Finite Group Databasebeta

← #7671749

Subgroups — #7671749

Order 512.

7502 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C212yesmaximal, complemented
2#59654C212yesmaximal, complemented
3#59428C212yesmaximal, complemented
4#59415C214yesmaximal, complemented
5#59315C214yesmaximal, complemented
6#59229C212yesmaximal, complemented
7#59213C212yesmaximal, complemented
8#39956C214yesmaximal, complemented
9#39952C214yesmaximal, complemented
10#39432C214yesmaximal, complemented
11#39350C212yesmaximal, complemented
12#39340C212yesmaximal, complemented
13#36645C211yesmaximal, characteristic, complemented
14#36468C212yesmaximal, complemented
15#36444C212yesmaximal, complemented
16#36261C212yesmaximal, complemented
17#36259C212yesmaximal, complemented
18#36149C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic, complemented
20#36129C212yesmaximal, complemented
21#36127C211yesmaximal, characteristic, complemented
22#36127C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#35606C214yesmaximal, complemented
25#35297C212yesmaximal, complemented
26#35170C212yesmaximal, complemented
27#34308C212yesmaximal, complemented
28C4×#532C211yesmaximal, characteristic, complemented
29C4×#532C211yesmaximal, characteristic, complemented
30#3511—232no—
31C2×#556C2214yes—
32C2×#555C2214yes—
33C2×#554C2214yes—
34C2×#553C2214yes—
35C2×#553C2214yes—
36C2×D4×Q8C2212yes—
37C2×#548C2214yes—
38C2×#548C2214yes—
39C2×#547C2212yes—
40C2×#547C2214yes—
41C2×#547C2212yes—
42C2×#542C2214yes—
43C2×#542C2214yes—
44C2×#537C2214yes—
45C2×#533C2212yes—
46C2×#533C2212yes—
47C2×#532C2212yes—
48C2×#532C2212yes—
49C2×#532C2211yescharacteristic
50C2×#532C2211yescharacteristic
51C22×C4⋊Q8C2212yes—
52C2×#520C2214yes—
53C2×C4×#41C2212yes—
54C2×C4×#41C2212yes—
55#2868C2211yescharacteristic
56#2868C2211yescharacteristic
57#2862C2212yes—
58#2859C2212yes—
59#2859C2212yes—
60#2857C2212yes—
61#2857C2212yes—
62#2857C2212yes—
63#2857C2212yes—
64#2857C2212yes—
65#2857C2212yes—
66#2857C2212yes—
67#2857C2212yes—
68#2857C2214yes—
69#2854C2214yes—
70#2717C2218yes—
71#2708C2218yes—
72#2698C2218yes—
73#2689C2218yes—
74#2686C2218yes—
75#2681C2218yes—
76#2672C2218yes—
77#2671C2218yes—
78#2663C2218yes—
79#2625C2214yes—
80#2616C2214yes—
81#2602C2218yes—
82#2584C2214yes—
83#2583C2218yes—
84#2581C2214yes—
85#2562C2214yes—
86#2559C2218yes—
87#2552C2212yes—
88#2551C2212yes—
89#2551C2212yes—
90#2550C2214yes—
91#2549C2218yes—
92#2547C2212yes—
93#2547C2212yes—
94#2547C2214yes—
95#2546C2212yes—
96#2542C2212yes—
97#2538C2212yes—
98#2537C2212yes—
99#2537C2212yes—
100#2537C2212yes—
101#2537C2212yes—
102#2537C2214yes—
103#2536C2214yes—
104#2535C2214yes—
105#2521C2218yes—
106#2496C2214yes—
107#2496C2214yes—
108#2492C2214yes—
109#2491C2214yes—
110#2486C2214yes—
111#2485C2214yes—
112#2485C2214yes—
113#2478C2218yes—
114#2474C2218yes—
115#2468C2218yes—
116#2461C2218yes—
117#2451C2214yes—
118#2447C2214yes—
119#2447C2214yes—
120#2446C2214yes—
121#2442C2214yes—
122#2441C2214yes—
123#2440C2214yes—
124#2440C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2439C2214yes—
128#2434C2214yes—
129#2432C2214yes—
130#2432C2214yes—
131#2429C2214yes—
132#2429C2214yes—
133#2428C2214yes—
134#2427C2214yes—
135#2427C2218yes—
136#2427C2214yes—
137#2425C2218yes—
138#2423C2214yes—
139#2422C2214yes—
140#2422C2214yes—
141#2422C2214yes—
142#2422C2214yes—
143#2420C2214yes—
144#2420C2214yes—
145#2417C2214yes—
146#2416C2214yes—
147#2415C2218yes—
148#2415C2214yes—
149#2415C2214yes—
150#2413C2218yes—
151#2409C2214yes—
152#2407C2214yes—
153#2407C2214yes—
154#2365C2212yes—
155#2361C2214yes—
156#2360C2214yes—
157#2359C2218yes—
158#2354C2212yes—
159#2352C2214yes—
160Q8×C4⋊C4C2212yes—
161#2349C2214yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168#2344C2214yes—
169Q8×C22⋊C4C2214yes—
170#2339C2214yes—
171#2339C2214yes—
172#2323C2214yes—
173#2323C2214yes—
174#2322C2218yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#127C2211yescharacteristic
185C4×#127C2211yescharacteristic
186C4×#127C2211yescharacteristic
187C4×#124C2212yes—
188C4×#124C2212yes—
189C4×#124C2212yes—
190C4×#124C2212yes—
191C4×#121C2214yes—
192C4×#121C2212yes—
193C4×#121C2212yes—
194C4×#121C2211yescharacteristic
195C4×#121C2212yes—
196C4×#121C2211yescharacteristic
197C4×#121C2211yescharacteristic
198C4×#121C2211yescharacteristic
199C4×#121C2212yes—
200C4×#121C2212yes—
201C4×#121C2212yes—
202#2297C2212yes—
203#2297C2212yes—
204#2293C2211yescharacteristic
205#2293C2212yes—
206#2293C2212yes—
207#2293C2212yes—
208#2293C2211yescharacteristic
209C2×#389C2214yes—
210#2285C2212yes—
211#2285C2212yes—
212#2285C2211yescharacteristic
213#2285C2211yescharacteristic
214C42×D4C2212yes—
215C42×D4C2211yescharacteristic
216C42×D4C2211yescharacteristic
217C42×D4C2212yes—
218C42×D4C2212yes—
219C2×C43C2211yescharacteristic
220C22×#41C2314yes—
221C22×#41C2312yes—
222C22×#41C2314yes—
223C22×#41C2312yes—
224C23×Q8C2314yes—
225#556—232no—
226#555—232no—
227#554—232no—
228#553—232no—
229#553—232no—
230D4×Q8—48no—
231#548—232no—
232#548—232no—
233#547—232no—
234#547—216no—
235#547—48no—
236#542—232no—
237#542—232no—
238#537—232no—
239#533—216no—
240#533—216no—
241#532—216no—
242#532—216no—
243#532—28no—
244#532D4116yescomplemented
245C2×C4⋊Q8—216no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2314yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2311yescharacteristic
258C2×#127C2311yescharacteristic
259C2×#127C2311yescharacteristic
260C2×#126C2318yes—
261C2×#126C2318yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2318yes—
268C2×#124C2318yes—
269C2×#124C2312yes—
270C2×#123C2318yes—
271C2×#123C2318yes—
272C2×#123C2318yes—
273C2×#123C2318yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2318yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2318yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2318yes—
291C2×#121C2318yes—
292C2×#121C2311yescharacteristic
293C2×#121C2318yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2311yescharacteristic
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300#520—232no—
301C4×#41—216no—
302C4×#41—48no—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2318yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2318yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2318yes—
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2314yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C22×C4⋊C4C2318yes—
352C22×C4⋊C4C2314yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2314yes—
356C22×C42C2311yescharacteristic
357C22×C42C2312yes—
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360C22×C42C2311yescharacteristic
361C22×C42C2311yescharacteristic
362C22×C42C2314yes—
363C22×C42C2311yescharacteristic
364C22×C42C2311yescharacteristic
365C22×C42C2311yescharacteristic
366#400C2318yes—
367#400C2318yes—
368#399C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#397C2318yes—
375#397C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#397C2318yes—
381#396C2318yes—
382#396C2318yes—
383#395C2318yes—
384#395C2318yes—
385#395C2318yes—
386#395C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2318yes—
396#393C2318yes—
397#392C2318yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2318yes—
411#391C2318yes—
412#390C2311yescharacteristic
413#390C2312yes—
414#390C2311yescharacteristic
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2312yes—
426#390C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2311yescharacteristic
444#389C2311yescharacteristic
445#389C2318yes—
446#389C2318yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2318yes—
458#389C2318yes—
459#389C2314yes—
460#388C2318yes—
461#388C2318yes—
462#388C2312yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2312yes—
468#388C2312yes—
469#388C2312yes—
470#388C2312yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2312yes—
475#388C2314yes—
476#388C2312yes—
477#388C2312yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#386C2318yes—
484#386C2318yes—
485#386C2318yes—
486#386C2318yes—
487#386C2318yes—
488#386C2314yes—
489#386C2312yes—
490#386C2312yes—
491#386C2312yes—
492#386C2314yes—
493#386C2312yes—
494#385C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#384C2311yescharacteristic
504#384C2311yescharacteristic
505#384C2311yescharacteristic
506#384C2311yescharacteristic
507#384C2312yes—
508#384C2312yes—
509#384C2312yes—
510#384C2312yes—
511#384C2314yes—
512#384C2312yes—
513#384C2312yes—
514#384C2312yes—
515#384C2312yes—
516#382C2312yes—
517#382C2314yes—
518#382C2314yes—
519#382C2312yes—
520#381C2318yes—
521#381C2318yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2318yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2318yes—
540#380C2312yes—
541#380C2312yes—
542#380C2312yes—
543#380C2311yescharacteristic
544#380C2311yescharacteristic
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2311yescharacteristic
551C4×C4⋊C4C2311yescharacteristic
552C4×C4⋊C4C2311yescharacteristic
553C4×C4⋊C4C2312yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2311yescharacteristic
557C4×C4⋊C4C2312yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2312yes—
560C4×C4⋊C4C2312yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2311yescharacteristic
563C4×C4⋊C4C2312yes—
564C4×C4⋊C4C2311yescharacteristic
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2312yes—
570C4×C22⋊C4C2318yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2312yes—
574C4×C22⋊C4C2312yes—
575C4×C22⋊C4C2312yes—
576C4×C22⋊C4C2312yes—
577C4×C22⋊C4C2312yes—
578C4×C22⋊C4C2312yes—
579C4×C22⋊C4C2312yes—
580C4×C22⋊C4C2312yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2312yes—
583C4×C22⋊C4C2314yes—
584C2×#95C2318yes—
585C43C2311yescharacteristic
586C43C2311yescharacteristic
587C43C2311yescharacteristic
588C43C2311yescharacteristic
589C43C2311yescharacteristic
590C43C2311yescharacteristic
591C43C2311yescharacteristic
592C43C2311yescharacteristic
593C2×#41—216no—
594C2×#41—216no—
595C2×#41—28no—
596C2×#41—28no—
597C2×#41—216no—
598C2×#41—44no—
599C2×#41—44no—
600C2×#41—44no—
601C2×#41—48no—
602C2×#41—48no—
603C2×#41—48no—
604C2×#41C2×D4116yes—
605C22×Q8—216no—
606C22×Q8—48no—
607C22×Q8—48no—
608C22×Q8C2414yes—
609C22×Q8C2414yes—
610C22×Q8C2412yes—
611C22×Q8C2412yes—
612C22×Q8C2418yes—
613C22×D4C2411yescharacteristic
614C22×D4C2412yes—
615C22×D4C2412yes—
616C22×D4C2412yes—
617C22×D4C2418yes—
618C22×D4C2412yes—
619C22×D4C2412yes—
620C22×D4C2412yes—
621C22×D4C2412yes—
622C22×D4C2411yescharacteristic
623C22×D4C2418yes—
624C22×D4C2414yes—
625C23×C4C2412yes—
626C23×C4C2414yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2411yescharacteristic
631C23×C4C2412yes—
632C23×C4C2418yes—
633C23×C4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2411yescharacteristic
638C23×C4C2412yes—
639C23×C4C2418yes—
640C23×C4C2418yes—
641C23×C4C2414yes—
642C23×C4C2411yescharacteristic
643C23×C4C2414yes—
644C4⋊Q8—216no—
645C4⋊Q8—216no—
646C4⋊Q8—216no—
647C4⋊Q8—24no—
648C4⋊Q8—28no—
649C4⋊Q8—28no—
650C4⋊Q8—28no—
651C4⋊Q8—28no—
652C4⋊Q8—48no—
653C4⋊Q8—44no—
654C4⋊Q8—44no—
655C4⋊Q8C2×D418yes—
656#127—24no—
657#127C2×D418yes—
658#126—232no—
659#126—232no—
660#125—216no—
661#125—216no—
662#124—216no—
663#124—216no—
664#124—232no—
665#124—232no—
666#124—28no—
667#124C2×D4116yes—
668#123—232no—
669#123—232no—
670#123—232no—
671#123—416no—
672C22⋊Q8—216no—
673C22⋊Q8—216no—
674C22⋊Q8—216no—
675C22⋊Q8—232no—
676C22⋊Q8—216no—
677C22⋊Q8—216no—
678C22⋊Q8—232no—
679C22⋊Q8—232no—
680C22⋊Q8—416no—
681C22⋊Q8—48no—
682C22⋊Q8—48no—
683C22⋊Q8—48no—
684#121—216no—
685#121—216no—
686#121—216no—
687#121—216no—
688#121—232no—
689#121—232no—
690#121—24no—
691#121—216no—
692#121—24no—
693#121—232no—
694#121—28no—
695#121—48no—
696#121C2×D4116yes—
697#121C2×D4116yes—
698C4×Q8—216no—
699C4×Q8—216no—
700C4×Q8—28no—
701C4×Q8—28no—
702C4×Q8—216no—
703C4×Q8—216no—
704C4×Q8—28no—
705C4×Q8—44no—
706C4×D4—216no—
707C4×D4—216no—
708C4×D4—216no—
709C4×D4—216no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—232no—
715C4×D4—28no—
716C4×D4—232no—
717C4×D4—28no—
718C4×D4—28no—
719C4×D4—24no—
720C4×D4—28no—
721C4×D4—28no—
722C4×D4—24no—
723C4×D4—24no—
724C4×D4—28no—
725C4×D4—24no—
726C4×D4—28no—
727C4×D4—24no—
728C4×D4—28no—
729C4×D4—44no—
730C4×D4—44no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—48no—
734C4×D4—48no—
735C4×D4C2×D4116yes—
736C4×D4C2×D4116yes—
737C4×D4#4118yescomplemented
738#117—28no—
739#117—216no—
740#117—216no—
741#117—232no—
742#117—28no—
743#117—28no—
744#117—48no—
745#117—44no—
746C2×C4⋊C4—232no—
747C2×C4⋊C4—216no—
748C2×C4⋊C4—216no—
749C2×C4⋊C4—216no—
750C2×C4⋊C4—48no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2418yes—
783C2×C4⋊C4C2418yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2418yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2418yes—
790C2×C4⋊C4C2418yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2418yes—
831C2×C22⋊C4C2418yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C42—28no—
836C2×C42—28no—
837C2×C42—24no—
838C2×C42—24no—
839C2×C42—24no—
840C2×C42—24no—
841C2×C42—48no—
842C2×C42—42no—
843C2×C42—42no—
844C2×C42C2×D418yes—
845C2×C42C2411yescharacteristic
846C2×C42C2412yes—
847C2×C42C2418yes—
848C2×C42C2418yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2411yescharacteristic
854C2×C42C2414yes—
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2412yes—
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884#95C2412yes—
885#95C2418yes—
886#95C2418yes—
887#95C2418yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2418yes—
906#95C2418yes—
907#95C2418yes—
908#95C2418yes—
909#95C2418yes—
910#95C2418yes—
911#95C2418yes—
912#95C2418yes—
913#95C2418yes—
914C24C2512yes—
915C24C2514yes—
916C24C2511yescharacteristic
917C24C2512yes—
918#41—432no—
919#41—432no—
920#41—464no—
921#41—832no—
922C2×Q8—24no—
923C2×Q8—28no—
924C2×Q8—28no—
925C2×Q8—216no—
926C2×Q8—28no—
927C2×Q8—24no—
928C2×Q8—24no—
929C2×Q8—28no—
930C2×Q8—24no—
931C2×Q8—28no—
932C2×Q8—28no—
933C2×Q8—42no—
934C2×Q8—48no—
935C2×Q8—48no—
936C2×Q8—832no—
937C2×Q8C22×D418yes—
938C2×D4—24no—
939C2×D4—24no—
940C2×D4—216no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—216no—
944C2×D4—24no—
945C2×D4—216no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—22no—
949C2×D4—24no—
950C2×D4—22no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—22no—
956C2×D4—24no—
957C2×D4—22no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—44no—
965C2×D4—48no—
966C2×D4—42no—
967C2×D4—48no—
968C2×D4—48no—
969C2×D4C22×D418yes—
970C2×D4C22×D418yes—
971C2×D4C22×D418yes—
972C2×D4C22×D4116yes—
973C2×D4C2×#4114yes—
974C22×C4—24no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—24no—
982C22×C4—216no—
983C22×C4—216no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—28no—
992C22×C4—216no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—24no—
1011C22×C4—216no—
1012C22×C4—28no—
1013C22×C4—44no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—44no—
1019C22×C4—48no—
1020C22×C4—44no—
1021C22×C4—48no—
1022C22×C4—48no—
1023C22×C4—44no—
1024C22×C4—48no—
1025C22×C4—48no—
1026C22×C4C22×D414yes—
1027C22×C4C22×D414yes—
1028C22×C4C22×D414yes—
1029C22×C4C22×D4116yes—
1030C22×C4C2×#4118yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2518yes—
1040C22×C4C2512yes—
1041C22×C4C2518yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2514yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C4⋊C4—24no—
1057C4⋊C4—216no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—216no—
1061C4⋊C4—216no—
1062C4⋊C4—216no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—216no—
1071C4⋊C4—216no—
1072C4⋊C4—28no—
1073C4⋊C4—216no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—22no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—48no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—48no—
1095C4⋊C4—48no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4C22×D418yes—
1101C4⋊C4C22×D418yes—
1102C4⋊C4C2×#4114yes—
1103C22⋊C4—216no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—216no—
1107C22⋊C4—216no—
1108C22⋊C4—216no—
1109C22⋊C4—216no—
1110C22⋊C4—24no—
1111C22⋊C4—216no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—216no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—48no—
1135C22⋊C4—48no—
1136C22⋊C4—48no—
1137C22⋊C4C22×D4116yes—
1138C22⋊C4C22×D4116yes—
1139C22⋊C4C2×#4118yes—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—216no—
1147C42—216no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—28no—
1155C42—22no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—22no—
1160C42—22no—
1161C42—22no—
1162C42—22no—
1163C42—22no—
1164C42—22no—
1165C42—41no—
1166C42—41no—
1167C42—41no—
1168C42—41no—
1169C42—44no—
1170C42—44no—
1171C42C22×D414yes—
1172C42C22×D414yes—
1173C42C22×D414yes—
1174C42C22×D414yes—
1175C42C2×#4114yes—
1176C42H(5,𝔽2)14yes—
1177C422−1+414yes—
1178C422−1+414yes—
1179C23—22no—
1180C23—24no—
1181C23—21no—
1182C23—22no—
1183C23—24no—
1184C23—21no—
1185C23—22no—
1186C23—24no—
1187C23—24no—
1188C23—22no—
1189C23—21no—
1190C23—21no—
1191C23—22no—
1192C23—24no—
1193C23—21no—
1194C23—21no—
1195C23—22no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23C23×D412yes—
1205C23C23×D418yes—
1206C23C22×#4114yes—
1207C23C2611yescharacteristic
1208Q8—216no—
1209Q8—48no—
1210Q8—416no—
1211Q8—416no—
1212Q8—816no—
1213D4—216no—
1214D4—216no—
1215D4—216no—
1216D4—28no—
1217D4—416no—
1218D4—48no—
1219D4—48no—
1220D4—48no—
1221D4—48no—
1222D4—432no—
1223D4—44no—
1224D4—816no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—24no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—28no—
1246C2×C4—216no—
1247C2×C4—28no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—28no—
1254C2×C4—22no—
1255C2×C4—28no—
1256C2×C4—21no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—28no—
1260C2×C4—21no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—28no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—24no—
1277C2×C4—28no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—28no—
1282C2×C4—416no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—432no—
1286C2×C4—44no—
1287C2×C4—48no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—44no—
1293C2×C4—416no—
1294C2×C4—88no—
1295C2×C4—816no—
1296C2×C4—816no—
1297C2×C4C23×D412yes—
1298C2×C4C23×D418yes—
1299C2×C4C23×D412yes—
1300C2×C4C23×D412yes—
1301C2×C4C23×D412yes—
1302C2×C4C23×D412yes—
1303C2×C4C23×D412yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4114yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C2×H(5,𝔽2)12yes—
1309C2×C4C2×H(5,𝔽2)12yes—
1310C2×C4C2×H(5,𝔽2)12yes—
1311C2×C4C2×2−1+412yes—
1312C2×C4C2×2−1+412yes—
1313C2×C4C2×2−1+412yes—
1314C2×C4C2×2−1+412yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4#58512yes—
1318C2×C4#58512yes—
1319C22—22no—
1320C22—28no—
1321C22—24no—
1322C22—22no—
1323C22—28no—
1324C22—24no—
1325C22—24no—
1326C22—22no—
1327C22—28no—
1328C22—42no—
1329C22—44no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—44no—
1334C22—41no—
1335C22—44no—
1336C22—42no—
1337C22—41no—
1338C22—42no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22C24×D411yescharacteristic
1348C22C23×#4111yescharacteristic
1349C22C22×H(5,𝔽2)11yescharacteristic
1350C22C22×2−1+411yescharacteristic
1351C22C22×2−1+411yescharacteristic
1352C22C2×#58511yescharacteristic
1353C22C2×#58511yescharacteristic
1354C4—22no—
1355C4—28no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—24no—
1363C4—22no—
1364C4—42no—
1365C4—42no—
1366C4—48no—
1367C4—41no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—41no—
1373C4—42no—
1374C4—48no—
1375C4D4×#4114yes—
1376C4#349614yes—
1377C4#349914yes—
1378C4#351114yescomplemented
1379C2—42no—
1380C2—48no—
1381C2—44no—
1382C2—82no—
1383C2C2×D4×#4111yescharacteristic
1384C2C2×#349611yescharacteristic
1385C2C2×#351111yescharacteristic
1386C2C2×#349911yescharacteristic
1387C2#6280511yescharacteristic
1388C2#6283511yescharacteristic
1389C2#6283811yescharacteristic
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×#3511C2semidirect
2. #59654C2semidirect
3. #59428C2semidirect
4. #59415C2semidirect
5. #59315C2semidirect
6. #59229C2semidirect
7. #59213C2semidirect
8. #39956C2semidirect
9. #39952C2semidirect
10. #39432C2semidirect
11. #39350C2semidirect
12. #39340C2semidirect
13. #36645C2semidirect
14. #36468C2semidirect
15. #36444C2semidirect
16. #36261C2semidirect
17. #36259C2semidirect
18. #36149C2semidirect
19. #36134C2semidirect
20. #36129C2semidirect
21. #36127C2semidirect
22. #36127C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #35606C2semidirect
25. #35297C2semidirect
26. #35170C2semidirect
27. #34308C2semidirect
28. C4×#532C2semidirect
29. C4×#532C2semidirect
244. #532D4semidirect
737. C4×D4#41semidirect
1378. C4#3511semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#596542
#594282
#594152
#593152
#592292
#592132
#399562
#399522
#394322
#393502
#393402
#366452
#364682
#364442
#362612
#362592
#361492
#361342
#361292
#361272
D4×C4⋊Q82
#356062
#352972
#351702
#343082
C4×#5322