2318yes—
439#382C2318yes—
440#382C2318yes—
441#382C2314yes—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381C2314yes—
445#381C2314yes—
446#381C2312yes—
447#381C2312yes—
448#381C2312yes—
449#381C2318yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453#380C2318yes—
454#380C2312yes—
455#380C2312yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#379C2312yes—
462#379C2312yes—
463#379C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2312yes—
494#376C2318yes—
495#376C2312yes—
496C2×#95C2314yes—
497C2×#95C2312yes—
498C2×#95C2314yes—
499C43C2312yes—
500C43C2312yes—
501C25C2411yescharacteristic
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×Q8C2414yes—
513C22×Q8C2414yes—
514C22×D4C2412yes—
515C22×D4C2411yescharacteristic
516C22×D4C2414yes—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4—44no—
521C23×C4—84no—
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2418yes—
533C23×C4C2414yes—
534C23×C4C2411yescharacteristic
535C4⋊Q8—28no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—88no—
542#126—216no—
543#126—88no—
544#125—28no—
545#125—44no—
546#125—44no—
547#125—44no—
548#125—44no—
549#124—216no—
550#124—44no—
551#123—28no—
552#123—48no—
553C22⋊Q8—28no—
554C22⋊Q8—216no—
555C22⋊Q8—48no—
556C22⋊Q8—48no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559C22⋊Q8—44no—
560C22⋊Q8—44no—
561C22⋊Q8—88no—
562C22⋊Q8—88no—
563#121—28no—
564#120—28no—
565C4×Q8—216no—
566C4×Q8—216no—
567C4×Q8—216no—
568C4×Q8—44no—
569C4×Q8—88no—
570C4×D4—216no—
571C4×D4—44no—
572C4×D4—48no—
573C4×D4—88no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—216no—
581#117—44no—
582#117#4118yes—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—48no—
587C2×C4⋊C4—48no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—84no—
592C2×C4⋊C4—84no—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C22⋊C4—28no—
641C2×C22⋊C4—44no—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C42—24no—
672C2×C42—24no—
673C2×C42C2412yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2411yescharacteristic
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2418yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694#95C2418yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735C24—22no—
736C24—24no—
737C24—22no—
738C24—22no—
739C24—42no—
740C24C2512yes—
741C24C2512yes—
742C24C2511yescharacteristic
743#41—416no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—28no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—22no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—44no—
758C2×Q8—48no—
759C2×Q8—48no—
760C2×Q8—416no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—28no—
764C2×D4—24no—
765C2×D4—28no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—44no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—48no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—44no—
801C22×C4—48no—
802C22×C4—416no—
803C22×C4—816no—
804C22×C4C2×#4114yes—
805C22×C4H(5,𝔽2)14yes—
806C22×C42−1+414yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C4⋊C4—24no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4C2×#4118yes—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4C2×#4118yes—
904C22⋊C42−1+418yes—
905C42—24no—
906C42—22no—
907C42—22no—
908C42—24no—
909C42—216no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—22no—
915C42—24no—
916C42—22no—
917C42—24no—
918C42—28no—
919C42—28no—
920C42—44no—
921C42—48no—
922C42—44no—
923C42—48no—
924C42—44no—
925C42C2×#4118yes—
926C23—22no—
927C23—22no—
928C23—28no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—22no—
939C23—24no—
940C23—48no—
941C23—48no—
942C23—44no—
943C23—44no—
944C23C22×#4112yes—
945C23C2×H(5,𝔽2)12yes—
946C23C2×2−1+414yes—
947C23C2×2−1+412yes—
948C23C2611yescharacteristic
949Q8—416no—
950Q8—48no—
951Q8—48no—
952Q8—44no—
953Q8—164no—
954Q8—164no—
955D4—416no—
956D4—48no—
957D4—44no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—24no—
1000C2×C4—28no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—44no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—84no—
1016C2×C4—816no—
1017C2×C4—164no—
1018C2×C4#542116yes—
1019C2×C4C22×#4118yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C2×H(5,𝔽2)12yes—
1023C2×C4C2×H(5,𝔽2)12yes—
1024C2×C4C2×2−1+414yes—
1025C2×C4C2×2−1+414yes—
1026C2×C4C2×2−1+412yes—
1027C2×C4C2×2−1+412yes—
1028C22—24no—
1029C22—22no—
1030C22—22no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—416no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—44no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—44no—
1045C22C2×#54214yes—
1046C22C23×#4111yescharacteristic
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C22×2−1+412yes—
1049C22C22×2−1+411yescharacteristic
1050C22H(7,𝔽2)12yes—
1051C4—24no—
1052C4—28no—
1053C4—24no—
1054C4—44no—
1055C4—42no—
1056C4—44no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—42no—
1064C4—42no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—44no—
1069C4—44no—
1070C4—42no—
1071C4C2×#54214yes—
1072C4C2×#54214yes—
1073C2—24no—
1074C2—44no—
1075C2—82no—
1076C2C22×#54211yescharacteristic
1077C2#6283311yescharacteristic
1078C2#6287611yescharacteristic
1079C2#6294512yes—
1080C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42772C2semidirect
2. #42561C2semidirect
3. #42513C2semidirect
4. #42512C2semidirect
5. #40847C2semidirect
6. #40154C2semidirect
7. #40000C2semidirect
8. #39660C2semidirect
9. #39633C2semidirect
10. #38511C2semidirect
11. #35662C2semidirect
13. #35644C2semidirect
14. #35619C2semidirect
15. #35557C2semidirect
16. #35532C2semidirect
17. #35312C2semidirect
18. #35275C2semidirect
19. #35224C2semidirect
20. #34814C2semidirect
22. C2×#2502C2semidirect
23. #34254C2semidirect
24. #34214C2semidirect
35. #2868C22semidirect
36. #2862C22semidirect
37. #2861C22semidirect
38. #2859C22semidirect
40. #2839C22semidirect
41. #2838C22semidirect
44. #2790C22semidirect
45. #2774C22semidirect
47. #2767C22semidirect
48. #2766C22semidirect
49. #2764C22semidirect
52. #2755C22semidirect
54. #2729C22semidirect
57. #2698C22semidirect
58. #2666C22semidirect
59. #2660C22semidirect
60. #2660C22semidirect
61. #2654C22semidirect
63. #2647C22semidirect
64. #2642C22semidirect
65. #2640C22semidirect
67. #2637C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
71. #2567C22semidirect
72. #2566C22semidirect
73. #2565C22semidirect
75. #2552C22semidirect
76. #2551C22semidirect
77. #2542C22semidirect
81. #2529C22semidirect
82. #2512C22semidirect
83. #2511C22semidirect
85. #2503C22semidirect
90. #2502C22semidirect
91. #2499C22semidirect
92. #2499C22semidirect
94. #2497C22semidirect
96. #2496C22semidirect
103. #2492C22semidirect
109. #2489C22semidirect
117. #2453C22semidirect
119. #2451C22semidirect
120. #2451C22semidirect
122. #2447C22semidirect
123. #2446C22semidirect
126. #2441C22semidirect
130. #2440C22semidirect
143. #2356C22semidirect
144. #2355C22semidirect
145. #2355C22semidirect
147. Q8×C4⋊C4C22semidirect
151. #2330C22semidirect
154. #2320C22semidirect
164. C4×C4⋊Q8C22semidirect
172. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#427722
#425612
#425132
#425122
#408472
#401542
#400002
#396602
#396332
#385112
#356622
#356612
#356442
#356192
#355572
#355322
#353122
#352752
#352242
#348142
#348132
C2×#25022
#342542
#342142
#342002