Finite Group Databasebeta

← #7652154

Subgroups — #7652154

Order 512.

4940 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42776C214yesmaximal, complemented
2#42708C214yesmaximal, complemented
3#42702C214yesmaximal, complemented
4#42702C214yesmaximal, complemented
5#41533C218yesmaximal, complemented
6#40079C214yesmaximal, complemented
7#40025C214yesmaximal, complemented
8#39656C214yesmaximal, complemented
9#39641C214yesmaximal, complemented
10#38607C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic, complemented
15#35621C211yesmaximal, characteristic
16#35619C211yesmaximal, characteristic, complemented
17#35317C211yesmaximal, characteristic
18#35316C211yesmaximal, characteristic, complemented
19#35182C211yesmaximal, characteristic, complemented
20C2×#2546C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic
23#34268C211yesmaximal, characteristic, complemented
24#34266C211yesmaximal, characteristic, complemented
25#34254C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2868C2212yes—
42#2858C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2853C2214yes—
46#2836C2218yes—
47#2836C2218yes—
48#2800C2218yes—
49#2791C2218yes—
50#2791C2218yes—
51#2791C2218yes—
52#2791C2218yes—
53#2780C2218yes—
54#2777C2218yes—
55#2777C2218yes—
56#2773C2218yes—
57#2773C2218yes—
58#2768C2218yes—
59#2768C2218yes—
60#2761C2218yes—
61#2738C2218yes—
62#2738C2218yes—
63#2707C2218yes—
64#2667C2218yes—
65#2667C2218yes—
66#2658C2212yes—
67#2658C2212yes—
68#2654C2218yes—
69#2654C2218yes—
70#2651C2218yes—
71#2647C2218yes—
72#2623C2214yes—
73#2621C2212yes—
74#2621C2212yes—
75#2547C2212yes—
76#2547C2214yes—
77#2546C2214yes—
78#2546C2212yes—
79#2546C2214yes—
80#2546C2214yes—
81#2546C2214yes—
82#2546C2214yes—
83#2546C2214yes—
84#2546C2214yes—
85#2546C2214yes—
86#2545C2212yes—
87#2545C2214yes—
88#2545C2214yes—
89#2545C2214yes—
90#2544C2212yes—
91#2542C2214yes—
92#2542C2214yes—
93#2531C2218yes—
94#2526C2218yes—
95#2522C2218yes—
96#2522C2218yes—
97#2509C2212yes—
98#2508C2212yes—
99#2507C2218yes—
100#2507C2218yes—
101#2507C2212yes—
102#2506C2212yes—
103#2505C2214yes—
104#2503C2212yes—
105#2502C2212yes—
106#2501C2218yes—
107#2499C2212yes—
108#2499C2212yes—
109#2486C2218yes—
110#2484C2218yes—
111#2473C2214yes—
112#2448C2214yes—
113#2448C2212yes—
114#2447C2214yes—
115#2447C2212yes—
116#2446C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2446C2214yes—
120#2446C2214yes—
121#2446C2214yes—
122#2446C2212yes—
123#2445C2212yes—
124#2444C2214yes—
125#2443C2214yes—
126#2429C2214yes—
127#2429C2214yes—
128#2429C2214yes—
129#2429C2214yes—
130#2429C2214yes—
131#2429C2214yes—
132#2425C2218yes—
133#2423C2214yes—
134#2421C2214yes—
135#2419C2218yes—
136#2417C2214yes—
137#2415C2214yes—
138#2413C2214yes—
139#2413C2214yes—
140#2413C2218yes—
141#2413C2214yes—
142#2413C2214yes—
143#2402C2214yes—
144#2395C2214yes—
145C2×#398C2214yes—
146#2367C2214yes—
147#2367C2214yes—
148#2365C2214yes—
149#2365C2214yes—
150#2362C2214yes—
151#2360C2214yes—
152#2359C2218yes—
153#2356C2214yes—
154#2355C2214yes—
155#2343C2218yes—
156#2335C2218yes—
157#2330C2218yes—
158#2323C2214yes—
159#2322C2214yes—
160#2320C2214yes—
161#2317C2211yescharacteristic
162#2311C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2211yescharacteristic
167C4×#125C2214yes—
168C4×C22⋊Q8C2214yes—
169C4×#123C2214yes—
170C4×#123C2214yes—
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2295C2214yes—
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#389C2214yes—
183#2285C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192#536—28no—
193#536—28no—
194#536—44no—
195#536—44no—
196#536—44no—
197#536—44no—
198#532—44no—
199C2×C4⋊Q8—44no—
200C2×C4⋊Q8—44no—
201C2×C4⋊Q8—44no—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×#127C2311yescharacteristic
218C2×#125C2314yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×#121C2314yes—
244#520—44no—
245#519—28no—
246#519—44no—
247C4×#41—44no—
248C2×C4×Q8—44no—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284C22×C42C2312yes—
285#400C2314yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2314yes—
291#400C2318yes—
292#400C2314yes—
293#400C2314yes—
294#399C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2314yes—
298#399C2318yes—
299#399C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2314yes—
313#398C2318yes—
314#398C2318yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2318yes—
320#398C2318yes—
321#398C2318yes—
322#397C2314yes—
323#397C2314yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2314yes—
330#397C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#394C2314yes—
339#394C2314yes—
340#394C2318yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2314yes—
356#391C2312yes—
357#391C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#390C2312yes—
363#390C2318yes—
364#390C2318yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2312yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2318yes—
395#389C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#388C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
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#387C2314yes—
433#386C2314yes—
434#386C2312yes—
435#386C2318yes—
436#386C2312yes—
437#386C2312yes—
438#386C2314yes—
439#386C2312yes—
440#386C2314yes—
441#385C2314yes—
442#385C2312yes—
443#385C2318yes—
444#385C2318yes—
445#385C2312yes—
446#385C2314yes—
447#385C2314yes—
448#385C2318yes—
449#385C2312yes—
450#385C2312yes—
451#385C2314yes—
452#385C2314yes—
453#384C2312yes—
454#384C2318yes—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2318yes—
458#383C2318yes—
459#382C2314yes—
460#382C2312yes—
461#382C2318yes—
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464#381C2314yes—
465#381C2314yes—
466#381C2314yes—
467#381C2314yes—
468#381C2314yes—
469#381C2318yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501#376C2312yes—
502#376C2318yes—
503C2×#95C2314yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C43C2312yes—
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—24no—
517C22×Q8—24no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×D4C2412yes—
531C22×D4C2412yes—
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558C4⋊Q8—42no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563#127—42no—
564#125—216no—
565#124—28no—
566#124—28no—
567#124—42no—
568#124—42no—
569#124—44no—
570#124—44no—
571#124—44no—
572#124—44no—
573#123—216no—
574#123—216no—
575#123—216no—
576#123—48no—
577#123—48no—
578#123—48no—
579#123—48no—
580C22⋊Q8—216no—
581C22⋊Q8—216no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—48no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589#121—48no—
590C4×Q8—216no—
591C4×Q8—216no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—44no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—44no—
598C4×D4—44no—
599C4×D4—44no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—48no—
603#117—24no—
604#117—24no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—216no—
609#117—44no—
610#117—48no—
611#117—44no—
612#117#4118yes—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C42—24no—
696C2×C42—24no—
697C2×C42—24no—
698C2×C42—44no—
699C2×C42—44no—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2418yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2412yes—
722#95C2418yes—
723#95C2418yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C24C2512yes—
763C24C2511yescharacteristic
764#41—416no—
765#41—416no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—416no—
791C2×Q8—416no—
792C2×Q8—416no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—28no—
806C2×D4—44no—
807C2×D4—44no—
808C22×C4—22no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—22no—
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—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4C2×#4114yes—
841C22×C4H(5,𝔽2)14yes—
842C22×C4H(5,𝔽2)14yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C4⋊C4—24no—
866C4⋊C4—216no—
867C4⋊C4—216no—
868C4⋊C4—216no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4C2×#4118yes—
912C4⋊C42−1+418yes—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—216no—
919C22⋊C4—216no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4C2×#4118yes—
939C42—24no—
940C42—216no—
941C42—22no—
942C42—22no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—22no—
948C42—22no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—44no—
955C42—48no—
956C42—44no—
957C42—48no—
958C42—44no—
959C42—48no—
960C42C2×#4118yes—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23C22×#4112yes—
974C23C2×H(5,𝔽2)12yes—
975C23C2×H(5,𝔽2)12yes—
976C23C2611yescharacteristic
977Q8—48no—
978Q8—48no—
979Q8—48no—
980Q8—48no—
981Q8—48no—
982Q8—48no—
983Q8—44no—
984Q8—44no—
985D4—48no—
986D4—48no—
987D4—44no—
988D4—44no—
989D4—88no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—44no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—88no—
1051C2×C4—84no—
1052C2×C4—164no—
1053C2×C4#540116yes—
1054C2×C4C22×#4118yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
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+414yes—
1062C2×C4C2×2−1+414yes—
1063C2×C4C2×2−1+414yes—
1064C22—24no—
1065C22—22no—
1066C22—22no—
1067C22—24no—
1068C22—44no—
1069C22—44no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—44no—
1077C22—44no—
1078C22C2×#54014yes—
1079C22C23×#4111yescharacteristic
1080C22C22×H(5,𝔽2)11yescharacteristic
1081C22C22×H(5,𝔽2)11yescharacteristic
1082C22C22×2−1+412yes—
1083C222−1+612yes—
1084C4—28no—
1085C4—24no—
1086C4—24no—
1087C4—24no—
1088C4—44no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—44no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—44no—
1098C4—44no—
1099C4—44no—
1100C4—44no—
1101C4—42no—
1102C4—42no—
1103C4—44no—
1104C4C2×#54014yes—
1105C4C2×#54014yes—
1106C2—24no—
1107C2—82no—
1108C2—82no—
1109C2C22×#54011yescharacteristic
1110C2#6283311yescharacteristic
1111C2#6288711yescharacteristic
1112C2#6294212yes—
1113C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42776C2semidirect
2. #42708C2semidirect
3. #42702C2semidirect
4. #42702C2semidirect
5. #41533C2semidirect
6. #40079C2semidirect
7. #40025C2semidirect
8. #39656C2semidirect
9. #39641C2semidirect
10. #38607C2semidirect
11. #35674C2semidirect
12. #35667C2semidirect
13. #35667C2semidirect
14. #35667C2semidirect
16. #35619C2semidirect
18. #35316C2semidirect
19. #35182C2semidirect
20. C2×#2546C2semidirect
21. #34815C2semidirect
23. #34268C2semidirect
24. #34266C2semidirect
25. #34254C2semidirect

Maximal subgroups

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

subgroupindex
#427762
#427082
#427022
#415332
#400792
#400252
#396562
#396412
#386072
#356742
#356672
#356212
#356192
#353172
#353162
#351822
C2×#25462
#348152
#347442
#342682
#342662
#342542