Finite Group Databasebeta

← #7671769

Subgroups — #7671769

Order 512.

5452 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C212yesmaximal, complemented
2#59457C212yesmaximal, complemented
3#59446C214yesmaximal, complemented
4#59146C214yesmaximal, complemented
5#59078C212yesmaximal, complemented
6#59064C212yesmaximal, complemented
7#40029C214yesmaximal, complemented
8#40025C214yesmaximal, complemented
9#39817C214yesmaximal, complemented
10#39736C212yesmaximal, complemented
11#39726C212yesmaximal, complemented
12#36644C211yesmaximal, characteristic
13#36609C212yesmaximal, complemented
14#36598C211yesmaximal, characteristic, complemented
15#36595C211yesmaximal, characteristic, complemented
16#36595C211yesmaximal, characteristic, complemented
17#36594C212yesmaximal, complemented
18#36593C211yesmaximal, characteristic, complemented
19#36538C212yesmaximal, complemented
20#36460C212yesmaximal, complemented
21#36302C212yesmaximal, complemented
22#36271C212yesmaximal, complemented
23#35561C214yesmaximal, complemented
24#35298C212yesmaximal, complemented
25#35186C212yesmaximal, complemented
26#34331C212yesmaximal, complemented
27#34226C212yesmaximal, complemented
28C4×#533C211yesmaximal, characteristic, complemented
29C4×#533C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#559C2212yes—
32C2×#557C2212yes—
33C2×#556C2214yes—
34C2×#533C2211yescharacteristic
35C2×#533C2211yescharacteristic
36C2×#532C2212yes—
37C2×#532C2212yes—
38C2×#532C2212yes—
39#2868C2211yescharacteristic
40#2868C2212yes—
41#2867C2211yescharacteristic
42#2862C2212yes—
43#2861C2214yes—
44#2860C2214yes—
45#2858C2212yes—
46#2858C2212yes—
47#2858C2212yes—
48#2858C2212yes—
49#2858C2212yes—
50#2856C2212yes—
51#2856C2212yes—
52#2856C2212yes—
53#2856C2212yes—
54#2800C2218yes—
55#2780C2218yes—
56#2761C2218yes—
57#2711C2218yes—
58#2708C2218yes—
59#2707C2218yes—
60#2691C2218yes—
61#2681C2218yes—
62#2651C2218yes—
63#2620C2214yes—
64#2620C2214yes—
65#2601C2218yes—
66#2592C2214yes—
67#2592C2214yes—
68#2582C2212yes—
69#2580C2214yes—
70#2571C2212yes—
71#2570C2214yes—
72#2568C2212yes—
73#2566C2214yes—
74#2566C2214yes—
75#2566C2214yes—
76#2560C2218yes—
77#2559C2218yes—
78#2558C2218yes—
79#2558C2218yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2212yes—
83#2552C2214yes—
84#2548C2212yes—
85#2548C2212yes—
86#2548C2212yes—
87#2548C2212yes—
88#2548C2212yes—
89#2548C2212yes—
90#2547C2214yes—
91#2546C2214yes—
92#2546C2212yes—
93#2545C2214yes—
94#2545C2214yes—
95#2545C2214yes—
96#2545C2214yes—
97#2545C2214yes—
98#2544C2214yes—
99#2544C2214yes—
100#2538C2214yes—
101#2538C2214yes—
102#2531C2218yes—
103#2526C2218yes—
104#2513C2214yes—
105#2513C2214yes—
106#2512C2214yes—
107#2512C2214yes—
108#2512C2214yes—
109#2512C2214yes—
110#2512C2214yes—
111#2511C2214yes—
112#2500C2214yes—
113#2500C2214yes—
114#2490C2214yes—
115#2476C2218yes—
116#2468C2218yes—
117#2466C2218yes—
118#2460C2218yes—
119#2454C2214yes—
120#2452C2214yes—
121#2450C2218yes—
122#2448C2214yes—
123#2448C2214yes—
124#2447C2214yes—
125#2447C2214yes—
126#2447C2214yes—
127#2446C2214yes—
128#2445C2214yes—
129#2445C2214yes—
130#2445C2214yes—
131#2445C2214yes—
132#2432C2214yes—
133#2432C2214yes—
134#2427C2214yes—
135#2426C2214yes—
136#2420C2214yes—
137#2419C2218yes—
138#2367C2214yes—
139#2367C2214yes—
140#2367C2214yes—
141#2367C2214yes—
142#2367C2214yes—
143#2366C2212yes—
144#2366C2212yes—
145#2366C2212yes—
146#2366C2212yes—
147#2365C2212yes—
148#2363C2214yes—
149#2363C2214yes—
150#2359C2218yes—
151#2357C2214yes—
152#2357C2214yes—
153#2355C2212yes—
154#2355C2212yes—
155#2354C2214yes—
156#2354C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159#2349C2214yes—
160#2349C2214yes—
161#2341C2214yes—
162#2339C2214yes—
163#2335C2218yes—
164#2326C2214yes—
165#2326C2214yes—
166#2324C2214yes—
167#2324C2214yes—
168#2319C2214yes—
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#127C2212yes—
180C4×#127C2212yes—
181C4×#127C2212yes—
182C4×#127C2212yes—
183C4×#127C2212yes—
184C4×#127C2212yes—
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×#125C2212yes—
188C4×#125C2212yes—
189C4×#124C2214yes—
190C4×C22⋊Q8C2212yes—
191C4×C22⋊Q8C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×C22⋊Q8C2212yes—
194C4×C22⋊Q8C2211yescharacteristic
195C4×C22⋊Q8C2212yes—
196C4×C22⋊Q8C2211yescharacteristic
197C4×C22⋊Q8C2212yes—
198C4×C22⋊Q8C2211yescharacteristic
199C4×C22⋊Q8C2211yescharacteristic
200#2296C2212yes—
201#2296C2212yes—
202#2295C2211yescharacteristic
203#2295C2212yes—
204#2295C2211yescharacteristic
205#2295C2212yes—
206#2295C2212yes—
207#2293C2214yes—
208#2285C2211yescharacteristic
209#2285C2211yescharacteristic
210#2275C2214yes—
211C42×Q8C2212yes—
212C42×Q8C2212yes—
213C42×Q8C2212yes—
214C42×Q8C2211yescharacteristic
215C42×Q8C2211yescharacteristic
216C4×#117C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2314yes—
220#559—216no—
221#559—48no—
222#557—48no—
223#556—416no—
224#533—28no—
225#533—28no—
226#532—216no—
227#532—48no—
228#532—48no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×#127C2312yes—
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#127C2312yes—
242C2×#127C2312yes—
243C2×#127C2312yes—
244C2×#127C2312yes—
245C2×#126C2318yes—
246C2×#126C2318yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2318yes—
251C2×#124C2314yes—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#124C2314yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#123C2318yes—
261C2×#123C2318yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2318yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2318yes—
310C2×#117C2312yes—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318#400C2318yes—
319#400C2318yes—
320#399C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#393C2318yes—
350#391C2312yes—
351#391C2314yes—
352#391C2312yes—
353#391C2314yes—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2311yescharacteristic
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2314yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2318yes—
391#390C2318yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2311yescharacteristic
417#389C2312yes—
418#389C2312yes—
419#389C2311yescharacteristic
420#389C2312yes—
421#389C2314yes—
422#389C2318yes—
423#389C2314yes—
424#389C2314yes—
425#389C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#387C2318yes—
445#387C2312yes—
446#387C2312yes—
447#387C2312yes—
448#387C2312yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2312yes—
453#387C2312yes—
454#387C2314yes—
455#387C2312yes—
456#387C2312yes—
457#387C2318yes—
458#387C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2318yes—
468#385C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2314yes—
474#385C2312yes—
475#385C2314yes—
476#385C2312yes—
477#385C2312yes—
478#385C2312yes—
479#384C2311yescharacteristic
480#384C2311yescharacteristic
481#384C2312yes—
482#384C2312yes—
483#384C2312yes—
484#384C2312yes—
485#384C2311yescharacteristic
486#384C2311yescharacteristic
487#384C2314yes—
488#384C2314yes—
489#384C2314yes—
490#384C2314yes—
491#382C2312yes—
492#382C2312yes—
493#382C2314yes—
494#382C2314yes—
495#382C2314yes—
496#381C2318yes—
497#381C2318yes—
498#380C2318yes—
499#380C2312yes—
500#380C2318yes—
501#380C2312yes—
502#380C2318yes—
503#380C2311yescharacteristic
504#380C2312yes—
505#380C2311yescharacteristic
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2314yes—
529C4×C4⋊C4C2311yescharacteristic
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2311yescharacteristic
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2311yescharacteristic
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2311yescharacteristic
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2311yescharacteristic
551C4×C4⋊C4C2312yes—
552C4×C22⋊C4C2318yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2318yes—
557C4×C22⋊C4C2318yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562#376C2312yes—
563#376C2312yes—
564#376C2314yes—
565C2×#95C2318yes—
566C43C2311yescharacteristic
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2312yes—
572C43C2312yes—
573C43C2311yescharacteristic
574C43C2311yescharacteristic
575C43C2311yescharacteristic
576C43C2314yes—
577C2×#41—216no—
578C2×#41—48no—
579C2×#41—48no—
580C22×Q8C2412yes—
581C22×Q8C2412yes—
582C22×Q8C2411yescharacteristic
583C22×Q8C2414yes—
584C22×Q8C2412yes—
585C22×Q8C2411yescharacteristic
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2418yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2418yes—
601C23×C4C2418yes—
602C23×C4C2411yescharacteristic
603C23×C4C2418yes—
604C4⋊Q8—24no—
605C4⋊Q8—24no—
606C4⋊Q8—28no—
607C4⋊Q8—24no—
608C4⋊Q8—24no—
609C4⋊Q8—28no—
610C4⋊Q8—44no—
611C4⋊Q8—48no—
612C4⋊Q8—48no—
613#127—28no—
614#127—28no—
615#127—28no—
616#127—28no—
617#127—44no—
618#127—44no—
619#127—44no—
620#126—416no—
621#126—416no—
622#125—28no—
623#125—28no—
624#125—48no—
625#125—416no—
626#124—216no—
627#124—216no—
628#124—216no—
629#124—216no—
630#124—48no—
631#124—48no—
632#124—48no—
633#124—48no—
634#124—48no—
635#123—232no—
636#123—416no—
637C22⋊Q8—24no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—24no—
641C22⋊Q8—28no—
642C22⋊Q8—416no—
643#121—216no—
644#121—216no—
645#121—48no—
646#121—48no—
647#121—48no—
648#121—48no—
649C4×Q8—28no—
650C4×Q8—24no—
651C4×Q8—28no—
652C4×Q8—28no—
653C4×Q8—28no—
654C4×Q8—28no—
655C4×Q8—28no—
656C4×Q8—24no—
657C4×Q8—28no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—44no—
662C4×Q8—44no—
663C4×Q8—48no—
664C4×Q8—48no—
665C4×Q8—48no—
666C4×Q8#4118yescomplemented
667C4×D4—216no—
668C4×D4—216no—
669C4×D4—216no—
670C4×D4—216no—
671C4×D4—48no—
672C4×D4—48no—
673C4×D4—48no—
674C4×D4—48no—
675C4×D4—48no—
676C4×D4—48no—
677C4×D4—48no—
678C4×D4—48no—
679C4×D4—48no—
680C4×D4—48no—
681#117—28no—
682#117—28no—
683#117—44no—
684#117—416no—
685#117—44no—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2418yes—
765C2×C42—24no—
766C2×C42—24no—
767C2×C42—24no—
768C2×C42—24no—
769C2×C42—42no—
770C2×C42—42no—
771C2×C42#4118yes—
772C2×C42C2414yes—
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2418yes—
804C2×C42C2414yes—
805C2×C42C2418yes—
806C2×C42C2414yes—
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820#95C2412yes—
821#95C2414yes—
822#95C2418yes—
823#95C2418yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2414yes—
829#95C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2418yes—
837#95C2414yes—
838#95C2412yes—
839#95C2414yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2414yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858C24C2518yes—
859C24C2511yescharacteristic
860#41—832no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—24no—
864C2×Q8—22no—
865C2×Q8—24no—
866C2×Q8—28no—
867C2×Q8—22no—
868C2×Q8—24no—
869C2×Q8—22no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—28no—
874C2×Q8—22no—
875C2×Q8—22no—
876C2×Q8—24no—
877C2×Q8—42no—
878C2×Q8C2×#4114yes—
879C2×D4—216no—
880C2×D4—28no—
881C2×D4—28no—
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—48no—
898C2×D4—48no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—216no—
918C22×C4—216no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4C2×#4114yes—
931C22×C4C2×#4114yes—
932C22×C4C2×#4114yes—
933C22×C4C2512yes—
934C22×C4C2511yescharacteristic
935C22×C4C2514yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2512yes—
943C22×C4C2518yes—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—48no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—44no—
1006C4⋊C4—48no—
1007C4⋊C4—48no—
1008C4⋊C4—48no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4C2×#4114yes—
1012C4⋊C4C2×#4118yes—
1013C22⋊C4—28no—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—216no—
1017C22⋊C4—216no—
1018C22⋊C4—216no—
1019C22⋊C4—216no—
1020C22⋊C4—216no—
1021C22⋊C4—216no—
1022C22⋊C4—216no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—44no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—48no—
1033C22⋊C4—48no—
1034C22⋊C4—48no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C22⋊C4—48no—
1038C22⋊C4—48no—
1039C42—22no—
1040C42—22no—
1041C42—22no—
1042C42—28no—
1043C42—24no—
1044C42—28no—
1045C42—22no—
1046C42—22no—
1047C42—22no—
1048C42—22no—
1049C42—22no—
1050C42—22no—
1051C42—28no—
1052C42—24no—
1053C42—24no—
1054C42—28no—
1055C42—24no—
1056C42—24no—
1057C42—22no—
1058C42—22no—
1059C42—22no—
1060C42—24no—
1061C42—24no—
1062C42—22no—
1063C42—22no—
1064C42—22no—
1065C42—22no—
1066C42—24no—
1067C42—24no—
1068C42—24no—
1069C42—24no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42—44no—
1075C42—48no—
1076C42—44no—
1077C42—48no—
1078C42C2×#4114yes—
1079C42C2×#4114yes—
1080C42C2×#4114yes—
1081C42C2×#4114yes—
1082C42C2×#4114yes—
1083C42C2×#4118yes—
1084C42H(5,𝔽2)14yes—
1085C42H(5,𝔽2)14yes—
1086C422−1+414yes—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—28no—
1094C23—28no—
1095C23—28no—
1096C23—28no—
1097C23—28no—
1098C23—28no—
1099C23—28no—
1100C23C22×#4112yes—
1101C23C2611yescharacteristic
1102Q8—28no—
1103Q8—48no—
1104Q8—48no—
1105Q8—48no—
1106Q8—416no—
1107Q8—44no—
1108D4—416no—
1109D4—416no—
1110D4—416no—
1111D4—416no—
1112D4—88no—
1113D4—88no—
1114D4—88no—
1115D4—816no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—21no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—28no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—28no—
1160C2×C4—28no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—44no—
1179C2×C4—44no—
1180C2×C4—44no—
1181C2×C4—44no—
1182C2×C4—816no—
1183C2×C4—816no—
1184C2×C4—168no—
1185C2×C4C22×#4112yes—
1186C2×C4C22×#4112yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4112yes—
1189C2×C4C22×#4114yes—
1190C2×C4C22×#4114yes—
1191C2×C4C22×#4112yes—
1192C2×C4C22×#4112yes—
1193C2×C4C22×#4112yes—
1194C2×C4C22×#4112yes—
1195C2×C4C22×#4112yes—
1196C2×C4C2×H(5,𝔽2)12yes—
1197C2×C4C2×H(5,𝔽2)12yes—
1198C2×C4C2×H(5,𝔽2)12yes—
1199C2×C4C2×H(5,𝔽2)12yes—
1200C2×C4C2×H(5,𝔽2)12yes—
1201C2×C4C2×H(5,𝔽2)12yes—
1202C2×C4C2×2−1+412yes—
1203C2×C4C2×2−1+412yes—
1204C2×C4C2×2−1+412yes—
1205C2×C4#58512yes—
1206C2×C4#58512yes—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—48no—
1215C22—48no—
1216C22—48no—
1217C22—48no—
1218C22—48no—
1219C22—48no—
1220C22—48no—
1221C22C23×#4111yescharacteristic
1222C22C23×#4111yescharacteristic
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C22×H(5,𝔽2)11yescharacteristic
1225C22C22×2−1+411yescharacteristic
1226C22C2×#58511yescharacteristic
1227C22C2×#58511yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—24no—
1231C4—22no—
1232C4—22no—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—48no—
1239C4—44no—
1240C4—41no—
1241C4—42no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—41no—
1248C4—44no—
1249C4—42no—
1250C4—44no—
1251C4#348014yes—
1252C4#350714yes—
1253C4#350814yes—
1254C4#351114yes—
1255C2—42no—
1256C2—88no—
1257C2C2×#348011yescharacteristic
1258C2C2×#350711yescharacteristic
1259C2C2×#350811yescharacteristic
1260C2C2×#351111yescharacteristic
1261C2#6280011yescharacteristic
1262C2#6283511yescharacteristic
1263C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36644C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59679C2semidirect
2. #59457C2semidirect
3. #59446C2semidirect
4. #59146C2semidirect
5. #59078C2semidirect
6. #59064C2semidirect
7. #40029C2semidirect
8. #40025C2semidirect
9. #39817C2semidirect
10. #39736C2semidirect
11. #39726C2semidirect
13. #36609C2semidirect
14. #36598C2semidirect
15. #36595C2semidirect
16. #36595C2semidirect
17. #36594C2semidirect
18. #36593C2semidirect
19. #36538C2semidirect
20. #36460C2semidirect
21. #36302C2semidirect
22. #36271C2semidirect
23. #35561C2semidirect
24. #35298C2semidirect
25. #35186C2semidirect
26. #34331C2semidirect
27. #34226C2semidirect
28. C4×#533C2semidirect
29. C4×#533C2semidirect
666. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#596792
#594572
#594462
#591462
#590782
#590642
#400292
#400252
#398172
#397362
#397262
#366442
#366092
#365982
#365952
#365942
#365932
#365382
#364602
#363022
#362712
#355612
#352982
#351862
#343312
#342262
C4×#5332