Finite Group Databasebeta

← #7986730

Subgroups — #7986730

Order 512.

7973 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3548C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#59458C212yesmaximal, complemented
4#59066C212yesmaximal, complemented
5#59057C212yesmaximal, complemented
6#51898C218yesmaximal, complemented
7#45484C214yesmaximal, complemented
8#45034C214yesmaximal, complemented
9#44884C214yesmaximal, complemented
10#42425C214yesmaximal, complemented
11#42421C214yesmaximal, complemented
12#39725C212yesmaximal, complemented
13#39386C212yesmaximal, complemented
14#39341C212yesmaximal, complemented
15#39341C212yesmaximal, complemented
16#39341C214yesmaximal, complemented
17#36592C211yesmaximal, characteristic, complemented
18#36128C212yesmaximal, complemented
19#36128C211yesmaximal, characteristic, complemented
20#36128C211yesmaximal, characteristic, complemented
21#36126C212yesmaximal, complemented
22#35171C212yesmaximal, complemented
23#35166C212yesmaximal, complemented
24#34929C211yesmaximal, characteristic, complemented
25#34925C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27#3548—232no—
28C2×#562C2218yes—
29C2×#554C2214yes—
30C2×#554C2212yes—
31C2×#554C2211yescharacteristic
32C2×#550C2212yes—
33C2×#550C2214yes—
34C2×#550C2212yes—
35C2×#550C2212yes—
36C2×#550C2212yes—
37C2×#550C2212yes—
38C2×#547C2214yes—
39C2×#547C2214yes—
40C2×#540C2214yes—
41C2×#540C2214yes—
42C2×#537C2214yes—
43C2×#537C2214yes—
44C2×#537C2218yes—
45C2×#537C2214yes—
46C2×#533C2212yes—
47C2×#532C2212yes—
48C2×#532C2212yes—
49C2×#532C2214yes—
50C2×#532C2212yes—
51C2×#532C2212yes—
52#2867C2211yescharacteristic
53#2867C2212yes—
54#2856C2212yes—
55#2856C2212yes—
56#2856C2214yes—
57#2856C2214yes—
58#2854C2214yes—
59#2813C2218yes—
60#2732C2214yes—
61#2730C2218yes—
62#2711C2218yes—
63#2696C2218yes—
64#2692C2218yes—
65#2681C2218yes—
66#2676C2218yes—
67#2676C2218yes—
68#2676C2218yes—
69#2676C2218yes—
70#2675C2218yes—
71#2675C2218yes—
72#2675C2218yes—
73#2673C2218yes—
74#2673C2218yes—
75#2671C2218yes—
76#2671C2218yes—
77#2661C2218yes—
78#2656C2218yes—
79#2619C2214yes—
80#2615C2214yes—
81#2615C2218yes—
82#2580C2214yes—
83#2556C2214yes—
84#2555C2214yes—
85#2552C2212yes—
86#2551C2211yescharacteristic
87#2551C2211yescharacteristic
88#2548C2212yes—
89#2548C2214yes—
90#2548C2212yes—
91#2546C2211yescharacteristic
92#2542C2214yes—
93#2542C2211yescharacteristic
94#2542C2212yes—
95#2541C2212yes—
96#2541C2212yes—
97#2541C2211yescharacteristic
98#2541C2212yes—
99#2541C2212yes—
100#2541C2214yes—
101#2541C2212yes—
102#2541C2214yes—
103#2541C2211yescharacteristic
104#2541C2214yes—
105#2541C2214yes—
106#2541C2212yes—
107#2541C2212yes—
108#2541C2214yes—
109#2541C2214yes—
110#2540C2214yes—
111#2540C2214yes—
112#2540C2218yes—
113#2538C2212yes—
114#2538C2211yescharacteristic
115#2538C2214yes—
116#2537C2211yescharacteristic
117#2506C2212yes—
118#2492C2212yes—
119#2491C2214yes—
120#2491C2212yes—
121#2491C2212yes—
122#2490C2214yes—
123#2464C2218yes—
124#2461C2218yes—
125#2454C2214yes—
126#2454C2214yes—
127#2452C2214yes—
128#2452C2214yes—
129#2452C2214yes—
130#2452C2212yes—
131#2449C2218yes—
132#2445C2214yes—
133#2445C2214yes—
134#2443C2218yes—
135#2432C2214yes—
136#2431C2214yes—
137#2431C2218yes—
138#2431C2214yes—
139#2430C2218yes—
140#2429C2212yes—
141#2428C2214yes—
142#2428C2218yes—
143#2428C2214yes—
144#2428C2214yes—
145#2428C2214yes—
146#2428C2214yes—
147#2428C2214yes—
148#2428C2214yes—
149#2428C2214yes—
150#2428C2212yes—
151#2428C2212yes—
152#2428C2214yes—
153#2428C2214yes—
154#2427C2214yes—
155#2422C2214yes—
156#2417C2214yes—
157#2416C2214yes—
158#2416C2218yes—
159#2416C2214yes—
160#2407C2214yes—
161#2407C2218yes—
162#2407C2214yes—
163#2396C2214yes—
164#2388C2214yes—
165#2370C2212yes—
166#2369C2211yescharacteristic
167#2368C2214yes—
168#2366C2212yes—
169#2366C2212yes—
170#2366C2212yes—
171#2366C2212yes—
172#2366C2214yes—
173#2366C2212yes—
174#2361C2214yes—
175#2360C2212yes—
176#2355C2211yescharacteristic
177#2349C2212yes—
178D4×C4⋊C4C2212yes—
179D4×C4⋊C4C2214yes—
180D4×C4⋊C4C2211yescharacteristic
181#2345C2212yes—
182#2324C2214yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×#127C2212yes—
187C4×#127C2211yescharacteristic
188C4×#125C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2214yes—
191C4×C22⋊Q8C2212yes—
192C4×#121C2212yes—
193C4×#121C2212yes—
194#2293C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2314yes—
201C22×#41C2314yes—
202C22×#41C2314yes—
203C22×#41C2318yes—
204C22×#41C2314yes—
205#562—264no—
206#554—216no—
207#554—232no—
208#554D4116yescomplemented
209#550—216no—
210#550—232no—
211#550—216no—
212#550—48no—
213#550—48no—
214#550—48no—
215#547—232no—
216#547—232no—
217#540—232no—
218#540—232no—
219#537—264no—
220#537—232no—
221#537—232no—
222#537—416no—
223#533—216no—
224#532—216no—
225#532—216no—
226#532—48no—
227#532—48no—
228#532—416no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2311yescharacteristic
236C2×#127C2312yes—
237C2×#127C2311yescharacteristic
238C2×#127C2312yes—
239C2×#127C2312yes—
240C2×#127C2314yes—
241C2×#127C2312yes—
242C2×#127C2314yes—
243C2×#127C2314yes—
244C2×#127C2314yes—
245C2×#127C2314yes—
246C2×#127C2312yes—
247C2×#127C2314yes—
248C2×#127C2312yes—
249C2×#127C2314yes—
250C2×#127C2312yes—
251C2×#127C2312yes—
252C2×#127C2314yes—
253C2×#127C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2318yes—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#123C2318yes—
263C2×#123C2318yes—
264C2×#123C2318yes—
265C2×#123C2318yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2318yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2318yes—
272C2×C22⋊Q8C2318yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2318yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2318yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2318yes—
280C2×#121C2314yes—
281C2×#121C2318yes—
282C2×#121C2314yes—
283C2×#121C2318yes—
284C2×#121C2318yes—
285C2×#121C2318yes—
286C2×#121C2314yes—
287C2×#121C2318yes—
288C2×#121C2312yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2318yes—
294C2×#121C2318yes—
295C2×#121C2318yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2318yes—
304C2×#121C2318yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2318yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2318yes—
312C2×#121C2318yes—
313C2×#121C2318yes—
314C2×#121C2318yes—
315C2×#121C2314yes—
316C2×#121C2318yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2318yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×#117C2314yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2318yes—
352C22×C4⋊C4C2312yes—
353C22×C42C2312yes—
354C22×C42C2312yes—
355C22×C42C2314yes—
356#400C2314yes—
357#399C2318yes—
358#399C2314yes—
359#399C2318yes—
360#399C2318yes—
361#398C2314yes—
362#398C2314yes—
363#398C2318yes—
364#397C2318yes—
365#396C2314yes—
366#396C2314yes—
367#396C2318yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#395C2314yes—
372#395C2314yes—
373#394C2318yes—
374#394C2318yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#393C2318yes—
387#393C2314yes—
388#393C2318yes—
389#393C2314yes—
390#392C2314yes—
391#392C2318yes—
392#392C2318yes—
393#392C2318yes—
394#392C2318yes—
395#392C2318yes—
396#392C2318yes—
397#392C2318yes—
398#392C2318yes—
399#392C2314yes—
400#392C2314yes—
401#392C2318yes—
402#392C2318yes—
403#392C2318yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2318yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2318yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2318yes—
433#390C2314yes—
434#390C2318yes—
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#388C2318yes—
458#388C2318yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2314yes—
480#386C2318yes—
481#386C2314yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2314yes—
486#385C2318yes—
487#385C2318yes—
488#385C2314yes—
489#385C2314yes—
490#385C2318yes—
491#385C2314yes—
492#384C2311yescharacteristic
493#384C2311yescharacteristic
494#384C2311yescharacteristic
495#384C2312yes—
496#384C2314yes—
497#382C2312yes—
498#380C2312yes—
499#380C2312yes—
500#380C2312yes—
501#380C2314yes—
502#380C2318yes—
503#380C2314yes—
504#380C2312yes—
505#380C2318yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2311yescharacteristic
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2311yescharacteristic
524C4×C4⋊C4C2311yescharacteristic
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2311yescharacteristic
529C4×C4⋊C4C2311yescharacteristic
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2314yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536C4×C22⋊C4C2312yes—
537C4×C22⋊C4C2314yes—
538C4×C22⋊C4C2314yes—
539C4×C22⋊C4C2312yes—
540C4×C22⋊C4C2312yes—
541C2×#95C2314yes—
542C43C2312yes—
543C43C2311yescharacteristic
544C2×#41—216no—
545C2×#41—216no—
546C2×#41—216no—
547C2×#41—232no—
548C2×#41—216no—
549C2×#41—48no—
550C2×#41—48no—
551C2×#41—48no—
552C2×#41—48no—
553C2×#41—416no—
554C2×#41—48no—
555C2×#41—48no—
556C2×#41—48no—
557C2×#41—84no—
558C2×#41—88no—
559C22×Q8C2412yes—
560C22×Q8C2414yes—
561C22×Q8C2411yescharacteristic
562C22×Q8C2414yes—
563C22×Q8C2412yes—
564C22×D4C2414yes—
565C22×D4C2412yes—
566C22×D4C2411yescharacteristic
567C22×D4C2412yes—
568C22×D4C2414yes—
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2411yescharacteristic
572C22×D4C2418yes—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2414yes—
576C22×D4C2414yes—
577C22×D4C2418yes—
578C22×D4C2414yes—
579C22×D4C2414yes—
580C22×D4C2418yes—
581C22×D4C2418yes—
582C22×D4C2418yes—
583C22×D4C2414yes—
584C22×D4C2418yes—
585C22×D4C2414yes—
586C22×D4C2418yes—
587C22×D4C2414yes—
588C22×D4C2418yes—
589C23×C4C2414yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2418yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2418yes—
597C23×C4C2418yes—
598C23×C4C2418yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—24no—
607C4⋊Q8—44no—
608C4⋊Q8C2×D418yes—
609#127—28no—
610#127—216no—
611#127—28no—
612#127—216no—
613#127—28no—
614#127—28no—
615#127—24no—
616#127—48no—
617#127—44no—
618#127—44no—
619#127—48no—
620#127—48no—
621#127—44no—
622#127—48no—
623#127—44no—
624#127—48no—
625#127—82no—
626#127—84no—
627#125—216no—
628#125—216no—
629#125C2×D4116yes—
630#124—216no—
631#124—216no—
632#124—48no—
633#124—48no—
634#124—416no—
635#123—232no—
636#123—232no—
637#123—232no—
638#123—232no—
639C22⋊Q8—28no—
640C22⋊Q8—232no—
641C22⋊Q8—216no—
642C22⋊Q8—28no—
643C22⋊Q8—232no—
644C22⋊Q8—216no—
645C22⋊Q8—232no—
646C22⋊Q8—232no—
647C22⋊Q8—28no—
648C22⋊Q8—416no—
649C22⋊Q8—48no—
650C22⋊Q8C2×D4116yes—
651C22⋊Q8C2×D4132yes—
652#121—28no—
653#121—232no—
654#121—216no—
655#121—232no—
656#121—216no—
657#121—216no—
658#121—28no—
659#121—232no—
660#121—232no—
661#121—216no—
662#121—232no—
663#121—28no—
664#121—216no—
665#121—216no—
666#121—232no—
667#121—232no—
668#121—232no—
669#121—232no—
670#121—48no—
671#121—416no—
672#121—416no—
673#121—48no—
674#121—416no—
675#121—416no—
676#121—416no—
677#121—416no—
678#121—44no—
679#121—48no—
680#121—44no—
681#121—44no—
682#121—48no—
683#121—48no—
684#121—48no—
685#121—48no—
686#121—416no—
687#121—48no—
688#121—84no—
689#121—88no—
690C4×Q8—24no—
691C4×Q8—216no—
692C4×Q8—28no—
693C4×Q8—24no—
694C4×Q8—44no—
695C4×Q8C2×D418yes—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—216no—
701C4×D4—216no—
702C4×D4—24no—
703C4×D4—28no—
704C4×D4—216no—
705C4×D4—24no—
706C4×D4—28no—
707C4×D4—24no—
708C4×D4—24no—
709C4×D4—48no—
710C4×D4—44no—
711C4×D4—42no—
712C4×D4—48no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—44no—
718C4×D4—416no—
719C4×D4C2×D418yes—
720C4×D4C2×D4116yes—
721#117—216no—
722C2×C4⋊C4—232no—
723C2×C4⋊C4—216no—
724C2×C4⋊C4—28no—
725C2×C4⋊C4C2×D4116yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C42—28no—
807C2×C42—28no—
808C2×C42—48no—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2411yescharacteristic
820C2×C42C2412yes—
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832#95C2412yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2414yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2412yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858C24C2512yes—
859C24C2514yes—
860C24C2518yes—
861C24C2512yes—
862#41—832no—
863#41—832no—
864#41—832no—
865#41—864no—
866#41—832no—
867C2×Q8—28no—
868C2×Q8—24no—
869C2×Q8—28no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—44no—
880C2×Q8C22×D414yes—
881C2×Q8C22×D418yes—
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—216no—
885C2×D4—216no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—24no—
889C2×D4—28no—
890C2×D4—216no—
891C2×D4—28no—
892C2×D4—216no—
893C2×D4—216no—
894C2×D4—28no—
895C2×D4—22no—
896C2×D4—28no—
897C2×D4—24no—
898C2×D4—22no—
899C2×D4—24no—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—216no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—28no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—28no—
912C2×D4—24no—
913C2×D4—28no—
914C2×D4—22no—
915C2×D4—24no—
916C2×D4—28no—
917C2×D4—44no—
918C2×D4—48no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—48no—
927C2×D4—44no—
928C2×D4—48no—
929C2×D4—48no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—48no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—48no—
938C2×D4—48no—
939C2×D4—44no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—48no—
947C2×D4—48no—
948C2×D4—48no—
949C2×D4—44no—
950C2×D4—48no—
951C2×D4—44no—
952C2×D4—48no—
953C2×D4—48no—
954C2×D4—44no—
955C2×D4—48no—
956C2×D4C22×D414yes—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—216no—
963C22×C4—28no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—216no—
968C22×C4—28no—
969C22×C4—24no—
970C22×C4—28no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—216no—
976C22×C4—216no—
977C22×C4—216no—
978C22×C4—24no—
979C22×C4—28no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—48no—
984C22×C4—44no—
985C22×C4—48no—
986C22×C4—48no—
987C22×C4—48no—
988C22×C4—48no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—48no—
992C22×C4—42no—
993C22×C4—48no—
994C22×C4C22×D418yes—
995C22×C4C22×D4116yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—216no—
1022C4⋊C4—216no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—22no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—22no—
1040C4⋊C4—28no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—24no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—48no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4C22×D418yes—
1053C4⋊C4C22×D4116yes—
1054C4⋊C4C22×D414yes—
1055C4⋊C4C22×D4116yes—
1056C4⋊C4C22×D418yes—
1057C4⋊C4C22×D414yes—
1058C4⋊C4C22×D418yes—
1059C4⋊C4H(5,𝔽2)14yes—
1060C4⋊C4H(5,𝔽2)14yes—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—216no—
1065C22⋊C4—216no—
1066C22⋊C4—216no—
1067C22⋊C4—216no—
1068C22⋊C4—28no—
1069C22⋊C4—216no—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—216no—
1073C22⋊C4—28no—
1074C22⋊C4—24no—
1075C22⋊C4—28no—
1076C22⋊C4—216no—
1077C22⋊C4—28no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—48no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—48no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—44no—
1091C22⋊C4—48no—
1092C22⋊C4—48no—
1093C22⋊C4—48no—
1094C22⋊C4—44no—
1095C22⋊C4—48no—
1096C22⋊C4C22×D4116yes—
1097C22⋊C4C22×D418yes—
1098C42—24no—
1099C42—24no—
1100C42—24no—
1101C42—28no—
1102C42—24no—
1103C42—24no—
1104C42—24no—
1105C42—24no—
1106C42—28no—
1107C42—22no—
1108C42—24no—
1109C42—22no—
1110C42—24no—
1111C42—24no—
1112C42—22no—
1113C42—44no—
1114C42—44no—
1115C42—41no—
1116C42—42no—
1117C42C22×D414yes—
1118C42C22×D418yes—
1119C42H(5,𝔽2)14yes—
1120C422−1+414yes—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—28no—
1129C23—24no—
1130C23—22no—
1131C23—22no—
1132C23—24no—
1133C23—28no—
1134C23—24no—
1135C23—28no—
1136C23—22no—
1137C23—24no—
1138C23—28no—
1139C23—22no—
1140C23—24no—
1141C23—28no—
1142C23—24no—
1143C23—28no—
1144C23—22no—
1145C23—22no—
1146C23—28no—
1147C23—24no—
1148C23C23×D414yes—
1149C23C2611yescharacteristic
1150Q8—28no—
1151Q8—48no—
1152Q8—416no—
1153Q8—48no—
1154Q8—88no—
1155D4—28no—
1156D4—416no—
1157D4—416no—
1158D4—48no—
1159D4—416no—
1160D4—44no—
1161D4—48no—
1162D4—416no—
1163D4—816no—
1164D4—88no—
1165D4—84no—
1166D4—88no—
1167D4—816no—
1168D4—88no—
1169D4—816no—
1170D4—88no—
1171D4—816no—
1172D4—816no—
1173D4—88no—
1174D4—88no—
1175D4—816no—
1176D4—88no—
1177D4—168no—
1178D4—164no—
1179D4—168no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—216no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—416no—
1230C2×C4—432no—
1231C2×C4—48no—
1232C2×C4—48no—
1233C2×C4—416no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—88no—
1237C2×C4—84no—
1238C2×C4—816no—
1239C2×C4—816no—
1240C2×C4—816no—
1241C2×C4C23×D412yes—
1242C2×C4C23×D414yes—
1243C2×C4C23×D414yes—
1244C2×C4C23×D418yes—
1245C2×C4C23×D414yes—
1246C2×C4C23×D412yes—
1247C2×C4C23×D412yes—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4C2×H(5,𝔽2)14yes—
1250C2×C4C2×H(5,𝔽2)14yes—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C2×C4C2×H(5,𝔽2)12yes—
1253C2×C4C2×H(5,𝔽2)12yes—
1254C2×C4C2×H(5,𝔽2)12yes—
1255C2×C4C2×2−1+412yes—
1256C2×C4C2×2−1+412yes—
1257C2×C4C2×2−1+412yes—
1258C2×C4#58512yes—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—48no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—48no—
1272C22—44no—
1273C22—48no—
1274C22—42no—
1275C22—42no—
1276C22—48no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—48no—
1281C22—48no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—44no—
1286C22—48no—
1287C22C24×D411yescharacteristic
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×H(5,𝔽2)11yescharacteristic
1291C22C22×2−1+411yescharacteristic
1292C22C2×#58511yescharacteristic
1293C22H(7,𝔽2)11yescharacteristic
1294C4—24no—
1295C4—28no—
1296C4—24no—
1297C4—22no—
1298C4—24no—
1299C4—24no—
1300C4—24no—
1301C4—22no—
1302C4—22no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—41no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4#349714yes—
1314C4#349814yes—
1315C4#354814yescomplemented
1316C2—44no—
1317C2—88no—
1318C2—82no—
1319C2—84no—
1320C2C2×#354811yescharacteristic
1321C2C2×#349711yescharacteristic
1322C2C2×#349811yescharacteristic
1323C2#6291711yescharacteristic
1324C2#6295511yescharacteristic
1325C2D4×H(5,𝔽2)11yescharacteristic
1326C2#6301411yescharacteristic
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×#3548C2semidirect
2. #59823C2semidirect
3. #59458C2semidirect
4. #59066C2semidirect
5. #59057C2semidirect
6. #51898C2semidirect
7. #45484C2semidirect
8. #45034C2semidirect
9. #44884C2semidirect
10. #42425C2semidirect
11. #42421C2semidirect
12. #39725C2semidirect
13. #39386C2semidirect
14. #39341C2semidirect
15. #39341C2semidirect
16. #39341C2semidirect
17. #36592C2semidirect
18. #36128C2semidirect
19. #36128C2semidirect
20. #36128C2semidirect
21. #36126C2semidirect
22. #35171C2semidirect
23. #35166C2semidirect
24. #34929C2semidirect
25. #34925C2semidirect
26. C4×#554C2semidirect
208. #554D4semidirect
1315. C4#3548semidirect

Maximal subgroups

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

subgroupindex
C2×#35482
#598232
#594582
#590662
#590572
#518982
#454842
#450342
#448842
#424252
#424212
#397252
#393862
#393412
#365922
#361282
#361262
#351712
#351662
#349292
#349252
C4×#5542