Finite Group Databasebeta

← #7643144

Subgroups — #7643144

Order 512.

6912 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3#39595C212yesmaximal, complemented
4#39467C212yesmaximal, complemented
5#39139C212yesmaximal, complemented
6#39136C212yesmaximal, complemented
7#39131C214yesmaximal, complemented
8#39127C212yesmaximal, complemented
9#39124C212yesmaximal, complemented
10#39123C212yesmaximal, complemented
11#39119C214yesmaximal, complemented
12#38919C212yesmaximal, complemented
13#38047C214yesmaximal, complemented
14#37843C214yesmaximal, complemented
15#37188C218yesmaximal, complemented
16#36625C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic, complemented
18#35664C214yesmaximal, complemented
19#35638C214yesmaximal, complemented
20#35325C212yesmaximal, complemented
21#35302C212yesmaximal, complemented
22#35240C211yesmaximal, characteristic, complemented
23#35236C211yesmaximal, characteristic, complemented
24#35172C212yesmaximal, complemented
25#35102C212yesmaximal, complemented
26#34196C211yesmaximal, characteristic, complemented
27#3523—216no—
28C2×#557C2212yescomplemented
29C2×#557C2211yescharacteristic, complemented
30C2×#557C2211yescharacteristic, complemented
31C2×#556C2212yescomplemented
32C2×#556C2211yescharacteristic, complemented
33C2×#552C2212yes—
34C2×#552C2214yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2211yescharacteristic, complemented
37C2×#541C2212yescomplemented
38C2×#541C2214yescomplemented
39C2×#533C2211yescharacteristic
40C2×#533C2212yes—
41C2×#529—216no—
42C2×#529C2211yescharacteristic
43C2×#529C2212yes—
44C2×#529C2212yes—
45C2×#529C2214yes—
46C2×#529C2212yes—
47C2×#529C2214yes—
48C2×#529C2212yes—
49C2×#529C2212yes—
50C22×#126C2212yes—
51C22×#125C2211yescharacteristic
52C22×#124C2211yescharacteristic
53C22×#123C2212yes—
54C22×C22⋊Q8C2211yescharacteristic
55C22×#121C2211yescharacteristic
56C2×#519C2212yescomplemented
57C22×C4×Q8C2211yescharacteristic
58C22×C4×D4C2212yes—
59C22×C4×D4C2211yescharacteristic
60C22×#117C2212yes—
61C23×C42C2211yescharacteristic
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2855C2212yes—
65#2855C2211yescharacteristic
66#2855C2212yes—
67#2854C2211yescharacteristic
68#2853C2212yes—
69#2852C2214yescomplemented
70#2851C2212yescomplemented
71#2851C2214yescomplemented
72#2850C2212yescomplemented
73#2849C2212yes—
74#2848C2211yescharacteristic
75#2848C2212yes—
76#2848C2212yes—
77#2848C2212yes—
78#2848C2212yes—
79#2848C2212yes—
80#2847C2211yescharacteristic
81#2847C2212yes—
82#2732C2218yescomplemented
83#2731C2218yescomplemented
84#2730C2218yescomplemented
85#2729C2218yescomplemented
86#2727C2218yescomplemented
87#2725C2218yescomplemented
88#2723C2218yescomplemented
89#2721C2218yescomplemented
90#2721C2218yescomplemented
91#2719C2218yescomplemented
92#2714C2218yes—
93#2711C2218yes—
94#2707C2218yescomplemented
95#2705C2218yescomplemented
96#2696C2218yescomplemented
97#2694C2218yescomplemented
98#2636C2214yescomplemented
99#2633C2214yescomplemented
100#2629C2214yescomplemented
101#2628C2214yescomplemented
102#2626C2214yes—
103#2626C2214yes—
104#2623C2214yes—
105#2621C2214yescomplemented
106#2620C2214yescomplemented
107#2613C2214yes—
108#2611C2218yescomplemented
109#2609C2218yescomplemented
110#2603C2218yescomplemented
111#2601C2218yescomplemented
112#2599C2218yescomplemented
113#2598C2218yescomplemented
114#2583C2214yes—
115#2580C2218yescomplemented
116#2579C2214yes—
117#2566C2218yescomplemented
118#2563C2214yescomplemented
119#2562C2214yescomplemented
120#2562C2212yescomplemented
121#2561C2214yes—
122#2558C2218yescomplemented
123#2554C2218yescomplemented
124#2552C2214yescomplemented
125#2547C2212yescomplemented
126#2545C2214yescomplemented
127#2542C2214yescomplemented
128#2542C2212yescomplemented
129#2540C2214yes—
130#2540C2214yescomplemented
131#2540C2212yescomplemented
132#2538C2214yescomplemented
133#2538C2214yescomplemented
134#2538C2214yescomplemented
135#2538C2212yescomplemented
136#2537C2212yescomplemented
137#2536C2214yescomplemented
138#2536C2214yescomplemented
139#2535C2214yescomplemented
140#2534C2214yes—
141#2519C2218yescomplemented
142#2512C2218yescomplemented
143#2502C2212yes—
144#2490C2214yes—
145#2489C2214yescomplemented
146#2487C2212yes—
147#2484C2214yes—
148#2482C2214yes—
149#2482C2214yes—
150#2479C2218yescomplemented
151#2471C2218yescomplemented
152#2469C2218yescomplemented
153#2458C2218yescomplemented
154#2453C2214yescomplemented
155#2448C2214yescomplemented
156#2441C2214yescomplemented
157#2436C2214yescomplemented
158#2435C2212yes—
159#2429C2214yescomplemented
160#2426C2214yes—
161#2426C2214yescomplemented
162#2423C2214yescomplemented
163#2414C2214yes—
164#2413C2214yes—
165#2411C2214yes—
166#2411C2214yes—
167#2409C2214yescomplemented
168#2408C2212yes—
169#2355C2214yescomplemented
170#2355C2212yescomplemented
171Q8×C4⋊C4C2212yescomplemented
172#2344C2212yes—
173#2344C2214yes—
174Q8×C22⋊C4C2212yes—
175#2326C2214yescomplemented
176#2324C2214yescomplemented
177#2324C2214yescomplemented
178#2323C2214yescomplemented
179#2323C2214yescomplemented
180#2323C2214yescomplemented
181#2321C2214yes—
182#2321C2214yes—
183#2320C2214yescomplemented
184#2320C2212yescomplemented
185#2317C2214yes—
186#2309C2214yes—
187C4×C22⋊Q8C2212yescomplemented
188C4×C22⋊Q8C2214yescomplemented
189C4×C22⋊Q8C2214yescomplemented
190C4×#123C2212yes—
191C4×#121C2212yescomplemented
192C4×#120C2212yes—
193#2296C2212yes—
194#2290C2214yescomplemented
195#2285C2211yescharacteristic
196#2285C2212yes—
197#2283C2211yescharacteristic
198#2283C2212yes—
199#2280C2212yes—
200#2276C2212yescomplemented
201C23×Q8C2312yes—
202C23×Q8C2311yescharacteristic
203C23×D4C2312yes—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C24×C4C2312yes—
208C24×C4C2311yescharacteristic
209#557—28no—
210#557—216no—
211#557—28no—
212#556—216no—
213#556—28no—
214#552—216no—
215#552—232no—
216D4×Q8—216no—
217D4×Q8—28no—
218#541—216no—
219#541—232no—
220#533—216no—
221#533—28no—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228#529—216no—
229#529—216no—
230#529—232no—
231#529—216no—
232#529—232no—
233#529—216no—
234#529—216no—
235#529—28no—
236C2×#126—216no—
237C2×#126C2312yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125—28no—
247C2×#125C2311yescharacteristic
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#124—28no—
260C2×#124C2311yescharacteristic
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#123—216no—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×C22⋊Q8—28no—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121—28no—
293C2×#121C2311yescharacteristic
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#120C2312yes—
301C2×#120C2314yes—
302#519—216no—
303C2×C4×Q8D4116yescomplemented
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4—216no—
322C2×C4×D4—28no—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×#117—216no—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C2×#117C2312yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2314yes—
348C2×#117C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2312yes—
359C22×C22⋊C4C2312yes—
360C22×C42—28no—
361C22×C42C2312yes—
362C22×C42C2312yes—
363C22×C42C2311yescharacteristic
364C22×C42C2311yescharacteristic
365C22×C42C2311yescharacteristic
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2318yes—
371#400C2314yes—
372#400C2318yes—
373#399C2318yes—
374#399C2318yes—
375#399C2318yes—
376#399C2318yes—
377#399C2318yes—
378#399C2314yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#395C2318yes—
399#394C2318yes—
400#394C2314yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#393C2318yes—
407#393C2318yes—
408#393C2318yes—
409#392C2318yes—
410#392C2318yes—
411#392C2314yes—
412#391C2314yes—
413#391C2318yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#390C2318yes—
419#390C2318yes—
420#390C2318yes—
421#390C2318yes—
422#390C2318yes—
423#390C2318yes—
424#390C2312yes—
425#390C2318yes—
426#390C2314yes—
427#390C2318yes—
428#390C2314yes—
429#389C2318yes—
430#389C2318yes—
431#389C2314yes—
432#389C2318yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2318yes—
437#389C2318yes—
438#389C2318yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#387C2318yes—
462#387C2318yes—
463#387C2318yes—
464#387C2318yes—
465#387C2318yes—
466#387C2318yes—
467#387C2314yes—
468#387C2314yes—
469#387C2318yes—
470#387C2318yes—
471#387C2314yes—
472#387C2314yes—
473#386C2312yes—
474#386C2314yes—
475#386C2318yes—
476#386C2318yes—
477#386C2312yes—
478#386C2318yes—
479#386C2318yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#385C2314yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2312yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2318yes—
494#385C2314yes—
495#385C2318yes—
496#385C2312yes—
497#385C2318yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#384C2318yes—
502#384C2314yes—
503#384C2312yes—
504#384C2314yes—
505#383C2312yes—
506#383C2314yes—
507#382C2318yes—
508#382C2314yes—
509#382C2312yes—
510#382C2312yes—
511#382C2314yes—
512#381C2312yes—
513#381C2314yes—
514#381C2312yes—
515#381C2314yes—
516#380C2314yes—
517#380C2312yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2312yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2311yescharacteristic
526#380C2312yes—
527#380C2311yescharacteristic
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#379C2314yes—
533#379C2314yes—
534#379C2312yes—
535#379C2314yes—
536#379C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2312yes—
553#376C2314yes—
554C25C2412yes—
555C25C2411yescharacteristic
556C22×Q8—28no—
557C22×Q8—44no—
558C22×Q8—48no—
559C22×Q8C2×D418yes—
560C22×Q8C2412yes—
561C22×Q8C2411yescharacteristic
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2414yes—
566C22×Q8C2412yes—
567C22×D4—28no—
568C22×D4—28no—
569C22×D4—24no—
570C22×D4—44no—
571C22×D4—44no—
572C22×D4C2412yes—
573C22×D4C2411yescharacteristic
574C22×D4C2412yes—
575C22×D4C2414yes—
576C22×D4C2414yes—
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2418yes—
580C23×C4—24no—
581C23×C4—28no—
582C23×C4—24no—
583C23×C4—24no—
584C23×C4—24no—
585C23×C4—44no—
586C23×C4—48no—
587C23×C4—44no—
588C23×C4—42no—
589C23×C4C2411yescharacteristic
590C23×C4C2412yes—
591C23×C4C2414yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—24no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—28no—
622#126—216no—
623#125—28no—
624#125—28no—
625#125—216no—
626#125—216no—
627#125—216no—
628#125—216no—
629#125—28no—
630#125—216no—
631#125—24no—
632#125—28no—
633#125—28no—
634#125—216no—
635#124—28no—
636#124—28no—
637#124—216no—
638#124—24no—
639#124—28no—
640#124—48no—
641#123—28no—
642#123—216no—
643#123—216no—
644#123—216no—
645#123—216no—
646#123—216no—
647#123—44no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—24no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—28no—
658C22⋊Q8—216no—
659C22⋊Q8—48no—
660C22⋊Q8—48no—
661C22⋊Q8—48no—
662C22⋊Q8—48no—
663C22⋊Q8—48no—
664C22⋊Q8—44no—
665#121—24no—
666#121—28no—
667#121—28no—
668#121—216no—
669#121—48no—
670#121—44no—
671#121—48no—
672#120—28no—
673#120—48no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—216no—
677C4×Q8—28no—
678C4×Q8—216no—
679C4×Q8—24no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—28no—
684C4×Q8—48no—
685C4×Q8C2×D418yes—
686C4×Q8C2×D418yes—
687C4×Q8C2×D4116yes—
688C4×Q8C2×D418yes—
689C4×Q8C2×D418yes—
690C4×Q8C2×D4116yes—
691C4×D4—28no—
692C4×D4—216no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—216no—
701C4×D4—24no—
702C4×D4—28no—
703C4×D4—48no—
704#117—28no—
705#117—216no—
706#117—28no—
707#117—216no—
708#117—216no—
709#117—216no—
710#117—216no—
711#117—216no—
712#117—28no—
713#117—216no—
714#117—44no—
715#117—48no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4C2×D418yes—
721C2×C4⋊C4C2×D4116yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—28no—
775C2×C22⋊C4—28no—
776C2×C22⋊C4—28no—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C42—24no—
816C2×C42—24no—
817C2×C42—24no—
818C2×C42—28no—
819C2×C42—28no—
820C2×C42—28no—
821C2×C42—28no—
822C2×C42C2×D4116yes—
823C2×C42C2×D418yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2418yes—
838C2×C42C2418yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847#95C2412yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2414yes—
859#95C2414yes—
860#95C2418yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864#95C2414yes—
865#95C2414yes—
866#95C2418yes—
867#95C2414yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872C24—22no—
873C24—22no—
874C24—24no—
875C24—24no—
876C24—24no—
877C24—42no—
878C24—42no—
879C24—44no—
880C24—44no—
881C242−1+414yes—
882C24C2514yes—
883C24C2512yes—
884C24C2512yes—
885C24C2511yescharacteristic
886C2×Q8—22no—
887C2×Q8—24no—
888C2×Q8—28no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—24no—
894C2×Q8—28no—
895C2×Q8—44no—
896C2×Q8—48no—
897C2×Q8—416no—
898C2×Q8—432no—
899C2×Q8C22×D414yes—
900C2×Q8C22×D414yes—
901C2×Q8C22×D418yes—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—22no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—432no—
920C2×D4—416no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—28no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—44no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—48no—
970C22×C4—416no—
971C22×C4—416no—
972C22×C4—416no—
973C22×C4—432no—
974C22×C4C22×D414yes—
975C22×C4C22×D414yes—
976C22×C4C22×D414yes—
977C22×C4C22×D418yes—
978C22×C4C22×D418yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2518yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—22no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—22no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—44no—
1034C4⋊C4—48no—
1035C4⋊C4—44no—
1036C4⋊C4—48no—
1037C4⋊C4—48no—
1038C4⋊C4—44no—
1039C4⋊C4—48no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4—48no—
1043C4⋊C4—44no—
1044C4⋊C4C22×D414yes—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D414yes—
1047C4⋊C4C22×D418yes—
1048C4⋊C4C22×D418yes—
1049C4⋊C4C22×D418yes—
1050C4⋊C4C22×D418yes—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—24no—
1055C22⋊C4—28no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—48no—
1077C22⋊C4—48no—
1078C22⋊C4—44no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—44no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C42—24no—
1090C42—24no—
1091C42—24no—
1092C42—24no—
1093C42—24no—
1094C42—24no—
1095C42—28no—
1096C42—28no—
1097C42—28no—
1098C42—28no—
1099C42—24no—
1100C42—28no—
1101C42—44no—
1102C42—48no—
1103C42—48no—
1104C42C22×D414yes—
1105C42C22×D414yes—
1106C42C22×D414yes—
1107C42C22×D414yes—
1108C42C22×D418yes—
1109C42C22×D418yes—
1110C42C22×D418yes—
1111C42C22×D418yes—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—28no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—48no—
1134C23—44no—
1135C23—44no—
1136C23—48no—
1137C23—48no—
1138C23—48no—
1139C23—48no—
1140C23—88no—
1141C23—88no—
1142C23C23×D412yes—
1143C23C2×2−1+414yes—
1144C23C2×2−1+412yes—
1145C23#58512yes—
1146C23C2611yescharacteristic
1147Q8—28no—
1148Q8—28no—
1149Q8—48no—
1150Q8—416no—
1151Q8—48no—
1152Q8—44no—
1153Q8—48no—
1154D4—416no—
1155D4—416no—
1156D4—48no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—88no—
1161D4—168no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—28no—
1175C2×C4—216no—
1176C2×C4—28no—
1177C2×C4—28no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—28no—
1194C2×C4—28no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—28no—
1199C2×C4—24no—
1200C2×C4—28no—
1201C2×C4—24no—
1202C2×C4—28no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—48no—
1211C2×C4—48no—
1212C2×C4—48no—
1213C2×C4—48no—
1214C2×C4—416no—
1215C2×C4—48no—
1216C2×C4—416no—
1217C2×C4—44no—
1218C2×C4—48no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—416no—
1225C2×C4C23×D412yes—
1226C2×C4C23×D414yes—
1227C2×C4C23×D412yes—
1228C2×C4C23×D412yes—
1229C2×C4C23×D414yes—
1230C2×C4C23×D412yes—
1231C2×C4C23×D414yes—
1232C2×C4C23×D414yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D412yes—
1235C2×C4#58514yes—
1236C2×C4#58514yes—
1237C22—22no—
1238C22—24no—
1239C22—24no—
1240C22—22no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—416no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—816no—
1262C22#348914yes—
1263C22C24×D411yescharacteristic
1264C22C22×2−1+411yescharacteristic
1265C22C2×#58512yes—
1266C22C2×#58511yescharacteristic
1267C22C2×#58512yes—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—24no—
1272C4—24no—
1273C4—22no—
1274C4—24no—
1275C4—24no—
1276C4—42no—
1277C4—44no—
1278C4—44no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—44no—
1284C4—48no—
1285C4—42no—
1286C4—42no—
1287C4—44no—
1288C4#344914yes—
1289C4#348714yes—
1290C2—24no—
1291C2—44no—
1292C2—82no—
1293C2—84no—
1294C2C2×#344911yescharacteristic
1295C2C2×#348711yescharacteristic
1296C2C2×#348911yescharacteristic
1297C2#6282312yes—
1298C2#6282712yes—
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×#3523C2semidirect
2. C22×#529C2semidirect
3. #39595C2semidirect
4. #39467C2semidirect
5. #39139C2semidirect
6. #39136C2semidirect
7. #39131C2semidirect
8. #39127C2semidirect
9. #39124C2semidirect
10. #39123C2semidirect
11. #39119C2semidirect
12. #38919C2semidirect
13. #38047C2semidirect
14. #37843C2semidirect
15. #37188C2semidirect
16. #36625C2semidirect
17. #36621C2semidirect
18. #35664C2semidirect
19. #35638C2semidirect
20. #35325C2semidirect
21. #35302C2semidirect
22. #35240C2semidirect
23. #35236C2semidirect
24. #35172C2semidirect
25. #35102C2semidirect
26. #34196C2semidirect
28. C2×#557C22semidirect
29. C2×#557C22semidirect
30. C2×#557C22semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
36. C2×D4×Q8C22semidirect
37. C2×#541C22semidirect
38. C2×#541C22semidirect
56. C2×#519C22semidirect
62. #2857C22semidirect
63. #2857C22semidirect
69. #2852C22semidirect
70. #2851C22semidirect
71. #2851C22semidirect
72. #2850C22semidirect
82. #2732C22semidirect
83. #2731C22semidirect
84. #2730C22semidirect
85. #2729C22semidirect
86. #2727C22semidirect
87. #2725C22semidirect
88. #2723C22semidirect
89. #2721C22semidirect
90. #2721C22semidirect
91. #2719C22semidirect
94. #2707C22semidirect
95. #2705C22semidirect
96. #2696C22semidirect
97. #2694C22semidirect
98. #2636C22semidirect
99. #2633C22semidirect
100. #2629C22semidirect
101. #2628C22semidirect
105. #2621C22semidirect
106. #2620C22semidirect
108. #2611C22semidirect
109. #2609C22semidirect
110. #2603C22semidirect
111. #2601C22semidirect
112. #2599C22semidirect
113. #2598C22semidirect
115. #2580C22semidirect
117. #2566C22semidirect
118. #2563C22semidirect
119. #2562C22semidirect
120. #2562C22semidirect
122. #2558C22semidirect
123. #2554C22semidirect
124. #2552C22semidirect
125. #2547C22semidirect
126. #2545C22semidirect
127. #2542C22semidirect
128. #2542C22semidirect
130. #2540C22semidirect
131. #2540C22semidirect
132. #2538C22semidirect
133. #2538C22semidirect
134. #2538C22semidirect
135. #2538C22semidirect
136. #2537C22semidirect
137. #2536C22semidirect
138. #2536C22semidirect
139. #2535C22semidirect
141. #2519C22semidirect
142. #2512C22semidirect
145. #2489C22semidirect
150. #2479C22semidirect
151. #2471C22semidirect
152. #2469C22semidirect
153. #2458C22semidirect
154. #2453C22semidirect
155. #2448C22semidirect
156. #2441C22semidirect
157. #2436C22semidirect
159. #2429C22semidirect
161. #2426C22semidirect
162. #2423C22semidirect
167. #2409C22semidirect
169. #2355C22semidirect
170. #2355C22semidirect
171. Q8×C4⋊C4C22semidirect
175. #2326C22semidirect
176. #2324C22semidirect
177. #2324C22semidirect
178. #2323C22semidirect
179. #2323C22semidirect
180. #2323C22semidirect
183. #2320C22semidirect
184. #2320C22semidirect
187. C4×C22⋊Q8C22semidirect
188. C4×C22⋊Q8C22semidirect
189. C4×C22⋊Q8C22semidirect
191. C4×#121C22semidirect
194. #2290C22semidirect
200. #2276C22semidirect
303. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C22×#5292
#395952
#394672
#391392
#391362
#391312
#391272
#391242
#391232
#391192
#389192
#380472
#378432
#371882
#366252
#366212
#356642
#356382
#353252
#353022
#352402
#352362
#351722
#351022
#341962