Finite Group Databasebeta

← #8095142

Subgroups — #8095142

Order 512.

4722 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53140C214yesmaximal, complemented
2#53070C214yesmaximal, complemented
3#52984C214yesmaximal, complemented
4#52975C214yesmaximal, complemented
5#52720C218yesmaximal, complemented
6#45734C218yesmaximal, complemented
7#45714C214yesmaximal, complemented
8#45711C214yesmaximal, complemented
9#45626C214yesmaximal, complemented
10#45619C214yesmaximal, complemented
11#35628C211yesmaximal, characteristic, complemented
12#35627C211yesmaximal, characteristic, complemented
13#35621C211yesmaximal, characteristic, complemented
14#35618C211yesmaximal, characteristic, complemented
15#35592C211yesmaximal, characteristic, complemented
16#35574C211yesmaximal, characteristic, complemented
17#35334C211yesmaximal, characteristic, complemented
18#35328C211yesmaximal, characteristic
19#35308C211yesmaximal, characteristic, complemented
20#35307C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic, complemented
22#35153C211yesmaximal, characteristic, complemented
23C2×#2568C211yesmaximal, 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×C4⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2857C2212yes—
39#2855C2214yes—
40#2854C2214yes—
41#2853C2214yes—
42#2851C2214yes—
43#2850C2212yes—
44#2850C2212yes—
45#2850C2212yes—
46#2839C2218yes—
47#2839C2218yes—
48#2837C2218yes—
49#2832C2218yes—
50#2831C2218yes—
51#2831C2218yes—
52#2831C2218yes—
53#2827C2218yes—
54#2826C2218yes—
55#2824C2218yes—
56#2806C2218yes—
57#2798C2218yes—
58#2798C2218yes—
59#2788C2218yes—
60#2781C2218yes—
61#2772C2218yes—
62#2755C2218yes—
63#2754C2218yes—
64#2754C2218yes—
65#2751C2218yes—
66#2750C2218yes—
67#2750C2218yes—
68#2744C2218yes—
69#2743C2218yes—
70#2739C2218yes—
71#2730C2218yes—
72#2710C2218yes—
73#2700C2218yes—
74#2692C2218yes—
75#2687C2218yes—
76#2628C2214yes—
77#2625C2214yes—
78#2623C2214yes—
79#2621C2212yes—
80#2621C2212yes—
81#2620C2212yes—
82#2619C2212yes—
83#2618C2214yes—
84#2592C2214yes—
85#2591C2214yes—
86#2581C2214yes—
87#2580C2214yes—
88#2579C2214yes—
89#2571C2214yes—
90#2570C2214yes—
91#2568C2214yes—
92#2568C2214yes—
93#2568C2214yes—
94#2568C2214yes—
95#2568C2214yes—
96#2564C2218yes—
97#2547C2212yes—
98#2546C2212yes—
99#2545C2212yes—
100#2544C2212yes—
101#2543C2218yes—
102#2536C2214yes—
103#2535C2214yes—
104#2509C2214yes—
105#2508C2214yes—
106#2505C2218yes—
107#2504C2212yes—
108#2503C2212yes—
109#2500C2212yes—
110#2499C2212yes—
111#2492C2214yes—
112#2492C2214yes—
113#2492C2214yes—
114#2491C2214yes—
115#2491C2214yes—
116#2489C2214yes—
117#2488C2218yes—
118#2454C2212yes—
119#2453C2212yes—
120#2452C2214yes—
121#2452C2212yes—
122#2451C2214yes—
123#2451C2212yes—
124#2450C2214yes—
125#2449C2214yes—
126#2448C2214yes—
127#2448C2212yes—
128#2447C2212yes—
129#2447C2214yes—
130#2446C2214yes—
131#2446C2214yes—
132#2446C2212yes—
133#2445C2212yes—
134#2444C2218yes—
135#2444C2214yes—
136#2443C2214yes—
137#2440C2214yes—
138#2439C2214yes—
139#2436C2214yes—
140#2429C2214yes—
141#2429C2214yes—
142#2429C2214yes—
143#2427C2214yes—
144#2426C2214yes—
145#2426C2214yes—
146#2425C2218yes—
147#2425C2218yes—
148#2423C2214yes—
149#2421C2214yes—
150#2421C2214yes—
151#2420C2214yes—
152#2419C2218yes—
153#2417C2214yes—
154#2415C2214yes—
155#2409C2214yes—
156#2396C2214yes—
157#2395C2214yes—
158C2×#400C2214yes—
159#2379C2218yes—
160#2378C2218yes—
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×#391C2214yes—
183C2×#382C2211yescharacteristic
184C2×#382C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2312yes—
192#537—44no—
193#537—44no—
194#536—44no—
195#536—44no—
196#536—44no—
197#533—44no—
198#532—44no—
199C2×C4⋊Q8—44no—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×#127C2311yescharacteristic
208C2×#125C2312yes—
209C2×#124C2312yes—
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2312yes—
213C2×#124C2318yes—
214C2×#124C2312yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237#520—44no—
238C4×#41—44no—
239C4×#41—44no—
240C2×C4×Q8—44no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2314yes—
290#400C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2314yes—
294#399C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2314yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2314yes—
318#396C2314yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2314yes—
324#396C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2314yes—
328#394C2314yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2314yes—
335#394C2318yes—
336#393C2318yes—
337#393C2314yes—
338#393C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#392C2318yes—
343#391C2314yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2318yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2318yes—
356#391C2314yes—
357#391C2312yes—
358#391C2318yes—
359#391C2318yes—
360#391C2318yes—
361#391C2314yes—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2318yes—
365#391C2318yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2311yescharacteristic
375#390C2318yes—
376#390C2311yescharacteristic
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#389C2312yes—
396#389C2312yes—
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#388C2318yes—
411#388C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2312yes—
436#386C2312yes—
437#386C2312yes—
438#386C2318yes—
439#386C2312yes—
440#386C2312yes—
441#386C2312yes—
442#386C2314yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#385C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2312yes—
452#385C2312yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#385C2314yes—
457#384C2312yes—
458#384C2312yes—
459#382C2314yes—
460#382C2314yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2312yes—
465#382C2318yes—
466#382C2312yes—
467#382C2312yes—
468#382C2318yes—
469#381C2314yes—
470#381C2318yes—
471#381C2318yes—
472#381C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C2×#95C2314yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
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×Q8—44no—
517C22×Q8—48no—
518C22×Q8C2412yes—
519C22×Q8C2411yescharacteristic
520C22×Q8C2412yes—
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2418yes—
524C22×Q8C2414yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C23×C4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2411yescharacteristic
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8—42no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556#127—42no—
557#125—44no—
558#124—42no—
559#124—42no—
560#124—44no—
561#124—44no—
562#124—44no—
563#124—416no—
564#123—48no—
565#123—48no—
566#123—48no—
567#123—48no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—416no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579#121—44no—
580#121—44no—
581#121—44no—
582#121—44no—
583#121—48no—
584#121—48no—
585#121—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—44no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—48no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—44no—
605#117—44no—
606#117—44no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C42—24no—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—44no—
691C2×C42—44no—
692C2×C42—44no—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2418yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
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—216no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—44no—
778C2×Q8—416no—
779C2×Q8—816no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—48no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—22no—
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—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—42no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4H(5,𝔽2)14yes—
842C22×C4H(5,𝔽2)14yes—
843C22×C42−1+414yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
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—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—44no—
952C42—44no—
953C42—48no—
954C42—44no—
955C42—48no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23C2×H(5,𝔽2)12yes—
974C23C2×H(5,𝔽2)12yes—
975C23C2×2−1+412yes—
976C23C2611yescharacteristic
977Q8—48no—
978Q8—48no—
979Q8—44no—
980Q8—44no—
981Q8—44no—
982Q8—816no—
983Q8—88no—
984D4—48no—
985D4—48no—
986D4—48no—
987D4—44no—
988D4—44no—
989D4—44no—
990D4—88no—
991D4—164no—
992D4—164no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—44no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—84no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—88no—
1056C2×C4—88no—
1057C2×C4—164no—
1058C2×C4#562116yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4#58514yes—
1066C22—22no—
1067C22—22no—
1068C22—24no—
1069C22—24no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22C2×#56214yes—
1086C22C22×H(5,𝔽2)11yescharacteristic
1087C22C22×H(5,𝔽2)11yescharacteristic
1088C22C22×2−1+411yescharacteristic
1089C22C2×#58512yes—
1090C222−1+612yes—
1091C4—24no—
1092C4—44no—
1093C4—44no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—44no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—44no—
1108C4—42no—
1109C4—44no—
1110C4C2×#56214yes—
1111C4C2×#56214yes—
1112C2—24no—
1113C2—82no—
1114C2—82no—
1115C2—82no—
1116C2C22×#56211yescharacteristic
1117C2#6282411yescharacteristic
1118C2#6288711yescharacteristic
1119C2#6295612yes—
1120C2#6296012yes—
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. #53140C2semidirect
2. #53070C2semidirect
3. #52984C2semidirect
4. #52975C2semidirect
5. #52720C2semidirect
6. #45734C2semidirect
7. #45714C2semidirect
8. #45711C2semidirect
9. #45626C2semidirect
10. #45619C2semidirect
11. #35628C2semidirect
12. #35627C2semidirect
13. #35621C2semidirect
14. #35618C2semidirect
15. #35592C2semidirect
16. #35574C2semidirect
17. #35334C2semidirect
19. #35308C2semidirect
20. #35307C2semidirect
21. #35182C2semidirect
22. #35153C2semidirect
23. C2×#2568C2semidirect
24. #34745C2semidirect
25. #34744C2semidirect

Maximal subgroups

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

subgroupindex
#531402
#530702
#529842
#529752
#527202
#457342
#457142
#457112
#456262
#456192
#356282
#356272
#356212
#356182
#355922
#355742
#353342
#353282
#353082
#353072
#351822
#351532
C2×#25682
#347452
#347442