Finite Group Databasebeta

← #7677886

Subgroups — #7677886

Order 512.

11108 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C212yesmaximal, complemented
2C2×#3497C211yesmaximal, characteristic, complemented
3C22×#537C211yesmaximal, characteristic, complemented
4#59005C214yesmaximal, complemented
5#59003C214yesmaximal, complemented
6#58998C214yesmaximal, complemented
7#58996C214yesmaximal, complemented
8#45245C214yesmaximal, complemented
9#45244C214yesmaximal, complemented
10#45091C214yesmaximal, complemented
11#44884C214yesmaximal, complemented
12#39359C214yesmaximal, complemented
13#37679C214yesmaximal, complemented
14#37673C214yesmaximal, complemented
15#36123C214yesmaximal, complemented
16#35660C212yesmaximal, complemented
17#35564C212yesmaximal, complemented
18#35223C211yesmaximal, characteristic, complemented
19#35166C211yesmaximal, characteristic, complemented
20#35153C211yesmaximal, characteristic, complemented
21#34738C212yesmaximal, complemented
22#34274C211yesmaximal, characteristic, complemented
23C2×#2360C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yescomplemented
25C23×#41C2212yes—
26#3497—216no—
27#3489—232no—
28C2×#550C2214yescomplemented
29C2×D4×Q8C2214yes—
30C2×D4×Q8C2214yescomplemented
31C2×#548C2214yescomplemented
32C2×#548C2214yescomplemented
33C2×#548C2214yescomplemented
34C2×#547C2214yescomplemented
35C2×#547C2218yescomplemented
36C2×#546C2218yes—
37C2×#546C2214yes—
38C2×#537—216no—
39C2×#537C2214yes—
40C2×#537C2214yes—
41C2×#537C2212yes—
42C2×#537C2211yescharacteristic
43C2×#537C2214yes—
44C2×#537C2211yescharacteristic
45C2×#537C2214yescomplemented
46C2×#537C2211yescharacteristic, complemented
47C2×#537C2214yescomplemented
48C2×#537C2212yescomplemented
49C2×#536C2214yescomplemented
50C2×#536C2212yescomplemented
51C2×#532C2214yescomplemented
52C2×#532C2212yescomplemented
53C2×#532C2212yescomplemented
54C2×#525C2214yes—
55C2×#525C2212yes—
56C22×C22⋊Q8C2214yes—
57C22×C22⋊Q8C2214yes—
58C22×C22⋊Q8C2211yescharacteristic
59C22×#121C2214yes—
60C22×#121C2214yes—
61C2×#520C2212yescomplemented
62C22×C4×Q8C2211yescharacteristic, complemented
63C23×C4⋊C4C2211yescharacteristic
64#2856C2214yescomplemented
65#2854C2214yescomplemented
66#2847C2214yes—
67#2683C2218yescomplemented
68#2682C2218yescomplemented
69#2681C2218yescomplemented
70#2681C2218yescomplemented
71#2677C2218yescomplemented
72#2676C2218yescomplemented
73#2676C2218yescomplemented
74#2675C2218yescomplemented
75#2674C2218yescomplemented
76#2673C2218yescomplemented
77#2672C2218yescomplemented
78#2671C2218yescomplemented
79#2656C2214yescomplemented
80#2618C2214yescomplemented
81#2618C2214yescomplemented
82#2555C2218yescomplemented
83#2543C2218yescomplemented
84#2542C2214yescomplemented
85#2541C2214yescomplemented
86#2540C2214yescomplemented
87#2540C2214yescomplemented
88#2491C2214yescomplemented
89#2472C2218yes—
90#2464C2218yescomplemented
91#2463C2218yescomplemented
92#2456C2218yescomplemented
93#2452C2218yescomplemented
94#2449C2218yes—
95#2449C2218yescomplemented
96#2443C2218yescomplemented
97#2440C2214yes—
98#2440C2218yescomplemented
99#2437C2218yes—
100#2436C2212yes—
101#2436C2214yescomplemented
102#2435C2212yes—
103#2434C2212yes—
104#2434C2214yescomplemented
105#2433C2214yes—
106#2433C2212yes—
107#2432C2212yescomplemented
108#2432C2214yescomplemented
109#2432C2212yescomplemented
110#2431C2214yescomplemented
111#2431C2212yescomplemented
112#2431C2212yescomplemented
113#2430C2218yescomplemented
114#2430C2218yescomplemented
115#2430C2214yescomplemented
116#2430C2214yescomplemented
117#2429C2214yescomplemented
118#2429C2214yescomplemented
119#2429C2214yescomplemented
120#2428C2214yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2428C2218yescomplemented
124#2427C2214yescomplemented
125#2426C2214yescomplemented
126#2426C2214yescomplemented
127#2426C2214yescomplemented
128#2424C2218yes—
129#2422C2214yescomplemented
130#2417C2214yes—
131#2417C2214yescomplemented
132#2417C2214yescomplemented
133#2416C2214yes—
134#2416C2218yescomplemented
135#2416C2218yescomplemented
136#2416C2214yescomplemented
137#2416C2214yescomplemented
138#2415C2214yescomplemented
139#2414C2214yescomplemented
140#2410C2214yes—
141#2410C2214yes—
142#2410C2218yes—
143#2409C2214yescomplemented
144#2409C2214yescomplemented
145#2407C2214yescomplemented
146#2407C2214yescomplemented
147#2388C2214yescomplemented
148#2388C2214yescomplemented
149#2363C2214yescomplemented
150#2362C2214yescomplemented
151#2361C2214yes—
152#2361C2214yescomplemented
153#2360C2214yes—
154#2360C2214yes—
155#2360C2214yescomplemented
156#2360C2214yescomplemented
157#2360C2214yescomplemented
158#2358C2218yes—
159D4×C22⋊C4C2214yes—
160#2325C2214yescomplemented
161#2316C2211yescharacteristic, complemented
162#2311C2212yescomplemented
163C4×#121C2214yescomplemented
164C4×#120C2214yes—
165C4×#120C2214yes—
166#2297C2212yescomplemented
167#2297C2212yescomplemented
168C2×#391C2211yescharacteristic, complemented
169C2×#389C2212yescomplemented
170C2×#389C2211yescharacteristic, complemented
171C2×#387C2212yescomplemented
172C2×#385C2212yes—
173C2×C4×C4⋊C4C2211yescharacteristic, complemented
174C2×C4×C22⋊C4C2212yes—
175C2×C4×C22⋊C4C2211yescharacteristic
176C2×2−1+4—216no—
177C2×2−1+4—216no—
178C2×2−1+4—48no—
179C22×#41—216no—
180C22×#41—216no—
181C22×#41—48no—
182C22×#41C2312yes—
183C22×#41C2312yes—
184C22×#41C2314yes—
185C22×#41C2314yes—
186C22×#41C2312yes—
187C22×#41C2312yes—
188C22×#41C2314yes—
189C22×#41C2314yes—
190C22×#41C2318yes—
191C22×#41C2312yes—
192C23×Q8C2312yes—
193C23×Q8C2314yes—
194C23×Q8C2314yes—
195C23×Q8C2311yescharacteristic
196C23×D4C2314yes—
197C23×D4C2312yes—
198C23×D4C2314yes—
199C24×C4C2314yes—
200C24×C4C2311yescharacteristic
201C24×C4C2312yes—
202#550—232no—
203D4×Q8—232no—
204D4×Q8—232no—
205#548—232no—
206#548—232no—
207#548—232no—
208#547—232no—
209#547—264no—
210#546—232no—
211#546—264no—
212#537—216no—
213#537—232no—
214#537—232no—
215#537—232no—
216#537—232no—
217#537—232no—
218#537—28no—
219#537—28no—
220#537—216no—
221#537D4116yescomplemented
222#536—216no—
223#536—232no—
224#532—216no—
225#532—232no—
226#532—48no—
227C2×C4⋊Q8C2318yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×#127C2314yes—
233C2×#127C2312yes—
234C2×#127C2312yes—
235C2×#127C2314yes—
236C2×#124C2318yes—
237C2×#124C2318yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243#525—216no—
244#525—232no—
245C2×#123C2318yes—
246C2×#123C2314yes—
247C2×#123C2318yes—
248C2×#123C2318yes—
249C2×#123C2318yes—
250C2×C22⋊Q8—232no—
251C2×C22⋊Q8—232no—
252C2×C22⋊Q8D4116yescomplemented
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2318yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2318yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2318yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2318yes—
269C2×C22⋊Q8C2318yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121—232no—
274C2×#121—232no—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2318yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2318yes—
282C2×#121C2318yes—
283C2×#121C2318yes—
284C2×#121C2314yes—
285C2×#121C2318yes—
286C2×#121C2314yes—
287C2×#121C2318yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2318yes—
295C2×#121C2314yes—
296C2×#121C2318yes—
297C2×#121C2318yes—
298C2×#121C2318yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2318yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#120C2314yes—
307C2×#120C2314yes—
308C2×#120C2318yes—
309C2×#120C2314yes—
310#520—216no—
311C2×C4×Q8—28no—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×D4C2318yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2318yes—
318C2×C4×D4C2318yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2318yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C22×C4⋊C4—28no—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2314yes—
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2314yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2318yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C22⋊C4C2318yes—
345C22×C22⋊C4C2318yes—
346C22×C22⋊C4C2311yescharacteristic
347C22×C22⋊C4C2311yescharacteristic
348C22×C22⋊C4C2312yes—
349C22×C42C2312yes—
350C22×C42C2311yescharacteristic
351C22×C42C2311yescharacteristic
352C22×C42C2312yes—
353#399C2318yes—
354#399C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#397C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#395C2314yes—
366#395C2314yes—
367#395C2318yes—
368#395C2318yes—
369#394C2318yes—
370#394C2318yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#393C2314yes—
383#393C2314yes—
384#393C2318yes—
385#393C2318yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2318yes—
393#392C2318yes—
394#392C2318yes—
395#392C2318yes—
396#392C2318yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2318yes—
409#390C2314yes—
410#390C2318yes—
411#390C2312yes—
412#390C2312yes—
413#390C2314yes—
414#390C2312yes—
415#390C2318yes—
416#390C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2318yes—
424#389C2318yes—
425#389C2314yes—
426#389C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#386C2318yes—
437#386C2314yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2314yes—
447#386C2314yes—
448#386C2318yes—
449#386C2318yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#385C2318yes—
457#385C2314yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2314yes—
465#385C2314yes—
466#385C2314yes—
467#385C2314yes—
468#385C2314yes—
469#384C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2318yes—
476#379C2314yes—
477#379C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C2×#95C2312yes—
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2312yes—
498C2×#95C2312yes—
499C2×#95C2312yes—
500C25C2414yes—
501C25C2411yescharacteristic
5022−1+4—4128no—
503C2×#41—216no—
504C2×#41—28no—
505C2×#41—216no—
506C2×#41—232no—
507C2×#41—216no—
508C2×#41—28no—
509C2×#41—216no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—28no—
513C2×#41—216no—
514C2×#41—28no—
515C2×#41—216no—
516C2×#41—28no—
517C2×#41—232no—
518C2×#41—28no—
519C2×#41—216no—
520C2×#41—28no—
521C2×#41—216no—
522C2×#41—28no—
523C2×#41—28no—
524C2×#41—28no—
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—416no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—48no—
531C2×#41—48no—
532C2×#41—4128no—
533C2×#41C2×D4116yes—
534C22×Q8—28no—
535C22×Q8—216no—
536C22×Q8—216no—
537C22×Q8—216no—
538C22×Q8—24no—
539C22×Q8—216no—
540C22×Q8—28no—
541C22×Q8—24no—
542C22×Q8—44no—
543C22×Q8—48no—
544C22×Q8—48no—
545C22×Q8C2×D418yescomplemented
546C22×Q8C2412yes—
547C22×Q8C2412yes—
548C22×Q8C2414yes—
549C22×Q8C2418yes—
550C22×Q8C2414yes—
551C22×Q8C2412yes—
552C22×D4—216no—
553C22×D4—28no—
554C22×D4—216no—
555C22×D4—216no—
556C22×D4—28no—
557C22×D4—44no—
558C22×D4—48no—
559C22×D4—48no—
560C22×D4—84no—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2412yes—
565C22×D4C2412yes—
566C22×D4C2414yes—
567C22×D4C2418yes—
568C22×D4C2414yes—
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2414yes—
572C22×D4C2412yes—
573C22×D4C2414yes—
574C22×D4C2414yes—
575C22×D4C2418yes—
576C22×D4C2414yes—
577C22×D4C2414yes—
578C22×D4C2418yes—
579C22×D4C2414yes—
580C22×D4C2414yes—
581C22×D4C2414yes—
582C23×C4—24no—
583C23×C4—24no—
584C23×C4—216no—
585C23×C4—216no—
586C23×C4—28no—
587C23×C4—48no—
588C23×C4—44no—
589C23×C4—82no—
590C23×C4C2×D418yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2418yes—
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2418yes—
600C23×C4C2414yes—
601C23×C4C2412yes—
602C23×C4C2411yescharacteristic
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2414yes—
606C23×C4C2411yescharacteristic
607C23×C4C2418yes—
608C23×C4C2411yescharacteristic
609C23×C4C2412yes—
610C23×C4C2414yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2411yescharacteristic
614C4⋊Q8—28no—
615C4⋊Q8—216no—
616C4⋊Q8—216no—
617C4⋊Q8—232no—
618C4⋊Q8—44no—
619#127—216no—
620#127—28no—
621#127—44no—
622#127—84no—
623#124—28no—
624#124—216no—
625#124—28no—
626#124—232no—
627#124—232no—
628#124—44no—
629#124—44no—
630#123—216no—
631#123—232no—
632#123—232no—
633#123—232no—
634#123—232no—
635C22⋊Q8—216no—
636C22⋊Q8—216no—
637C22⋊Q8—216no—
638C22⋊Q8—28no—
639C22⋊Q8—216no—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—232no—
643C22⋊Q8—216no—
644C22⋊Q8—232no—
645C22⋊Q8—232no—
646C22⋊Q8—216no—
647C22⋊Q8—232no—
648C22⋊Q8—216no—
649C22⋊Q8—232no—
650C22⋊Q8—232no—
651C22⋊Q8—232no—
652C22⋊Q8C2×D4132yes—
653C22⋊Q8C2×D4132yes—
654C22⋊Q8C2×D4132yescomplemented
655#121—216no—
656#121—216no—
657#121—232no—
658#121—232no—
659#121—216no—
660#121—216no—
661#121—232no—
662#121—216no—
663#121—216no—
664#121—28no—
665#121—28no—
666#121—216no—
667#121—232no—
668#121—216no—
669#121—216no—
670#121—216no—
671#121—232no—
672#121—216no—
673#121—216no—
674#121—232no—
675#121—232no—
676#121—232no—
677#121—232no—
678#121—232no—
679#121—48no—
680#121—48no—
681#121—48no—
682#121—88no—
683#121—84no—
684#121C2×D4132yes—
685#121C2×D4132yes—
686#120—216no—
687#120—232no—
688#120—216no—
689#120—48no—
690C4×Q8—216no—
691C4×Q8—216no—
692C4×Q8—216no—
693C4×D4—216no—
694C4×D4—232no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—232no—
701C4×D4—216no—
702C4×D4—232no—
703C4×D4—232no—
704C4×D4—48no—
705C4×D4—48no—
706C4×D4—84no—
707#117—28no—
708#117—216no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—216no—
716C2×C4⋊C4—232no—
717C2×C4⋊C4—82no—
718C2×C4⋊C4C2×D418yes—
719C2×C4⋊C4C2×D418yescomplemented
720C2×C4⋊C4C2×D4116yescomplemented
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2418yes—
726C2×C4⋊C4C2418yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C22⋊C4—232no—
747C2×C22⋊C4—232no—
748C2×C22⋊C4—24no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4C2×D4116yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2411yescharacteristic
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2418yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C42—28no—
793C2×C42—24no—
794C2×C42—24no—
795C2×C42—82no—
796C2×C42C2414yes—
797C2×C42C2418yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2414yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806#95C2412yes—
807#95C2412yes—
808#95C2412yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2418yes—
815#95C2418yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2418yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2418yes—
826#95C2418yes—
827C24—22no—
828C24—22no—
829C24—22no—
830C24—22no—
831C24—28no—
832C24—28no—
833C24—28no—
834C24—28no—
835C24—41no—
836C24—41no—
837C24—44no—
838C24—44no—
839C24—44no—
840C24C22×D414yes—
841C24C2514yes—
842C24C2514yes—
843C24C2514yes—
844C24C2511yescharacteristic
845C24C2511yescharacteristic
846C24C2511yescharacteristic
847#41—264no—
848#41—464no—
849#41—464no—
850#41—432no—
851#41—4128no—
852#41—432no—
853#41—464no—
854#41—464no—
855#41—432no—
856#41—432no—
857C2×Q8—232no—
858C2×Q8—24no—
859C2×Q8—28no—
860C2×Q8—24no—
861C2×Q8—28no—
862C2×Q8—24no—
863C2×Q8—216no—
864C2×Q8—216no—
865C2×Q8—24no—
866C2×Q8—28no—
867C2×Q8—24no—
868C2×Q8—28no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—48no—
873C2×Q8—44no—
874C2×Q8—432no—
875C2×Q8—464no—
876C2×Q8—464no—
877C2×Q8C22×D418yes—
878C2×Q8C22×D4116yes—
879C2×D4—28no—
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—216no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—216no—
899C2×D4—24no—
900C2×D4—216no—
901C2×D4—28no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—28no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—216no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—432no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—48no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—48no—
931C2×D4—44no—
932C2×D4—48no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—48no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—464no—
941C2×D4—832no—
942C2×D4C22×D4116yes—
943C2×D4C22×D418yes—
944C2×D4C22×D4116yes—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—232no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—22no—
957C22×C4—216no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—22no—
961C22×C4—28no—
962C22×C4—22no—
963C22×C4—24no—
964C22×C4—22no—
965C22×C4—28no—
966C22×C4—28no—
967C22×C4—216no—
968C22×C4—28no—
969C22×C4—216no—
970C22×C4—216no—
971C22×C4—28no—
972C22×C4—28no—
973C22×C4—28no—
974C22×C4—28no—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—216no—
982C22×C4—28no—
983C22×C4—41no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—41no—
993C22×C4—48no—
994C22×C4—48no—
995C22×C4—464no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—42no—
1000C22×C4—48no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—48no—
1005C22×C4—41no—
1006C22×C4—816no—
1007C22×C4C22×D418yes—
1008C22×C4C22×D414yes—
1009C22×C4C22×D4116yes—
1010C22×C4C22×D418yes—
1011C22×C4C22×D418yes—
1012C22×C4C22×D418yes—
1013C22×C4C22×D418yes—
1014C22×C4C22×D414yes—
1015C22×C4C22×D414yes—
1016C22×C4H(5,𝔽2)14yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2512yes—
1034C4⋊C4—216no—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—216no—
1039C4⋊C4—216no—
1040C4⋊C4—216no—
1041C4⋊C4—28no—
1042C4⋊C4—216no—
1043C4⋊C4—216no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—216no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4C22×D4116yes—
1056C4⋊C4C22×D4116yes—
1057C4⋊C4C22×D4132yes—
1058C4⋊C4C22×D4116yes—
1059C22⋊C4—28no—
1060C22⋊C4—216no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—22no—
1066C22⋊C4—24no—
1067C22⋊C4—216no—
1068C22⋊C4—216no—
1069C22⋊C4—216no—
1070C22⋊C4—216no—
1071C22⋊C4—216no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—216no—
1075C22⋊C4—28no—
1076C22⋊C4—216no—
1077C22⋊C4—28no—
1078C22⋊C4—216no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—42no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—48no—
1094C22⋊C4—44no—
1095C22⋊C4—48no—
1096C22⋊C4C22×D4116yes—
1097C22⋊C4C22×D4132yes—
1098C22⋊C4C22×D4116yes—
1099C22⋊C42−1+414yescomplemented
1100C42—28no—
1101C42—24no—
1102C42—28no—
1103C42—24no—
1104C42—216no—
1105C42—28no—
1106C42—24no—
1107C42—24no—
1108C42—44no—
1109C42—44no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—24no—
1119C23—21no—
1120C23—21no—
1121C23—24no—
1122C23—21no—
1123C23—24no—
1124C23—21no—
1125C23—24no—
1126C23—24no—
1127C23—21no—
1128C23—24no—
1129C23—21no—
1130C23—28no—
1131C23—28no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—24no—
1146C23—44no—
1147C23—44no—
1148C23—44no—
1149C23—44no—
1150C23—44no—
1151C23—416no—
1152C23—416no—
1153C23—416no—
1154C23—416no—
1155C23—88no—
1156C23—88no—
1157C23—88no—
1158C23C23×D412yes—
1159C23C23×D418yes—
1160C23C23×D412yes—
1161C23C23×D412yes—
1162C23C23×D412yes—
1163C23C2×H(5,𝔽2)12yes—
1164C23C2×2−1+412yes—
1165C23#58512yes—
1166C23C2611yescharacteristic
1167Q8—232no—
1168Q8—216no—
1169Q8—432no—
1170Q8—416no—
1171Q8—48no—
1172Q8—48no—
1173D4—232no—
1174D4—216no—
1175D4—416no—
1176D4—416no—
1177D4—416no—
1178D4—416no—
1179D4—432no—
1180D4—416no—
1181D4—416no—
1182D4—416no—
1183D4—416no—
1184D4—48no—
1185D4—48no—
1186D4—88no—
1187D4—816no—
1188D4—88no—
1189D4—88no—
1190D4—88no—
1191D4—88no—
1192D4—816no—
1193D4—88no—
1194C2×C4—21no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—21no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—21no—
1208C2×C4—28no—
1209C2×C4—216no—
1210C2×C4—216no—
1211C2×C4—216no—
1212C2×C4—232no—
1213C2×C4—21no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—21no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—416no—
1243C2×C4—432no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—416no—
1247C2×C4—416no—
1248C2×C4—416no—
1249C2×C4—432no—
1250C2×C4—416no—
1251C2×C4—416no—
1252C2×C4—816no—
1253C2×C4—88no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4—84no—
1257C2×C4D42116yes—
1258C2×C4C23×D418yes—
1259C2×C4C23×D418yes—
1260C2×C4C23×D418yes—
1261C2×C4C23×D418yes—
1262C2×C4C23×D414yes—
1263C2×C4C23×D414yes—
1264C2×C4C23×D414yes—
1265C2×C4C2×H(5,𝔽2)14yes—
1266C2×C4C2×2−1+412yes—
1267C2×C4C2×2−1+412yes—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—28no—
1281C22—28no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—28no—
1286C22—416no—
1287C22—41no—
1288C22—41no—
1289C22—44no—
1290C22—44no—
1291C22—41no—
1292C22—44no—
1293C22—41no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—832no—
1310C22C2×D4214yes—
1311C22#349714yescomplemented
1312C22C24×D411yescharacteristic
1313C22C24×D411yescharacteristic
1314C22C22×H(5,𝔽2)11yescharacteristic
1315C22C22×2−1+411yescharacteristic
1316C22C2×#58511yescharacteristic
1317C22H(7,𝔽2)11yescharacteristic
1318C222−1+611yescharacteristic
1319C4—28no—
1320C4—22no—
1321C4—28no—
1322C4—22no—
1323C4—24no—
1324C4—28no—
1325C4—28no—
1326C4—44no—
1327C4—42no—
1328C4—41no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—41no—
1333C4—44no—
1334C4—44no—
1335C4C2×D4218yes—
1336C2—24no—
1337C2—24no—
1338C2—42no—
1339C2—48no—
1340C2—84no—
1341C2—84no—
1342C2C22×D4211yescharacteristic
1343C2C2×#349711yescharacteristic
1344C2#6285311yescharacteristic
1345C2#6292711yescharacteristic
1346C2#6294411yescharacteristic
1347C2#6298711yescharacteristic
1348C2D4×2−1+411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3489C2semidirect
2. C2×#3497C2semidirect
3. C22×#537C2semidirect
4. #59005C2semidirect
5. #59003C2semidirect
6. #58998C2semidirect
7. #58996C2semidirect
8. #45245C2semidirect
9. #45244C2semidirect
10. #45091C2semidirect
11. #44884C2semidirect
12. #39359C2semidirect
13. #37679C2semidirect
14. #37673C2semidirect
15. #36123C2semidirect
16. #35660C2semidirect
17. #35564C2semidirect
18. #35223C2semidirect
19. #35166C2semidirect
20. #35153C2semidirect
21. #34738C2semidirect
22. #34274C2semidirect
23. C2×#2360C2semidirect
24. C22×2−1+4C22semidirect
28. C2×#550C22semidirect
30. C2×D4×Q8C22semidirect
31. C2×#548C22semidirect
32. C2×#548C22semidirect
33. C2×#548C22semidirect
34. C2×#547C22semidirect
35. C2×#547C22semidirect
45. C2×#537C22semidirect
46. C2×#537C22semidirect
47. C2×#537C22semidirect
48. C2×#537C22semidirect
49. C2×#536C22semidirect
50. C2×#536C22semidirect
51. C2×#532C22semidirect
52. C2×#532C22semidirect
53. C2×#532C22semidirect
61. C2×#520C22semidirect
62. C22×C4×Q8C22semidirect
64. #2856C22semidirect
65. #2854C22semidirect
67. #2683C22semidirect
68. #2682C22semidirect
69. #2681C22semidirect
70. #2681C22semidirect
71. #2677C22semidirect
72. #2676C22semidirect
73. #2676C22semidirect
74. #2675C22semidirect
75. #2674C22semidirect
76. #2673C22semidirect
77. #2672C22semidirect
78. #2671C22semidirect
79. #2656C22semidirect
80. #2618C22semidirect
81. #2618C22semidirect
82. #2555C22semidirect
83. #2543C22semidirect
84. #2542C22semidirect
85. #2541C22semidirect
86. #2540C22semidirect
87. #2540C22semidirect
88. #2491C22semidirect
90. #2464C22semidirect
91. #2463C22semidirect
92. #2456C22semidirect
93. #2452C22semidirect
95. #2449C22semidirect
96. #2443C22semidirect
98. #2440C22semidirect
101. #2436C22semidirect
104. #2434C22semidirect
107. #2432C22semidirect
108. #2432C22semidirect
109. #2432C22semidirect
110. #2431C22semidirect
111. #2431C22semidirect
112. #2431C22semidirect
113. #2430C22semidirect
114. #2430C22semidirect
115. #2430C22semidirect
116. #2430C22semidirect
117. #2429C22semidirect
118. #2429C22semidirect
119. #2429C22semidirect
120. #2428C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2428C22semidirect
124. #2427C22semidirect
125. #2426C22semidirect
126. #2426C22semidirect
127. #2426C22semidirect
129. #2422C22semidirect
131. #2417C22semidirect
132. #2417C22semidirect
134. #2416C22semidirect
135. #2416C22semidirect
136. #2416C22semidirect
137. #2416C22semidirect
138. #2415C22semidirect
139. #2414C22semidirect
143. #2409C22semidirect
144. #2409C22semidirect
145. #2407C22semidirect
146. #2407C22semidirect
147. #2388C22semidirect
148. #2388C22semidirect
149. #2363C22semidirect
150. #2362C22semidirect
152. #2361C22semidirect
155. #2360C22semidirect
156. #2360C22semidirect
157. #2360C22semidirect
160. #2325C22semidirect
161. #2316C22semidirect
162. #2311C22semidirect
163. C4×#121C22semidirect
166. #2297C22semidirect
167. #2297C22semidirect
168. C2×#391C22semidirect
169. C2×#389C22semidirect
170. C2×#389C22semidirect
171. C2×#387C22semidirect
173. C2×C4×C4⋊C4C22semidirect
221. #537D4semidirect
252. C2×C22⋊Q8D4semidirect
545. C22×Q8C2×D4semidirect
654. C22⋊Q8C2×D4semidirect
719. C2×C4⋊C4C2×D4semidirect
720. C2×C4⋊C4C2×D4semidirect
1099. C22⋊C42−1+4semidirect
1311. C22#3497semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#34972
C22×#5372
#590052
#590032
#589982
#589962
#452452
#452442
#450912
#448842
#393592
#376792
#376732
#361232
#356602
#355642
#352232
#351662
#351532
#347382
#342742
C2×#23602