Finite Group Databasebeta

← #7806365

Subgroups — #7806365

Order 512.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3523C211yesmaximal, characteristic, complemented
3#59809C214yesmaximal, complemented
4#59317C214yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#59134C212yesmaximal, complemented
7#59096C214yesmaximal, complemented
8#59075C214yesmaximal, complemented
9#59071C212yesmaximal, complemented
10#59042C212yesmaximal, complemented
11#47769C218yesmaximal, complemented
12#42812C212yesmaximal, complemented
13#42811C212yesmaximal, complemented
14#42793C212yesmaximal, complemented
15#42790C212yesmaximal, complemented
16#42150C214yesmaximal, complemented
17#37617C211yesmaximal, characteristic, complemented
18#36070C214yesmaximal, complemented
19#35938C212yesmaximal, complemented
20#35910C212yesmaximal, complemented
21#35738C212yesmaximal, complemented
22#35711C212yesmaximal, complemented
23#34971C211yesmaximal, characteristic, complemented
24#34964C211yesmaximal, characteristic
25C2×#2568C211yesmaximal, characteristic, complemented
26#34235C211yesmaximal, characteristic, complemented
27#3523—216no—
28#3503—216no—
29C2×Q82C2212yes—
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34C2×#556C2212yes—
35C2×#556C2211yescharacteristic
36C2×#554C2212yes—
37C2×#554C2214yes—
38C2×#552C2214yes—
39C2×#552C2212yes—
40C2×D4×Q8C2212yes—
41C2×D4×Q8C2212yes—
42C2×D4×Q8C2211yescharacteristic
43C2×D4×Q8C2214yes—
44C2×#544C2214yes—
45C2×#544C2212yes—
46C2×#541C2212yes—
47C2×#541C2214yes—
48C2×#533C2212yes—
49C2×#533C2212yes—
50C2×#533C2211yescharacteristic
51C22×C4⋊Q8C2212yes—
52C22×C4⋊Q8C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#520C2212yes—
56C2×#519C2212yes—
57C2×C4×#41C2211yescharacteristic
58C22×C4×Q8C2211yescharacteristic
59#2822C2214yes—
60#2821C2214yes—
61#2821C2214yes—
62#2723C2218yes—
63#2719C2218yes—
64#2719C2218yes—
65#2716C2218yes—
66#2716C2218yes—
67#2713C2218yes—
68#2713C2218yes—
69#2713C2218yes—
70#2704C2218yes—
71#2702C2218yes—
72#2692C2218yes—
73#2690C2218yes—
74#2664C2214yes—
75#2658C2212yes—
76#2642C2214yes—
77#2642C2212yes—
78#2636C2214yes—
79#2634C2214yes—
80#2634C2214yes—
81#2628C2212yes—
82#2628C2212yes—
83#2628C2214yes—
84#2623C2214yes—
85#2611C2214yes—
86#2604C2214yes—
87#2601C2214yes—
88#2599C2214yes—
89#2598C2214yes—
90#2592C2211yescharacteristic
91#2584C2211yescharacteristic
92#2581C2211yescharacteristic
93#2581C2214yes—
94#2581C2211yescharacteristic
95#2568C2212yes—
96#2568C2212yes—
97#2568C2212yes—
98#2568C2212yes—
99#2568C2214yes—
100#2568C2212yes—
101#2568C2214yes—
102#2568C2212yes—
103#2562C2214yes—
104#2562C2211yescharacteristic
105#2556C2218yes—
106#2550C2214yes—
107#2549C2218yes—
108#2547C2212yes—
109#2546C2214yes—
110#2546C2212yes—
111#2545C2214yes—
112#2540C2211yescharacteristic
113#2536C2211yescharacteristic
114#2536C2214yes—
115#2536C2211yescharacteristic
116#2519C2218yes—
117#2498C2212yes—
118#2492C2214yes—
119#2492C2218yes—
120#2492C2214yes—
121#2489C2218yes—
122#2489C2214yes—
123#2488C2218yes—
124#2487C2214yes—
125#2486C2212yes—
126#2484C2212yes—
127#2481C2218yes—
128#2477C2218yes—
129#2477C2218yes—
130#2475C2218yes—
131#2473C2218yes—
132#2465C2218yes—
133#2453C2214yes—
134#2451C2214yes—
135#2451C2214yes—
136#2451C2218yes—
137#2450C2218yes—
138#2450C2218yes—
139#2446C2214yes—
140#2446C2214yes—
141#2446C2214yes—
142#2442C2214yes—
143#2439C2218yes—
144#2439C2214yes—
145#2438C2218yes—
146#2436C2214yes—
147#2436C2212yes—
148#2434C2214yes—
149#2434C2212yes—
150#2430C2212yes—
151#2429C2214yes—
152#2429C2214yes—
153#2427C2214yes—
154#2425C2218yes—
155#2421C2214yes—
156#2421C2214yes—
157#2417C2214yes—
158#2417C2212yes—
159#2416C2212yes—
160#2409C2214yes—
161#2409C2212yes—
162#2406C2212yes—
163#2399C2212yes—
164#2398C2212yes—
165#2398C2214yes—
166#2396C2212yes—
167#2396C2214yes—
168C2×#400C2214yes—
169#2392C2212yes—
170#2367C2214yes—
171#2365C2212yes—
172#2365C2214yes—
173#2365C2212yes—
174#2364C2218yes—
175#2360C2214yes—
176#2360C2214yes—
177#2359C2218yes—
178#2356C2212yes—
179#2352C2214yes—
180#2351C2212yes—
181#2351C2214yes—
182#2343C2214yes—
183Q8×C22⋊C4C2214yes—
184Q8×C22⋊C4C2214yes—
185Q8×C22⋊C4C2214yes—
186#2336C2214yes—
187#2320C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×C22⋊Q8C2214yes—
192C4×#123C2214yes—
193C4×#121C2214yes—
194C4×#121C2212yes—
195C2×#391C2212yes—
196C2×#391C2214yes—
197#2283C2211yescharacteristic
198C2×#382C2212yes—
199#2276C2212yes—
200C2×C4×C4⋊C4C2211yescharacteristic
201C22×#41C2311yescharacteristic
202C23×Q8C2312yes—
203C23×Q8C2311yescharacteristic
204C23×Q8C2314yes—
205C23×Q8C2312yes—
206Q82—216no—
207#557—28no—
208#557—28no—
209#557—216no—
210#557—216no—
211#556—28no—
212#556—216no—
213#554—232no—
214#554—216no—
215#552—216no—
216#552—232no—
217D4×Q8—28no—
218D4×Q8—232no—
219D4×Q8—216no—
220D4×Q8—216no—
221#544—232no—
222#544—216no—
223#541—232no—
224#541—216no—
225#533—216no—
226#533—216no—
227#533D4116yescomplemented
228C2×C4⋊Q8—216no—
229C2×C4⋊Q8—28no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2318yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246#529—216no—
247#529—28no—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2314yes—
254C2×#125C2311yescharacteristic
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2318yes—
264C2×#125C2312yes—
265C2×#124C2311yescharacteristic
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2318yes—
281C2×C22⋊Q8C2318yes—
282C2×C22⋊Q8C2318yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2314yes—
288C2×#121C2311yescharacteristic
289C2×#121C2312yes—
290#520—216no—
291#519—216no—
292C4×#41—28no—
293C2×C4×Q8—28no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2318yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2314yes—
328C2×#117C2314yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2311yescharacteristic
334C2×#117C2314yes—
335C2×#117C2314yes—
336C2×#117C2312yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2314yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C42C2312yes—
345C22×C42C2312yes—
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2318yes—
354#400C2318yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2318yes—
359#400C2318yes—
360#400C2314yes—
361#400C2318yes—
362#400C2318yes—
363#400C2318yes—
364#400C2318yes—
365#399C2312yes—
366#399C2314yes—
367#399C2318yes—
368#399C2314yes—
369#398C2318yes—
370#398C2318yes—
371#398C2312yes—
372#398C2312yes—
373#398C2318yes—
374#398C2318yes—
375#398C2318yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#397C2318yes—
383#397C2318yes—
384#397C2312yes—
385#397C2314yes—
386#397C2318yes—
387#396C2314yes—
388#396C2314yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#395C2314yes—
393#395C2314yes—
394#395C2318yes—
395#395C2312yes—
396#395C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2318yes—
400#395C2318yes—
401#394C2312yes—
402#394C2312yes—
403#394C2312yes—
404#394C2314yes—
405#394C2318yes—
406#393C2314yes—
407#393C2314yes—
408#393C2318yes—
409#393C2312yes—
410#393C2314yes—
411#393C2318yes—
412#393C2318yes—
413#392C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2318yes—
422#391C2318yes—
423#391C2314yes—
424#391C2318yes—
425#391C2318yes—
426#391C2318yes—
427#391C2314yes—
428#391C2312yes—
429#391C2318yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2318yes—
435#391C2318yes—
436#391C2314yes—
437#390C2312yes—
438#390C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2318yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2318yes—
447#389C2318yes—
448#389C2314yes—
449#389C2318yes—
450#389C2314yes—
451#389C2318yes—
452#389C2314yes—
453#389C2318yes—
454#388C2314yes—
455#388C2318yes—
456#388C2318yes—
457#388C2314yes—
458#388C2318yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#387C2318yes—
467#387C2314yes—
468#387C2314yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#386C2318yes—
484#386C2318yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2318yes—
489#386C2318yes—
490#386C2314yes—
491#385C2318yes—
492#385C2318yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2314yes—
500#383C2312yes—
501#383C2314yes—
502#382C2314yes—
503#382C2314yes—
504#382C2314yes—
505#382C2314yes—
506#382C2314yes—
507#382C2318yes—
508#382C2311yescharacteristic
509#382C2311yescharacteristic
510#381C2312yes—
511#381C2314yes—
512#380C2312yes—
513#380C2312yes—
514#380C2318yes—
515#380C2318yes—
516#380C2314yes—
517#380C2318yes—
518#380C2312yes—
519#380C2314yes—
520#380C2312yes—
521#380C2314yes—
522#380C2312yes—
523C4×C4⋊C4C2311yescharacteristic
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2311yescharacteristic
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2318yes—
530C4×C4⋊C4C2318yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C22⋊C4C2318yes—
538C4×C22⋊C4C2318yes—
539C4×C22⋊C4C2318yes—
540C4×C22⋊C4C2314yes—
541C4×C22⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2318yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2314yes—
546#376C2312yes—
547#376C2314yes—
548C2×#95C2312yes—
549C2×#95C2318yes—
550C2×#95C2318yes—
551C2×#41—28no—
552C2×#41—24no—
553C22×Q8—28no—
554C22×Q8—24no—
555C22×Q8—28no—
556C22×Q8—216no—
557C22×Q8—24no—
558C22×Q8—28no—
559C22×Q8—42no—
560C22×Q8—44no—
561C22×Q8—48no—
562C22×Q8—48no—
563C22×Q8—48no—
564C22×Q8C2411yescharacteristic
565C22×Q8C2411yescharacteristic
566C22×Q8C2411yescharacteristic
567C22×Q8C2414yes—
568C22×Q8C2412yes—
569C22×Q8C2414yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2418yes—
574C22×Q8C2414yes—
575C22×D4C2411yescharacteristic
576C22×D4C2412yes—
577C22×D4C2411yescharacteristic
578C22×D4C2412yes—
579C22×D4C2414yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2414yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2414yes—
591C23×C4C2418yes—
592C23×C4C2414yes—
593C4⋊Q8—216no—
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—216no—
597C4⋊Q8—216no—
598C4⋊Q8—28no—
599C4⋊Q8—216no—
600C4⋊Q8—232no—
601C4⋊Q8—28no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—216no—
606C4⋊Q8—48no—
607C4⋊Q8C2×D418yes—
608C4⋊Q8C2×D418yes—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—28no—
613#126—216no—
614#125—28no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—232no—
622#125—24no—
623#125—216no—
624#125—216no—
625#125C2×D4116yes—
626#124—28no—
627#124—24no—
628#124—48no—
629#123—216no—
630#123—28no—
631#123—216no—
632C22⋊Q8—216no—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—24no—
636C22⋊Q8—216no—
637C22⋊Q8—216no—
638C22⋊Q8—216no—
639C22⋊Q8—28no—
640C22⋊Q8—232no—
641C22⋊Q8—232no—
642C22⋊Q8—216no—
643C22⋊Q8—232no—
644C22⋊Q8—44no—
645C22⋊Q8—44no—
646C22⋊Q8C2×D4116yes—
647C22⋊Q8C2×D4116yes—
648#121—216no—
649#121—24no—
650#121—44no—
651C4×Q8—28no—
652C4×Q8—28no—
653C4×Q8—216no—
654C4×Q8—28no—
655C4×Q8—216no—
656C4×Q8—28no—
657C4×Q8—216no—
658C4×Q8—28no—
659C4×Q8—24no—
660C4×Q8—28no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—28no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—216no—
668C4×Q8—216no—
669C4×Q8—24no—
670C4×Q8—48no—
671C4×Q8—48no—
672C4×Q8C2×D4116yes—
673C4×Q8C2×D4116yes—
674C4×D4—28no—
675C4×D4—28no—
676C4×D4—28no—
677C4×D4—28no—
678C4×D4—232no—
679C4×D4—216no—
680C4×D4—24no—
681C4×D4—24no—
682C4×D4—216no—
683C4×D4—24no—
684C4×D4—48no—
685#117—24no—
686#117—216no—
687#117—28no—
688#117—216no—
689#117—216no—
690#117—28no—
691#117—28no—
692#117—216no—
693#117C2×D4116yes—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—28no—
696C2×C4⋊C4—28no—
697C2×C4⋊C4—28no—
698C2×C4⋊C4—216no—
699C2×C4⋊C4—216no—
700C2×C4⋊C4—44no—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2418yes—
781C2×C22⋊C4C2414yes—
782C2×C42—28no—
783C2×C42—28no—
784C2×C42—44no—
785C2×C42C2×D418yes—
786C2×C42C2412yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2414yes—
792C2×C42C2418yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2414yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2418yes—
801C2×C42C2418yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2411yescharacteristic
805C2×C42C2414yes—
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809#95C2412yes—
810#95C2418yes—
811#95C2418yes—
812#95C2412yes—
813#95C2414yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819#95C2418yes—
820#95C2412yes—
821#95C2414yes—
822#95C2412yes—
823#95C2418yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2418yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2412yes—
833#95C2418yes—
834#95C2418yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2418yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848C24C2512yes—
849C24C2512yes—
850C24C2511yescharacteristic
851#41—232no—
852C2×Q8—22no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×Q8—28no—
856C2×Q8—24no—
857C2×Q8—22no—
858C2×Q8—28no—
859C2×Q8—216no—
860C2×Q8—28no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—24no—
864C2×Q8—28no—
865C2×Q8—22no—
866C2×Q8—24no—
867C2×Q8—28no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—24no—
871C2×Q8—28no—
872C2×Q8—28no—
873C2×Q8—42no—
874C2×Q8—44no—
875C2×Q8—48no—
876C2×Q8—48no—
877C2×Q8—48no—
878C2×Q8—416no—
879C2×Q8—432no—
880C2×Q8—816no—
881C2×Q8—832no—
882C2×Q8C22×D418yes—
883C2×Q8C22×D418yes—
884C2×Q82−1+414yes—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—24no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D42−1+418yes—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—28no—
907C22×C4—28no—
908C22×C4—28no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—28no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—28no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—216no—
922C22×C4—44no—
923C22×C4—42no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4C22×D414yes—
930C22×C4C22×D414yes—
931C22×C4C22×D414yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2518yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2514yes—
949C22×C4C2511yescharacteristic
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—216no—
960C4⋊C4—28no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—216no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—22no—
979C4⋊C4—28no—
980C4⋊C4—24no—
981C4⋊C4—22no—
982C4⋊C4—216no—
983C4⋊C4—216no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—48no—
1003C4⋊C4—48no—
1004C4⋊C4C22×D418yes—
1005C4⋊C4C22×D418yes—
1006C4⋊C4C22×D418yes—
1007C4⋊C4C22×D4116yes—
1008C4⋊C4C22×D418yes—
1009C4⋊C4C22×D4116yes—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—24no—
1017C22⋊C4—28no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—216no—
1022C22⋊C4—28no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—48no—
1034C22⋊C4—48no—
1035C22⋊C4C22×D4116yes—
1036C42—24no—
1037C42—24no—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—28no—
1044C42—28no—
1045C42—216no—
1046C42—28no—
1047C42—24no—
1048C42—28no—
1049C42—28no—
1050C42—42no—
1051C42—42no—
1052C42—48no—
1053C42—48no—
1054C42C22×D414yes—
1055C42C22×D414yes—
1056C42C22×D414yes—
1057C42C22×D414yes—
1058C42C22×D4116yes—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—24no—
1070C23—22no—
1071C23—24no—
1072C23—22no—
1073C23C23×D412yes—
1074C23C2×2−1+414yes—
1075C23C2×2−1+414yes—
1076C23C2611yescharacteristic
1077Q8—28no—
1078Q8—28no—
1079Q8—216no—
1080Q8—216no—
1081Q8—48no—
1082Q8—416no—
1083Q8—44no—
1084Q8—44no—
1085Q8—416no—
1086Q8—88no—
1087Q8—816no—
1088D4—28no—
1089D4—216no—
1090D4—48no—
1091D4—44no—
1092D4—88no—
1093C2×C4—216no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—24no—
1101C2×C4—21no—
1102C2×C4—24no—
1103C2×C4—28no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—28no—
1107C2×C4—28no—
1108C2×C4—28no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—28no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—28no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—28no—
1144C2×C4—416no—
1145C2×C4—48no—
1146C2×C4—48no—
1147C2×C4—48no—
1148C2×C4—48no—
1149C2×C4—48no—
1150C2×C4—816no—
1151C2×C4—88no—
1152C2×C4—88no—
1153C2×C4C23×D412yes—
1154C2×C4C23×D418yes—
1155C2×C4C23×D412yes—
1156C2×C4C23×D418yes—
1157C2×C4C23×D412yes—
1158C2×C4C23×D412yes—
1159C2×C4C23×D412yes—
1160C2×C4C23×D412yes—
1161C2×C4C2×2−1+414yes—
1162C2×C4C2×2−1+414yes—
1163C2×C4C2×2−1+412yes—
1164C2×C4#58512yes—
1165C2×C4#58514yes—
1166C22—24no—
1167C22—24no—
1168C22—22no—
1169C22—22no—
1170C22—24no—
1171C22—24no—
1172C22—24no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—44no—
1178C22—44no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22#348614yes—
1183C22C24×D411yescharacteristic
1184C22C22×2−1+412yes—
1185C22C22×2−1+411yescharacteristic
1186C22C2×#58511yescharacteristic
1187C22C2×#58512yes—
1188C4—22no—
1189C4—22no—
1190C4—24no—
1191C4—22no—
1192C4—24no—
1193C4—28no—
1194C4—22no—
1195C4—28no—
1196C4—44no—
1197C4—44no—
1198C4—44no—
1199C4—44no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—48no—
1208C4—42no—
1209C4#348914yes—
1210C4#350014yes—
1211C2—24no—
1212C2—44no—
1213C2—82no—
1214C2C2×#348611yescharacteristic
1215C2C2×#348911yescharacteristic
1216C2C2×#350011yescharacteristic
1217C2#6302512yes—
1218C2#6303212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34964C2
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×#3503C2semidirect
2. C2×#3523C2semidirect
3. #59809C2semidirect
4. #59317C2semidirect
5. #59144C2semidirect
6. #59134C2semidirect
7. #59096C2semidirect
8. #59075C2semidirect
9. #59071C2semidirect
10. #59042C2semidirect
11. #47769C2semidirect
12. #42812C2semidirect
13. #42811C2semidirect
14. #42793C2semidirect
15. #42790C2semidirect
16. #42150C2semidirect
17. #37617C2semidirect
18. #36070C2semidirect
19. #35938C2semidirect
20. #35910C2semidirect
21. #35738C2semidirect
22. #35711C2semidirect
23. #34971C2semidirect
25. C2×#2568C2semidirect
26. #34235C2semidirect
227. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#35232
#598092
#593172
#591442
#591342
#590962
#590752
#590712
#590422
#477692
#428122
#428112
#427932
#427902
#421502
#376172
#360702
#359382
#359102
#357382
#357112
#349712
#349642
C2×#25682
#342352