Finite Group Databasebeta

← #7652666

Subgroups — #7652666

Order 512.

8388 conjugacy classes of subgroups.

The subgroup lattice has 1383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#42890C214yesmaximal, complemented
4#42889C214yesmaximal, complemented
5#42876C214yesmaximal, complemented
6#42805C214yesmaximal, complemented
7#41934C218yesmaximal, complemented
8#39954C214yesmaximal, complemented
9#39858C214yesmaximal, complemented
10#39745C214yesmaximal, complemented
11#39138C214yesmaximal, complemented
12#38366C218yesmaximal, complemented
13#35676C211yesmaximal, characteristic, complemented
14#35660C211yesmaximal, characteristic, complemented
15#35565C211yesmaximal, characteristic, complemented
16#35556C211yesmaximal, characteristic, complemented
17#35528C211yesmaximal, characteristic, complemented
18#35514C211yesmaximal, characteristic, complemented
19#35274C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#34813C211yesmaximal, characteristic, complemented
23#34743C211yesmaximal, characteristic, complemented
24C2×#2431C211yesmaximal, characteristic, complemented
25#34254C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C23×#41C2211yescharacteristic
28#3510—216no—
29#3487—216no—
30C2×#559C2214yescomplemented
31C2×#556C2214yescomplemented
32C2×#551C2218yes—
33C2×#550C2214yescomplemented
34C2×#550C2214yescomplemented
35C2×#548C2214yescomplemented
36C2×#548C2214yescomplemented
37C2×#542C2214yescomplemented
38C2×#537C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#535C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2214yes—
43C2×#535C2211yescharacteristic
44C2×#535C2211yescharacteristic
45C2×#535C2211yescharacteristic
46C2×#535C2211yescharacteristic
47C2×#533C2211yescharacteristic
48C2×#532C2211yescharacteristic
49C22×#127C2211yescharacteristic
50C2×#529C2214yescomplemented
51C22×#124C2211yescharacteristic
52C2×#525C2211yescharacteristic
53C2×#525C2214yes—
54C2×#525C2211yescharacteristic
55C2×#525C2211yescharacteristic
56C22×#121C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C2×#518C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60#2867C2212yescomplemented
61#2858C2212yescomplemented
62#2856C2212yescomplemented
63#2850C2212yescomplemented
64#2849C2214yes—
65#2819C2218yescomplemented
66#2818C2218yescomplemented
67#2723C2218yescomplemented
68#2714C2218yescomplemented
69#2714C2218yescomplemented
70#2714C2218yescomplemented
71#2696C2218yescomplemented
72#2696C2218yescomplemented
73#2692C2218yescomplemented
74#2676C2218yescomplemented
75#2676C2218yescomplemented
76#2676C2218yescomplemented
77#2673C2218yescomplemented
78#2673C2218yescomplemented
79#2673C2218yescomplemented
80#2673C2218yescomplemented
81#2673C2218yescomplemented
82#2673C2218yescomplemented
83#2662C2218yescomplemented
84#2657C2218yescomplemented
85#2657C2212yescomplemented
86#2657C2212yescomplemented
87#2636C2218yescomplemented
88#2631C2218yescomplemented
89#2631C2218yescomplemented
90#2620C2212yescomplemented
91#2619C2212yescomplemented
92#2619C2218yescomplemented
93#2613C2214yes—
94#2610C2218yescomplemented
95#2603C2218yescomplemented
96#2598C2218yescomplemented
97#2592C2214yescomplemented
98#2548C2214yescomplemented
99#2544C2218yescomplemented
100#2544C2214yescomplemented
101#2541C2214yescomplemented
102#2541C2214yescomplemented
103#2541C2218yescomplemented
104#2541C2214yescomplemented
105#2541C2214yescomplemented
106#2541C2214yescomplemented
107#2540C2214yescomplemented
108#2540C2214yescomplemented
109#2539C2214yes—
110#2537C2214yescomplemented
111#2535C2214yescomplemented
112#2535C2218yescomplemented
113#2492C2212yescomplemented
114#2491C2214yescomplemented
115#2491C2212yescomplemented
116#2490C2214yescomplemented
117#2490C2212yescomplemented
118#2489C2212yescomplemented
119#2488C2214yes—
120#2472C2214yes—
121#2472C2218yes—
122#2436C2214yescomplemented
123#2436C2212yescomplemented
124#2436C2212yescomplemented
125#2436C2212yescomplemented
126#2434C2212yescomplemented
127#2433C2218yes—
128#2433C2214yes—
129#2432C2214yescomplemented
130#2432C2212yescomplemented
131#2431C2214yes—
132#2431C2214yes—
133#2431C2214yes—
134#2431C2214yes—
135#2431C2212yescomplemented
136#2431C2214yescomplemented
137#2431C2214yescomplemented
138#2431C2212yescomplemented
139#2431C2212yescomplemented
140#2430C2218yes—
141#2429C2212yescomplemented
142#2428C2214yescomplemented
143#2428C2212yescomplemented
144#2428C2214yescomplemented
145#2428C2214yescomplemented
146#2428C2214yescomplemented
147#2427C2214yescomplemented
148#2427C2212yescomplemented
149#2426C2214yescomplemented
150#2426C2212yescomplemented
151#2425C2214yes—
152#2424C2214yes—
153#2424C2218yes—
154#2412C2214yes—
155#2410C2214yes—
156#2410C2218yes—
157#2409C2214yescomplemented
158#2407C2214yescomplemented
159#2407C2214yescomplemented
160#2407C2214yescomplemented
161#2404C2218yes—
162#2398C2214yescomplemented
163#2392C2214yescomplemented
164C2×#392C2214yes—
165#2356C2214yescomplemented
166#2355C2214yescomplemented
167#2343C2218yes—
168#2328C2218yescomplemented
169#2324C2218yescomplemented
170#2320C2214yescomplemented
171#2317C2211yescharacteristic
172#2311C2211yescharacteristic
173#2310C2211yescharacteristic
174#2309C2211yescharacteristic
175C4×#124C2214yescomplemented
176C4×#121C2214yescomplemented
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2211yescharacteristic
180#2296C2211yescharacteristic
181#2295C2214yescomplemented
182C2×#391C2211yescharacteristic
183C2×#390C2211yescharacteristic
184C2×#386C2214yes—
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic
187C4×#117C2211yescharacteristic
188C2×C4×C22⋊C4C2211yescharacteristic
189C2×2−1+4—28no—
190C2×2−1+4—44no—
191C2×2−1+4—44no—
192C22×#41—28no—
193C22×#41—44no—
194C22×#41—44no—
195C22×#41C2311yescharacteristic
196C22×#41C2311yescharacteristic
197C22×#41C2311yescharacteristic
198C22×#41C2314yes—
199C22×#41C2314yes—
200C22×#41C2314yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2311yescharacteristic
204C23×Q8C2312yes—
205C23×Q8C2312yes—
206C23×D4C2311yescharacteristic
207C23×D4C2311yescharacteristic
208C23×D4C2312yes—
209C23×D4C2314yes—
210C23×D4C2312yes—
211C24×C4C2311yescharacteristic
212C24×C4C2312yes—
213#559—232no—
214#556—232no—
215#551—264no—
216#550—232no—
217#550—232no—
218#548—232no—
219#548—232no—
220#542—232no—
221#537—44no—
222#536—28no—
223#535—28no—
224#535—28no—
225#535—232no—
226#535—28no—
227#535—44no—
228#535—44no—
229#535—44no—
230#533—28no—
231#532—44no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×#127—44no—
236C2×#127C2318yes—
237C2×#127C2312yes—
238C2×#127C2312yes—
239C2×#127C2312yes—
240C2×#127C2318yes—
241C2×#127C2312yes—
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2314yes—
247C2×#127C2312yes—
248C2×#127C2318yes—
249C2×#127C2318yes—
250#529—232no—
251C2×#126C2318yes—
252C2×#126C2318yes—
253C2×#125C2312yes—
254C2×#124—28no—
255C2×#124C2318yes—
256C2×#124C2318yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2311yescharacteristic
267C2×#124C2311yescharacteristic
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2318yes—
271#525—28no—
272#525—28no—
273#525—232no—
274#525—44no—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2312yes—
278C2×#123C2318yes—
279C2×#123C2318yes—
280C2×#123C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2318yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2318yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×#121—44no—
291C2×#121C2318yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2318yes—
296C2×#121C2318yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2318yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2318yes—
314C2×#121C2318yes—
315C2×#121C2318yes—
316C2×#120C2312yes—
317C2×#120C2314yes—
318C2×#120C2314yes—
319C2×#120C2312yes—
320C2×#120C2314yes—
321C2×#120C2314yes—
322C2×#120C2312yes—
323C2×#120C2314yes—
324C2×#120C2314yes—
325#519D4116yescomplemented
326#518—28no—
327C4×#41—28no—
328C2×C4×Q8C2314yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2314yes—
332C2×C4×D4C2318yes—
333C2×C4×D4C2318yes—
334C2×C4×D4C2318yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×#117C2311yescharacteristic
344C2×#117C2311yescharacteristic
345C2×#117C2311yescharacteristic
346C2×#117C2318yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C2×#117C2314yes—
350C2×#117C2311yescharacteristic
351C22×C4⋊C4C2311yescharacteristic
352C22×C22⋊C4C2314yes—
353C22×C22⋊C4C2314yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2314yes—
357C22×C42C2312yes—
358C22×C42C2311yescharacteristic
359C22×C42C2311yescharacteristic
360#400C2314yes—
361#400C2314yes—
362#399C2318yes—
363#398C2314yes—
364#397C2318yes—
365#397C2318yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#396C2318yes—
370#396C2314yes—
371#396C2314yes—
372#395C2318yes—
373#394C2314yes—
374#394C2314yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2314yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2314yes—
386#394C2318yes—
387#394C2314yes—
388#394C2318yes—
389#393C2314yes—
390#393C2318yes—
391#393C2318yes—
392#393C2318yes—
393#393C2318yes—
394#393C2314yes—
395#392C2318yes—
396#392C2318yes—
397#392C2318yes—
398#392C2318yes—
399#392C2318yes—
400#392C2318yes—
401#392C2318yes—
402#392C2318yes—
403#392C2318yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#392C2318yes—
408#392C2318yes—
409#392C2318yes—
410#392C2318yes—
411#392C2318yes—
412#392C2318yes—
413#392C2318yes—
414#392C2314yes—
415#392C2318yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2311yescharacteristic
423#391C2314yes—
424#391C2311yescharacteristic
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2312yes—
431#390C2318yes—
432#390C2318yes—
433#390C2318yes—
434#390C2318yes—
435#390C2318yes—
436#390C2314yes—
437#390C2312yes—
438#390C2311yescharacteristic
439#390C2318yes—
440#390C2318yes—
441#390C2314yes—
442#390C2311yescharacteristic
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2314yes—
450#389C2312yes—
451#388C2314yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#387C2318yes—
461#387C2318yes—
462#387C2318yes—
463#387C2318yes—
464#386C2314yes—
465#386C2318yes—
466#386C2318yes—
467#386C2314yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2318yes—
480#386C2314yes—
481#386C2318yes—
482#386C2318yes—
483#386C2318yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#385C2314yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2318yes—
492#385C2314yes—
493#384C2312yes—
494#383C2318yes—
495#382C2318yes—
496#382C2312yes—
497#382C2314yes—
498#381C2314yes—
499#381C2312yes—
500#380C2314yes—
501#380C2318yes—
502#380C2312yes—
503#380C2312yes—
504#380C2314yes—
505#379C2314yes—
506#379C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2318yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525#376C2312yes—
526#376C2318yes—
527C2×#95C2314yes—
528C2×#95C2312yes—
529C43C2312yes—
530C25C2412yes—
531C25C2411yescharacteristic
532C25C2412yes—
5332−1+4—464no—
534C2×#41—216no—
535C2×#41—216no—
536C2×#41—28no—
537C2×#41—28no—
538C2×#41—24no—
539C2×#41—216no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—24no—
546C2×#41—24no—
547C2×#41—24no—
548C2×#41—48no—
549C2×#41—48no—
550C2×#41—48no—
551C2×#41—48no—
552C2×#41—48no—
553C2×#41—48no—
554C2×#41—44no—
555C2×#41—44no—
556C2×#41—44no—
557C2×#41—44no—
558C2×#41—464no—
559C22×Q8—28no—
560C22×Q8—28no—
561C22×Q8—24no—
562C22×Q8—24no—
563C22×Q8—44no—
564C22×Q8—44no—
565C22×Q8—44no—
566C22×Q8—44no—
567C22×Q8C2×D418yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2412yes—
573C22×Q8C2414yes—
574C22×Q8C2414yes—
575C22×D4—24no—
576C22×D4—28no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—48no—
583C22×D4—44no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4—48no—
587C22×D4—84no—
588C22×D4—84no—
589C22×D4C2412yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2411yescharacteristic
593C22×D4C2412yes—
594C22×D4C2412yes—
595C22×D4C2412yes—
596C22×D4C2411yescharacteristic
597C22×D4C2412yes—
598C22×D4C2411yescharacteristic
599C22×D4C2418yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2418yes—
603C22×D4C2418yes—
604C22×D4C2414yes—
605C22×D4C2418yes—
606C22×D4C2414yes—
607C22×D4C2418yes—
608C22×D4C2414yes—
609C22×D4C2414yes—
610C22×D4C2414yes—
611C22×D4C2418yes—
612C22×D4C2414yes—
613C22×D4C2414yes—
614C22×D4C2414yes—
615C22×D4C2418yes—
616C22×D4C2418yes—
617C23×C4—28no—
618C23×C4—24no—
619C23×C4—24no—
620C23×C4—24no—
621C23×C4—44no—
622C23×C4—44no—
623C23×C4C2411yescharacteristic
624C23×C4C2412yes—
625C23×C4C2412yes—
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2412yes—
631C23×C4C2412yes—
632C23×C4C2412yes—
633C23×C4C2418yes—
634C23×C4C2414yes—
635C23×C4C2414yes—
636C23×C4C2414yes—
637C23×C4C2418yes—
638C23×C4C2411yescharacteristic
639C4⋊Q8—28no—
640C4⋊Q8—28no—
641C4⋊Q8—42no—
642#127—28no—
643#127—232no—
644#127—28no—
645#127—28no—
646#127—48no—
647#127—44no—
648#127—44no—
649#127—416no—
650#127—42no—
651#127—44no—
652#127—44no—
653#127—44no—
654#127—88no—
655#127—88no—
656#126—232no—
657#126—232no—
658#125—28no—
659#124—28no—
660#124—28no—
661#124—216no—
662#124—28no—
663#124—28no—
664#124—232no—
665#124—28no—
666#124—28no—
667#124—232no—
668#124—48no—
669#124—42no—
670#124—42no—
671#124—44no—
672#124—44no—
673#124—44no—
674#124—88no—
675#123—216no—
676#123—232no—
677#123—232no—
678#123—28no—
679#123—28no—
680#123—44no—
681C22⋊Q8—216no—
682C22⋊Q8—28no—
683C22⋊Q8—28no—
684C22⋊Q8—232no—
685C22⋊Q8—232no—
686C22⋊Q8—216no—
687C22⋊Q8—44no—
688C22⋊Q8—44no—
689C22⋊Q8—44no—
690#121—28no—
691#121—28no—
692#121—232no—
693#121—216no—
694#121—216no—
695#121—216no—
696#121—232no—
697#121—232no—
698#121—48no—
699#121—416no—
700#121—48no—
701#121—48no—
702#121—44no—
703#121—44no—
704#121—44no—
705#121—44no—
706#121—44no—
707#121—48no—
708#121—44no—
709#121—44no—
710#121—48no—
711#121—48no—
712#121—88no—
713#121—88no—
714#121—88no—
715#120—28no—
716#120—216no—
717#120—216no—
718#120—28no—
719#120—216no—
720#120—44no—
721#120—48no—
722#120—48no—
723#120—48no—
724C4×Q8—28no—
725C4×Q8—216no—
726C4×Q8C2×D4132yescomplemented
727C4×Q8C2×D4132yescomplemented
728C4×D4—28no—
729C4×D4—216no—
730C4×D4—216no—
731C4×D4—216no—
732C4×D4—216no—
733C4×D4—232no—
734C4×D4—232no—
735C4×D4—216no—
736C4×D4—232no—
737C4×D4—48no—
738C4×D4—48no—
739#117—24no—
740#117—24no—
741#117—24no—
742#117—28no—
743#117—232no—
744#117C2×D418yes—
745#117C2×D418yes—
746#117C2×D4132yes—
747C2×C4⋊C4—24no—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2418yes—
770C2×C22⋊C4—216no—
771C2×C22⋊C4—216no—
772C2×C22⋊C4—44no—
773C2×C22⋊C4—44no—
774C2×C22⋊C4—84no—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C42—24no—
822C2×C42—24no—
823C2×C42—28no—
824C2×C42C2414yes—
825C2×C42C2411yescharacteristic
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2414yes—
834C2×C42C2411yescharacteristic
835C2×C42C2418yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2418yes—
839C2×C42C2412yes—
840#95C2418yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2418yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2418yes—
861#95C2414yes—
862#95C2418yes—
863C24—22no—
864C24—24no—
865C24—24no—
866C24—24no—
867C24—22no—
868C24—24no—
869C24—22no—
870C24—24no—
871C24—24no—
872C24—42no—
873C24—44no—
874C24—44no—
875C24—42no—
876C24—44no—
877C24—44no—
878C24C2514yes—
879C24C2512yes—
880C24C2514yes—
881C24C2512yes—
882C24C2512yes—
883C24C2512yes—
884C24C2511yescharacteristic
885#41—464no—
886#41—464no—
887#41—464no—
888#41—432no—
889#41—432no—
890#41—416no—
891#41—416no—
892#41—416no—
893C2×Q8—232no—
894C2×Q8—22no—
895C2×Q8—28no—
896C2×Q8—22no—
897C2×Q8—22no—
898C2×Q8—28no—
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—22no—
904C2×Q8—22no—
905C2×Q8—22no—
906C2×Q8—22no—
907C2×Q8—22no—
908C2×Q8—22no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×Q8—44no—
912C2×Q8—44no—
913C2×Q8—432no—
914C2×Q8—432no—
915C2×Q8C22×D418yes—
916C2×Q8C22×D418yes—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—22no—
929C2×D4—216no—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—28no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—28no—
936C2×D4—216no—
937C2×D4—28no—
938C2×D4—216no—
939C2×D4—216no—
940C2×D4—24no—
941C2×D4—24no—
942C2×D4—22no—
943C2×D4—24no—
944C2×D4—22no—
945C2×D4—24no—
946C2×D4—22no—
947C2×D4—24no—
948C2×D4—24no—
949C2×D4—22no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—22no—
954C2×D4—28no—
955C2×D4—216no—
956C2×D4—48no—
957C2×D4—48no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—432no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—48no—
964C2×D4—48no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—48no—
969C2×D4—48no—
970C2×D4—48no—
971C2×D4—44no—
972C2×D4—48no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—48no—
976C2×D4—48no—
977C2×D4—44no—
978C2×D4—48no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—48no—
982C2×D4—48no—
983C2×D4—48no—
984C2×D4—48no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—48no—
991C2×D4—48no—
992C2×D4—48no—
993C2×D4—48no—
994C2×D4—48no—
995C2×D4—48no—
996C2×D4—48no—
997C2×D4—416no—
998C2×D4—416no—
999C2×D4—832no—
1000C2×D4—816no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—22no—
1004C22×C4—24no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—216no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—28no—
1029C22×C4—216no—
1030C22×C4—48no—
1031C22×C4—48no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—48no—
1042C22×C4—44no—
1043C22×C4—48no—
1044C22×C4—432no—
1045C22×C4—416no—
1046C22×C4C22×D418yes—
1047C22×C4C22×D414yes—
1048C22×C4H(5,𝔽2)14yes—
1049C22×C4H(5,𝔽2)14yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—216no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—48no—
1087C4⋊C4C22×D418yes—
1088C4⋊C4C22×D418yes—
1089C4⋊C4C22×D4132yes—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—216no—
1094C22⋊C4—216no—
1095C22⋊C4—216no—
1096C22⋊C4—28no—
1097C22⋊C4—216no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—216no—
1101C22⋊C4—28no—
1102C22⋊C4—216no—
1103C22⋊C4—28no—
1104C22⋊C4—216no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—48no—
1111C22⋊C4—48no—
1112C22⋊C4—48no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—48no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—48no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—48no—
1130C22⋊C4—48no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4C22×D418yes—
1135C22⋊C4C22×D418yes—
1136C42—22no—
1137C42—28no—
1138C42—22no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—22no—
1143C42—22no—
1144C42—24no—
1145C42—24no—
1146C42—28no—
1147C42—48no—
1148C42—44no—
1149C42C22×D418yes—
1150C42C22×D4132yes—
1151C42C22×D418yes—
1152C23—22no—
1153C23—22no—
1154C23—24no—
1155C23—22no—
1156C23—22no—
1157C23—24no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—24no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—24no—
1167C23—24no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—24no—
1176C23—28no—
1177C23—24no—
1178C23—28no—
1179C23—24no—
1180C23—28no—
1181C23—24no—
1182C23—22no—
1183C23—24no—
1184C23—28no—
1185C23—22no—
1186C23—44no—
1187C23—416no—
1188C23—44no—
1189C23—48no—
1190C23—44no—
1191C23—48no—
1192C23—84no—
1193C23—88no—
1194C23—84no—
1195C23—84no—
1196C23—84no—
1197C23—84no—
1198C23—88no—
1199C23—88no—
1200C23—84no—
1201C23C23×D412yes—
1202C23C2×H(5,𝔽2)12yes—
1203C23C2×H(5,𝔽2)12yes—
1204C23C2611yescharacteristic
1205Q8—216no—
1206Q8—216no—
1207Q8—416no—
1208Q8—44no—
1209Q8—44no—
1210Q8—44no—
1211Q8—88no—
1212D4—432no—
1213D4—416no—
1214D4—48no—
1215D4—48no—
1216D4—48no—
1217D4—48no—
1218D4—48no—
1219D4—48no—
1220D4—48no—
1221D4—44no—
1222D4—44no—
1223D4—44no—
1224D4—816no—
1225D4—88no—
1226D4—816no—
1227D4—88no—
1228D4—816no—
1229D4—88no—
1230D4—816no—
1231D4—88no—
1232D4—816no—
1233D4—816no—
1234D4—164no—
1235D4—164no—
1236D4—164no—
1237D4—164no—
1238D4—164no—
1239D4—168no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—216no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—28no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—48no—
1283C2×C4—432no—
1284C2×C4—416no—
1285C2×C4—416no—
1286C2×C4—44no—
1287C2×C4—48no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—88no—
1293C2×C4—816no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4#535116yes—
1297C2×C4C23×D418yes—
1298C2×C4C23×D418yes—
1299C2×C4C23×D418yes—
1300C2×C4C23×D412yes—
1301C2×C4C23×D412yes—
1302C2×C4C2×H(5,𝔽2)12yes—
1303C2×C4C2×H(5,𝔽2)12yes—
1304C2×C4C2×H(5,𝔽2)12yes—
1305C2×C4C2×H(5,𝔽2)12yes—
1306C2×C4#58514yes—
1307C22—24no—
1308C22—22no—
1309C22—22no—
1310C22—24no—
1311C22—44no—
1312C22—48no—
1313C22—44no—
1314C22—44no—
1315C22—42no—
1316C22—42no—
1317C22—48no—
1318C22—42no—
1319C22—42no—
1320C22—44no—
1321C22—44no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—44no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—44no—
1330C22—48no—
1331C22—44no—
1332C22—48no—
1333C22—42no—
1334C22—44no—
1335C22—44no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—44no—
1343C22—88no—
1344C22—816no—
1345C22—168no—
1346C22C2×#53514yes—
1347C22C24×D411yescharacteristic
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×H(5,𝔽2)11yescharacteristic
1350C22C2×#58512yes—
1351C22H(7,𝔽2)12yes—
1352C4—28no—
1353C4—28no—
1354C4—24no—
1355C4—28no—
1356C4—42no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4C2×#53514yes—
1369C4C2×#53514yes—
1370C2—24no—
1371C2—82no—
1372C2—82no—
1373C2—82no—
1374C2—84no—
1375C2—82no—
1376C2—84no—
1377C2C22×#53511yescharacteristic
1378C2#6283611yescharacteristic
1379C2#6287611yescharacteristic
1380C2#6292412yes—
1381C2#6300312yes—
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×#3510C2semidirect
2. C2×#3487C2semidirect
3. #42890C2semidirect
4. #42889C2semidirect
5. #42876C2semidirect
6. #42805C2semidirect
7. #41934C2semidirect
8. #39954C2semidirect
9. #39858C2semidirect
10. #39745C2semidirect
11. #39138C2semidirect
12. #38366C2semidirect
13. #35676C2semidirect
14. #35660C2semidirect
15. #35565C2semidirect
16. #35556C2semidirect
17. #35528C2semidirect
18. #35514C2semidirect
19. #35274C2semidirect
20. #35256C2semidirect
21. #35149C2semidirect
22. #34813C2semidirect
23. #34743C2semidirect
24. C2×#2431C2semidirect
25. #34254C2semidirect
30. C2×#559C22semidirect
31. C2×#556C22semidirect
33. C2×#550C22semidirect
34. C2×#550C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#542C22semidirect
50. C2×#529C22semidirect
60. #2867C22semidirect
61. #2858C22semidirect
62. #2856C22semidirect
63. #2850C22semidirect
65. #2819C22semidirect
66. #2818C22semidirect
67. #2723C22semidirect
68. #2714C22semidirect
69. #2714C22semidirect
70. #2714C22semidirect
71. #2696C22semidirect
72. #2696C22semidirect
73. #2692C22semidirect
74. #2676C22semidirect
75. #2676C22semidirect
76. #2676C22semidirect
77. #2673C22semidirect
78. #2673C22semidirect
79. #2673C22semidirect
80. #2673C22semidirect
81. #2673C22semidirect
82. #2673C22semidirect
83. #2662C22semidirect
84. #2657C22semidirect
85. #2657C22semidirect
86. #2657C22semidirect
87. #2636C22semidirect
88. #2631C22semidirect
89. #2631C22semidirect
90. #2620C22semidirect
91. #2619C22semidirect
92. #2619C22semidirect
94. #2610C22semidirect
95. #2603C22semidirect
96. #2598C22semidirect
97. #2592C22semidirect
98. #2548C22semidirect
99. #2544C22semidirect
100. #2544C22semidirect
101. #2541C22semidirect
102. #2541C22semidirect
103. #2541C22semidirect
104. #2541C22semidirect
105. #2541C22semidirect
106. #2541C22semidirect
107. #2540C22semidirect
108. #2540C22semidirect
110. #2537C22semidirect
111. #2535C22semidirect
112. #2535C22semidirect
113. #2492C22semidirect
114. #2491C22semidirect
115. #2491C22semidirect
116. #2490C22semidirect
117. #2490C22semidirect
118. #2489C22semidirect
122. #2436C22semidirect
123. #2436C22semidirect
124. #2436C22semidirect
125. #2436C22semidirect
126. #2434C22semidirect
129. #2432C22semidirect
130. #2432C22semidirect
135. #2431C22semidirect
136. #2431C22semidirect
137. #2431C22semidirect
138. #2431C22semidirect
139. #2431C22semidirect
141. #2429C22semidirect
142. #2428C22semidirect
143. #2428C22semidirect
144. #2428C22semidirect
145. #2428C22semidirect
146. #2428C22semidirect
147. #2427C22semidirect
148. #2427C22semidirect
149. #2426C22semidirect
150. #2426C22semidirect
157. #2409C22semidirect
158. #2407C22semidirect
159. #2407C22semidirect
160. #2407C22semidirect
162. #2398C22semidirect
163. #2392C22semidirect
165. #2356C22semidirect
166. #2355C22semidirect
168. #2328C22semidirect
169. #2324C22semidirect
170. #2320C22semidirect
175. C4×#124C22semidirect
176. C4×#121C22semidirect
181. #2295C22semidirect
325. #519D4semidirect
726. C4×Q8C2×D4semidirect
727. C4×Q8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#34872
#428902
#428892
#428762
#428052
#419342
#399542
#398582
#397452
#391382
#383662
#356762
#356602
#355652
#355562
#355282
#355142
#352742
#352562
#351492
#348132
#347432
C2×#24312
#342542