Finite Group Databasebeta

← #7673903

Subgroups — #7673903

Order 512.

7008 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3503C211yesmaximal, characteristic, complemented
3#45338C212yesmaximal, complemented
4#45337C212yesmaximal, complemented
5#45271C212yesmaximal, complemented
6#45270C212yesmaximal, complemented
7#45143C212yesmaximal, complemented
8#45142C212yesmaximal, complemented
9#44938C212yesmaximal, complemented
10#44937C212yesmaximal, complemented
11#39166C218yesmaximal, complemented
12#39160C218yesmaximal, complemented
13#37757C214yesmaximal, complemented
14#37756C214yesmaximal, complemented
15#37711C214yesmaximal, complemented
16#37704C214yesmaximal, complemented
17#35575C212yesmaximal, complemented
18#35564C212yesmaximal, complemented
19#35334C211yesmaximal, characteristic, complemented
20#35328C211yesmaximal, characteristic, complemented
21#35158C212yesmaximal, complemented
22#34637C211yesmaximal, characteristic, complemented
23#34274C212yesmaximal, complemented
24C2×#2331C211yesmaximal, characteristic, complemented
25#34070C211yesmaximal, characteristic, complemented
26#3511—216no—
27#3503—216no—
28C2×Q82C2212yes—
29C2×#557C2212yes—
30C2×#556C2212yes—
31C2×#555C2212yes—
32C2×#554C2212yes—
33C2×#554C2212yes—
34C2×#554C2214yes—
35C2×#553C2214yes—
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2214yes—
38C2×#548C2214yes—
39C2×#547C2212yes—
40C2×#544C2212yes—
41C2×#544C2214yes—
42C2×#542C2214yes—
43C2×#537C2212yes—
44C2×#537C2212yes—
45C2×#533C2211yescharacteristic
46C2×#533C2212yes—
47C2×#533C2212yes—
48C2×#532C2211yescharacteristic
49C2×#532C2211yescharacteristic
50C2×#532C2212yes—
51C22×C4⋊Q8C2212yes—
52C22×C4⋊Q8C2211yescharacteristic
53C2×#520C2212yes—
54C2×#520C2212yes—
55C2×C4×#41C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57#2851C2214yes—
58#2850C2214yes—
59#2850C2218yes—
60#2731C2218yes—
61#2731C2218yes—
62#2730C2218yes—
63#2730C2218yes—
64#2729C2218yes—
65#2729C2218yes—
66#2728C2218yes—
67#2728C2218yes—
68#2723C2218yes—
69#2719C2218yes—
70#2716C2218yes—
71#2711C2218yes—
72#2696C2218yes—
73#2690C2218yes—
74#2676C2218yes—
75#2674C2218yes—
76#2642C2212yes—
77#2641C2212yes—
78#2640C2212yes—
79#2640C2212yes—
80#2639C2214yes—
81#2639C2214yes—
82#2639C2218yes—
83#2628C2212yes—
84#2628C2212yes—
85#2621C2212yes—
86#2619C2212yes—
87#2581C2212yes—
88#2581C2212yes—
89#2580C2212yes—
90#2580C2212yes—
91#2564C2214yes—
92#2564C2214yes—
93#2564C2218yes—
94#2543C2214yes—
95#2543C2214yes—
96#2543C2218yes—
97#2536C2212yes—
98#2536C2212yes—
99#2535C2212yes—
100#2535C2212yes—
101#2492C2214yes—
102#2492C2214yes—
103#2491C2214yes—
104#2491C2214yes—
105#2490C2214yes—
106#2490C2214yes—
107#2489C2214yes—
108#2489C2214yes—
109#2481C2218yes—
110#2477C2218yes—
111#2475C2218yes—
112#2469C2218yes—
113#2463C2218yes—
114#2460C2218yes—
115#2458C2218yes—
116#2454C2214yes—
117#2453C2214yes—
118#2452C2214yes—
119#2451C2214yes—
120#2448C2218yes—
121#2446C2218yes—
122#2443C2218yes—
123#2442C2214yes—
124#2441C2214yes—
125#2440C2214yes—
126#2439C2214yes—
127#2436C2218yes—
128#2432C2218yes—
129#2429C2214yes—
130#2428C2214yes—
131#2427C2214yes—
132#2426C2214yes—
133#2421C2218yes—
134#2421C2218yes—
135#2417C2214yes—
136#2417C2218yes—
137#2416C2214yes—
138#2416C2218yes—
139#2415C2214yes—
140#2414C2214yes—
141#2409C2218yes—
142#2407C2218yes—
143#2398C2212yes—
144#2398C2212yes—
145#2398C2212yes—
146#2398C2212yes—
147#2363C2214yes—
148#2363C2214yes—
149#2362C2214yes—
150#2362C2214yes—
151#2361C2214yes—
152#2361C2214yes—
153#2360C2214yes—
154#2360C2214yes—
155#2331C2212yes—
156#2331C2212yes—
157#2331C2214yes—
158#2331C2212yes—
159#2331C2212yes—
160#2331C2214yes—
161#2328C2211yescharacteristic
162#2328C2211yescharacteristic
163#2327C2211yescharacteristic
164#2327C2211yescharacteristic
165#2326C2211yescharacteristic
166#2326C2211yescharacteristic
167#2326C2211yescharacteristic
168#2326C2211yescharacteristic
169#2325C2214yes—
170#2325C2214yes—
171#2325C2218yes—
172#2316C2212yes—
173#2311C2212yes—
174#2311C2212yes—
175C4×#121C2218yes—
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2212yes—
179#2297C2212yes—
180C2×#391C2214yes—
181C2×#389C2212yes—
182#2290C2214yes—
183#2290C2214yes—
184C2×#387C2214yes—
185#2285C2211yescharacteristic
186C2×#382C2211yescharacteristic
187C2×C4×C4⋊C4C2212yes—
188C2×#376C2211yescharacteristic
189C22×#41C2311yescharacteristic
190C22×#41C2312yes—
191C22×#41C2311yescharacteristic
192C22×#41C2314yes—
193C23×Q8C2314yes—
194C23×Q8C2312yes—
195Q82—216no—
196#557—216no—
197#556—216no—
198#555—216no—
199#554—216no—
200#554—216no—
201#554—232no—
202#553—232no—
203D4×Q8—232no—
204D4×Q8—216no—
205#548—232no—
206#547—216no—
207#544—232no—
208#544—216no—
209#542—232no—
210#537—216no—
211#537—216no—
212#533—216no—
213#533—216no—
214#533—28no—
215#532—28no—
216#532—216no—
217#532—28no—
218C2×C4⋊Q8—216no—
219C2×C4⋊Q8D4116yescomplemented
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2318yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#126C2318yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#125C2318yes—
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2318yes—
246C2×#124C2318yes—
247C2×#123C2318yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2318yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2318yes—
262C2×#121C2314yes—
263C2×#121C2318yes—
264C2×#121C2314yes—
265C2×#121C2318yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2318yes—
273#520—216no—
274#520—216no—
275C4×#41—28no—
276C4×#41—28no—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2318yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2318yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2318yes—
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2311yescharacteristic
308C2×#117C2314yes—
309C2×#117C2314yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C42C2312yes—
321C22×C42C2312yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2314yes—
325C22×C42C2311yescharacteristic
326#400C2314yes—
327#400C2314yes—
328#400C2318yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2318yes—
334#400C2318yes—
335#399C2314yes—
336#399C2314yes—
337#399C2318yes—
338#398C2314yes—
339#398C2314yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2318yes—
350#397C2318yes—
351#397C2318yes—
352#396C2318yes—
353#396C2318yes—
354#396C2318yes—
355#396C2318yes—
356#395C2314yes—
357#395C2314yes—
358#395C2318yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#393C2314yes—
371#393C2314yes—
372#393C2318yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2318yes—
378#393C2318yes—
379#392C2314yes—
380#392C2314yes—
381#392C2318yes—
382#391C2314yes—
383#391C2314yes—
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2318yes—
389#391C2318yes—
390#391C2318yes—
391#391C2318yes—
392#391C2318yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2318yes—
398#390C2314yes—
399#390C2314yes—
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2318yes—
405#390C2312yes—
406#390C2312yes—
407#390C2318yes—
408#390C2312yes—
409#390C2312yes—
410#390C2318yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2318yes—
420#389C2318yes—
421#389C2318yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#386C2318yes—
453#386C2314yes—
454#386C2318yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2314yes—
467#386C2314yes—
468#386C2318yes—
469#386C2318yes—
470#385C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2318yes—
474#385C2314yes—
475#385C2314yes—
476#385C2314yes—
477#385C2314yes—
478#385C2318yes—
479#385C2318yes—
480#384C2311yescharacteristic
481#384C2311yescharacteristic
482#382C2312yes—
483#382C2312yes—
484#382C2311yescharacteristic
485#382C2311yescharacteristic
486#382C2312yes—
487#382C2312yes—
488#382C2318yes—
489#380C2318yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2318yes—
496#380C2318yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511#376C2311yescharacteristic
512#376C2311yescharacteristic
513#376C2311yescharacteristic
514#376C2311yescharacteristic
515#376C2312yes—
516#376C2312yes—
517C2×#95C2312yes—
518C2×#95C2312yes—
519C2×#95C2314yes—
520C2×#95C2312yes—
521C2×#95C2312yes—
522C2×#95C2314yes—
523C2×#41—216no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—24no—
530C2×#41—24no—
531C2×#41—28no—
532C2×#41—88no—
533C2×#41#4118yescomplemented
534C22×Q8—216no—
535C22×Q8—84no—
536C22×Q8—88no—
537C22×Q8C2×D4116yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2418yes—
544C22×Q8C2414yes—
545C22×Q8C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2411yescharacteristic
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2412yes—
553C22×D4C2418yes—
554C22×D4C2414yes—
555C22×D4C2412yes—
556C22×D4C2418yes—
557C23×C4C2414yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2418yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2414yes—
564C23×C4C2418yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C4⋊Q8—216no—
574C4⋊Q8—232no—
575C4⋊Q8—24no—
576C4⋊Q8—216no—
577C4⋊Q8—216no—
578C4⋊Q8—216no—
579C4⋊Q8—24no—
580C4⋊Q8—24no—
581C4⋊Q8—24no—
582C4⋊Q8C2×D4116yes—
583C4⋊Q8C2×D4116yes—
584C4⋊Q8C2×D4116yes—
585C4⋊Q8C2×D4116yes—
586#127—24no—
587#127—24no—
588#126—232no—
589#125—216no—
590#125—216no—
591#125—232no—
592#125—216no—
593#125—28no—
594#124—216no—
595#124—232no—
596#124—24no—
597#124—24no—
598#124—28no—
599#124—88no—
600#123—232no—
601C22⋊Q8—216no—
602C22⋊Q8—216no—
603C22⋊Q8—232no—
604C22⋊Q8—232no—
605C22⋊Q8—216no—
606C22⋊Q8—28no—
607C22⋊Q8—28no—
608C22⋊Q8—232no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—232no—
614C22⋊Q8—88no—
615#121—216no—
616#121—216no—
617#121—232no—
618#121—28no—
619#121—28no—
620#121—232no—
621#121—216no—
622#121—216no—
623#121—216no—
624#121—216no—
625#121—88no—
626C4×Q8—216no—
627C4×Q8—216no—
628C4×Q8—216no—
629C4×Q8—216no—
630C4×Q8—216no—
631C4×Q8—24no—
632C4×Q8—24no—
633C4×Q8—24no—
634C4×Q8—24no—
635C4×Q8—28no—
636C4×Q8—28no—
637C4×D4—28no—
638C4×D4—28no—
639C4×D4—28no—
640C4×D4—28no—
641C4×D4—232no—
642C4×D4—232no—
643C4×D4—216no—
644C4×D4—216no—
645C4×D4—216no—
646C4×D4—216no—
647C4×D4—24no—
648C4×D4—24no—
649C4×D4—24no—
650C4×D4—24no—
651C4×D4—28no—
652C4×D4—28no—
653C4×D4—88no—
654#117—24no—
655#117—24no—
656#117—28no—
657#117—216no—
658#117—216no—
659#117—216no—
660#117—28no—
661#117—28no—
662C2×C4⋊C4—28no—
663C2×C4⋊C4—216no—
664C2×C4⋊C4—216no—
665C2×C4⋊C4—216no—
666C2×C4⋊C4—84no—
667C2×C4⋊C4C2×D4116yes—
668C2×C4⋊C4C2×D4116yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C42—24no—
739C2×C42—24no—
740C2×C42—28no—
741C2×C42—28no—
742C2×C42—84no—
743C2×C42C2×D418yes—
744C2×C42C2412yes—
745C2×C42C2418yes—
746C2×C42C2412yes—
747C2×C42C2414yes—
748C2×C42C2418yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2412yes—
759C2×C42C2418yes—
760C2×C42C2418yes—
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770#95C2412yes—
771#95C2412yes—
772#95C2412yes—
773#95C2418yes—
774#95C2418yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2418yes—
786#95C2414yes—
787#95C2418yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800#95C2418yes—
801C24C2514yes—
802C24C2512yes—
803C24C2512yes—
804C24C2511yescharacteristic
805#41—232no—
806#41—416no—
807#41—432no—
808#41—832no—
809C2×Q8—22no—
810C2×Q8—24no—
811C2×Q8—22no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—216no—
815C2×Q8—24no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—48no—
821C2×Q8—44no—
822C2×Q8—48no—
823C2×Q8—44no—
824C2×Q8—48no—
825C2×Q8—48no—
826C2×Q8—816no—
827C2×Q8—832no—
828C2×Q8C22×D4116yes—
829C2×Q8C22×D4116yes—
830C2×Q8C2×#4114yes—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—216no—
841C2×D4—22no—
842C2×D4—24no—
843C2×D4—22no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—216no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—48no—
855C2×D4—44no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—48no—
859C2×D4—44no—
860C2×D4C2×#4118yes—
861C2×D4C2×#4114yes—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—28no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—28no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—24no—
877C22×C4—216no—
878C22×C4—216no—
879C22×C4—42no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—42no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—42no—
896C22×C4—44no—
897C22×C4C22×D414yes—
898C22×C4C22×D414yes—
899C22×C4C22×D4116yes—
900C22×C4C22×D414yes—
901C22×C4C2×#4118yes—
902C22×C4C2×#4114yes—
903C22×C42−1+414yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2518yes—
908C22×C4C2512yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2518yes—
922C22×C4C2512yes—
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—216no—
929C4⋊C4—216no—
930C4⋊C4—216no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—216no—
943C4⋊C4—216no—
944C4⋊C4—28no—
945C4⋊C4—216no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—216no—
951C4⋊C4—48no—
952C4⋊C4—48no—
953C4⋊C4—44no—
954C4⋊C4—48no—
955C4⋊C4—48no—
956C4⋊C4—44no—
957C4⋊C4C22×D4116yes—
958C4⋊C4C22×D4116yes—
959C4⋊C4C22×D4116yes—
960C4⋊C4C22×D4116yes—
961C22⋊C4—24no—
962C22⋊C4—28no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—216no—
966C22⋊C4—216no—
967C22⋊C4—216no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—216no—
973C22⋊C4—216no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—216no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—48no—
990C22⋊C4—44no—
991C22⋊C4—48no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—24no—
1000C42—216no—
1001C42—216no—
1002C42—28no—
1003C42—24no—
1004C42—22no—
1005C42—22no—
1006C42—24no—
1007C42—22no—
1008C42—22no—
1009C42—48no—
1010C42—48no—
1011C42C22×D414yes—
1012C42C22×D414yes—
1013C42C22×D414yes—
1014C42C22×D414yes—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—24no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—22no—
1025C23—24no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23C23×D412yes—
1034C23C22×#4114yes—
1035C23C22×#4112yes—
1036C23C2×2−1+412yes—
1037C23C2611yescharacteristic
1038Q8—28no—
1039Q8—416no—
1040Q8—416no—
1041Q8—48no—
1042Q8—48no—
1043Q8—48no—
1044Q8—44no—
1045Q8—816no—
1046D4—216no—
1047D4—28no—
1048D4—48no—
1049D4—48no—
1050D4—48no—
1051D4—416no—
1052D4—48no—
1053D4—44no—
1054D4—816no—
1055D4—816no—
1056D4—88no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—28no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—216no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—28no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—44no—
1102C2×C4—416no—
1103C2×C4—44no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—416no—
1111C2×C4—816no—
1112C2×C4—816no—
1113C2×C4—84no—
1114C2×C4—88no—
1115C2×C4#548116yes—
1116C2×C4C23×D412yes—
1117C2×C4C23×D412yes—
1118C2×C4C23×D412yes—
1119C2×C4C23×D412yes—
1120C2×C4C23×D4116yes—
1121C2×C4C23×D412yes—
1122C2×C4C23×D412yes—
1123C2×C4C22×#4114yes—
1124C2×C4C22×#4112yes—
1125C2×C4C22×#4112yes—
1126C2×C4C2×2−1+412yes—
1127C2×C4C2×2−1+412yes—
1128C22—22no—
1129C22—22no—
1130C22—24no—
1131C22—24no—
1132C22—28no—
1133C22—24no—
1134C22—42no—
1135C22—42no—
1136C22—44no—
1137C22—42no—
1138C22—44no—
1139C22—42no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—42no—
1148C22—44no—
1149C22C2×#54814yes—
1150C22C24×D411yescharacteristic
1151C22C23×#4111yescharacteristic
1152C22C22×2−1+411yescharacteristic
1153C22H(7,𝔽2)12yes—
1154C222−1+612yes—
1155C4—22no—
1156C4—22no—
1157C4—216no—
1158C4—22no—
1159C4—22no—
1160C4—24no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—42no—
1165C4—42no—
1166C4—44no—
1167C4—42no—
1168C4—48no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—44no—
1174C4C2×#54814yes—
1175C4C2×#54814yes—
1176C2—24no—
1177C2—44no—
1178C2—82no—
1179C2—84no—
1180C2C22×#54811yescharacteristic
1181C2#6284211yescharacteristic
1182C2#6284811yescharacteristic
1183C2#6285712yes—
1184C2#6287712yes—
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. C2×#3503C2semidirect
3. #45338C2semidirect
4. #45337C2semidirect
5. #45271C2semidirect
6. #45270C2semidirect
7. #45143C2semidirect
8. #45142C2semidirect
9. #44938C2semidirect
10. #44937C2semidirect
11. #39166C2semidirect
12. #39160C2semidirect
13. #37757C2semidirect
14. #37756C2semidirect
15. #37711C2semidirect
16. #37704C2semidirect
17. #35575C2semidirect
18. #35564C2semidirect
19. #35334C2semidirect
20. #35328C2semidirect
21. #35158C2semidirect
22. #34637C2semidirect
23. #34274C2semidirect
24. C2×#2331C2semidirect
25. #34070C2semidirect
219. C2×C4⋊Q8D4semidirect
533. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#35032
#453382
#453372
#452712
#452702
#451432
#451422
#449382
#449372
#391662
#391602
#377572
#377562
#377112
#377042
#355752
#355642
#353342
#353282
#351582
#346372
#342742
C2×#23312
#340702