Finite Group Databasebeta

← #7708765

Subgroups — #7708765

Order 512.

7028 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C212yesmaximal, complemented
2#59651C214yesmaximal, complemented
3#59312C212yesmaximal, complemented
4#59127C212yesmaximal, complemented
5#45787C214yesmaximal, complemented
6#45485C214yesmaximal, complemented
7#39615C212yesmaximal, complemented
8#39487C212yesmaximal, complemented
9#39435C214yesmaximal, complemented
10#39421C214yesmaximal, complemented
11#39384C212yesmaximal, complemented
12#39368C212yesmaximal, complemented
13#39353C212yesmaximal, complemented
14#39343C212yesmaximal, complemented
15#37861C214yesmaximal, complemented
16#37442C212yesmaximal, complemented
17#36742C214yesmaximal, complemented
18#36624C211yesmaximal, characteristic
19C2×#2857C211yesmaximal, characteristic, complemented
20Q8×#121C212yesmaximal, complemented
21#36186C212yesmaximal, complemented
22#36183C214yesmaximal, complemented
23#35167C212yesmaximal, complemented
24#35006C212yesmaximal, complemented
25C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
26#3538—232no—
27C2×#563C2218yes—
28C2×#552C2214yes—
29C2×#552C2214yes—
30C2×#551C2218yes—
31C2×D4×Q8C2214yes—
32C2×D4×Q8C2214yes—
33C2×D4×Q8C2212yescomplemented
34C2×#544C2214yes—
35C2×#544C2214yes—
36C2×#541C2214yes—
37C2×#539C2214yes—
38C2×#539C2214yes—
39C2×#536C2214yes—
40C2×#532C2211yescharacteristic
41C22×C4⋊Q8C2211yescharacteristic
42C2×#525C2212yes—
43C22×C22⋊Q8C2212yes—
44C22×C22⋊Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C23×C42C2211yescharacteristic
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2211yescharacteristic
56#2857C2211yescharacteristic
57#2857C2214yes—
58#2856C2211yescharacteristic
59#2856C2211yescharacteristic
60#2854C2212yes—
61#2854C2212yes—
62#2854C2214yes—
63#2850C2212yes—
64#2850C2212yes—
65#2847C2212yes—
66#2847C2212yes—
67#2814C2218yes—
68#2734C2214yescomplemented
69#2732C2214yescomplemented
70#2729C2218yescomplemented
71#2727C2214yescomplemented
72#2726C2214yescomplemented
73#2725C2218yescomplemented
74#2722C2218yes—
75#2721C2218yescomplemented
76#2719C2218yescomplemented
77#2716C2218yescomplemented
78#2715C2218yes—
79#2713C2218yescomplemented
80#2695C2218yes—
81#2694C2218yescomplemented
82#2690C2218yescomplemented
83#2677C2218yescomplemented
84#2674C2218yescomplemented
85#2672C2218yes—
86#2659C2214yes—
87#2659C2214yes—
88#2639C2214yes—
89#2627C2214yes—
90#2625C2214yes—
91#2618C2214yes—
92#2618C2214yes—
93#2616C2214yes—
94#2564C2218yes—
95#2560C2218yescomplemented
96#2558C2218yescomplemented
97#2553C2218yes—
98#2552C2212yescomplemented
99#2552C2214yescomplemented
100#2552C2214yescomplemented
101#2551C2214yescomplemented
102#2551C2214yescomplemented
103#2550C2218yescomplemented
104#2550C2218yescomplemented
105#2546C2214yescomplemented
106#2546C2212yescomplemented
107#2542C2212yescomplemented
108#2538C2214yescomplemented
109#2538C2212yescomplemented
110#2521C2218yes—
111#2519C2218yescomplemented
112#2512C2214yescomplemented
113#2512C2214yescomplemented
114#2506C2214yescomplemented
115#2506C2214yescomplemented
116#2501C2214yes—
117#2498C2218yes—
118#2498C2218yes—
119#2496C2214yes—
120#2496C2214yes—
121#2491C2214yes—
122#2489C2214yescomplemented
123#2488C2218yes—
124#2486C2214yes—
125#2453C2214yescomplemented
126#2452C2214yescomplemented
127#2449C2218yes—
128#2446C2214yescomplemented
129#2445C2214yescomplemented
130#2441C2214yescomplemented
131#2440C2214yes—
132#2438C2218yes—
133#2434C2214yescomplemented
134#2429C2214yescomplemented
135#2429C2214yescomplemented
136#2429C2218yescomplemented
137#2425C2218yes—
138#2423C2214yescomplemented
139#2422C2214yes—
140#2417C2214yes—
141#2417C2214yes—
142#2417C2218yes—
143#2415C2214yescomplemented
144#2413C2218yes—
145#2412C2218yes—
146#2409C2214yes—
147#2409C2214yescomplemented
148#2365C2212yescomplemented
149#2362C2214yescomplemented
150#2361C2214yes—
151#2359C2218yes—
152#2354C2212yescomplemented
153Q8×C4⋊C4C2212yescomplemented
154#2344C2214yes—
155Q8×C22⋊C4C2214yescomplemented
156#2325C2214yes—
157#2316C2214yes—
158C4×C22⋊Q8C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2212yes—
162C4×C22⋊Q8C2212yes—
163C4×C22⋊Q8C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×C22⋊Q8C2212yes—
166C4×#121C2212yes—
167C4×#121C2212yes—
168C4×#121C2212yes—
169C4×#121C2212yes—
170C4×#121C2214yes—
171#2297C2212yes—
172C2×#391C2212yes—
173C2×#391C2211yescharacteristic
174C2×#389C2212yes—
175C2×#389C2212yes—
176C2×#389C2211yescharacteristic
177C2×#387C2212yes—
178C2×#385C2212yes—
179#2285C2211yescharacteristic
180#2285C2214yes—
181C2×#384C2211yescharacteristic
182C2×#380C2212yes—
183C2×#380C2212yes—
184C2×#380C2211yescharacteristic
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C4×C4⋊C4C2212yes—
187C2×C4×C22⋊C4C2212yes—
188C22×#41C2312yes—
189C23×Q8C2314yes—
190C23×Q8C2312yes—
191C23×Q8C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2311yescharacteristic
195#563—264no—
196#552—232no—
197#552—232no—
198#551—264no—
199D4×Q8—232no—
200D4×Q8—232no—
201D4×Q8—48no—
202#544—232no—
203#544—232no—
204#541—232no—
205#539—232no—
206#539—232no—
207#536—232no—
208#532—44no—
209C2×C4⋊Q8—44no—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2318yes—
212C2×C4⋊Q8C2318yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2314yes—
220C2×#127C2311yescharacteristic
221C2×#126C2318yes—
222C2×#126C2318yes—
223C2×#126C2318yes—
224C2×#126C2318yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2314yes—
228C2×#125C2318yes—
229C2×#125C2318yes—
230C2×#124C2318yes—
231C2×#124C2312yes—
232#525—216no—
233C2×#123C2314yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×C22⋊Q8—216no—
240C2×C22⋊Q8D4116yescomplemented
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2318yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#120C2314yes—
269C2×C4×Q8—44no—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×D4C2318yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2318yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×#117C2318yes—
284C2×#117C2318yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2311yescharacteristic
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C42—44no—
303C22×C42C2312yes—
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2312yes—
316C22×C42C2311yescharacteristic
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#399C2318yes—
322#399C2318yes—
323#399C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#397C2318yes—
336#397C2318yes—
337#397C2318yes—
338#397C2318yes—
339#397C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yes—
346#395C2318yes—
347#395C2318yes—
348#395C2318yes—
349#395C2318yes—
350#395C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#393C2318yes—
356#393C2318yes—
357#391C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2318yes—
362#391C2314yes—
363#391C2318yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2318yes—
400#389C2314yes—
401#389C2314yes—
402#389C2318yes—
403#389C2314yes—
404#389C2312yes—
405#389C2312yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#386C2318yes—
433#386C2314yes—
434#386C2318yes—
435#386C2314yes—
436#386C2314yes—
437#386C2314yes—
438#386C2314yes—
439#386C2314yes—
440#386C2318yes—
441#386C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2314yes—
447#385C2314yes—
448#385C2314yes—
449#385C2314yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#384C2314yes—
457#384C2314yes—
458#384C2314yes—
459#382C2312yes—
460#382C2318yes—
461#381C2318yes—
462#380C2314yes—
463#380C2318yes—
464#380C2312yes—
465#380C2314yes—
466#380C2318yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C22⋊C4C2318yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C2×#95C2312yes—
507C2×#95C2312yes—
508C2×#95C2314yes—
509C2×#95C2312yes—
510C2×#95C2314yes—
511C2×#95C2312yes—
512C2×#95C2312yes—
513C25C2411yescharacteristic
514C2×#41—28no—
515C2×#41—44no—
516C2×#41—44no—
517C22×Q8—216no—
518C22×Q8—28no—
519C22×Q8—42no—
520C22×Q8—42no—
521C22×Q8—44no—
522C22×Q8—48no—
523C22×Q8—44no—
524C22×Q8—48no—
525C22×Q8C2×D418yes—
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2414yes—
537C22×D4C2412yes—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—42no—
542C23×C4—42no—
543C23×C4—42no—
544C23×C4—42no—
545C23×C4—42no—
546C23×C4C2×D418yes—
547C23×C4C2414yes—
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2412yes—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2418yes—
567C23×C4C2411yescharacteristic
568C23×C4C2412yes—
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C4⋊Q8—216no—
574C4⋊Q8—232no—
575C4⋊Q8—232no—
576C4⋊Q8—232no—
577C4⋊Q8—28no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580C4⋊Q8—42no—
581C4⋊Q8—48no—
582C4⋊Q8—44no—
583#127—42no—
584#126—232no—
585#126—232no—
586#126—232no—
587#126—232no—
588#125—232no—
589#125—232no—
590#125—216no—
591#125—232no—
592#125—232no—
593#124—232no—
594#124—44no—
595#123—216no—
596#123—232no—
597#123—232no—
598#123—232no—
599#123—232no—
600#123—416no—
601C22⋊Q8—216no—
602C22⋊Q8—232no—
603C22⋊Q8—216no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—28no—
608C22⋊Q8—28no—
609C22⋊Q8—232no—
610C22⋊Q8—216no—
611C22⋊Q8—232no—
612C22⋊Q8—232no—
613C22⋊Q8—416no—
614C22⋊Q8—48no—
615C22⋊Q8—48no—
616C22⋊Q8C2×D4116yes—
617C22⋊Q8C2×D4116yes—
618C22⋊Q8C2×D4116yes—
619C22⋊Q8C2×D4116yes—
620#121—28no—
621#121—28no—
622#121—28no—
623#121—28no—
624#121—28no—
625#121—44no—
626#121—44no—
627#121—44no—
628#120—216no—
629C4×Q8—216no—
630C4×Q8—216no—
631C4×Q8—28no—
632C4×Q8—44no—
633C4×Q8—44no—
634C4×Q8—44no—
635C4×D4—216no—
636C4×D4—216no—
637C4×D4—232no—
638C4×D4—232no—
639C4×D4—28no—
640C4×D4—48no—
641C4×D4—44no—
642#117—28no—
643#117—232no—
644#117—216no—
645#117—232no—
646C2×C4⋊C4—216no—
647C2×C4⋊C4—28no—
648C2×C4⋊C4—28no—
649C2×C4⋊C4—28no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—44no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4C2×D4116yes—
657C2×C4⋊C4C2×D418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2412yes—
704C2×C22⋊C4—216no—
705C2×C22⋊C4—44no—
706C2×C22⋊C4C2×D4116yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C42—28no—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—24no—
735C2×C42—44no—
736C2×C42—42no—
737C2×C42—42no—
738C2×C42—42no—
739C2×C42—42no—
740C2×C42—42no—
741C2×C42—42no—
742C2×C42—42no—
743C2×C42—42no—
744C2×C42—42no—
745C2×C42C2418yes—
746C2×C42C2414yes—
747C2×C42C2418yes—
748C2×C42C2418yes—
749C2×C42C2411yescharacteristic
750C2×C42C2414yes—
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2414yes—
791#95C2414yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797C24—22no—
798C24—22no—
799C24—22no—
800C24—22no—
801C24—41no—
802C24—41no—
803C24C22×D414yes—
804C24C2514yes—
805C24C2511yescharacteristic
806C24C2511yescharacteristic
807C24C2511yescharacteristic
808#41—816no—
809C2×Q8—28no—
810C2×Q8—28no—
811C2×Q8—216no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—28no—
815C2×Q8—24no—
816C2×Q8—28no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—48no—
820C2×Q8—42no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×Q8—48no—
824C2×Q8—42no—
825C2×Q8—416no—
826C2×Q8—816no—
827C2×Q8—832no—
828C2×Q8C22×D418yes—
829C2×Q8C22×D418yes—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—42no—
843C2×D4—44no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—28no—
864C22×C4—28no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—28no—
869C22×C4—22no—
870C22×C4—28no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—28no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—28no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—28no—
888C22×C4—216no—
889C22×C4—416no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—42no—
908C22×C4—416no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—42no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—44no—
917C22×C4—416no—
918C22×C4C22×D418yes—
919C22×C4C22×D414yes—
920C22×C4C22×D414yes—
921C22×C4C22×D414yes—
922C22×C4C22×D418yes—
923C22×C4C22×D414yes—
924C22×C4C22×D414yes—
925C22×C4C22×D414yes—
926C22×C42−1+414yes—
927C22×C42−1+414yes—
928C22×C42−1+414yes—
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2514yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2518yes—
936C22×C4C2514yes—
937C22×C4C2518yes—
938C22×C4C2514yes—
939C22×C4C2511yescharacteristic
940C22×C4C2514yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C4⋊C4—28no—
951C4⋊C4—216no—
952C4⋊C4—216no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—216no—
957C4⋊C4—216no—
958C4⋊C4—216no—
959C4⋊C4—216no—
960C4⋊C4—216no—
961C4⋊C4—216no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—216no—
965C4⋊C4—216no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—28no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—48no—
989C4⋊C4—48no—
990C4⋊C4—48no—
991C4⋊C4—48no—
992C4⋊C4C22×D418yes—
993C4⋊C4C22×D4116yes—
994C4⋊C4C22×D4116yes—
995C4⋊C4C22×D418yes—
996C22⋊C4—216no—
997C22⋊C4—216no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—216no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—216no—
1006C22⋊C4—216no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—48no—
1014C22⋊C4—44no—
1015C22⋊C4—48no—
1016C22⋊C4—48no—
1017C22⋊C4—48no—
1018C22⋊C4C22×D4116yes—
1019C22⋊C4C22×D4116yes—
1020C42—216no—
1021C42—28no—
1022C42—216no—
1023C42—216no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—22no—
1029C42—22no—
1030C42—22no—
1031C42—22no—
1032C42—22no—
1033C42—28no—
1034C42—28no—
1035C42—28no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42—41no—
1040C42—41no—
1041C42—41no—
1042C42—44no—
1043C42H(5,𝔽2)14yes—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—28no—
1059C23—28no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23—24no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—44no—
1068C23—44no—
1069C23—44no—
1070C23—44no—
1071C23—44no—
1072C23C23×D412yes—
1073C23C23×D412yes—
1074C23C23×D412yes—
1075C23C2×2−1+412yes—
1076C23C2×2−1+412yes—
1077C23C2×2−1+412yes—
1078C23#58512yes—
1079C23C2611yescharacteristic
1080Q8—216no—
1081Q8—48no—
1082Q8—416no—
1083Q8—88no—
1084Q8—816no—
1085Q8—84no—
1086D4—416no—
1087D4—416no—
1088D4—48no—
1089D4—84no—
1090D4—84no—
1091D4—88no—
1092C2×C4—28no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—24no—
1113C2×C4—216no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—28no—
1117C2×C4—28no—
1118C2×C4—28no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—28no—
1122C2×C4—24no—
1123C2×C4—28no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—28no—
1134C2×C4—24no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—24no—
1142C2×C4—28no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—48no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—416no—
1159C2×C4—416no—
1160C2×C4—44no—
1161C2×C4—816no—
1162C2×C4—84no—
1163C2×C4—84no—
1164C2×C4—88no—
1165C2×C4C23×D418yes—
1166C2×C4C23×D418yes—
1167C2×C4C23×D412yes—
1168C2×C4C23×D412yes—
1169C2×C4C23×D412yes—
1170C2×C4C23×D412yes—
1171C2×C4C2×H(5,𝔽2)12yes—
1172C2×C4C2×H(5,𝔽2)12yes—
1173C2×C4C2×H(5,𝔽2)12yes—
1174C2×C4C2×2−1+412yes—
1175C2×C4C2×2−1+412yes—
1176C2×C4C2×2−1+412yes—
1177C2×C4C2×2−1+412yes—
1178C2×C4C2×2−1+412yes—
1179C2×C4C2×2−1+412yes—
1180C2×C4#58512yes—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—416no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22#349714yes—
1209C22#349914yes—
1210C22C24×D411yescharacteristic
1211C22C22×H(5,𝔽2)11yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22C2×#58511yescharacteristic
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—28no—
1223C4—28no—
1224C4—22no—
1225C4—22no—
1226C4—22no—
1227C4—41no—
1228C4—44no—
1229C4—44no—
1230C4—48no—
1231C4—48no—
1232C4—44no—
1233C4—44no—
1234C4—41no—
1235C4—44no—
1236C4#349614yes—
1237C4#353814yescomplemented
1238C2—24no—
1239C2—24no—
1240C2—42no—
1241C2—84no—
1242C2C2×#353811yescharacteristic
1243C2#6275211yescharacteristic
1244C2C2×#349611yescharacteristic
1245C2C2×#349711yescharacteristic
1246C2C2×#349911yescharacteristic
1247C2#6281911yescharacteristic
1248C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
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×#3538C2semidirect
2. #59651C2semidirect
3. #59312C2semidirect
4. #59127C2semidirect
5. #45787C2semidirect
6. #45485C2semidirect
7. #39615C2semidirect
8. #39487C2semidirect
9. #39435C2semidirect
10. #39421C2semidirect
11. #39384C2semidirect
12. #39368C2semidirect
13. #39353C2semidirect
14. #39343C2semidirect
15. #37861C2semidirect
16. #37442C2semidirect
17. #36742C2semidirect
19. C2×#2857C2semidirect
20. Q8×#121C2semidirect
21. #36186C2semidirect
22. #36183C2semidirect
23. #35167C2semidirect
24. #35006C2semidirect
25. C2×C4×C22⋊Q8C2semidirect
33. C2×D4×Q8C22semidirect
68. #2734C22semidirect
69. #2732C22semidirect
70. #2729C22semidirect
71. #2727C22semidirect
72. #2726C22semidirect
73. #2725C22semidirect
75. #2721C22semidirect
76. #2719C22semidirect
77. #2716C22semidirect
79. #2713C22semidirect
81. #2694C22semidirect
82. #2690C22semidirect
83. #2677C22semidirect
84. #2674C22semidirect
95. #2560C22semidirect
96. #2558C22semidirect
98. #2552C22semidirect
99. #2552C22semidirect
100. #2552C22semidirect
101. #2551C22semidirect
102. #2551C22semidirect
103. #2550C22semidirect
104. #2550C22semidirect
105. #2546C22semidirect
106. #2546C22semidirect
107. #2542C22semidirect
108. #2538C22semidirect
109. #2538C22semidirect
111. #2519C22semidirect
112. #2512C22semidirect
113. #2512C22semidirect
114. #2506C22semidirect
115. #2506C22semidirect
122. #2489C22semidirect
125. #2453C22semidirect
126. #2452C22semidirect
128. #2446C22semidirect
129. #2445C22semidirect
130. #2441C22semidirect
133. #2434C22semidirect
134. #2429C22semidirect
135. #2429C22semidirect
136. #2429C22semidirect
138. #2423C22semidirect
143. #2415C22semidirect
147. #2409C22semidirect
148. #2365C22semidirect
149. #2362C22semidirect
152. #2354C22semidirect
153. Q8×C4⋊C4C22semidirect
155. Q8×C22⋊C4C22semidirect
240. C2×C22⋊Q8D4semidirect
1237. C4#3538semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
#596512
#593122
#591272
#457872
#454852
#396152
#394872
#394352
#394212
#393842
#393682
#393532
#393432
#378612
#374422
#367422
#366242
C2×#28572
Q8×#1212
#361862
#361832
#351672
#350062
C2×C4×C22⋊Q82