Finite Group Databasebeta

← #7671750

Subgroups — #7671750

Order 512.

5356 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59642C212yesmaximal, complemented
2#59461C214yesmaximal, complemented
3#59413C212yesmaximal, complemented
4#59323C214yesmaximal, complemented
5#59052C212yesmaximal, complemented
6#59036C212yesmaximal, complemented
7#39980C214yesmaximal, complemented
8#39976C214yesmaximal, complemented
9#39690C214yesmaximal, complemented
10#39606C212yesmaximal, complemented
11#39596C212yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36573C212yesmaximal, complemented
14#36563C212yesmaximal, complemented
15#36563C211yesmaximal, characteristic, complemented
16#36560C211yesmaximal, characteristic, complemented
17#36559C211yesmaximal, characteristic, complemented
18Q8×#127C211yesmaximal, characteristic, complemented
19#36476C212yesmaximal, complemented
20#36445C212yesmaximal, complemented
21#36276C212yesmaximal, complemented
22#36274C212yesmaximal, complemented
23#35580C214yesmaximal, complemented
24#35294C212yesmaximal, complemented
25#35176C212yesmaximal, complemented
26#34334C212yesmaximal, complemented
27#34226C212yesmaximal
28C4×#533C211yesmaximal, characteristic, complemented
29C4×#532C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#554C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×#533C2211yescharacteristic
36C2×#533C2212yes—
37C2×#532C2211yescharacteristic
38C2×C4×#41C2212yes—
39#2868C2211yescharacteristic
40#2868C2211yescharacteristic
41#2868C2212yes—
42#2862C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2859C2212yes—
47#2859C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2214yes—
53#2855C2214yes—
54#2807C2218yes—
55#2768C2218yes—
56#2748C2218yes—
57#2732C2218yes—
58#2720C2218yes—
59#2704C2218yes—
60#2692C2218yes—
61#2692C2218yes—
62#2667C2218yes—
63#2629C2214yes—
64#2628C2214yes—
65#2607C2218yes—
66#2589C2218yes—
67#2589C2218yes—
68#2582C2212yes—
69#2582C2214yes—
70#2580C2214yes—
71#2580C2214yes—
72#2580C2214yes—
73#2570C2214yes—
74#2570C2214yes—
75#2568C2212yes—
76#2567C2212yes—
77#2567C2214yes—
78#2566C2214yes—
79#2565C2214yes—
80#2563C2212yes—
81#2556C2218yes—
82#2552C2214yes—
83#2552C2212yes—
84#2550C2214yes—
85#2550C2214yes—
86#2550C2214yes—
87#2550C2214yes—
88#2550C2214yes—
89#2549C2218yes—
90#2549C2218yes—
91#2546C2212yes—
92#2546C2212yes—
93#2542C2214yes—
94#2542C2214yes—
95#2542C2214yes—
96#2542C2214yes—
97#2542C2212yes—
98#2542C2212yes—
99#2542C2212yes—
100#2538C2212yes—
101#2538C2214yes—
102#2538C2212yes—
103#2522C2218yes—
104#2507C2214yes—
105#2507C2214yes—
106#2507C2214yes—
107#2506C2214yes—
108#2506C2214yes—
109#2502C2214yes—
110#2492C2214yes—
111#2465C2218yes—
112#2454C2218yes—
113#2454C2214yes—
114#2454C2214yes—
115#2454C2214yes—
116#2454C2214yes—
117#2454C2214yes—
118#2454C2214yes—
119#2452C2214yes—
120#2452C2214yes—
121#2451C2214yes—
122#2451C2214yes—
123#2451C2214yes—
124#2450C2218yes—
125#2441C2218yes—
126#2441C2214yes—
127#2441C2214yes—
128#2439C2214yes—
129#2439C2214yes—
130#2438C2218yes—
131#2434C2214yes—
132#2429C2214yes—
133#2423C2214yes—
134#2423C2218yes—
135#2423C2214yes—
136#2417C2214yes—
137#2409C2214yes—
138#2369C2214yes—
139#2369C2212yes—
140#2368C2218yes—
141#2367C2214yes—
142#2367C2214yes—
143#2365C2212yes—
144#2365C2212yes—
145#2363C2214yes—
146#2363C2214yes—
147#2360C2214yes—
148#2357C2214yes—
149#2355C2212yes—
150#2355C2214yes—
151Q8×C4⋊C4C2214yes—
152Q8×C4⋊C4C2212yes—
153#2349C2214yes—
154#2349C2214yes—
155#2349C2214yes—
156#2349C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2341C2214yes—
160Q8×C22⋊C4C2214yes—
161#2339C2214yes—
162#2331C2214yes—
163#2330C2214yes—
164#2329C2218yes—
165#2324C2214yes—
166#2324C2214yes—
167#2319C2214yes—
168C4×C4⋊Q8C2211yescharacteristic
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#127C2212yes—
181C4×#127C2212yes—
182C4×#127C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×#125C2212yes—
186C4×#124C2212yes—
187C4×#124C2212yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2211yescharacteristic
191C4×C22⋊Q8C2211yescharacteristic
192C4×C22⋊Q8C2211yescharacteristic
193C4×C22⋊Q8C2211yescharacteristic
194C4×C22⋊Q8C2212yes—
195C4×#121C2212yes—
196C4×#121C2212yes—
197C4×#121C2212yes—
198C4×#121C2212yes—
199#2297C2212yes—
200#2296C2212yes—
201#2295C2211yescharacteristic
202#2295C2211yescharacteristic
203#2295C2212yes—
204C2×#391C2214yes—
205#2293C2212yes—
206#2293C2212yes—
207#2285C2212yes—
208#2285C2212yes—
209#2285C2211yescharacteristic
210#2285C2211yescharacteristic
211#2275C2214yes—
212C42×Q8C2211yescharacteristic
213C42×Q8C2211yescharacteristic
214C42×Q8C2212yes—
215C42×D4C2212yes—
216C42×D4C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2314yes—
221#557—48no—
222#554—48no—
223D4×Q8—216no—
224D4×Q8—48no—
225D4×Q8—48no—
226#533—28no—
227#533—48no—
228#532Q8116yescomplemented
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2318yes—
249C2×#124C2312yes—
250C2×C22⋊Q8C2318yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2318yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C4×#41—48no—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2314yes—
301C2×#117C2314yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2314yes—
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2314yes—
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312#400C2318yes—
313#400C2318yes—
314#399C2318yes—
315#399C2318yes—
316#399C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C2318yes—
320#399C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#395C2318yes—
338#395C2318yes—
339#395C2318yes—
340#395C2318yes—
341#393C2318yes—
342#393C2318yes—
343#393C2318yes—
344#391C2312yes—
345#391C2314yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#391C2314yes—
350#391C2311yescharacteristic
351#391C2314yes—
352#391C2311yescharacteristic
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2318yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2318yes—
363#391C2318yes—
364#391C2318yes—
365#391C2318yes—
366#391C2318yes—
367#390C2314yes—
368#390C2312yes—
369#390C2314yes—
370#390C2314yes—
371#390C2312yes—
372#390C2312yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2312yes—
377#390C2312yes—
378#390C2312yes—
379#390C2318yes—
380#390C2318yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2311yescharacteristic
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2311yescharacteristic
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2318yes—
415#389C2314yes—
416#389C2314yes—
417#389C2318yes—
418#389C2318yes—
419#389C2314yes—
420#389C2314yes—
421#389C2318yes—
422#389C2318yes—
423#389C2314yes—
424#389C2314yes—
425#389C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#387C2312yes—
435#387C2312yes—
436#387C2312yes—
437#387C2312yes—
438#387C2312yes—
439#387C2312yes—
440#387C2312yes—
441#387C2312yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2314yes—
454#386C2314yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2312yes—
466#385C2312yes—
467#385C2312yes—
468#385C2312yes—
469#384C2311yescharacteristic
470#384C2312yes—
471#384C2311yescharacteristic
472#384C2312yes—
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#384C2312yes—
476#384C2312yes—
477#384C2312yes—
478#384C2312yes—
479#384C2312yes—
480#384C2314yes—
481#384C2318yes—
482#384C2314yes—
483#384C2314yes—
484#384C2314yes—
485#384C2312yes—
486#382C2312yes—
487#382C2314yes—
488#382C2314yes—
489#382C2312yes—
490#382C2314yes—
491#382C2314yes—
492#382C2314yes—
493#381C2318yes—
494#380C2314yes—
495#380C2314yes—
496#380C2318yes—
497#380C2314yes—
498#380C2318yes—
499#380C2314yes—
500#380C2314yes—
501#380C2314yes—
502#380C2318yes—
503#380C2318yes—
504#380C2312yes—
505#380C2311yescharacteristic
506#380C2312yes—
507#380C2312yes—
508#380C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2311yescharacteristic
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2311yescharacteristic
529C4×C4⋊C4C2314yes—
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2311yescharacteristic
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2318yes—
542C4×C4⋊C4C2311yescharacteristic
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2311yescharacteristic
549C4×C4⋊C4C2312yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552C4×C22⋊C4C2314yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2318yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563#376C2312yes—
564#376C2312yes—
565C2×#95C2318yes—
566C2×#95C2318yes—
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2312yes—
571C43C2312yes—
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2311yescharacteristic
575C43C2311yescharacteristic
576C43C2311yescharacteristic
577C2×#41—44no—
578C2×#41—44no—
579C2×#41C2×Q8116yescomplemented
580C22×Q8—216no—
581C22×Q8—48no—
582C22×Q8—48no—
583C22×Q8C2411yescharacteristic
584C22×Q8C2414yes—
585C22×Q8C2412yes—
586C22×Q8C2412yes—
587C22×Q8C2411yescharacteristic
588C22×Q8C2414yes—
589C22×Q8C2418yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C23×C4C2414yes—
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2414yes—
602C23×C4C2418yes—
603C23×C4C2411yescharacteristic
604C23×C4C2418yes—
605C23×C4C2414yes—
606C4⋊Q8—24no—
607C4⋊Q8—24no—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—44no—
614C4⋊Q8—44no—
615C4⋊Q8—48no—
616C4⋊Q8—48no—
617C4⋊Q8—48no—
618C4⋊Q8C2×Q818yescomplemented
619#127C2×Q818yes—
620#125—28no—
621#125—48no—
622#125—48no—
623#125—48no—
624#125—48no—
625#125—416no—
626#124C2×Q8116yescomplemented
627C22⋊Q8—24no—
628C22⋊Q8—24no—
629C22⋊Q8—28no—
630C22⋊Q8—232no—
631C22⋊Q8—216no—
632C22⋊Q8—416no—
633C22⋊Q8—416no—
634C22⋊Q8—416no—
635C22⋊Q8—48no—
636C22⋊Q8—48no—
637C22⋊Q8—48no—
638C22⋊Q8—48no—
639C22⋊Q8—48no—
640#121C2×Q8116yescomplemented
641#121C2×Q8116yescomplemented
642C4×Q8—28no—
643C4×Q8—24no—
644C4×Q8—28no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—28no—
650C4×Q8—44no—
651C4×Q8—48no—
652C4×Q8—44no—
653C4×Q8—48no—
654C4×Q8—48no—
655C4×Q8—48no—
656C4×Q8—48no—
657C4×Q8#4118yescomplemented
658C4×D4—28no—
659C4×D4—216no—
660C4×D4—28no—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—44no—
664C4×D4—48no—
665C4×D4—48no—
666C4×D4—44no—
667C4×D4—48no—
668C4×D4—48no—
669C4×D4—48no—
670C4×D4—48no—
671C4×D4—48no—
672C4×D4C2×Q8116yescomplemented
673C4×D4C2×Q8116yescomplemented
674#117—28no—
675#117—44no—
676#117—48no—
677#117—44no—
678#117—48no—
679C2×C4⋊C4—48no—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C42—24no—
761C2×C42—24no—
762C2×C42—24no—
763C2×C42—24no—
764C2×C42—48no—
765C2×C42—42no—
766C2×C42—42no—
767C2×C42C2×Q818yescomplemented
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2411yescharacteristic
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2411yescharacteristic
778C2×C42C2414yes—
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2414yes—
797C2×C42C2418yes—
798C2×C42C2414yes—
799C2×C42C2418yes—
800C2×C42C2418yes—
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2412yes—
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814#95C2412yes—
815#95C2412yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819#95C2418yes—
820#95C2418yes—
821#95C2418yes—
822#95C2412yes—
823#95C2412yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2412yes—
836#95C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854C24C2511yescharacteristic
855C24C2514yes—
856#41—432no—
857C2×Q8—24no—
858C2×Q8—22no—
859C2×Q8—28no—
860C2×Q8—216no—
861C2×Q8—24no—
862C2×Q8—22no—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—22no—
866C2×Q8—28no—
867C2×Q8—28no—
868C2×Q8—28no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—42no—
872C2×Q8—48no—
873C2×Q8—48no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—832no—
877C2×Q8C22×Q818yes—
878C2×Q8C2×#4114yes—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4C22×Q818yes—
888C2×D4C22×Q818yes—
889C2×D4C22×Q818yes—
890C2×D4C22×Q8116yes—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—28no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—28no—
905C22×C4—28no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—216no—
909C22×C4—28no—
910C22×C4—44no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—44no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4C22×Q814yes—
924C22×C4C22×Q814yes—
925C22×C4C22×Q814yes—
926C22×C4C22×Q8116yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2518yes—
933C22×C4C2511yescharacteristic
934C22×C4C2514yes—
935C22×C4C2518yes—
936C22×C4C2512yes—
937C22×C4C2511yescharacteristic
938C22×C4C2512yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2514yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—28no—
964C4⋊C4—216no—
965C4⋊C4—22no—
966C4⋊C4—28no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—22no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—48no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—44no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—48no—
997C4⋊C4—42no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—48no—
1001C4⋊C4—48no—
1002C4⋊C4—48no—
1003C4⋊C4—48no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4—48no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4C22×Q818yes—
1011C4⋊C4C22×Q818yes—
1012C4⋊C4C2×#4118yes—
1013C4⋊C4C2×#4114yes—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—28no—
1017C22⋊C4—216no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—48no—
1026C22⋊C4—44no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4C22×Q8116yes—
1033C22⋊C4C22×Q8116yes—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—24no—
1038C42—22no—
1039C42—22no—
1040C42—22no—
1041C42—22no—
1042C42—22no—
1043C42—22no—
1044C42—28no—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—24no—
1049C42—22no—
1050C42—22no—
1051C42—22no—
1052C42—24no—
1053C42—24no—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—22no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—24no—
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—44no—
1067C42—44no—
1068C42—48no—
1069C42—48no—
1070C42—48no—
1071C42C22×Q814yes—
1072C42C22×Q814yes—
1073C42C22×Q814yes—
1074C42C22×Q814yes—
1075C42C2×#4114yes—
1076C42C2×#4118yes—
1077C42H(5,𝔽2)14yes—
1078C42H(5,𝔽2)14yes—
1079C422−1+414yes—
1080C23—21no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—21no—
1085C23—21no—
1086C23—24no—
1087C23—21no—
1088C23—21no—
1089C23—24no—
1090C23—24no—
1091C23—21no—
1092C23C23×Q818yes—
1093C23C23×Q812yes—
1094C23C2611yescharacteristic
1095Q8—216no—
1096Q8—28no—
1097Q8—48no—
1098Q8—44no—
1099Q8—416no—
1100Q8—88no—
1101Q8—816no—
1102D4—216no—
1103D4—216no—
1104D4—216no—
1105D4—416no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—21no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—28no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—28no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—416no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—416no—
1173C2×C4—88no—
1174C2×C4—816no—
1175C2×C4—168no—
1176C2×C4C23×Q812yes—
1177C2×C4C23×Q812yes—
1178C2×C4C23×Q812yes—
1179C2×C4C23×Q818yes—
1180C2×C4C23×Q812yes—
1181C2×C4C23×Q812yes—
1182C2×C4C23×Q812yes—
1183C2×C4C22×#4112yes—
1184C2×C4C22×#4114yes—
1185C2×C4C22×#4114yes—
1186C2×C4C22×#4112yes—
1187C2×C4C22×#4112yes—
1188C2×C4C2×H(5,𝔽2)12yes—
1189C2×C4C2×H(5,𝔽2)12yes—
1190C2×C4C2×H(5,𝔽2)12yes—
1191C2×C4C2×H(5,𝔽2)12yes—
1192C2×C4C2×H(5,𝔽2)12yes—
1193C2×C4C2×H(5,𝔽2)12yes—
1194C2×C4C2×2−1+412yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+412yes—
1197C2×C4#58512yes—
1198C2×C4#58512yes—
1199C22—22no—
1200C22—28no—
1201C22—22no—
1202C22—28no—
1203C22—22no—
1204C22—28no—
1205C22—44no—
1206C22—41no—
1207C22—41no—
1208C22—44no—
1209C22—41no—
1210C22—44no—
1211C22—41no—
1212C22—44no—
1213C22C24×Q811yescharacteristic
1214C22C23×#4111yescharacteristic
1215C22C22×H(5,𝔽2)11yescharacteristic
1216C22C22×H(5,𝔽2)11yescharacteristic
1217C22C22×2−1+411yescharacteristic
1218C22C2×#58511yescharacteristic
1219C22C2×#58511yescharacteristic
1220C4—22no—
1221C4—28no—
1222C4—22no—
1223C4—24no—
1224C4—22no—
1225C4—22no—
1226C4—24no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—41no—
1232C4—44no—
1233C4—48no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—41no—
1241C4—42no—
1242C4—48no—
1243C4Q8×#4114yes—
1244C4#350114yes—
1245C4#350314yes—
1246C4#350814yes—
1247C2—42no—
1248C2—48no—
1249C2C2×Q8×#4111yescharacteristic
1250C2C2×#350111yescharacteristic
1251C2C2×#350311yescharacteristic
1252C2C2×#350811yescharacteristic
1253C2#6280511yescharacteristic
1254C2#6283511yescharacteristic
1255C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59642C2semidirect
2. #59461C2semidirect
3. #59413C2semidirect
4. #59323C2semidirect
5. #59052C2semidirect
6. #59036C2semidirect
7. #39980C2semidirect
8. #39976C2semidirect
9. #39690C2semidirect
10. #39606C2semidirect
11. #39596C2semidirect
12. #36645C2semidirect
13. #36573C2semidirect
14. #36563C2semidirect
15. #36563C2semidirect
16. #36560C2semidirect
17. #36559C2semidirect
18. Q8×#127C2semidirect
19. #36476C2semidirect
20. #36445C2semidirect
21. #36276C2semidirect
22. #36274C2semidirect
23. #35580C2semidirect
24. #35294C2semidirect
25. #35176C2semidirect
26. #34334C2semidirect
28. C4×#533C2semidirect
228. #532Q8semidirect
579. C2×#41C2×Q8semidirect
618. C4⋊Q8C2×Q8semidirect
626. #124C2×Q8semidirect
640. #121C2×Q8semidirect
641. #121C2×Q8semidirect
657. C4×Q8#41semidirect
672. C4×D4C2×Q8semidirect
673. C4×D4C2×Q8semidirect
767. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#596422
#594612
#594132
#593232
#590522
#590362
#399802
#399762
#396902
#396062
#395962
#366452
#365732
#365632
#365602
#365592
Q8×#1272
#364762
#364452
#362762
#362742
#355802
#352942
#351762
#343342
#342262
C4×#5332
C4×#5322