Finite Group Databasebeta

← #8075558

Subgroups — #8075558

Order 512.

6855 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C212yesmaximal, complemented
2#59836C211yesmaximal, characteristic, complemented
3#59835C212yesmaximal, complemented
4#59179C212yesmaximal, complemented
5#58998C214yesmaximal, complemented
6#51532C214yesmaximal, complemented
7#51530C212yesmaximal, complemented
8#51326C212yesmaximal, complemented
9#50887C212yesmaximal, complemented
10#47945C214yesmaximal, complemented
11#47867C214yesmaximal, complemented
12#47799C212yesmaximal, complemented
13#47688C214yesmaximal, complemented
14#45418C212yesmaximal, complemented
15#44879C214yesmaximal, complemented
16#44775C214yesmaximal, complemented
17#44581C214yesmaximal, complemented
18#44162C214yesmaximal, complemented
19#39369C212yesmaximal, complemented
20#39360C211yesmaximal, characteristic, complemented
21#37721C214yesmaximal, complemented
22#37653C212yesmaximal, complemented
23#34523C211yesmaximal, characteristic, complemented
24#3538—232no—
25C2×#563C2212yes—
26C2×#563C2211yescharacteristic
27C2×#563C2214yescomplemented
28C2×#552C2214yes—
29C2×#552C2214yescomplemented
30C2×#551C2212yes—
31C2×#551C2212yes—
32C2×#551C2214yescomplemented
33C2×D4×Q8C2214yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2214yescomplemented
36C2×D4×Q8C2211yescharacteristic, complemented
37C2×#547C2211yescharacteristic
38C2×#544C2214yescomplemented
39C2×#544C2214yescomplemented
40C2×#541C2214yescomplemented
41C2×#539C2214yes—
42C2×#539C2214yes—
43C2×#536C2212yes—
44C2×#536C2212yes—
45C2×#525C2212yes—
46C22×C22⋊Q8C2214yescomplemented
47C22×C22⋊Q8C2212yescomplemented
48#2868C2211yescharacteristic, complemented
49#2849C2212yescomplemented
50#2822C2212yescomplemented
51#2734C2212yescomplemented
52#2732C2212yes—
53#2732C2214yescomplemented
54#2729C2214yescomplemented
55#2729C2214yescomplemented
56#2728C2212yes—
57#2727C2212yescomplemented
58#2726C2212yescomplemented
59#2725C2214yescomplemented
60#2724C2211yescharacteristic
61#2723C2214yescomplemented
62#2722C2214yescomplemented
63#2720C2214yescomplemented
64#2720C2214yescomplemented
65#2719C2214yescomplemented
66#2719C2214yescomplemented
67#2718C2214yescomplemented
68#2717C2212yes—
69#2716C2214yescomplemented
70#2713C2214yescomplemented
71#2707C2214yescomplemented
72#2704C2214yescomplemented
73#2704C2214yescomplemented
74#2698C2214yescomplemented
75#2696C2214yes—
76#2695C2214yes—
77#2695C2214yescomplemented
78#2694C2214yescomplemented
79#2693C2214yes—
80#2690C2214yescomplemented
81#2689C2214yescomplemented
82#2689C2214yescomplemented
83#2687C2214yes—
84#2684C2212yes—
85#2683C2214yes—
86#2683C2212yes—
87#2683C2214yescomplemented
88#2682C2212yes—
89#2681C2214yes—
90#2680C2214yescomplemented
91#2680C2214yescomplemented
92#2679C2211yescharacteristic
93#2678C2214yes—
94#2677C2214yescomplemented
95#2677C2214yescomplemented
96#2677C2214yescomplemented
97#2677C2214yescomplemented
98#2677C2214yescomplemented
99#2677C2214yescomplemented
100#2676C2214yes—
101#2674C2214yescomplemented
102#2663C2214yescomplemented
103#2638C2214yes—
104#2628C2214yescomplemented
105#2621C2212yescomplemented
106#2618C2212yescomplemented
107#2614C2212yescomplemented
108#2611C2214yescomplemented
109#2609C2212yes—
110#2609C2212yes—
111#2609C2214yescomplemented
112#2602C2214yes—
113#2584C2214yescomplemented
114#2566C2214yescomplemented
115#2560C2214yescomplemented
116#2559C2214yes—
117#2558C2214yescomplemented
118#2556C2214yescomplemented
119#2556C2214yescomplemented
120#2554C2214yescomplemented
121#2553C2214yes—
122#2553C2214yes—
123#2552C2212yescomplemented
124#2551C2212yescomplemented
125#2551C2214yescomplemented
126#2550C2214yescomplemented
127#2547C2211yescharacteristic
128#2546C2211yescharacteristic, complemented
129#2542C2214yes—
130#2539C2212yescomplemented
131#2536C2212yes—
132#2536C2214yescomplemented
133#2536C2212yescomplemented
134#2534C2212yes—
135#2521C2214yescomplemented
136#2506C2214yescomplemented
137#2481C2214yescomplemented
138#2480C2214yescomplemented
139#2478C2214yescomplemented
140#2477C2214yes—
141#2475C2214yescomplemented
142#2475C2214yescomplemented
143#2473C2214yescomplemented
144#2473C2214yescomplemented
145#2471C2214yes—
146#2470C2214yes—
147#2469C2214yescomplemented
148#2468C2214yes—
149#2466C2214yes—
150#2463C2214yes—
151#2463C2214yes—
152#2463C2214yescomplemented
153#2463C2214yescomplemented
154#2462C2214yescomplemented
155#2461C2214yes—
156#2455C2214yes—
157#2454C2214yescomplemented
158#2452C2214yes—
159#2452C2214yescomplemented
160#2452C2214yescomplemented
161#2449C2214yes—
162#2449C2214yes—
163#2449C2214yes—
164#2449C2214yes—
165#2443C2214yes—
166#2441C2214yescomplemented
167#2440C2214yescomplemented
168#2440C2214yescomplemented
169#2440C2214yescomplemented
170#2440C2214yescomplemented
171#2439C2214yescomplemented
172#2437C2214yescomplemented
173#2437C2214yescomplemented
174#2434C2214yescomplemented
175#2434C2214yescomplemented
176#2434C2212yescomplemented
177#2432C2212yes—
178#2429C2214yescomplemented
179#2429C2214yescomplemented
180#2424C2214yes—
181#2422C2214yescomplemented
182#2418C2214yes—
183#2418C2214yescomplemented
184#2417C2214yes—
185#2417C2214yes—
186#2413C2212yescomplemented
187#2411C2212yescomplemented
188#2409C2214yes—
189#2409C2214yescomplemented
190#2409C2214yescomplemented
191#2406C2212yes—
192#2404C2212yes—
193#2397C2212yes—
194#2396C2214yescomplemented
195#2382C2212yescomplemented
196#2379C2211yescharacteristic
197#2374C2212yes—
198#2373C2214yescomplemented
199#2369C2212yescomplemented
200#2363C2214yes—
201#2361C2214yes—
202#2360C2214yescomplemented
203#2360C2214yescomplemented
204#2358C2214yes—
205#2358C2214yes—
206#2354C2212yes—
207D4×C4⋊C4C2212yes—
208#2344C2212yescomplemented
209#2334C2214yescomplemented
210#2332C2214yescomplemented
211#2327C2212yescomplemented
212#2327C2212yescomplemented
213#2324C2214yes—
214#2322C2212yes—
215C4×#125C2212yescomplemented
216C4×#124C2211yescharacteristic
217C4×#120C2214yes—
218#2293C2212yes—
219#2293C2211yescharacteristic, complemented
220C22×#41C2312yes—
221C23×Q8C2312yes—
222C23×Q8C2314yes—
223C23×Q8C2312yes—
224C24×C4C2312yes—
225#563—216no—
226#563—232no—
227#563D4116yescomplemented
228#552—232no—
229#552—232no—
230#551—232no—
231#551—216no—
232#551—216no—
233D4×Q8—232no—
234D4×Q8—232no—
235D4×Q8—44no—
236D4×Q8—48no—
237#547—44no—
238#544—232no—
239#544—232no—
240#541—232no—
241#539—232no—
242#539—232no—
243#536—216no—
244#536—216no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2314yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2314yes—
258C2×C4⋊Q8C2312yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2312yes—
275C2×#124C2314yes—
276C2×#124C2312yes—
277C2×#124C2311yescharacteristic
278#525—216no—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×C22⋊Q8—232no—
294C2×C22⋊Q8—48no—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#120C2314yes—
326C2×#120C2312yes—
327C2×#120C2312yes—
328C2×#120C2312yes—
329C2×C4×Q8C2314yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×#117C2314yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C22⋊C4C2314yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2312yes—
363C22×C22⋊C4C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2312yes—
439#394C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2311yescharacteristic
465#391C2314yes—
466#391C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2312yes—
475#390C2311yescharacteristic
476#390C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#386C2314yes—
549#386C2312yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#384C2314yes—
593#384C2312yes—
594#384C2312yes—
595#384C2314yes—
596#382C2312yes—
597#382C2314yes—
598#382C2312yes—
599#382C2312yes—
600#382C2311yescharacteristic
601#381C2312yes—
602#381C2312yes—
603#381C2312yes—
604#381C2312yes—
605#380C2314yes—
606#380C2312yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2314yes—
614#379C2312yes—
615#379C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2311yescharacteristic
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2312yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636#376C2312yes—
637C43C2311yescharacteristic
638C25C2412yes—
639C2×#41—28no—
640C2×#41—44no—
641C2×#41—82no—
642C22×Q8—216no—
643C22×Q8—28no—
644C22×Q8—28no—
645C22×Q8—44no—
646C22×Q8—44no—
647C22×Q8—48no—
648C22×Q8—82no—
649C22×Q8—84no—
650C22×Q8—82no—
651C22×Q8C2414yes—
652C22×Q8C2414yes—
653C22×Q8C2414yes—
654C22×Q8C2414yes—
655C22×Q8C2412yes—
656C22×Q8C2412yes—
657C22×Q8C2412yes—
658C22×Q8C2411yescharacteristic
659C22×D4C2414yes—
660C22×D4C2412yes—
661C22×D4C2414yes—
662C22×D4C2411yescharacteristic
663C22×D4C2414yes—
664C22×D4C2412yes—
665C22×D4C2412yes—
666C22×D4C2411yescharacteristic
667C22×D4C2412yes—
668C23×C4—28no—
669C23×C4—44no—
670C23×C4—82no—
671C23×C4C2414yes—
672C23×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2414yes—
679C23×C4C2414yes—
680C23×C4C2412yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C4⋊Q8—28no—
686C4⋊Q8—216no—
687C4⋊Q8—216no—
688C4⋊Q8—216no—
689C4⋊Q8—216no—
690C4⋊Q8—216no—
691C4⋊Q8—28no—
692C4⋊Q8—28no—
693C4⋊Q8—42no—
694C4⋊Q8—42no—
695C4⋊Q8—48no—
696C4⋊Q8—84no—
697C4⋊Q8—82no—
698C4⋊Q8C2×D4116yes—
699#126—216no—
700#126—216no—
701#126—216no—
702#126—216no—
703#126—216no—
704#126—216no—
705#126C2×D4132yes—
706#125—216no—
707#125—216no—
708#125—216no—
709#125—216no—
710#125—216no—
711#125—216no—
712#125—216no—
713#125—216no—
714#125C2×D4116yes—
715#124—28no—
716#124—216no—
717#124C2×D418yes—
718#123—28no—
719#123—28no—
720#123—28no—
721#123—216no—
722#123—216no—
723#123—216no—
724#123—28no—
725#123—216no—
726#123—216no—
727#123—216no—
728#123—44no—
729#123—44no—
730#123—82no—
731#123C2×D4116yes—
732C22⋊Q8—216no—
733C22⋊Q8—216no—
734C22⋊Q8—216no—
735C22⋊Q8—216no—
736C22⋊Q8—216no—
737C22⋊Q8—216no—
738C22⋊Q8—216no—
739C22⋊Q8—216no—
740C22⋊Q8—216no—
741C22⋊Q8—216no—
742C22⋊Q8—216no—
743C22⋊Q8—216no—
744C22⋊Q8—216no—
745C22⋊Q8—216no—
746C22⋊Q8—216no—
747C22⋊Q8—216no—
748C22⋊Q8—216no—
749C22⋊Q8—216no—
750C22⋊Q8—48no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753C22⋊Q8—48no—
754C22⋊Q8—48no—
755C22⋊Q8—48no—
756C22⋊Q8—44no—
757C22⋊Q8—44no—
758C22⋊Q8C2×D4132yes—
759#121—216no—
760#121—216no—
761#121—44no—
762#120—28no—
763#120—216no—
764#120—28no—
765#120—82no—
766C4×Q8—216no—
767C4×Q8—216no—
768C4×Q8—42no—
769C4×Q8—44no—
770C4×D4—28no—
771C4×D4—216no—
772C4×D4—216no—
773C4×D4—216no—
774C4×D4—24no—
775C4×D4—216no—
776C4×D4—216no—
777C4×D4—216no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—42no—
781C4×D4—48no—
782C4×D4—84no—
783C4×D4—84no—
784#117—216no—
785#117—216no—
786#117—28no—
787#117—28no—
788#117—28no—
789#117—216no—
790#117—216no—
791C2×C4⋊C4—216no—
792C2×C4⋊C4—216no—
793C2×C4⋊C4—216no—
794C2×C4⋊C4—28no—
795C2×C4⋊C4—44no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C22⋊C4—216no—
860C2×C22⋊C4—216no—
861C2×C22⋊C4—44no—
862C2×C22⋊C4—44no—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964C24—24no—
965C24—28no—
966C24—42no—
967C24—44no—
968C24—42no—
969C24C2512yes—
970C24C2512yes—
971C24C2514yes—
972#41—816no—
973C2×Q8—28no—
974C2×Q8—28no—
975C2×Q8—28no—
976C2×Q8—28no—
977C2×Q8—24no—
978C2×Q8—24no—
979C2×Q8—28no—
980C2×Q8—28no—
981C2×Q8—41no—
982C2×Q8—42no—
983C2×Q8—42no—
984C2×Q8—41no—
985C2×Q8—44no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—42no—
989C2×Q8—44no—
990C2×Q8—42no—
991C2×Q8—44no—
992C2×Q8—44no—
993C2×Q8—42no—
994C2×Q8—42no—
995C2×Q8—816no—
996C2×Q8—832no—
997C2×Q8—816no—
998C2×Q8C22×D418yes—
999C2×Q8C22×D414yes—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—28no—
1003C2×D4—28no—
1004C2×D4—24no—
1005C2×D4—24no—
1006C2×D4—28no—
1007C2×D4—28no—
1008C2×D4—22no—
1009C2×D4—42no—
1010C2×D4—41no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—41no—
1017C2×D4—44no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4C22×D414yes—
1024C2×D42−1+418yes—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—24no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—816no—
1065C22×C4C22×D418yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—41no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4C22×D418yes—
1143C4⋊C4C22×D4116yes—
1144C4⋊C4C22×D4116yes—
1145C4⋊C4C22×D418yes—
1146C4⋊C4C22×D4116yes—
1147C4⋊C4H(5,𝔽2)14yes—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4C22×D4116yes—
1189C22⋊C4C22×D4116yes—
1190C22⋊C4C22×D418yes—
1191C42—24no—
1192C42—28no—
1193C42—28no—
1194C42—28no—
1195C42—28no—
1196C42—28no—
1197C42—22no—
1198C42—24no—
1199C42—24no—
1200C42—44no—
1201C42—42no—
1202C42—44no—
1203C42—44no—
1204C42—42no—
1205C42—44no—
1206C42—41no—
1207C42C22×D414yes—
1208C42C22×D418yes—
1209C23—24no—
1210C23—24no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—22no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—22no—
1220C23—22no—
1221C23—24no—
1222C23—22no—
1223C23—24no—
1224C23—416no—
1225C23—48no—
1226C23—84no—
1227C23—88no—
1228C23—84no—
1229C23C23×D414yes—
1230C23C2×2−1+418yes—
1231C23C2611yescharacteristic
1232Q8—48no—
1233Q8—44no—
1234Q8—416no—
1235Q8—416no—
1236Q8—88no—
1237Q8—88no—
1238Q8—84no—
1239Q8—84no—
1240D4—44no—
1241D4—48no—
1242D4—416no—
1243D4—44no—
1244D4—416no—
1245D4—48no—
1246D4—88no—
1247D4—84no—
1248D4—84no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—48no—
1298C2×C4—416no—
1299C2×C4—48no—
1300C2×C4—416no—
1301C2×C4—416no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—84no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4—88no—
1308C2×C4—88no—
1309C2×C4—84no—
1310C2×C4—84no—
1311C2×C4C23×D418yes—
1312C2×C4C23×D414yes—
1313C2×C4C23×D412yes—
1314C2×C4C23×D418yes—
1315C2×C4C23×D414yes—
1316C2×C4C2×H(5,𝔽2)12yes—
1317C2×C4C2×H(5,𝔽2)14yes—
1318C2×C4C2×2−1+414yes—
1319C22—24no—
1320C22—28no—
1321C22—28no—
1322C22—28no—
1323C22—28no—
1324C22—44no—
1325C22—44no—
1326C22—42no—
1327C22—44no—
1328C22—44no—
1329C22—42no—
1330C22—44no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—816no—
1337C22C24×D411yescharacteristic
1338C22C22×H(5,𝔽2)11yescharacteristic
1339C22C22×2−1+412yes—
1340C22H(7,𝔽2)11yescharacteristic
1341C222−1+612yes—
1342C4—24no—
1343C4—28no—
1344C4—22no—
1345C4—24no—
1346C4—24no—
1347C4—28no—
1348C4—24no—
1349C4—22no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—44no—
1354C4—44no—
1355C4—44no—
1356C4—44no—
1357C4—41no—
1358C4—42no—
1359C4—44no—
1360C4—44no—
1361C4—42no—
1362C2—44no—
1363C2—48no—
1364C2—82no—
1365C2#6286512yes—
1366C2#6288611yescharacteristic
1367C2D4×H(5,𝔽2)11yescharacteristic
1368C2D4×2−1+412yes—
1369C2#6301611yescharacteristic
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×#3538C2semidirect
2. #59836C2semidirect
3. #59835C2semidirect
4. #59179C2semidirect
5. #58998C2semidirect
6. #51532C2semidirect
7. #51530C2semidirect
8. #51326C2semidirect
9. #50887C2semidirect
10. #47945C2semidirect
11. #47867C2semidirect
12. #47799C2semidirect
13. #47688C2semidirect
14. #45418C2semidirect
15. #44879C2semidirect
16. #44775C2semidirect
17. #44581C2semidirect
18. #44162C2semidirect
19. #39369C2semidirect
20. #39360C2semidirect
21. #37721C2semidirect
22. #37653C2semidirect
23. #34523C2semidirect
27. C2×#563C22semidirect
29. C2×#552C22semidirect
32. C2×#551C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×D4×Q8C22semidirect
38. C2×#544C22semidirect
39. C2×#544C22semidirect
40. C2×#541C22semidirect
46. C22×C22⋊Q8C22semidirect
47. C22×C22⋊Q8C22semidirect
48. #2868C22semidirect
49. #2849C22semidirect
50. #2822C22semidirect
51. #2734C22semidirect
53. #2732C22semidirect
54. #2729C22semidirect
55. #2729C22semidirect
57. #2727C22semidirect
58. #2726C22semidirect
59. #2725C22semidirect
61. #2723C22semidirect
62. #2722C22semidirect
63. #2720C22semidirect
64. #2720C22semidirect
65. #2719C22semidirect
66. #2719C22semidirect
67. #2718C22semidirect
69. #2716C22semidirect
70. #2713C22semidirect
71. #2707C22semidirect
72. #2704C22semidirect
73. #2704C22semidirect
74. #2698C22semidirect
77. #2695C22semidirect
78. #2694C22semidirect
80. #2690C22semidirect
81. #2689C22semidirect
82. #2689C22semidirect
87. #2683C22semidirect
90. #2680C22semidirect
91. #2680C22semidirect
94. #2677C22semidirect
95. #2677C22semidirect
96. #2677C22semidirect
97. #2677C22semidirect
98. #2677C22semidirect
99. #2677C22semidirect
101. #2674C22semidirect
102. #2663C22semidirect
104. #2628C22semidirect
105. #2621C22semidirect
106. #2618C22semidirect
107. #2614C22semidirect
108. #2611C22semidirect
111. #2609C22semidirect
113. #2584C22semidirect
114. #2566C22semidirect
115. #2560C22semidirect
117. #2558C22semidirect
118. #2556C22semidirect
119. #2556C22semidirect
120. #2554C22semidirect
123. #2552C22semidirect
124. #2551C22semidirect
125. #2551C22semidirect
126. #2550C22semidirect
128. #2546C22semidirect
130. #2539C22semidirect
132. #2536C22semidirect
133. #2536C22semidirect
135. #2521C22semidirect
136. #2506C22semidirect
137. #2481C22semidirect
138. #2480C22semidirect
139. #2478C22semidirect
141. #2475C22semidirect
142. #2475C22semidirect
143. #2473C22semidirect
144. #2473C22semidirect
147. #2469C22semidirect
152. #2463C22semidirect
153. #2463C22semidirect
154. #2462C22semidirect
157. #2454C22semidirect
159. #2452C22semidirect
160. #2452C22semidirect
166. #2441C22semidirect
167. #2440C22semidirect
168. #2440C22semidirect
169. #2440C22semidirect
170. #2440C22semidirect
171. #2439C22semidirect
172. #2437C22semidirect
173. #2437C22semidirect
174. #2434C22semidirect
175. #2434C22semidirect
176. #2434C22semidirect
178. #2429C22semidirect
179. #2429C22semidirect
181. #2422C22semidirect
183. #2418C22semidirect
186. #2413C22semidirect
187. #2411C22semidirect
189. #2409C22semidirect
190. #2409C22semidirect
194. #2396C22semidirect
195. #2382C22semidirect
198. #2373C22semidirect
199. #2369C22semidirect
202. #2360C22semidirect
203. #2360C22semidirect
208. #2344C22semidirect
209. #2334C22semidirect
210. #2332C22semidirect
211. #2327C22semidirect
212. #2327C22semidirect
215. C4×#125C22semidirect
219. #2293C22semidirect
227. #563D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
#598362
#598352
#591792
#589982
#515322
#515302
#513262
#508872
#479452
#478672
#477992
#476882
#454182
#448792
#447752
#445812
#441622
#393692
#393602
#377212
#376532
#345232