Finite Group Databasebeta

← #8095363

Subgroups — #8095363

Order 512.

4558 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53146C214yesmaximal, complemented
2#53140C214yesmaximal, complemented
3#53037C214yesmaximal, complemented
4#53013C214yesmaximal, complemented
5#52722C218yesmaximal, complemented
6#46057C214yesmaximal, complemented
7#46007C214yesmaximal, complemented
8#45752C218yesmaximal, complemented
9#45634C214yesmaximal, complemented
10#45500C214yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35674C211yesmaximal, characteristic, complemented
13#35668C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic
15#35667C211yesmaximal, characteristic
16#35662C211yesmaximal, characteristic, complemented
17#35320C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic
19#35312C211yesmaximal, characteristic
20#35307C211yesmaximal, characteristic
21#35182C211yesmaximal, characteristic
22#35154C211yesmaximal, characteristic, complemented
23C2×#2546C211yesmaximal, characteristic, complemented
24#34815C211yesmaximal, characteristic, complemented
25#34745C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2862C2212yes—
39#2862C2214yes—
40#2861C2212yes—
41#2857C2212yes—
42#2857C2212yes—
43#2855C2214yes—
44#2855C2214yes—
45#2853C2214yes—
46#2845C2218yes—
47#2841C2218yes—
48#2839C2218yes—
49#2839C2218yes—
50#2839C2218yes—
51#2839C2218yes—
52#2836C2218yes—
53#2836C2218yes—
54#2831C2218yes—
55#2831C2218yes—
56#2806C2218yes—
57#2806C2218yes—
58#2802C2218yes—
59#2802C2218yes—
60#2802C2218yes—
61#2802C2218yes—
62#2798C2218yes—
63#2788C2218yes—
64#2783C2218yes—
65#2772C2218yes—
66#2768C2218yes—
67#2755C2218yes—
68#2755C2218yes—
69#2755C2218yes—
70#2755C2218yes—
71#2754C2218yes—
72#2747C2218yes—
73#2744C2218yes—
74#2739C2218yes—
75#2704C2218yes—
76#2642C2214yes—
77#2642C2212yes—
78#2640C2212yes—
79#2627C2214yes—
80#2625C2214yes—
81#2623C2214yes—
82#2621C2212yes—
83#2621C2212yes—
84#2582C2214yes—
85#2581C2214yes—
86#2568C2214yes—
87#2568C2212yes—
88#2568C2214yes—
89#2567C2212yes—
90#2565C2212yes—
91#2565C2212yes—
92#2547C2214yes—
93#2546C2214yes—
94#2546C2214yes—
95#2546C2214yes—
96#2546C2212yes—
97#2546C2214yes—
98#2546C2212yes—
99#2546C2214yes—
100#2546C2214yes—
101#2545C2212yes—
102#2545C2214yes—
103#2545C2212yes—
104#2509C2212yes—
105#2508C2212yes—
106#2507C2212yes—
107#2506C2212yes—
108#2505C2214yes—
109#2503C2218yes—
110#2492C2214yes—
111#2489C2214yes—
112#2488C2218yes—
113#2486C2218yes—
114#2484C2214yes—
115#2484C2218yes—
116#2484C2214yes—
117#2473C2214yes—
118#2454C2212yes—
119#2453C2214yes—
120#2453C2214yes—
121#2453C2214yes—
122#2453C2214yes—
123#2453C2212yes—
124#2452C2212yes—
125#2451C2214yes—
126#2451C2214yes—
127#2451C2214yes—
128#2451C2214yes—
129#2451C2212yes—
130#2450C2214yes—
131#2449C2214yes—
132#2448C2214yes—
133#2447C2214yes—
134#2446C2214yes—
135#2446C2214yes—
136#2446C2214yes—
137#2446C2214yes—
138#2446C2214yes—
139#2446C2214yes—
140#2446C2214yes—
141#2446C2214yes—
142#2446C2214yes—
143#2446C2214yes—
144#2438C2218yes—
145#2438C2218yes—
146#2429C2214yes—
147#2429C2214yes—
148#2429C2214yes—
149#2429C2214yes—
150#2423C2214yes—
151#2421C2214yes—
152#2419C2218yes—
153#2413C2214yes—
154#2413C2218yes—
155#2413C2214yes—
156#2402C2214yes—
157#2396C2214yes—
158C2×#398C2214yes—
159#2382C2218yes—
160#2378C2218yes—
161#2317C2211yescharacteristic
162#2316C2211yescharacteristic
163#2311C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2211yescharacteristic
167#2310C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2211yescharacteristic
171C4×#125C2214yes—
172C4×C22⋊Q8C2214yes—
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#391C2211yescharacteristic
183C2×#389C2214yes—
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191#544—44no—
192#536—44no—
193#536—44no—
194#536—44no—
195#533—44no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8—44no—
198C2×C4⋊Q8—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231#519—44no—
232#519—44no—
233C4×#41—44no—
234C2×C4×Q8—44no—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2312yes—
268C22×C42C2312yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2318yes—
289#399C2314yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2314yes—
314#398C2314yes—
315#398C2318yes—
316#398C2318yes—
317#398C2314yes—
318#398C2314yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#396C2314yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2314yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2314yes—
335#393C2314yes—
336#393C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#391C2314yes—
357#391C2312yes—
358#391C2312yes—
359#391C2318yes—
360#391C2318yes—
361#391C2318yes—
362#391C2314yes—
363#391C2318yes—
364#391C2318yes—
365#391C2312yes—
366#391C2311yescharacteristic
367#391C2318yes—
368#391C2312yes—
369#391C2311yescharacteristic
370#391C2312yes—
371#391C2314yes—
372#391C2314yes—
373#390C2312yes—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2318yes—
385#389C2312yes—
386#389C2312yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2312yes—
391#389C2318yes—
392#389C2318yes—
393#389C2312yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2318yes—
407#389C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2314yes—
438#387C2318yes—
439#387C2318yes—
440#386C2314yes—
441#386C2312yes—
442#386C2312yes—
443#386C2314yes—
444#385C2314yes—
445#385C2312yes—
446#385C2312yes—
447#385C2312yes—
448#385C2318yes—
449#385C2312yes—
450#385C2312yes—
451#385C2312yes—
452#385C2314yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#385C2314yes—
457#384C2311yescharacteristic
458#384C2312yes—
459#384C2311yescharacteristic
460#382C2314yes—
461#382C2311yescharacteristic
462#382C2312yes—
463#382C2311yescharacteristic
464#382C2318yes—
465#382C2318yes—
466#382C2318yes—
467#381C2314yes—
468#381C2314yes—
469#381C2314yes—
470#381C2314yes—
471#381C2314yes—
472#381C2314yes—
473#381C2314yes—
474#381C2318yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499#376C2312yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2412yes—
521C22×Q8C2412yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2414yes—
524C22×Q8C2414yes—
525C22×D4C2412yes—
526C22×D4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2414yes—
537C23×C4C2411yescharacteristic
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—48no—
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552#125—216no—
553#125—44no—
554#125—44no—
555#125—44no—
556#124—44no—
557#124—44no—
558#124—44no—
559#123—48no—
560#123—48no—
561#123—48no—
562C22⋊Q8—216no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565C22⋊Q8—48no—
566C22⋊Q8—44no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C4×Q8—48no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—44no—
574C4×Q8—48no—
575C4×Q8—44no—
576C4×Q8—48no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×D4—44no—
581C4×D4—48no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—24no—
588#117—24no—
589#117—44no—
590#117—48no—
591#117—48no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—28no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—48no—
598C2×C4⋊C4—48no—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
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×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
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⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C42—24no—
672C2×C42—24no—
673C2×C42—24no—
674C2×C42—44no—
675C2×C42—44no—
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2414yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
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#95C2418yes—
727#95C2418yes—
728#95C2418yes—
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—
742#95C2418yes—
743C24C2512yes—
744C24C2511yescharacteristic
745#41—416no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
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—24no—
766C2×Q8—22no—
767C2×Q8—28no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—48no—
772C2×Q8—416no—
773C2×Q8—416no—
774C2×Q8—416no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C22×C4—22no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
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—28no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4H(5,𝔽2)14yes—
809C22×C4H(5,𝔽2)14yes—
810C22×C42−1+414yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C42−1+418yes—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C42—22no—
907C42—22no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—22no—
913C42—22no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—28no—
922C42—44no—
923C42—48no—
924C42—44no—
925C42—44no—
926C42—48no—
927C42—44no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23C2×H(5,𝔽2)12yes—
936C23C2×H(5,𝔽2)12yes—
937C23C2×2−1+412yes—
938C23C2611yescharacteristic
939Q8—48no—
940Q8—48no—
941Q8—48no—
942Q8—48no—
943Q8—48no—
944Q8—48no—
945Q8—44no—
946Q8—88no—
947Q8—164no—
948D4—48no—
949D4—44no—
950C2×C4—28no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—88no—
1012C2×C4—84no—
1013C2×C4#562116yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4C2×H(5,𝔽2)12yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×2−1+414yes—
1019C2×C4C2×2−1+414yes—
1020C2×C4C2×2−1+414yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C22—22no—
1024C22—22no—
1025C22—24no—
1026C22—24no—
1027C22—42no—
1028C22—42no—
1029C22—44no—
1030C22—42no—
1031C22—44no—
1032C22C2×#56214yes—
1033C22C22×H(5,𝔽2)11yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+412yes—
1036C22C22×2−1+411yescharacteristic
1037C222−1+612yes—
1038C4—24no—
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—44no—
1050C4—42no—
1051C4—42no—
1052C4—44no—
1053C4—44no—
1054C4—42no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4C2×#56214yes—
1060C4C2×#56214yes—
1061C2—24no—
1062C2—82no—
1063C2C22×#56211yescharacteristic
1064C2#6283311yescharacteristic
1065C2#6288711yescharacteristic
1066C2#6294212yes—
1067C2#6294712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53146C2semidirect
2. #53140C2semidirect
3. #53037C2semidirect
4. #53013C2semidirect
5. #52722C2semidirect
6. #46057C2semidirect
7. #46007C2semidirect
8. #45752C2semidirect
9. #45634C2semidirect
10. #45500C2semidirect
11. #35674C2semidirect
12. #35674C2semidirect
13. #35668C2semidirect
16. #35662C2semidirect
17. #35320C2semidirect
22. #35154C2semidirect
23. C2×#2546C2semidirect
24. #34815C2semidirect

Maximal subgroups

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

subgroupindex
#531462
#531402
#530372
#530132
#527222
#460572
#460072
#457522
#456342
#455002
#356742
#356682
#356672
#356622
#353202
#353162
#353122
#353072
#351822
#351542
C2×#25462
#348152
#347452