Finite Group Databasebeta

← #8095551

Subgroups — #8095551

Order 512.

4706 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53141C214yesmaximal, complemented
2#53126C214yesmaximal, complemented
3#53037C214yesmaximal, complemented
4#53027C214yesmaximal, complemented
5#52348C218yesmaximal, complemented
6#46074C214yesmaximal, complemented
7#46057C214yesmaximal, complemented
8#45675C214yesmaximal, complemented
9#45589C218yesmaximal, complemented
10#45512C214yesmaximal, complemented
11#35677C211yesmaximal, characteristic
12#35674C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35626C211yesmaximal, characteristic, complemented
15#35617C211yesmaximal, characteristic
16#35529C211yesmaximal, characteristic, complemented
17#35338C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35312C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic
21#35182C211yesmaximal, characteristic, complemented
22#35154C211yesmaximal, characteristic, complemented
23C2×#2545C211yesmaximal, characteristic, complemented
24#34815C211yesmaximal, characteristic, complemented
25#34745C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×#518C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2862C2212yescomplemented
39#2861C2214yes—
40#2861C2212yescomplemented
41#2857C2212yescomplemented
42#2857C2212yescomplemented
43#2855C2214yes—
44#2854C2214yes—
45#2853C2214yes—
46#2841C2218yescomplemented
47#2837C2218yescomplemented
48#2836C2218yescomplemented
49#2836C2218yescomplemented
50#2832C2218yescomplemented
51#2831C2218yescomplemented
52#2831C2218yescomplemented
53#2830C2218yescomplemented
54#2827C2218yescomplemented
55#2814C2218yescomplemented
56#2800C2218yescomplemented
57#2798C2218yescomplemented
58#2788C2218yescomplemented
59#2786C2218yescomplemented
60#2783C2218yescomplemented
61#2781C2218yescomplemented
62#2772C2218yescomplemented
63#2768C2218yescomplemented
64#2754C2218yescomplemented
65#2751C2218yescomplemented
66#2750C2218yescomplemented
67#2747C2218yescomplemented
68#2744C2218yescomplemented
69#2741C2218yescomplemented
70#2740C2218yescomplemented
71#2739C2218yescomplemented
72#2704C2218yescomplemented
73#2694C2218yescomplemented
74#2692C2218yescomplemented
75#2687C2218yescomplemented
76#2642C2212yescomplemented
77#2640C2214yes—
78#2640C2212yescomplemented
79#2627C2214yes—
80#2624C2214yes—
81#2623C2214yes—
82#2621C2212yescomplemented
83#2621C2212yescomplemented
84#2592C2214yes—
85#2592C2214yes—
86#2582C2214yescomplemented
87#2581C2214yescomplemented
88#2566C2212yes—
89#2566C2212yes—
90#2563C2212yes—
91#2561C2218yes—
92#2548C2214yes—
93#2547C2212yes—
94#2547C2212yes—
95#2547C2214yescomplemented
96#2546C2214yescomplemented
97#2545C2214yes—
98#2545C2214yes—
99#2545C2214yes—
100#2545C2214yes—
101#2545C2214yes—
102#2544C2212yes—
103#2544C2212yes—
104#2542C2212yes—
105#2509C2212yescomplemented
106#2508C2212yescomplemented
107#2507C2212yescomplemented
108#2506C2212yescomplemented
109#2505C2214yes—
110#2492C2214yescomplemented
111#2489C2214yescomplemented
112#2488C2218yes—
113#2486C2218yes—
114#2484C2218yes—
115#2483C2214yes—
116#2483C2214yes—
117#2473C2214yes—
118#2454C2214yes—
119#2454C2212yescomplemented
120#2453C2214yescomplemented
121#2453C2214yescomplemented
122#2453C2214yescomplemented
123#2453C2212yescomplemented
124#2452C2214yes—
125#2452C2212yescomplemented
126#2451C2214yescomplemented
127#2451C2212yescomplemented
128#2451C2214yescomplemented
129#2451C2214yescomplemented
130#2450C2214yes—
131#2449C2214yes—
132#2448C2214yes—
133#2448C2214yescomplemented
134#2447C2214yes—
135#2447C2214yes—
136#2447C2214yes—
137#2447C2214yes—
138#2446C2214yescomplemented
139#2446C2214yescomplemented
140#2446C2214yescomplemented
141#2446C2214yescomplemented
142#2446C2214yescomplemented
143#2445C2214yes—
144#2438C2218yes—
145#2437C2218yes—
146#2427C2214yes—
147#2427C2214yes—
148#2426C2214yes—
149#2426C2214yes—
150#2423C2214yescomplemented
151#2421C2214yescomplemented
152#2418C2218yes—
153#2412C2218yes—
154#2411C2214yes—
155#2411C2214yes—
156#2402C2214yescomplemented
157#2396C2214yescomplemented
158C2×#396C2214yes—
159#2378C2218yescomplemented
160#2376C2218yescomplemented
161#2317C2211yescharacteristic
162#2316C2211yescharacteristic
163#2311C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2211yescharacteristic
167#2310C2211yescharacteristic
168#2310C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic
171C4×#125C2214yescomplemented
172C4×C22⋊Q8C2214yescomplemented
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#390C2211yescharacteristic
183C2×#388C2214yes—
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191#544—44no—
192#536—44no—
193#536—44no—
194#535—44no—
195#533—44no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2312yes—
205C2×#127C2312yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#124—44no—
211C2×#124—44no—
212C2×#124C2314yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×#123C2318yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×#121C2314yes—
232C2×#120C2314yes—
233#519—44no—
234#518—44no—
235C4×#41—44no—
236C2×C4×Q8—44no—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2314yes—
266C22×C22⋊C4C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271C22×C42C2312yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2314yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2314yes—
302#398C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2314yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2314yes—
326#395C2318yes—
327#395C2314yes—
328#395C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2314yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2312yes—
352#391C2312yes—
353#391C2314yes—
354#391C2312yes—
355#391C2318yes—
356#391C2318yes—
357#391C2318yes—
358#391C2314yes—
359#391C2312yes—
360#391C2311yescharacteristic
361#391C2312yes—
362#391C2311yescharacteristic
363#391C2312yes—
364#391C2314yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2312yes—
372#390C2312yes—
373#390C2318yes—
374#390C2311yescharacteristic
375#390C2318yes—
376#390C2311yescharacteristic
377#390C2314yes—
378#390C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2312yes—
387#389C2312yes—
388#389C2318yes—
389#389C2312yes—
390#389C2318yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2314yes—
432#387C2318yes—
433#386C2314yes—
434#386C2318yes—
435#386C2312yes—
436#386C2318yes—
437#386C2312yes—
438#386C2318yes—
439#386C2314yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2312yes—
445#385C2312yes—
446#385C2312yes—
447#385C2312yes—
448#385C2312yes—
449#385C2312yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2311yescharacteristic
459#382C2314yes—
460#382C2311yescharacteristic
461#382C2312yes—
462#382C2311yescharacteristic
463#382C2318yes—
464#381C2314yes—
465#381C2314yes—
466#381C2314yes—
467#381C2314yes—
468#381C2314yes—
469#381C2318yes—
470#381C2318yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477#380C2314yes—
478#380C2318yes—
479#380C2314yes—
480#379C2314yes—
481#379C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500#376C2312yes—
501C2×#95C2314yes—
502C2×#95C2312yes—
503C43C2312yes—
504C25C2412yes—
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×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4C2412yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2411yescharacteristic
528C22×D4C2418yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2411yescharacteristic
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546C4⋊Q8—48no—
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549#127—44no—
550#125—44no—
551#125—44no—
552#125—44no—
553#125—48no—
554#124—48no—
555#124—48no—
556#124—48no—
557#124—44no—
558#124—44no—
559#124—44no—
560#124—44no—
561#124—44no—
562#123—416no—
563#123—48no—
564#123—48no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—416no—
568C22⋊Q8—48no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573#121—48no—
574#120—48no—
575C4×Q8—48no—
576C4×Q8—48no—
577C4×Q8—48no—
578C4×Q8—44no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—48no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—44no—
595#117—48no—
596C2×C4⋊C4—24no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—48no—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C22⋊C4—48no—
648C2×C22⋊C4—48no—
649C2×C22⋊C4—44no—
650C2×C22⋊C4—44no—
651C2×C22⋊C4—48no—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C42—24no—
683C2×C42—24no—
684C2×C42—24no—
685C2×C42—44no—
686C2×C42—44no—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2418yes—
712#95C2418yes—
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#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746C24—24no—
747C24—24no—
748C24—24no—
749C24—44no—
750C24—44no—
751C24C2514yes—
752C24C2512yes—
753C24C2511yescharacteristic
754#41—416no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—48no—
775C2×Q8—416no—
776C2×Q8—416no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—416no—
793C22×C4—22no—
794C22×C4—22no—
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—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4H(5,𝔽2)14yes—
822C22×C4H(5,𝔽2)14yes—
823C22×C42−1+414yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—216no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C42—22no—
924C42—22no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—22no—
930C42—22no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—44no—
939C42—48no—
940C42—44no—
941C42—48no—
942C42—44no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—28no—
952C23—24no—
953C23—24no—
954C23—28no—
955C23—48no—
956C23—84no—
957C23—84no—
958C23—88no—
959C23—88no—
960C23C2×H(5,𝔽2)12yes—
961C23C2×H(5,𝔽2)12yes—
962C23C2×2−1+412yes—
963C23C2611yescharacteristic
964Q8—48no—
965Q8—48no—
966Q8—48no—
967Q8—48no—
968Q8—44no—
969Q8—88no—
970Q8—164no—
971D4—48no—
972D4—48no—
973D4—48no—
974D4—44no—
975D4—168no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—48no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—48no—
1034C2×C4—88no—
1035C2×C4—84no—
1036C2×C4—84no—
1037C2×C4—164no—
1038C2×C4—164no—
1039C2×C4#562116yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4#58514yes—
1047C22—22no—
1048C22—22no—
1049C22—24no—
1050C22—24no—
1051C22—44no—
1052C22—42no—
1053C22—44no—
1054C22—42no—
1055C22—44no—
1056C22—48no—
1057C22—42no—
1058C22—44no—
1059C22—44no—
1060C22—48no—
1061C22—168no—
1062C22C2×#56214yes—
1063C22C22×H(5,𝔽2)11yescharacteristic
1064C22C22×H(5,𝔽2)11yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C2×#58512yes—
1067C222−1+612yes—
1068C4—24no—
1069C4—42no—
1070C4—44no—
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—42no—
1078C4—44no—
1079C4—42no—
1080C4—44no—
1081C4—44no—
1082C4—42no—
1083C4—42no—
1084C4—44no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4C2×#56214yes—
1089C4C2×#56214yes—
1090C2—24no—
1091C2—82no—
1092C2—84no—
1093C2C22×#56211yescharacteristic
1094C2#6283611yescharacteristic
1095C2#6288711yescharacteristic
1096C2#6293212yes—
1097C2#6295412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
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. #53126C2semidirect
3. #53037C2semidirect
4. #53027C2semidirect
5. #52348C2semidirect
6. #46074C2semidirect
7. #46057C2semidirect
8. #45675C2semidirect
9. #45589C2semidirect
10. #45512C2semidirect
12. #35674C2semidirect
13. #35662C2semidirect
14. #35626C2semidirect
16. #35529C2semidirect
17. #35338C2semidirect
18. #35316C2semidirect
19. #35312C2semidirect
21. #35182C2semidirect
22. #35154C2semidirect
23. C2×#2545C2semidirect
24. #34815C2semidirect
25. #34745C2semidirect
38. #2862C22semidirect
40. #2861C22semidirect
41. #2857C22semidirect
42. #2857C22semidirect
46. #2841C22semidirect
47. #2837C22semidirect
48. #2836C22semidirect
49. #2836C22semidirect
50. #2832C22semidirect
51. #2831C22semidirect
52. #2831C22semidirect
53. #2830C22semidirect
54. #2827C22semidirect
55. #2814C22semidirect
56. #2800C22semidirect
57. #2798C22semidirect
58. #2788C22semidirect
59. #2786C22semidirect
60. #2783C22semidirect
61. #2781C22semidirect
62. #2772C22semidirect
63. #2768C22semidirect
64. #2754C22semidirect
65. #2751C22semidirect
66. #2750C22semidirect
67. #2747C22semidirect
68. #2744C22semidirect
69. #2741C22semidirect
70. #2740C22semidirect
71. #2739C22semidirect
72. #2704C22semidirect
73. #2694C22semidirect
74. #2692C22semidirect
75. #2687C22semidirect
76. #2642C22semidirect
78. #2640C22semidirect
82. #2621C22semidirect
83. #2621C22semidirect
86. #2582C22semidirect
87. #2581C22semidirect
95. #2547C22semidirect
96. #2546C22semidirect
105. #2509C22semidirect
106. #2508C22semidirect
107. #2507C22semidirect
108. #2506C22semidirect
110. #2492C22semidirect
111. #2489C22semidirect
119. #2454C22semidirect
120. #2453C22semidirect
121. #2453C22semidirect
122. #2453C22semidirect
123. #2453C22semidirect
125. #2452C22semidirect
126. #2451C22semidirect
127. #2451C22semidirect
128. #2451C22semidirect
129. #2451C22semidirect
133. #2448C22semidirect
138. #2446C22semidirect
139. #2446C22semidirect
140. #2446C22semidirect
141. #2446C22semidirect
142. #2446C22semidirect
150. #2423C22semidirect
151. #2421C22semidirect
156. #2402C22semidirect
157. #2396C22semidirect
159. #2378C22semidirect
160. #2376C22semidirect
171. C4×#125C22semidirect
172. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#531412
#531262
#530372
#530272
#523482
#460742
#460572
#456752
#455892
#455122
#356772
#356742
#356622
#356262
#356172
#355292
#353382
#353162
#353122
#352542
#351822
#351542
C2×#25452
#348152
#347452