Finite Group Databasebeta

← #8093607

Subgroups — #8093607

Order 512.

4506 conjugacy classes of subgroups.

The subgroup lattice has 1093 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53141C214yesmaximal, complemented
2#53140C214yesmaximal, complemented
3#53070C214yesmaximal, complemented
4#53050C214yesmaximal, complemented
5#53027C214yesmaximal, complemented
6#53024C214yesmaximal, complemented
7#53013C214yesmaximal, complemented
8#53010C214yesmaximal, complemented
9#52722C218yesmaximal, complemented
10#52719C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35672C211yesmaximal, characteristic, complemented
13#35668C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic, complemented
15#35662C211yesmaximal, characteristic, complemented
16#35661C211yesmaximal, characteristic
17#35644C211yesmaximal, characteristic, complemented
18#35633C211yesmaximal, characteristic
19#35628C211yesmaximal, characteristic, complemented
20#35627C211yesmaximal, characteristic, complemented
21#35620C211yesmaximal, characteristic, complemented
22#35619C211yesmaximal, characteristic, complemented
23#34635C211yesmaximal, characteristic
24#34634C211yesmaximal, characteristic, complemented
25C2×#2621C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2845C2218yescomplemented
39#2841C2218yescomplemented
40#2839C2218yescomplemented
41#2839C2218yescomplemented
42#2839C2218yescomplemented
43#2837C2218yes—
44#2836C2218yes—
45#2836C2218yes—
46#2836C2218yescomplemented
47#2832C2218yes—
48#2831C2218yes—
49#2831C2218yes—
50#2831C2218yescomplemented
51#2831C2218yescomplemented
52#2830C2218yes—
53#2827C2218yes—
54#2806C2218yescomplemented
55#2802C2218yescomplemented
56#2800C2218yes—
57#2798C2218yes—
58#2783C2218yes—
59#2781C2218yes—
60#2772C2218yes—
61#2768C2218yescomplemented
62#2755C2218yescomplemented
63#2755C2218yescomplemented
64#2754C2218yes—
65#2754C2218yescomplemented
66#2751C2218yes—
67#2747C2218yescomplemented
68#2744C2218yescomplemented
69#2740C2218yes—
70#2629C2212yes—
71#2629C2212yes—
72#2628C2212yes—
73#2628C2212yes—
74#2627C2214yes—
75#2626C2214yes—
76#2625C2212yes—
77#2625C2212yes—
78#2624C2212yes—
79#2624C2212yes—
80#2623C2214yes—
81#2622C2214yes—
82#2621C2214yes—
83#2621C2214yes—
84#2621C2214yes—
85#2621C2214yes—
86#2592C2214yescomplemented
87#2582C2214yescomplemented
88#2581C2214yescomplemented
89#2571C2214yescomplemented
90#2570C2214yescomplemented
91#2568C2214yescomplemented
92#2568C2212yescomplemented
93#2568C2212yescomplemented
94#2567C2212yescomplemented
95#2566C2212yescomplemented
96#2565C2212yescomplemented
97#2565C2212yescomplemented
98#2565C2212yescomplemented
99#2563C2212yescomplemented
100#2561C2214yes—
101#2546C2212yescomplemented
102#2546C2212yescomplemented
103#2545C2212yescomplemented
104#2545C2212yescomplemented
105#2538C2214yes—
106#2536C2214yes—
107#2534C2214yes—
108#2509C2214yescomplemented
109#2508C2214yescomplemented
110#2505C2218yes—
111#2503C2214yes—
112#2503C2212yescomplemented
113#2502C2212yescomplemented
114#2499C2212yescomplemented
115#2499C2212yescomplemented
116#2492C2214yes—
117#2492C2214yes—
118#2492C2214yescomplemented
119#2489C2214yes—
120#2489C2214yes—
121#2489C2214yescomplemented
122#2488C2218yes—
123#2486C2214yes—
124#2484C2214yes—
125#2484C2218yes—
126#2482C2214yes—
127#2453C2214yescomplemented
128#2453C2214yescomplemented
129#2451C2214yescomplemented
130#2451C2214yescomplemented
131#2450C2218yes—
132#2447C2214yescomplemented
133#2446C2214yescomplemented
134#2446C2214yescomplemented
135#2446C2214yescomplemented
136#2446C2214yescomplemented
137#2446C2214yescomplemented
138#2442C2214yescomplemented
139#2439C2214yescomplemented
140#2438C2218yes—
141#2438C2218yes—
142#2429C2214yes—
143#2429C2214yes—
144#2429C2214yescomplemented
145#2429C2214yescomplemented
146#2427C2214yes—
147#2426C2214yes—
148#2423C2214yes—
149#2423C2214yes—
150#2421C2214yes—
151#2421C2214yes—
152#2419C2218yes—
153#2417C2214yes—
154#2415C2214yes—
155#2413C2214yes—
156#2413C2218yes—
157#2411C2214yes—
158#2396C2214yes—
159#2396C2214yes—
160#2395C2214yes—
161#2395C2214yes—
162C2×#398C2214yes—
163C2×#397C2214yes—
164#2317C2211yescharacteristic
165#2317C2211yescharacteristic
166#2317C2211yescharacteristic
167#2316C2211yescharacteristic
168#2311C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2211yescharacteristic
171#2310C2211yescharacteristic
172#2310C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2211yescharacteristic
181#2285C2211yescharacteristic
182C2×#382C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191#544—44no—
192#536—44no—
193#536—44no—
194#533—44no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209#525—44no—
210C2×#123C2312yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×C22⋊Q8—44no—
214C2×C22⋊Q8—44no—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×#121C2312yes—
226C2×#120C2312yes—
227#520—44no—
228#519—44no—
229#519—44no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×#117—44no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#399C2318yes—
287#399C2314yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2314yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2314yes—
311#398C2314yes—
312#398C2318yes—
313#398C2314yes—
314#398C2314yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#397C2314yes—
323#397C2318yes—
324#397C2318yes—
325#397C2314yes—
326#397C2314yes—
327#397C2318yes—
328#397C2318yes—
329#397C2314yes—
330#397C2314yes—
331#396C2318yes—
332#396C2314yes—
333#396C2318yes—
334#396C2314yes—
335#396C2318yes—
336#396C2318yes—
337#396C2314yes—
338#396C2318yes—
339#396C2318yes—
340#396C2314yes—
341#395C2318yes—
342#395C2318yes—
343#395C2314yes—
344#395C2314yes—
345#394C2314yes—
346#394C2318yes—
347#394C2314yes—
348#394C2318yes—
349#394C2314yes—
350#394C2314yes—
351#393C2318yes—
352#393C2318yes—
353#393C2314yes—
354#393C2318yes—
355#393C2314yes—
356#391C2312yes—
357#391C2311yescharacteristic
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2312yes—
371#391C2312yes—
372#391C2311yescharacteristic
373#391C2318yes—
374#391C2318yes—
375#391C2318yes—
376#391C2314yes—
377#391C2318yes—
378#391C2318yes—
379#391C2314yes—
380#391C2312yes—
381#391C2312yes—
382#390C2311yescharacteristic
383#390C2312yes—
384#390C2311yescharacteristic
385#390C2318yes—
386#390C2312yes—
387#389C2318yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2312yes—
399#389C2312yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#386C2314yes—
434#386C2318yes—
435#386C2314yes—
436#386C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#384C2311yescharacteristic
447#384C2312yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2312yes—
451#382C2312yes—
452#382C2312yes—
453#382C2311yescharacteristic
454#382C2312yes—
455#382C2312yes—
456#382C2311yescharacteristic
457#382C2318yes—
458#382C2312yes—
459#382C2314yes—
460#382C2318yes—
461#382C2318yes—
462#381C2314yes—
463#381C2314yes—
464#381C2314yes—
465#381C2314yes—
466#381C2318yes—
467#381C2312yes—
468#381C2312yes—
469#381C2312yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#379C2312yes—
482#379C2312yes—
483#379C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2314yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2411yescharacteristic
519C22×Q8C2414yes—
520C22×Q8C2414yes—
521C22×D4C2412yes—
522C22×D4C2411yescharacteristic
523C22×D4C2414yes—
524C23×C4—24no—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C23×C4C2411yescharacteristic
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547#125—44no—
548#125—44no—
549#125—44no—
550#124—44no—
551#124—44no—
552#123—44no—
553#123—48no—
554#123—48no—
555C22⋊Q8—48no—
556C22⋊Q8—48no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560C22⋊Q8—48no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564C22⋊Q8—48no—
565#121—44no—
566#120—44no—
567C4×Q8—48no—
568C4×Q8—48no—
569C4×Q8—48no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—44no—
574C4×Q8—44no—
575C4×D4—44no—
576C4×D4—48no—
577C4×D4—48no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—24no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—44no—
586#117—44no—
587#117—44no—
588#117—44no—
589#117—48no—
590#117—48no—
591#117—44no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—48no—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C22⋊C4—44no—
650C2×C22⋊C4—44no—
651C2×C22⋊C4—44no—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C42—24no—
683C2×C42—24no—
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2412yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—42no—
746C24—42no—
747C24C2512yes—
748C24C2512yes—
749C24C2511yescharacteristic
750#41—416no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—48no—
771C2×Q8—416no—
772C2×Q8—416no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—44no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—416no—
813C22×C4H(5,𝔽2)14yes—
814C22×C4H(5,𝔽2)14yes—
815C22×C42−1+414yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C42—24no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—24no—
923C42—22no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—48no—
932C42—44no—
933C42—44no—
934C42—44no—
935C42—48no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—44no—
951C23—44no—
952C23—44no—
953C23—84no—
954C23—84no—
955C23C2×H(5,𝔽2)12yes—
956C23C2×H(5,𝔽2)12yes—
957C23C2×2−1+412yes—
958C23C2611yescharacteristic
959Q8—48no—
960Q8—48no—
961Q8—48no—
962Q8—48no—
963Q8—44no—
964Q8—88no—
965Q8—164no—
966D4—48no—
967D4—44no—
968D4—88no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—48no—
1022C2×C4—44no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—48no—
1028C2×C4—84no—
1029C2×C4—84no—
1030C2×C4—84no—
1031C2×C4—164no—
1032C2×C4#562116yes—
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4C2×H(5,𝔽2)12yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×2−1+412yes—
1038C2×C4C2×2−1+412yes—
1039C22—24no—
1040C22—22no—
1041C22—22no—
1042C22—24no—
1043C22—42no—
1044C22—44no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—44no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—88no—
1056C22C2×#56214yes—
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22C22×H(5,𝔽2)11yescharacteristic
1059C22C22×2−1+411yescharacteristic
1060C222−1+612yes—
1061C222−1+612yes—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4—42no—
1066C4—44no—
1067C4—44no—
1068C4—44no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—44no—
1073C4—44no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—44no—
1078C4—42no—
1079C4—42no—
1080C4—44no—
1081C4—44no—
1082C4C2×#56214yes—
1083C4C2×#56214yes—
1084C2—24no—
1085C2—82no—
1086C2—82no—
1087C2C22×#56211yescharacteristic
1088C2#6288612yes—
1089C2#6288711yescharacteristic
1090C2#6288711yescharacteristic
1091C2#6288912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53141C2semidirect
2. #53140C2semidirect
3. #53070C2semidirect
4. #53050C2semidirect
5. #53027C2semidirect
6. #53024C2semidirect
7. #53013C2semidirect
8. #53010C2semidirect
9. #52722C2semidirect
10. #52719C2semidirect
11. #35674C2semidirect
12. #35672C2semidirect
13. #35668C2semidirect
14. #35667C2semidirect
15. #35662C2semidirect
17. #35644C2semidirect
19. #35628C2semidirect
20. #35627C2semidirect
21. #35620C2semidirect
22. #35619C2semidirect
24. #34634C2semidirect
25. C2×#2621C2semidirect
38. #2845C22semidirect
39. #2841C22semidirect
40. #2839C22semidirect
41. #2839C22semidirect
42. #2839C22semidirect
46. #2836C22semidirect
50. #2831C22semidirect
51. #2831C22semidirect
54. #2806C22semidirect
55. #2802C22semidirect
61. #2768C22semidirect
62. #2755C22semidirect
63. #2755C22semidirect
65. #2754C22semidirect
67. #2747C22semidirect
68. #2744C22semidirect
86. #2592C22semidirect
87. #2582C22semidirect
88. #2581C22semidirect
89. #2571C22semidirect
90. #2570C22semidirect
91. #2568C22semidirect
92. #2568C22semidirect
93. #2568C22semidirect
94. #2567C22semidirect
95. #2566C22semidirect
96. #2565C22semidirect
97. #2565C22semidirect
98. #2565C22semidirect
99. #2563C22semidirect
101. #2546C22semidirect
102. #2546C22semidirect
103. #2545C22semidirect
104. #2545C22semidirect
108. #2509C22semidirect
109. #2508C22semidirect
112. #2503C22semidirect
113. #2502C22semidirect
114. #2499C22semidirect
115. #2499C22semidirect
118. #2492C22semidirect
121. #2489C22semidirect
127. #2453C22semidirect
128. #2453C22semidirect
129. #2451C22semidirect
130. #2451C22semidirect
132. #2447C22semidirect
133. #2446C22semidirect
134. #2446C22semidirect
135. #2446C22semidirect
136. #2446C22semidirect
137. #2446C22semidirect
138. #2442C22semidirect
139. #2439C22semidirect
144. #2429C22semidirect
145. #2429C22semidirect

Maximal subgroups

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

subgroupindex
#531412
#531402
#530702
#530502
#530272
#530242
#530132
#530102
#527222
#527192
#356742
#356722
#356682
#356672
#356622
#356612
#356442
#356332
#356282
#356272
#356202
#356192
#346352
#346342
C2×#26212