Finite Group Databasebeta

← #7679699

Subgroups — #7679699

Order 512.

6746 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C212yesmaximal, complemented
2#59831C214yesmaximal, complemented
3#59828C212yesmaximal, complemented
4#59823C212yesmaximal, complemented
5#59667C212yesmaximal, complemented
6#59458C212yesmaximal, complemented
7#59314C214yesmaximal, complemented
8#45424C214yesmaximal, complemented
9#45139C214yesmaximal, complemented
10#43529C218yesmaximal, complemented
11#39370C212yesmaximal, complemented
12#39369C212yesmaximal, complemented
13#37691C214yesmaximal, complemented
14#37687C214yesmaximal, complemented
15#36134C212yesmaximal, complemented
16D4×#125C212yesmaximal, complemented
17#35639C212yesmaximal, complemented
18#35519C212yesmaximal, complemented
19#35275C211yesmaximal, characteristic, complemented
20#35257C212yesmaximal, complemented
21#34938C211yesmaximal, characteristic, complemented
22C2×#2552C211yesmaximal, characteristic, complemented
23#34207C211yesmaximal, characteristic
24#34206C211yesmaximal, characteristic
25#34141C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic, complemented
27#3504—232no—
28C2×#557C2214yes—
29C2×#557C2214yes—
30C2×#554C2218yes—
31C2×#554C2218yes—
32C2×#554C2214yes—
33C2×#554C2214yes—
34C2×#544C2214yes—
35C2×#544C2214yes—
36C2×#544C2212yes—
37C2×#544C2211yescharacteristic
38C2×#533C2214yes—
39C2×#533C2212yes—
40C2×#532C2211yescharacteristic
41C22×#125C2214yes—
42C22×#125C2212yes—
43C2×#520C2212yes—
44C2×#520C2212yes—
45C2×C4×#41C2212yes—
46#2868C2212yes—
47#2859C2212yes—
48#2857C2214yes—
49#2851C2214yes—
50#2732C2218yes—
51#2729C2218yes—
52#2729C2218yes—
53#2726C2218yes—
54#2720C2218yes—
55#2720C2218yes—
56#2720C2218yes—
57#2713C2218yes—
58#2704C2218yes—
59#2704C2218yes—
60#2692C2218yes—
61#2677C2218yes—
62#2660C2214yes—
63#2629C2214yes—
64#2628C2214yes—
65#2582C2214yes—
66#2581C2214yes—
67#2580C2214yes—
68#2579C2218yes—
69#2552C2211yescharacteristic
70#2552C2212yes—
71#2552C2212yes—
72#2552C2211yescharacteristic
73#2552C2214yes—
74#2552C2212yes—
75#2552C2212yes—
76#2552C2214yes—
77#2552C2212yes—
78#2552C2212yes—
79#2551C2212yes—
80#2551C2214yes—
81#2551C2212yes—
82#2551C2211yescharacteristic
83#2551C2211yescharacteristic
84#2550C2212yes—
85#2550C2212yes—
86#2549C2214yes—
87#2546C2214yes—
88#2542C2214yes—
89#2542C2214yes—
90#2538C2214yes—
91#2538C2214yes—
92#2538C2214yes—
93#2506C2214yes—
94#2506C2214yes—
95#2506C2214yes—
96#2506C2214yes—
97#2487C2218yes—
98#2473C2218yes—
99#2473C2218yes—
100#2473C2218yes—
101#2465C2218yes—
102#2462C2218yes—
103#2454C2214yes—
104#2454C2214yes—
105#2454C2214yes—
106#2453C2214yes—
107#2453C2214yes—
108#2453C2214yes—
109#2452C2214yes—
110#2452C2214yes—
111#2452C2214yes—
112#2451C2214yes—
113#2450C2218yes—
114#2450C2218yes—
115#2449C2218yes—
116#2449C2218yes—
117#2449C2218yes—
118#2446C2218yes—
119#2442C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2441C2214yes—
123#2441C2214yes—
124#2441C2214yes—
125#2440C2214yes—
126#2440C2218yes—
127#2440C2214yes—
128#2440C2212yes—
129#2440C2212yes—
130#2440C2214yes—
131#2439C2214yes—
132#2429C2218yes—
133#2423C2218yes—
134#2423C2218yes—
135#2417C2218yes—
136#2399C2214yes—
137C2×#398C2214yes—
138#2367C2212yes—
139#2367C2214yes—
140#2367C2212yes—
141#2366C2211yescharacteristic
142#2366C2212yes—
143#2366C2211yescharacteristic
144#2365C2211yescharacteristic
145#2365C2214yes—
146#2365C2212yes—
147#2365C2211yescharacteristic
148#2364C2214yes—
149#2361C2214yes—
150#2361C2212yes—
151#2361C2212yes—
152#2361C2214yes—
153#2354C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156#2352C2214yes—
157Q8×C4⋊C4C2214yes—
158D4×C4⋊C4C2214yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2212yes—
163#2331C2212yes—
164#2331C2212yes—
165#2330C2212yes—
166#2330C2212yes—
167#2329C2214yes—
168#2326C2214yes—
169#2325C2214yes—
170#2317C2211yescharacteristic
171#2317C2211yescharacteristic
172#2317C2212yes—
173#2316C2211yescharacteristic
174#2311C2212yes—
175#2311C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×#127C2212yes—
182C4×#125C2212yes—
183C4×#125C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×#121C2214yes—
186#2297C2212yes—
187#2296C2212yes—
188#2293C2212yes—
189C2×#389C2212yes—
190C2×#389C2212yes—
191#2290C2214yes—
192#2285C2211yescharacteristic
193C2×#384C2211yescharacteristic
194C2×#384C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C2×C4×C4⋊C4C2211yescharacteristic
200C22×#41C2312yes—
201#557—232no—
202#557—232no—
203#554—232no—
204#554—232no—
205#554—264no—
206#554—264no—
207#544—232no—
208#544—232no—
209#544—216no—
210#544D4116yescomplemented
211#533—232no—
212#533—216no—
213#532Q8116yescomplemented
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2318yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#125—232no—
229C2×#125—216no—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×#125C2318yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2318yes—
238C2×#125C2312yes—
239C2×#125C2318yes—
240C2×#125C2314yes—
241C2×#125C2318yes—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#124C2312yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2318yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C2318yes—
256C2×C22⋊Q8C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259#520—216no—
260#520—216no—
261C4×#41—216no—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2318yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2318yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2318yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2314yes—
290C2×#117C2314yes—
291C2×#117C2314yes—
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2314yes—
297C22×C4⋊C4C2314yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2318yes—
300C22×C4⋊C4C2318yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C42C2314yes—
309C22×C42C2312yes—
310C22×C42C2312yes—
311C22×C42C2311yescharacteristic
312#400C2318yes—
313#400C2318yes—
314#400C2318yes—
315#400C2318yes—
316#399C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C2318yes—
320#398C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2318yes—
335#398C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#395C2318yes—
343#395C2318yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2318yes—
349#395C2318yes—
350#393C2318yes—
351#393C2318yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2318yes—
361#391C2314yes—
362#391C2318yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2312yes—
397#389C2314yes—
398#389C2312yes—
399#389C2318yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2314yes—
411#389C2312yes—
412#389C2318yes—
413#389C2318yes—
414#389C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#387C2314yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#386C2318yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#385C2318yes—
446#385C2314yes—
447#385C2314yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2314yes—
459#385C2314yes—
460#385C2314yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2312yes—
466#384C2314yes—
467#384C2312yes—
468#384C2311yescharacteristic
469#384C2312yes—
470#384C2314yes—
471#384C2312yes—
472#384C2314yes—
473#384C2311yescharacteristic
474#384C2314yes—
475#384C2318yes—
476#384C2314yes—
477#382C2312yes—
478#382C2312yes—
479#382C2314yes—
480#382C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2312yes—
487#380C2318yes—
488#380C2318yes—
489#380C2318yes—
490#380C2318yes—
491#380C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2311yescharacteristic
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2318yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2314yes—
531#376C2312yes—
532#376C2312yes—
533C2×#95C2312yes—
534C2×#95C2312yes—
535C2×#95C2314yes—
536C43C2312yes—
537C43C2312yes—
538C2×#41—28no—
539C2×#41—28no—
540C2×#41C2×Q8116yes—
541C22×Q8C2412yes—
542C22×Q8C2414yes—
543C22×Q8C2418yes—
544C22×Q8C2414yes—
545C22×Q8C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C22×D4C2412yes—
550C23×C4C2411yescharacteristic
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2418yes—
555C23×C4C2418yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2414yes—
559C23×C4C2414yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C4⋊Q8—232no—
564C4⋊Q8—28no—
565C4⋊Q8—28no—
566C4⋊Q8—216no—
567C4⋊Q8—232no—
568C4⋊Q8—216no—
569C4⋊Q8—44no—
570C4⋊Q8—48no—
571C4⋊Q8—44no—
572C4⋊Q8—84no—
573C4⋊Q8C2×D4116yes—
574C4⋊Q8C2×D4116yes—
575C4⋊Q8C2×Q818yes—
576#127C2×Q818yes—
577#125—28no—
578#125—216no—
579#125—216no—
580#125—232no—
581#125—232no—
582#125—216no—
583#125—216no—
584#125—28no—
585#125—232no—
586#125—216no—
587#125—232no—
588#125—216no—
589#125C2×D4116yes—
590#125C2×D4116yes—
591#124C2×Q8116yes—
592C22⋊Q8—232no—
593C22⋊Q8—232no—
594C22⋊Q8—232no—
595C22⋊Q8—232no—
596C22⋊Q8—232no—
597C22⋊Q8—232no—
598C22⋊Q8—216no—
599C22⋊Q8—216no—
600C22⋊Q8—232no—
601C22⋊Q8—88no—
602C22⋊Q8—88no—
603C22⋊Q8C2×D4132yes—
604#121C2×Q8116yes—
605#121C2×Q8116yes—
606C4×Q8—232no—
607C4×Q8—28no—
608C4×Q8—28no—
609C4×Q8—216no—
610C4×Q8—232no—
611C4×Q8—216no—
612C4×Q8—216no—
613C4×Q8—216no—
614C4×Q8—48no—
615C4×D4—232no—
616C4×D4—28no—
617C4×D4—28no—
618C4×D4—216no—
619C4×D4—216no—
620C4×D4—216no—
621C4×D4—232no—
622C4×D4—216no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—84no—
628C4×D4C2×Q8116yes—
629C4×D4C2×Q8116yes—
630#117—28no—
631#117—24no—
632#117—24no—
633#117—216no—
634#117—216no—
635#117—216no—
636#117C2×D418yes—
637#117C2×D418yes—
638C2×C4⋊C4—28no—
639C2×C4⋊C4—216no—
640C2×C4⋊C4—216no—
641C2×C4⋊C4—24no—
642C2×C4⋊C4—216no—
643C2×C4⋊C4—216no—
644C2×C4⋊C4—232no—
645C2×C4⋊C4—232no—
646C2×C4⋊C4—42no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—82no—
650C2×C4⋊C4—84no—
651C2×C4⋊C4C2×D418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C42—28no—
738C2×C42—216no—
739C2×C42—44no—
740C2×C42C2×Q818yes—
741C2×C42C2412yes—
742C2×C42C2418yes—
743C2×C42C2414yes—
744C2×C42C2418yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2414yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768#95C2412yes—
769#95C2414yes—
770#95C2414yes—
771#95C2412yes—
772#95C2412yes—
773#95C2412yes—
774#95C2418yes—
775#95C2418yes—
776#95C2412yes—
777#95C2412yes—
778#95C2412yes—
779#95C2412yes—
780#95C2412yes—
781#95C2412yes—
782#95C2412yes—
783#95C2412yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2418yes—
805#95C2418yes—
806C24C2514yes—
807C24C2511yescharacteristic
808#41—264no—
809C2×Q8—24no—
810C2×Q8—28no—
811C2×Q8—216no—
812C2×Q8—28no—
813C2×Q8—24no—
814C2×Q8—44no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—48no—
818C2×Q8—44no—
819C2×Q8—44no—
820C2×Q8—48no—
821C2×Q8—44no—
822C2×Q8C22×D4116yes—
823C2×Q8C22×Q818yes—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4C22×Q818yes—
833C2×D4C22×Q8116yes—
834C2×D4C22×Q818yes—
835C2×D4C22×Q818yes—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—216no—
847C22×C4—216no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—41no—
851C22×C4—42no—
852C22×C4—41no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—42no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—42no—
868C22×C4C22×D418yes—
869C22×C4C22×D414yes—
870C22×C4C22×Q814yes—
871C22×C4C22×Q8116yes—
872C22×C4C22×Q814yes—
873C22×C4C22×Q814yes—
874C22×C42−1+414yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2512yes—
884C22×C4C2514yes—
885C22×C4C2512yes—
886C22×C4C2518yes—
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2514yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—216no—
902C4⋊C4—216no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—216no—
906C4⋊C4—216no—
907C4⋊C4—28no—
908C4⋊C4—216no—
909C4⋊C4—216no—
910C4⋊C4—216no—
911C4⋊C4—216no—
912C4⋊C4—24no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—216no—
919C4⋊C4—28no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—28no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—42no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—48no—
950C4⋊C4—44no—
951C4⋊C4—48no—
952C4⋊C4—44no—
953C4⋊C4—42no—
954C4⋊C4C22×D414yes—
955C4⋊C4C22×D418yes—
956C4⋊C4C22×D4116yes—
957C4⋊C4C22×D4116yes—
958C4⋊C4C22×D418yes—
959C4⋊C4C22×D414yes—
960C4⋊C4C22×D414yes—
961C4⋊C4C22×D414yes—
962C4⋊C4C22×D4116yes—
963C4⋊C4C22×Q818yes—
964C4⋊C4C22×Q818yes—
965C22⋊C4—28no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—216no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—216no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—48no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4C22×D418yes—
981C22⋊C4C22×D418yes—
982C22⋊C4C22×Q8116yes—
983C22⋊C4C22×Q8116yes—
984C42—24no—
985C42—24no—
986C42—28no—
987C42—28no—
988C42—24no—
989C42—24no—
990C42—216no—
991C42—216no—
992C42—28no—
993C42—24no—
994C42—24no—
995C42—28no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—24no—
1000C42—44no—
1001C42—42no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42C22×D418yes—
1006C42C22×D418yes—
1007C42C22×Q814yes—
1008C42C22×Q814yes—
1009C42C22×Q814yes—
1010C42C22×Q814yes—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23C23×D412yes—
1022C23C23×Q818yes—
1023C23C23×Q812yes—
1024C23C2×2−1+412yes—
1025C23C2611yescharacteristic
1026Q8—216no—
1027Q8—416no—
1028Q8—88no—
1029Q8—88no—
1030Q8—816no—
1031D4—232no—
1032D4—216no—
1033D4—216no—
1034D4—48no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—232no—
1054C2×C4—28no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—28no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—28no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—48no—
1092C2×C4—44no—
1093C2×C4—48no—
1094C2×C4—816no—
1095C2×C4—88no—
1096C2×C4—816no—
1097C2×C4—88no—
1098C2×C4—84no—
1099C2×C4—84no—
1100C2×C4—88no—
1101C2×C4D4×Q8116yes—
1102C2×C4C23×D414yes—
1103C2×C4C23×D414yes—
1104C2×C4C23×D414yes—
1105C2×C4C23×D418yes—
1106C2×C4C23×D414yes—
1107C2×C4C23×D412yes—
1108C2×C4C23×D412yes—
1109C2×C4C23×Q812yes—
1110C2×C4C23×Q812yes—
1111C2×C4C23×Q812yes—
1112C2×C4C23×Q818yes—
1113C2×C4C23×Q812yes—
1114C2×C4C23×Q812yes—
1115C2×C4C23×Q812yes—
1116C2×C4C2×2−1+412yes—
1117C2×C4C2×2−1+412yes—
1118C2×C4#58512yes—
1119C2×C4#58512yes—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—28no—
1127C22—28no—
1128C22—28no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22C2×D4×Q814yes—
1134C22C24×D411yescharacteristic
1135C22C24×Q811yescharacteristic
1136C22C22×2−1+411yescharacteristic
1137C22C2×#58511yescharacteristic
1138C22C2×#58511yescharacteristic
1139C22H(7,𝔽2)11yescharacteristic
1140C222−1+611yescharacteristic
1141C4—28no—
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—28no—
1150C4—42no—
1151C4—44no—
1152C4—42no—
1153C4—42no—
1154C4—48no—
1155C4—42no—
1156C4—44no—
1157C4—42no—
1158C4—42no—
1159C4—44no—
1160C4—42no—
1161C4—42no—
1162C4C2×D4×Q814yes—
1163C4C2×D4×Q814yes—
1164C4#350414yescomplemented
1165C2—24no—
1166C2—48no—
1167C2C22×D4×Q811yescharacteristic
1168C2C2×#350411yescharacteristic
1169C2#6285411yescharacteristic
1170C2#6292611yescharacteristic
1171C2#6295611yescharacteristic
1172C2#6298811yescharacteristic
1173C2#6300311yescharacteristic
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. C2×#3504C2semidirect
2. #59831C2semidirect
3. #59828C2semidirect
4. #59823C2semidirect
5. #59667C2semidirect
6. #59458C2semidirect
7. #59314C2semidirect
8. #45424C2semidirect
9. #45139C2semidirect
10. #43529C2semidirect
11. #39370C2semidirect
12. #39369C2semidirect
13. #37691C2semidirect
14. #37687C2semidirect
15. #36134C2semidirect
16. D4×#125C2semidirect
17. #35639C2semidirect
18. #35519C2semidirect
19. #35275C2semidirect
20. #35257C2semidirect
21. #34938C2semidirect
22. C2×#2552C2semidirect
26. C4×#544C2semidirect
210. #544D4semidirect
213. #532Q8semidirect
1164. C4#3504semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
#598312
#598282
#598232
#596672
#594582
#593142
#454242
#451392
#435292
#393702
#393692
#376912
#376872
#361342
D4×#1252
#356392
#355192
#352752
#352572
#349382
C2×#25522
#342072
#342062
#341412
C4×#5442