Finite Group Databasebeta

← #8095590

Subgroups — #8095590

Order 512.

4690 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53105C214yesmaximal, complemented
2#53069C214yesmaximal, complemented
3#53024C214yesmaximal, complemented
4#53013C214yesmaximal, complemented
5#52350C218yesmaximal, complemented
6#45703C214yesmaximal, complemented
7#45662C214yesmaximal, complemented
8#45625C214yesmaximal, complemented
9#45586C218yesmaximal, complemented
10#45525C214yesmaximal, complemented
11#35649C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35628C211yesmaximal, characteristic, complemented
14#35627C211yesmaximal, characteristic, complemented
15#35621C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic
18#35308C211yesmaximal, characteristic, complemented
19#35307C211yesmaximal, characteristic, complemented
20#35280C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic, complemented
22#35153C211yesmaximal, characteristic, complemented
23C2×#2565C211yesmaximal, characteristic, complemented
24#34745C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2857C2214yes—
39#2857C2212yes—
40#2855C2214yes—
41#2854C2214yes—
42#2853C2214yes—
43#2850C2212yes—
44#2850C2212yes—
45#2850C2212yes—
46#2845C2218yes—
47#2839C2218yes—
48#2836C2218yes—
49#2836C2218yes—
50#2836C2218yes—
51#2829C2218yes—
52#2829C2218yes—
53#2827C2218yes—
54#2827C2218yes—
55#2814C2218yes—
56#2802C2218yes—
57#2798C2218yes—
58#2783C2218yes—
59#2783C2218yes—
60#2781C2218yes—
61#2779C2218yes—
62#2772C2218yes—
63#2768C2218yes—
64#2761C2218yes—
65#2755C2218yes—
66#2754C2218yes—
67#2747C2218yes—
68#2747C2218yes—
69#2743C2218yes—
70#2741C2218yes—
71#2740C2218yes—
72#2732C2218yes—
73#2706C2218yes—
74#2696C2218yes—
75#2687C2218yes—
76#2629C2214yes—
77#2625C2214yes—
78#2623C2214yes—
79#2621C2212yes—
80#2621C2212yes—
81#2620C2212yes—
82#2619C2212yes—
83#2618C2214yes—
84#2592C2214yes—
85#2591C2214yes—
86#2582C2214yes—
87#2579C2214yes—
88#2571C2214yes—
89#2570C2214yes—
90#2568C2214yes—
91#2565C2214yes—
92#2565C2214yes—
93#2565C2214yes—
94#2565C2214yes—
95#2547C2212yes—
96#2546C2212yes—
97#2545C2212yes—
98#2544C2212yes—
99#2543C2218yes—
100#2538C2214yes—
101#2536C2214yes—
102#2535C2214yes—
103#2509C2214yes—
104#2508C2214yes—
105#2505C2218yes—
106#2504C2214yes—
107#2502C2212yes—
108#2501C2212yes—
109#2500C2212yes—
110#2499C2212yes—
111#2492C2214yes—
112#2490C2214yes—
113#2490C2214yes—
114#2489C2214yes—
115#2489C2214yes—
116#2489C2214yes—
117#2488C2218yes—
118#2487C2214yes—
119#2454C2214yes—
120#2454C2212yes—
121#2453C2214yes—
122#2453C2212yes—
123#2452C2212yes—
124#2451C2212yes—
125#2450C2214yes—
126#2449C2214yes—
127#2448C2212yes—
128#2448C2214yes—
129#2447C2214yes—
130#2447C2212yes—
131#2446C2212yes—
132#2446C2214yes—
133#2446C2214yes—
134#2445C2212yes—
135#2444C2214yes—
136#2443C2218yes—
137#2443C2214yes—
138#2442C2214yes—
139#2441C2214yes—
140#2429C2214yes—
141#2429C2214yes—
142#2429C2214yes—
143#2427C2214yes—
144#2426C2214yes—
145#2426C2214yes—
146#2425C2218yes—
147#2425C2218yes—
148#2423C2214yes—
149#2423C2214yes—
150#2422C2214yes—
151#2421C2214yes—
152#2419C2218yes—
153#2417C2218yes—
154#2417C2214yes—
155#2415C2214yes—
156#2396C2214yes—
157#2395C2214yes—
158C2×#398C2214yes—
159#2378C2218yes—
160#2376C2218yes—
161#2317C2211yescharacteristic
162#2317C2211yescharacteristic
163#2316C2211yescharacteristic
164#2316C2211yescharacteristic
165#2311C2211yescharacteristic
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2310C2211yescharacteristic
170C4×C22⋊Q8C2214yes—
171C4×#123C2214yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#387C2214yes—
183C2×#384C2211yescharacteristic
184C2×#382C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191#537—44no—
192#537—44no—
193#536—44no—
194#536—44no—
195#536—44no—
196#533—44no—
197#532—44no—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×#127C2311yescharacteristic
204C2×#125—44no—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#124C2312yes—
209C2×#124C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×#123C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236#520—44no—
237C4×#41—44no—
238C4×#41—44no—
239C2×C4×Q8—44no—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2312yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2318yes—
286#400C2318yes—
287#399C2314yes—
288#399C2318yes—
289#399C2314yes—
290#399C2318yes—
291#399C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2314yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2314yes—
328#396C2318yes—
329#396C2318yes—
330#396C2314yes—
331#396C2318yes—
332#395C2314yes—
333#394C2314yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2314yes—
339#394C2318yes—
340#394C2318yes—
341#393C2318yes—
342#393C2314yes—
343#392C2318yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2312yes—
356#391C2312yes—
357#391C2318yes—
358#391C2318yes—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2314yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#390C2312yes—
369#390C2318yes—
370#390C2318yes—
371#390C2312yes—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2312yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2312yes—
391#389C2318yes—
392#389C2312yes—
393#389C2318yes—
394#389C2312yes—
395#389C2312yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2318yes—
410#388C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2312yes—
434#386C2312yes—
435#386C2312yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2312yes—
440#386C2312yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#385C2314yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2314yes—
449#385C2314yes—
450#385C2312yes—
451#385C2312yes—
452#385C2314yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#384C2314yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#382C2314yes—
462#382C2312yes—
463#382C2312yes—
464#382C2318yes—
465#382C2312yes—
466#382C2312yes—
467#382C2318yes—
468#382C2318yes—
469#381C2314yes—
470#381C2318yes—
471#381C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2318yes—
481#380C2318yes—
482#380C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C2×#95C2314yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C2×#95C2312yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C22×Q8—24no—
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8C2412yes—
517C22×Q8C2411yescharacteristic
518C22×Q8C2412yes—
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2414yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2414yes—
529C22×D4C2414yes—
530C22×D4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2411yescharacteristic
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2411yescharacteristic
546C4⋊Q8—44no—
547C4⋊Q8—42no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551#127—42no—
552#125—48no—
553#125—48no—
554#125—44no—
555#124—42no—
556#124—42no—
557#124—44no—
558#124—44no—
559#124—44no—
560#123—416no—
561#123—48no—
562#123—48no—
563#123—48no—
564#123—48no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—416no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576#121—44no—
577#121—44no—
578#121—44no—
579#121—44no—
580#121—48no—
581#121—48no—
582#121—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—44no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4—48no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—44no—
602#117—44no—
603#117—44no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C42—24no—
690C2×C42—24no—
691C2×C42—24no—
692C2×C42—44no—
693C2×C42—44no—
694C2×C42—44no—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750C24C2512yes—
751C24C2512yes—
752C24C2512yes—
753C24C2511yescharacteristic
754#41—416no—
755#41—416no—
756#41—416no—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—28no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—416no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—48no—
800C2×D4—48no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4H(5,𝔽2)14yes—
838C22×C4H(5,𝔽2)14yes—
839C22×C42−1+414yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—216no—
875C4⋊C4—24no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—44no—
951C42—44no—
952C42—48no—
953C42—48no—
954C42—44no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23C2×H(5,𝔽2)12yes—
973C23C2×H(5,𝔽2)12yes—
974C23C2×2−1+412yes—
975C23C2611yescharacteristic
976Q8—48no—
977Q8—48no—
978Q8—44no—
979Q8—44no—
980Q8—44no—
981Q8—88no—
982D4—48no—
983D4—48no—
984D4—48no—
985D4—44no—
986D4—44no—
987D4—44no—
988D4—88no—
989D4—164no—
990D4—164no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—48no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—88no—
1050C2×C4—84no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4—88no—
1055C2×C4—164no—
1056C2×C4#562116yes—
1057C2×C4C2×H(5,𝔽2)12yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4#58514yes—
1064C22—22no—
1065C22—22no—
1066C22—24no—
1067C22—24no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22C2×#56214yes—
1084C22C22×H(5,𝔽2)11yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C2×#58512yes—
1088C222−1+612yes—
1089C4—24no—
1090C4—42no—
1091C4—44no—
1092C4—44no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4C2×#56214yes—
1109C4C2×#56214yes—
1110C2—24no—
1111C2—82no—
1112C2—82no—
1113C2—82no—
1114C2C22×#56211yescharacteristic
1115C2#6283611yescharacteristic
1116C2#6288711yescharacteristic
1117C2#6292712yes—
1118C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35328C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53105C2semidirect
2. #53069C2semidirect
3. #53024C2semidirect
4. #53013C2semidirect
5. #52350C2semidirect
6. #45703C2semidirect
7. #45662C2semidirect
8. #45625C2semidirect
9. #45586C2semidirect
10. #45525C2semidirect
11. #35649C2semidirect
12. #35639C2semidirect
13. #35628C2semidirect
14. #35627C2semidirect
15. #35621C2semidirect
16. #35530C2semidirect
18. #35308C2semidirect
19. #35307C2semidirect
20. #35280C2semidirect
21. #35182C2semidirect
22. #35153C2semidirect
23. C2×#2565C2semidirect
24. #34745C2semidirect
25. #34744C2semidirect

Maximal subgroups

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

subgroupindex
#531052
#530692
#530242
#530132
#523502
#457032
#456622
#456252
#455862
#455252
#356492
#356392
#356282
#356272
#356212
#355302
#353282
#353082
#353072
#352802
#351822
#351532
C2×#25652
#347452
#347442