Finite Group Databasebeta

← #7683355

Subgroups — #7683355

Order 512.

5564 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59881C218yesmaximal, complemented
2#59478C214yesmaximal, complemented
3#59477C214yesmaximal, complemented
4#59276C214yesmaximal, complemented
5#59274C214yesmaximal, complemented
6#45292C214yesmaximal, complemented
7#45290C214yesmaximal, complemented
8#45082C214yesmaximal, complemented
9#44920C214yesmaximal, complemented
10#43978C218yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35660C211yesmaximal, characteristic
13#35592C211yesmaximal, characteristic, complemented
14#35574C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17C2×#2567C211yesmaximal, characteristic, complemented
18#34816C211yesmaximal, characteristic, complemented
19#34744C211yesmaximal, characteristic, complemented
20#34266C211yesmaximal, characteristic, complemented
21#34259C211yesmaximal, characteristic, complemented
22#34257C211yesmaximal, characteristic, complemented
23#34254C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#532C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2798C2218yes—
37#2796C2218yes—
38#2763C2218yes—
39#2759C2218yes—
40#2755C2218yes—
41#2745C2218yes—
42#2742C2218yes—
43#2737C2218yes—
44#2737C2218yes—
45#2723C2218yes—
46#2717C2218yes—
47#2705C2218yes—
48#2610C2218yes—
49#2605C2218yes—
50#2602C2218yes—
51#2601C2218yes—
52#2591C2214yes—
53#2589C2218yes—
54#2588C2218yes—
55#2586C2218yes—
56#2579C2214yes—
57#2574C2218yes—
58#2573C2218yes—
59#2567C2214yes—
60#2567C2214yes—
61#2567C2214yes—
62#2567C2214yes—
63#2564C2218yes—
64#2553C2218yes—
65#2526C2218yes—
66#2522C2218yes—
67#2521C2218yes—
68#2518C2218yes—
69#2514C2212yes—
70#2513C2212yes—
71#2512C2212yes—
72#2512C2214yes—
73#2511C2212yes—
74#2511C2214yes—
75#2510C2214yes—
76#2505C2218yes—
77#2502C2212yes—
78#2501C2212yes—
79#2500C2212yes—
80#2499C2212yes—
81#2498C2218yes—
82#2497C2214yes—
83#2496C2214yes—
84#2492C2214yes—
85#2492C2214yes—
86#2491C2214yes—
87#2491C2214yes—
88#2481C2214yes—
89#2481C2218yes—
90#2461C2218yes—
91#2452C2214yes—
92#2451C2214yes—
93#2448C2214yes—
94#2448C2212yes—
95#2447C2212yes—
96#2446C2214yes—
97#2446C2212yes—
98#2445C2212yes—
99#2444C2214yes—
100#2443C2214yes—
101#2443C2218yes—
102#2440C2214yes—
103#2439C2214yes—
104#2438C2218yes—
105#2436C2214yes—
106#2436C2212yes—
107#2434C2212yes—
108#2432C2212yes—
109#2431C2212yes—
110#2430C2218yes—
111#2423C2214yes—
112#2423C2214yes—
113#2422C2214yes—
114#2421C2214yes—
115#2409C2214yes—
116#2409C2214yes—
117#2407C2214yes—
118#2401C2214yes—
119#2395C2214yes—
120C2×#395C2214yes—
121#2373C2218yes—
122#2367C2214yes—
123#2365C2214yes—
124#2362C2214yes—
125#2361C2218yes—
126#2360C2214yes—
127#2359C2218yes—
128#2356C2214yes—
129#2355C2214yes—
130#2355C2214yes—
131#2354C2214yes—
132#2354C2214yes—
133#2352C2218yes—
134D4×C4⋊C4C2214yes—
135#2343C2218yes—
136#2341C2214yes—
137#2341C2214yes—
138Q8×C22⋊C4C2214yes—
139Q8×C22⋊C4C2214yes—
140Q8×C22⋊C4C2214yes—
141#2339C2214yes—
142#2339C2218yes—
143#2326C2212yes—
144#2326C2212yes—
145#2322C2214yes—
146#2320C2214yes—
147#2317C2211yescharacteristic
148#2316C2211yescharacteristic
149#2314C2214yes—
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2212yes—
154#2311C2211yescharacteristic
155#2311C2211yescharacteristic
156#2311C2214yes—
157#2310C2211yescharacteristic
158#2310C2212yes—
159C4×C4⋊Q8C2212yes—
160C4×#127C2212yes—
161C4×#126C2214yes—
162C4×#123C2214yes—
163C4×#123C2214yes—
164#2297C2211yescharacteristic
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2212yes—
170#2297C2211yescharacteristic
171#2297C2214yes—
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2295C2214yes—
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2212yes—
178C2×#389C2214yes—
179#2285C2211yescharacteristic
180#2285C2214yes—
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—28no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2314yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C22×#41C2311yescharacteristic
196C23×Q8C2312yes—
197C23×Q8C2312yes—
198C23×Q8C2311yescharacteristic
199C23×Q8C2312yes—
200#537—44no—
201#536—28no—
202#532—28no—
203C2×C4⋊Q8—44no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×#127C2311yescharacteristic
209C2×#126C2314yes—
210C2×#126C2318yes—
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2312yes—
214C2×#124C2318yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2318yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2318yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226#520—44no—
227#520—44no—
228#519—28no—
229C4×#41—28no—
230C2×C4×Q8—44no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2318yes—
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2314yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2312yes—
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271#401C2314yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#399C2318yes—
281#399C2314yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2314yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2314yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2318yes—
309#394C2314yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#392C2318yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2311yescharacteristic
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2311yescharacteristic
342#390C2312yes—
343#390C2312yes—
344#390C2318yes—
345#390C2312yes—
346#390C2311yescharacteristic
347#390C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2311yescharacteristic
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#386C2314yes—
407#386C2318yes—
408#386C2314yes—
409#386C2312yes—
410#386C2312yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2318yes—
416#386C2312yes—
417#386C2312yes—
418#386C2312yes—
419#386C2312yes—
420#386C2318yes—
421#386C2314yes—
422#386C2318yes—
423#386C2314yes—
424#386C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2312yes—
431#385C2312yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#383C2314yes—
446#383C2318yes—
447#382C2312yes—
448#382C2312yes—
449#382C2318yes—
450#382C2318yes—
451#381C2318yes—
452#381C2314yes—
453#381C2314yes—
454#380C2318yes—
455#380C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497#376C2312yes—
498#376C2318yes—
499C2×#95C2318yes—
500C2×#95C2314yes—
501C2×#95C2314yes—
502C2×#95C2312yes—
503C43C2312yes—
5042−1+4—464no—
505C2×#41—28no—
506C2×#41—28no—
507C2×#41—216no—
508C2×#41—28no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—216no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—48no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41#4118yes—
523C22×Q8—28no—
524C22×Q8—28no—
525C22×Q8—28no—
526C22×Q8—24no—
527C22×Q8—28no—
528C22×Q8—24no—
529C22×Q8—44no—
530C22×Q8—44no—
531C22×Q8—44no—
532C22×Q8—84no—
533C22×Q8#4118yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2418yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2412yes—
548C22×D4C2411yescharacteristic
549C22×D4C2414yes—
550C23×C4C2411yescharacteristic
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2414yes—
557C23×C4C2414yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2411yescharacteristic
564C23×C4C2414yes—
565C23×C4C2414yes—
566C23×C4C2411yescharacteristic
567C4⋊Q8—24no—
568C4⋊Q8—28no—
569C4⋊Q8—48no—
570C4⋊Q8—48no—
571#127—24no—
572#126—216no—
573#126—88no—
574#124—24no—
575#124—28no—
576#124—24no—
577#124—88no—
578#123—216no—
579#123—216no—
580#123—88no—
581C22⋊Q8—216no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—88no—
585#121—216no—
586#121—44no—
587#121—44no—
588#121—48no—
589C4×Q8—28no—
590C4×Q8—216no—
591C4×Q8—216no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—44no—
595C4×Q8—44no—
596C4×D4—216no—
597C4×D4—28no—
598C4×D4—216no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—48no—
602C4×D4—48no—
603C4×D4—88no—
604#117—28no—
605#117—24no—
606#117—216no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—44no—
612#117—44no—
613#117—88no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—84no—
623C2×C4⋊C4—84no—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
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×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C42—28no—
692C2×C42—24no—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—44no—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2418yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757C24C2512yes—
758C24C2512yes—
759C24C2512yes—
760C24C2511yescharacteristic
761#41—232no—
762#41—464no—
763#41—432no—
764#41—432no—
765#41—416no—
766#41—416no—
767C2×Q8—232no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—44no—
783C2×Q8—48no—
784C2×Q8—48no—
785C2×Q8—48no—
786C2×Q8—432no—
787C2×Q8—432no—
788C2×Q8—816no—
789C2×Q8C2×#4118yes—
790C2×Q8C2×#4114yes—
791C2×Q8C2×#4118yes—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—28no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—28no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—28no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—48no—
816C2×D4C2×#4118yes—
817C2×D4C2×#4114yes—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4C2×#4118yes—
858C22×C4C2×#4118yes—
859C22×C4C2×#4114yes—
860C22×C4C2×#4114yes—
861C22×C4H(5,𝔽2)14yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—216no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—216no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C42−1+418yescomplemented
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—28no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—216no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C42—22no—
951C42—24no—
952C42—22no—
953C42—24no—
954C42—28no—
955C42—24no—
956C42—22no—
957C42—22no—
958C42—216no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—28no—
966C42—48no—
967C42—44no—
968C42—44no—
969C42—48no—
970C42—48no—
971C42—44no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23C22×#4114yes—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2611yescharacteristic
993Q8—216no—
994Q8—216no—
995Q8—28no—
996Q8—416no—
997Q8—44no—
998Q8—44no—
999Q8—816no—
1000D4—216no—
1001D4—28no—
1002D4—416no—
1003D4—416no—
1004D4—48no—
1005D4—48no—
1006D4—44no—
1007D4—44no—
1008D4—164no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—216no—
1021C2×C4—216no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—416no—
1060C2×C4—48no—
1061C2×C4—416no—
1062C2×C4—48no—
1063C2×C4—416no—
1064C2×C4—44no—
1065C2×C4—48no—
1066C2×C4—48no—
1067C2×C4—84no—
1068C2×C4—84no—
1069C2×C4—84no—
1070C2×C4—164no—
1071C2×C4—164no—
1072C2×C4#551116yes—
1073C2×C4C22×#4118yes—
1074C2×C4C22×#4114yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×H(5,𝔽2)12yes—
1081C2×C4C2×2−1+414yes—
1082C2×C4C2×2−1+414yes—
1083C2×C4C2×2−1+414yes—
1084C22—24no—
1085C22—24no—
1086C22—22no—
1087C22—22no—
1088C22—28no—
1089C22—24no—
1090C22—44no—
1091C22—42no—
1092C22—42no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22C2×#55114yes—
1104C22C23×#4111yescharacteristic
1105C22C23×#4111yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×2−1+412yes—
1108C22H(7,𝔽2)12yes—
1109C4—24no—
1110C4—24no—
1111C4—24no—
1112C4—24no—
1113C4—28no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4C2×#55114yes—
1129C4C2×#55114yes—
1130C2—24no—
1131C2—44no—
1132C2—82no—
1133C2—82no—
1134C2C22×#55111yescharacteristic
1135C2#6283311yescharacteristic
1136C2#6287611yescharacteristic
1137C2#6299912yes—
1138C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35660C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59881C2semidirect
2. #59478C2semidirect
3. #59477C2semidirect
4. #59276C2semidirect
5. #59274C2semidirect
6. #45292C2semidirect
7. #45290C2semidirect
8. #45082C2semidirect
9. #44920C2semidirect
10. #43978C2semidirect
11. #35673C2semidirect
13. #35592C2semidirect
14. #35574C2semidirect
15. #35557C2semidirect
16. #35530C2semidirect
17. C2×#2567C2semidirect
18. #34816C2semidirect
19. #34744C2semidirect
20. #34266C2semidirect
21. #34259C2semidirect
22. #34257C2semidirect
23. #34254C2semidirect
24. #34207C2semidirect
25. #34188C2semidirect
919. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#598812
#594782
#594772
#592762
#592742
#452922
#452902
#450822
#449202
#439782
#356732
#356602
#355922
#355742
#355572
#355302
C2×#25672
#348162
#347442
#342662
#342592
#342572
#342542
#342072
#341882