Finite Group Databasebeta

← #7671760

Subgroups — #7671760

Order 512.

4972 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59481C214yesmaximal, complemented
2#59464C212yesmaximal, complemented
3#59437C212yesmaximal, complemented
4#59295C214yesmaximal, complemented
5#59071C212yesmaximal, complemented
6#59042C212yesmaximal
7#40100C214yesmaximal, complemented
8#40096C214yesmaximal, complemented
9#39159C212yesmaximal, complemented
10#38923C212yesmaximal
11#38263C214yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36560C211yesmaximal, characteristic, complemented
15#36449C212yesmaximal
16#36446C212yesmaximal, complemented
17#36313C212yesmaximal, complemented
18#36288C212yesmaximal, complemented
19#36209C212yesmaximal, complemented
20#36188C211yesmaximal, characteristic, complemented
21#36129C212yesmaximal, complemented
22D4×C4⋊Q8C211yesmaximal, characteristic, complemented
23#35608C214yesmaximal, complemented
24#35291C212yesmaximal, complemented
25#35199C212yesmaximal, complemented
26#34322C212yesmaximal, complemented
27#34216C212yesmaximal, complemented
28C4×#533C211yesmaximal, characteristic, complemented
29C4×#529C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#556C2212yes—
32C2×D4×Q8C2212yes—
33C2×#533C2211yescharacteristic
34C2×#533C2212yes—
35C22×C4⋊Q8C2212yes—
36C2×#529C2211yescharacteristic
37#2868C2211yescharacteristic
38#2868C2211yescharacteristic
39#2863C2214yes—
40#2862C2212yes—
41#2862C2212yes—
42#2862C2214yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2787C2218yes—
53#2774C2218yes—
54#2758C2218yes—
55#2745C2218yes—
56#2722C2218yes—
57#2719C2218yes—
58#2695C2218yes—
59#2690C2218yes—
60#2666C2218yes—
61#2645C2214yes—
62#2625C2214yes—
63#2612C2218yes—
64#2588C2218yes—
65#2582C2212yes—
66#2578C2218yes—
67#2577C2218yes—
68#2574C2218yes—
69#2571C2212yes—
70#2570C2214yes—
71#2568C2214yes—
72#2568C2212yes—
73#2568C2212yes—
74#2568C2212yes—
75#2565C2214yes—
76#2551C2212yes—
77#2551C2212yes—
78#2550C2214yes—
79#2547C2214yes—
80#2547C2212yes—
81#2547C2212yes—
82#2546C2212yes—
83#2546C2212yes—
84#2546C2212yes—
85#2536C2214yes—
86#2530C2218yes—
87#2528C2218yes—
88#2524C2218yes—
89#2520C2218yes—
90#2514C2214yes—
91#2514C2214yes—
92#2511C2214yes—
93#2509C2214yes—
94#2508C2214yes—
95#2508C2214yes—
96#2508C2214yes—
97#2506C2214yes—
98#2506C2214yes—
99#2499C2214yes—
100#2496C2214yes—
101#2496C2214yes—
102#2495C2214yes—
103#2495C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2492C2214yes—
107#2492C2214yes—
108#2489C2218yes—
109#2489C2214yes—
110#2489C2218yes—
111#2489C2214yes—
112#2489C2214yes—
113#2485C2214yes—
114#2485C2214yes—
115#2477C2218yes—
116#2475C2218yes—
117#2453C2214yes—
118#2453C2214yes—
119#2451C2214yes—
120#2451C2214yes—
121#2446C2214yes—
122#2446C2214yes—
123#2446C2214yes—
124#2442C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2439C2214yes—
128#2434C2214yes—
129#2429C2214yes—
130#2429C2214yes—
131#2427C2214yes—
132#2421C2214yes—
133#2421C2214yes—
134#2417C2214yes—
135#2409C2214yes—
136#2373C2218yes—
137#2369C2214yes—
138#2369C2214yes—
139#2367C2214yes—
140#2365C2212yes—
141#2365C2212yes—
142#2365C2212yes—
143#2365C2214yes—
144#2365C2212yes—
145#2365C2212yes—
146#2365C2214yes—
147#2360C2214yes—
148#2356C2214yes—
149#2355C2212yes—
150#2355C2212yes—
151#2352C2214yes—
152#2351C2214yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2212yes—
155#2346C2214yes—
156#2346C2214yes—
157#2345C2214yes—
158#2345C2214yes—
159Q8×C22⋊C4C2214yes—
160Q8×C22⋊C4C2214yes—
161Q8×C22⋊C4C2214yes—
162#2334C2218yes—
163#2331C2214yes—
164#2331C2214yes—
165#2323C2214yes—
166#2320C2214yes—
167#2316C2214yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#125C2212yes—
179C4×#125C2211yescharacteristic
180C4×#125C2212yes—
181C4×#125C2211yescharacteristic
182C4×#126C2212yes—
183C4×#126C2212yes—
184C4×#124C2214yes—
185C4×#124C2211yescharacteristic
186C4×#124C2211yescharacteristic
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×C22⋊Q8C2211yescharacteristic
192C4×C22⋊Q8C2211yescharacteristic
193C4×#123C2212yes—
194C4×#123C2212yes—
195C4×#121C2211yescharacteristic
196C4×#121C2211yescharacteristic
197#2298C2212yes—
198#2296C2212yes—
199#2295C2214yes—
200#2295C2212yes—
201#2295C2212yes—
202#2295C2211yescharacteristic
203#2293C2211yescharacteristic
204#2290C2212yes—
205#2285C2212yes—
206#2285C2212yes—
207#2285C2212yes—
208#2285C2211yescharacteristic
209#2283C2211yescharacteristic
210#2274C2214yes—
211C42×Q8C2212yes—
212C42×Q8C2212yes—
213C42×Q8C2211yescharacteristic
214C42×D4C2211yescharacteristic
215C42×D4C2212yes—
216C4×#117C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C23×Q8C2314yes—
220#557—48no—
221#556—216no—
222D4×Q8—48no—
223#533—28no—
224#533—48no—
225C2×C4⋊Q8—216no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2311yescharacteristic
239#529—28no—
240C2×#126C2312yes—
241C2×#126C2318yes—
242C2×#125C2311yescharacteristic
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#125C2318yes—
247C2×#124C2314yes—
248C2×#124C2311yescharacteristic
249C2×#123C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2318yes—
258C2×#121C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2311yescharacteristic
281C2×#117C2312yes—
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C42C2311yescharacteristic
290C22×C42C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297#401C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#396C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#394C2318yes—
328#393C2318yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2318yes—
343#391C2318yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2318yes—
349#391C2314yes—
350#391C2314yes—
351#391C2318yes—
352#391C2318yes—
353#391C2318yes—
354#391C2314yes—
355#391C2311yescharacteristic
356#391C2314yes—
357#391C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2314yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#388C2312yes—
400#388C2312yes—
401#388C2312yes—
402#388C2312yes—
403#388C2312yes—
404#388C2312yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2312yes—
413#388C2312yes—
414#387C2312yes—
415#387C2312yes—
416#387C2312yes—
417#387C2312yes—
418#387C2312yes—
419#387C2312yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2312yes—
424#387C2314yes—
425#387C2312yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#386C2312yes—
445#386C2318yes—
446#386C2312yes—
447#385C2312yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2312yes—
453#385C2314yes—
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#383C2312yes—
465#383C2318yes—
466#383C2318yes—
467#382C2312yes—
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2314yes—
471#382C2314yes—
472#382C2314yes—
473#382C2314yes—
474#382C2314yes—
475#382C2318yes—
476#382C2318yes—
477#382C2318yes—
478#382C2314yes—
479#382C2314yes—
480#381C2312yes—
481#380C2318yes—
482#380C2318yes—
483#380C2314yes—
484#380C2318yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2311yescharacteristic
495#380C2312yes—
496#380C2312yes—
497#380C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2311yescharacteristic
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2314yes—
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2311yescharacteristic
531C4×C4⋊C4C2318yes—
532C4×C4⋊C4C2318yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2311yescharacteristic
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2312yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2318yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561#376C2312yes—
562#376C2312yes—
563#376C2318yes—
564#376C2314yes—
565C43C2311yescharacteristic
566C43C2311yescharacteristic
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2312yes—
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2314yes—
575C22×Q8—216no—
576C22×Q8—48no—
577C22×Q8—48no—
578C22×Q8C2412yes—
579C22×Q8C2411yescharacteristic
580C22×Q8C2414yes—
581C22×Q8C2414yes—
582C22×Q8C2412yes—
583C22×Q8C2418yes—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C23×C4C2418yes—
597C4⋊Q8—216no—
598C4⋊Q8—216no—
599C4⋊Q8—216no—
600C4⋊Q8—28no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—48no—
607C4⋊Q8—44no—
608C4⋊Q8—48no—
609C4⋊Q8#4118yes—
610#126—28no—
611#126—232no—
612#125—24no—
613#125—28no—
614#125—48no—
615#125—48no—
616#125—416no—
617#124—24no—
618#124—216no—
619#123—28no—
620C22⋊Q8—28no—
621C22⋊Q8—216no—
622C22⋊Q8—24no—
623C22⋊Q8—28no—
624C22⋊Q8—416no—
625C22⋊Q8—48no—
626C22⋊Q8—48no—
627C22⋊Q8—48no—
628#121—24no—
629C4×Q8—28no—
630C4×Q8—28no—
631C4×Q8—216no—
632C4×Q8—24no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8—24no—
636C4×Q8—28no—
637C4×Q8—24no—
638C4×Q8—44no—
639C4×Q8—48no—
640C4×Q8—48no—
641C4×Q8—48no—
642C4×Q8—48no—
643C4×Q8—48no—
644C4×D4—28no—
645C4×D4—28no—
646C4×D4—24no—
647C4×D4—24no—
648C4×D4—48no—
649C4×D4—44no—
650C4×D4#4118yes—
651#117—28no—
652#117—216no—
653#117—28no—
654#117—28no—
655#117—28no—
656#117—48no—
657C2×C4⋊C4—216no—
658C2×C4⋊C4—216no—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2418yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—28no—
735C2×C42—24no—
736C2×C42—24no—
737C2×C42—24no—
738C2×C42—24no—
739C2×C42—42no—
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2418yes—
744C2×C42C2414yes—
745C2×C42C2412yes—
746C2×C42C2414yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2414yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757C2×C42C2414yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2418yes—
777C2×C42C2418yes—
778C2×C42C2414yes—
779C2×C42C2418yes—
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787#95C2412yes—
788#95C2414yes—
789#95C2418yes—
790#95C2412yes—
791#95C2412yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2414yes—
797#95C2412yes—
798#95C2412yes—
799#95C2414yes—
800#95C2414yes—
801#95C2418yes—
802#95C2418yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2412yes—
807#95C2412yes—
808#95C2412yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816#95C2414yes—
817#95C2414yes—
818#95C2412yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2412yes—
823#95C2412yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837C24C2512yes—
838C24C2511yescharacteristic
839C2×Q8—24no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8—28no—
843C2×Q8—28no—
844C2×Q8—216no—
845C2×Q8—24no—
846C2×Q8—22no—
847C2×Q8—28no—
848C2×Q8—28no—
849C2×Q8—24no—
850C2×Q8—22no—
851C2×Q8—28no—
852C2×Q8—24no—
853C2×Q8—28no—
854C2×Q8—48no—
855C2×Q8—48no—
856C2×Q8—832no—
857C2×Q8C2×#4118yes—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—42no—
863C2×D4C2×#4114yes—
864C22×C4—22no—
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—24no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—22no—
889C22×C4—24no—
890C22×C4—216no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4C2×#4118yes—
896C22×C42−1+414yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2511yescharacteristic
908C22×C4C2512yes—
909C22×C4C2518yes—
910C22×C4C2518yes—
911C22×C4C2511yescharacteristic
912C22×C4C2512yes—
913C22×C4C2511yescharacteristic
914C22×C4C2514yes—
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C4⋊C4—216no—
925C4⋊C4—216no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—28no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—22no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—216no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—22no—
945C4⋊C4—28no—
946C4⋊C4—22no—
947C4⋊C4—28no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—24no—
964C4⋊C4—42no—
965C4⋊C4—44no—
966C4⋊C4—48no—
967C4⋊C4—48no—
968C4⋊C4—48no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4C2×#4118yes—
976C4⋊C4C2×#4118yes—
977C4⋊C4C2×#4114yes—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—216no—
981C22⋊C4—24no—
982C22⋊C4—216no—
983C22⋊C4—28no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—48no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—48no—
996C22⋊C4C2×#4118yes—
997C42—22no—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—22no—
1003C42—24no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—28no—
1008C42—216no—
1009C42—28no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—28no—
1014C42—24no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—22no—
1020C42—22no—
1021C42—22no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—28no—
1026C42—24no—
1027C42—24no—
1028C42—28no—
1029C42—24no—
1030C42—22no—
1031C42—22no—
1032C42—24no—
1033C42—41no—
1034C42—41no—
1035C42—48no—
1036C42—44no—
1037C42—48no—
1038C42—48no—
1039C42C2×#4114yes—
1040C42C2×#4114yes—
1041C42H(5,𝔽2)14yes—
1042C422−1+414yes—
1043C422−1+414yes—
1044C23—21no—
1045C23—21no—
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23C22×#4114yes—
1057C23C2×2−1+412yes—
1058C23C2611yescharacteristic
1059Q8—216no—
1060Q8—48no—
1061Q8—44no—
1062Q8—416no—
1063Q8—416no—
1064Q8—816no—
1065D4—28no—
1066D4—48no—
1067C2×C4—28no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—24no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—24no—
1084C2×C4—216no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—28no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—28no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—28no—
1106C2×C4—28no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—28no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—21no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—48no—
1137C2×C4—48no—
1138C2×C4—816no—
1139C2×C4C22×#4114yes—
1140C2×C4C22×#4112yes—
1141C2×C4C22×#4118yes—
1142C2×C4C22×#4112yes—
1143C2×C4C22×#4112yes—
1144C2×C4C22×#4112yes—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C2×H(5,𝔽2)12yes—
1148C2×C4C2×H(5,𝔽2)12yes—
1149C2×C4C2×H(5,𝔽2)12yes—
1150C2×C4C2×2−1+412yes—
1151C2×C4C2×2−1+412yes—
1152C2×C4C2×2−1+412yes—
1153C2×C4C2×2−1+412yes—
1154C2×C4C2×2−1+412yes—
1155C2×C4C2×2−1+412yes—
1156C2×C4C2×2−1+412yes—
1157C2×C4C2×2−1+412yes—
1158C2×C4#58512yes—
1159C22—22no—
1160C22—24no—
1161C22—22no—
1162C22—24no—
1163C22—22no—
1164C22—24no—
1165C22—42no—
1166C22—41no—
1167C22—42no—
1168C22—41no—
1169C22—42no—
1170C22—41no—
1171C22—42no—
1172C22—41no—
1173C22C23×#4111yescharacteristic
1174C22C23×#4111yescharacteristic
1175C22C22×H(5,𝔽2)11yescharacteristic
1176C22C22×2−1+411yescharacteristic
1177C22C22×2−1+411yescharacteristic
1178C22C22×2−1+411yescharacteristic
1179C22C2×#58511yescharacteristic
1180C4—28no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—22no—
1186C4—22no—
1187C4—24no—
1188C4—41no—
1189C4—42no—
1190C4—48no—
1191C4—42no—
1192C4—41no—
1193C4—42no—
1194C4—48no—
1195C4—44no—
1196C4—41no—
1197C4—42no—
1198C4—42no—
1199C4—44no—
1200C4—42no—
1201C4—41no—
1202C4—44no—
1203C4#348214yes—
1204C4#351114yes—
1205C4#351414yes—
1206C4#352314yes—
1207C2—42no—
1208C2—44no—
1209C2C2×#348211yescharacteristic
1210C2C2×#351411yescharacteristic
1211C2C2×#352311yescharacteristic
1212C2C2×#351111yescharacteristic
1213C2#6280511yescharacteristic
1214C2#6283311yescharacteristic
1215C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59481C2semidirect
2. #59464C2semidirect
3. #59437C2semidirect
4. #59295C2semidirect
5. #59071C2semidirect
7. #40100C2semidirect
8. #40096C2semidirect
9. #39159C2semidirect
11. #38263C2semidirect
12. #36645C2semidirect
13. #36598C2semidirect
14. #36560C2semidirect
16. #36446C2semidirect
17. #36313C2semidirect
18. #36288C2semidirect
19. #36209C2semidirect
20. #36188C2semidirect
21. #36129C2semidirect
22. D4×C4⋊Q8C2semidirect
23. #35608C2semidirect
24. #35291C2semidirect
25. #35199C2semidirect
26. #34322C2semidirect
27. #34216C2semidirect
28. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#594812
#594642
#594372
#592952
#590712
#590422
#401002
#400962
#391592
#389232
#382632
#366452
#365982
#365602
#364492
#364462
#363132
#362882
#362092
#361882
#361292
D4×C4⋊Q82
#356082
#352912
#351992
#343222
#342162
C4×#5332
C4×#5292