Finite Group Databasebeta

← #7987103

Subgroups — #7987103

Order 512.

6283 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C212yesmaximal, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59667C212yesmaximal, complemented
4#59244C212yesmaximal, complemented
5#59081C212yesmaximal, complemented
6#51540C218yesmaximal, complemented
7#45485C214yesmaximal, complemented
8#45343C214yesmaximal, complemented
9#45326C214yesmaximal, complemented
10#42649C214yesmaximal, complemented
11#42644C214yesmaximal, complemented
12#39724C212yesmaximal, complemented
13#39385C212yesmaximal, complemented
14#39353C212yesmaximal, complemented
15#39353C214yesmaximal, complemented
16#38923C212yesmaximal, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36188C212yesmaximal, complemented
19#36188C211yesmaximal, characteristic, complemented
20#36186C212yesmaximal, complemented
21#36134C211yesmaximal, characteristic, complemented
22#35170C212yesmaximal
23#35167C212yesmaximal, complemented
24#34932C211yesmaximal, characteristic
25#34929C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27#3555—232no—
28C2×#563C2218yes—
29C2×Q82C2212yes—
30C2×#557C2214yes—
31C2×#557C2212yes—
32C2×#556C2212yes—
33C2×#556C2214yes—
34C2×#556C2214yes—
35C2×#554C2211yescharacteristic
36C2×#552C2214yes—
37C2×#544C2214yes—
38C2×#542C2214yes—
39C2×#541C2214yes—
40C2×#541C2214yes—
41C2×#541C2218yes—
42C2×#533C2212yes—
43C2×#533C2212yes—
44C2×#529C2212yes—
45#2868C2211yescharacteristic
46#2868C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2214yes—
50#2857C2214yes—
51#2854C2214yes—
52#2814C2218yes—
53#2734C2214yes—
54#2729C2218yes—
55#2725C2218yes—
56#2722C2218yes—
57#2722C2218yes—
58#2722C2218yes—
59#2721C2218yes—
60#2721C2218yes—
61#2719C2218yes—
62#2719C2218yes—
63#2719C2218yes—
64#2716C2218yes—
65#2715C2218yes—
66#2715C2218yes—
67#2713C2218yes—
68#2695C2218yes—
69#2690C2218yes—
70#2663C2218yes—
71#2659C2218yes—
72#2625C2214yes—
73#2625C2218yes—
74#2621C2214yes—
75#2582C2212yes—
76#2581C2214yes—
77#2568C2214yes—
78#2568C2212yes—
79#2556C2214yes—
80#2553C2214yes—
81#2552C2211yescharacteristic
82#2552C2212yes—
83#2552C2214yes—
84#2552C2212yes—
85#2552C2214yes—
86#2552C2212yes—
87#2552C2214yes—
88#2552C2214yes—
89#2551C2214yes—
90#2551C2212yes—
91#2551C2211yescharacteristic
92#2551C2212yes—
93#2550C2214yes—
94#2550C2218yes—
95#2550C2214yes—
96#2547C2214yes—
97#2547C2212yes—
98#2547C2211yescharacteristic
99#2547C2212yes—
100#2546C2212yes—
101#2546C2214yes—
102#2546C2211yescharacteristic
103#2546C2214yes—
104#2542C2212yes—
105#2542C2211yescharacteristic
106#2542C2211yescharacteristic
107#2538C2212yes—
108#2538C2211yescharacteristic
109#2537C2211yescharacteristic
110#2521C2218yes—
111#2519C2218yes—
112#2512C2214yes—
113#2512C2214yes—
114#2506C2214yes—
115#2506C2214yes—
116#2506C2212yes—
117#2499C2214yes—
118#2499C2218yes—
119#2498C2218yes—
120#2496C2218yes—
121#2496C2214yes—
122#2496C2214yes—
123#2496C2214yes—
124#2496C2214yes—
125#2496C2214yes—
126#2496C2212yes—
127#2492C2214yes—
128#2492C2212yes—
129#2491C2214yes—
130#2489C2212yes—
131#2489C2214yes—
132#2485C2214yes—
133#2469C2218yes—
134#2462C2218yes—
135#2453C2214yes—
136#2453C2218yes—
137#2453C2214yes—
138#2452C2212yes—
139#2451C2214yes—
140#2451C2214yes—
141#2451C2214yes—
142#2446C2214yes—
143#2446C2218yes—
144#2441C2214yes—
145#2439C2214yes—
146#2429C2214yes—
147#2429C2212yes—
148#2429C2214yes—
149#2429C2214yes—
150#2427C2214yes—
151#2427C2212yes—
152#2423C2214yes—
153#2422C2212yes—
154#2421C2214yes—
155#2417C2214yes—
156#2396C2214yes—
157#2395C2214yes—
158#2370C2212yes—
159#2369C2211yescharacteristic
160#2368C2214yes—
161#2365C2212yes—
162#2365C2212yes—
163#2365C2214yes—
164#2365C2212yes—
165#2365C2214yes—
166#2365C2212yes—
167#2365C2212yes—
168#2362C2214yes—
169#2360C2212yes—
170#2355C2211yescharacteristic
171#2354C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174Q8×C4⋊C4C2212yes—
175#2349C2212yes—
176D4×C4⋊C4C2211yescharacteristic
177#2345C2212yes—
178#2323C2214yes—
179#2316C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2214yes—
190C4×#121C2212yes—
191#2293C2212yes—
192#2285C2214yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200#563—264no—
201Q82—216no—
202#557—232no—
203#557—216no—
204#556—232no—
205#556—232no—
206#556—216no—
207#554D4116yescomplemented
208#552—232no—
209#544—232no—
210#542—232no—
211#541—232no—
212#541—232no—
213#541—264no—
214#533—216no—
215#533—216no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2318yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2318yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2311yescharacteristic
232#529—216no—
233C2×#126C2314yes—
234C2×#126C2318yes—
235C2×#126C2318yes—
236C2×#126C2318yes—
237C2×#126C2318yes—
238C2×#126C2318yes—
239C2×#126C2318yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2318yes—
244C2×#125C2318yes—
245C2×#125C2318yes—
246C2×#125C2318yes—
247C2×#125C2318yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#124C2312yes—
251C2×#124C2314yes—
252C2×#124C2318yes—
253C2×#123C2318yes—
254C2×#123C2314yes—
255C2×C22⋊Q8C2318yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2318yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2318yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2314yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×#117C2314yes—
296C2×#117C2314yes—
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2318yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C42C2312yes—
303C22×C42C2312yes—
304C22×C42C2314yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C2318yes—
309#400C2314yes—
310#400C2318yes—
311#400C2314yes—
312#400C2318yes—
313#399C2314yes—
314#399C2314yes—
315#399C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C2318yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2314yes—
334#397C2318yes—
335#397C2318yes—
336#397C2318yes—
337#397C2318yes—
338#397C2314yes—
339#397C2314yes—
340#397C2318yes—
341#396C2314yes—
342#396C2314yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yes—
346#395C2318yes—
347#395C2314yes—
348#395C2318yes—
349#395C2318yes—
350#395C2318yes—
351#394C2314yes—
352#394C2314yes—
353#394C2318yes—
354#393C2314yes—
355#393C2318yes—
356#391C2312yes—
357#391C2312yes—
358#391C2314yes—
359#391C2312yes—
360#391C2314yes—
361#391C2314yes—
362#391C2312yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2318yes—
368#391C2314yes—
369#391C2318yes—
370#391C2312yes—
371#391C2318yes—
372#391C2314yes—
373#391C2312yes—
374#391C2318yes—
375#390C2312yes—
376#390C2314yes—
377#390C2312yes—
378#390C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2318yes—
400#389C2312yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2318yes—
411#389C2314yes—
412#389C2318yes—
413#389C2318yes—
414#389C2314yes—
415#389C2312yes—
416#389C2318yes—
417#389C2312yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2318yes—
425#388C2314yes—
426#388C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#386C2318yes—
447#386C2314yes—
448#385C2314yes—
449#385C2314yes—
450#385C2314yes—
451#385C2314yes—
452#385C2314yes—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2312yes—
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2314yes—
459#384C2314yes—
460#384C2312yes—
461#384C2314yes—
462#384C2314yes—
463#384C2312yes—
464#384C2312yes—
465#384C2314yes—
466#384C2312yes—
467#384C2312yes—
468#382C2312yes—
469#382C2314yes—
470#382C2318yes—
471#382C2314yes—
472#380C2318yes—
473#380C2318yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2314yes—
478#380C2312yes—
479#380C2314yes—
480#380C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2312yes—
488#380C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2318yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2311yescharacteristic
522C4×C4⋊C4C2311yescharacteristic
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2314yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2314yes—
534C2×#95C2314yes—
535C43C2312yes—
536C43C2311yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2414yes—
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2414yes—
542C22×Q8C2418yes—
543C22×Q8C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C22×D4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2414yes—
555C4⋊Q8—28no—
556C4⋊Q8—232no—
557C4⋊Q8—28no—
558C4⋊Q8—216no—
559C4⋊Q8—216no—
560C4⋊Q8—232no—
561C4⋊Q8—28no—
562C4⋊Q8—216no—
563C4⋊Q8—24no—
564C4⋊Q8—28no—
565C4⋊Q8—24no—
566C4⋊Q8—44no—
567C4⋊Q8—48no—
568C4⋊Q8—44no—
569C4⋊Q8—48no—
570C4⋊Q8C2×D418yes—
571#126—232no—
572#126—232no—
573#126—216no—
574#126—232no—
575#126—232no—
576#126—232no—
577#126—232no—
578#125—28no—
579#125—216no—
580#125—216no—
581#125—232no—
582#125—232no—
583#125—232no—
584#125—232no—
585#125—232no—
586#125—216no—
587#125C2×D4116yes—
588#124—28no—
589#124—216no—
590#124—232no—
591#123—232no—
592#123—216no—
593C22⋊Q8—28no—
594C22⋊Q8—216no—
595C22⋊Q8—232no—
596C22⋊Q8—216no—
597C22⋊Q8—232no—
598C22⋊Q8—28no—
599C22⋊Q8—216no—
600C22⋊Q8—28no—
601C22⋊Q8—216no—
602C22⋊Q8—28no—
603C22⋊Q8—48no—
604C22⋊Q8—44no—
605C22⋊Q8C2×D4116yes—
606C22⋊Q8C2×D4132yes—
607#121—28no—
608#121—44no—
609C4×Q8—216no—
610C4×Q8—216no—
611C4×Q8—216no—
612C4×Q8—216no—
613C4×Q8—232no—
614C4×Q8—216no—
615C4×Q8—216no—
616C4×Q8—24no—
617C4×Q8—28no—
618C4×Q8—216no—
619C4×Q8—28no—
620C4×Q8—216no—
621C4×Q8—24no—
622C4×Q8—44no—
623C4×Q8C2×D418yes—
624C4×D4—216no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—42no—
629C4×D4—44no—
630C4×D4—42no—
631C4×D4C2×D418yes—
632C4×D4C2×D4116yes—
633#117—216no—
634#117—232no—
635#117—216no—
636#117—216no—
637#117—216no—
638C2×C4⋊C4—28no—
639C2×C4⋊C4C2×D4116yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2414yes—
726C2×C42—28no—
727C2×C42—28no—
728C2×C42—48no—
729C2×C42C2418yes—
730C2×C42C2412yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2412yes—
739C2×C42C2418yes—
740C2×C42C2412yes—
741C2×C42C2414yes—
742C2×C42C2411yescharacteristic
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2412yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757#95C2412yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2412yes—
769#95C2412yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2412yes—
775#95C2412yes—
776#95C2418yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2414yes—
785#95C2418yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2418yes—
792#95C2414yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797C24C2512yes—
798C24C2512yes—
799C2×Q8—24no—
800C2×Q8—28no—
801C2×Q8—24no—
802C2×Q8—28no—
803C2×Q8—216no—
804C2×Q8—22no—
805C2×Q8—22no—
806C2×Q8—24no—
807C2×Q8—28no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—28no—
811C2×Q8—24no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—44no—
815C2×Q8—48no—
816C2×Q8—44no—
817C2×Q8—48no—
818C2×Q8C22×D414yes—
819C2×Q8C22×D418yes—
820C2×D4—28no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4C22×D414yes—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C22×D418yes—
852C22×C4C22×D4116yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2511yescharacteristic
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2518yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—216no—
889C4⋊C4—216no—
890C4⋊C4—216no—
891C4⋊C4—216no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—216no—
895C4⋊C4—28no—
896C4⋊C4—216no—
897C4⋊C4—28no—
898C4⋊C4—216no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—42no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—44no—
933C4⋊C4C22×D414yes—
934C4⋊C4C22×D418yes—
935C4⋊C4C22×D4116yes—
936C4⋊C4C22×D414yes—
937C4⋊C4C22×D418yes—
938C4⋊C4C22×D4116yes—
939C4⋊C4C22×D418yes—
940C4⋊C42−1+414yes—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—216no—
945C22⋊C4—216no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—28no—
954C22⋊C4—44no—
955C22⋊C4—42no—
956C22⋊C4—44no—
957C22⋊C4—42no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4C22×D418yes—
962C22⋊C4C22×D4116yes—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—216no—
967C42—28no—
968C42—28no—
969C42—216no—
970C42—216no—
971C42—216no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—22no—
977C42—24no—
978C42—24no—
979C42—28no—
980C42—22no—
981C42—24no—
982C42—22no—
983C42—44no—
984C42—44no—
985C42—41no—
986C42—42no—
987C42C22×D414yes—
988C42C22×D418yes—
989C422−1+414yes—
990C422−1+414yes—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23C23×D414yes—
1005C23C2611yescharacteristic
1006Q8—28no—
1007Q8—48no—
1008Q8—416no—
1009Q8—48no—
1010Q8—48no—
1011Q8—88no—
1012Q8—816no—
1013D4—28no—
1014D4—44no—
1015D4—88no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—24no—
1032C2×C4—216no—
1033C2×C4—22no—
1034C2×C4—28no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—28no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—416no—
1073C2×C4—48no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—84no—
1077C2×C4—88no—
1078C2×C4—84no—
1079C2×C4C23×D414yes—
1080C2×C4C23×D414yes—
1081C2×C4C23×D418yes—
1082C2×C4C23×D412yes—
1083C2×C4C23×D414yes—
1084C2×C4C23×D412yes—
1085C2×C4C23×D412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+414yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4#58512yes—
1095C2×C4#58512yes—
1096C22—24no—
1097C22—24no—
1098C22—24no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22C24×D411yescharacteristic
1111C22C22×2−1+411yescharacteristic
1112C22C22×2−1+411yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C2×#58511yescharacteristic
1115C22C2×#58511yescharacteristic
1116C222−1+611yescharacteristic
1117C4—24no—
1118C4—28no—
1119C4—22no—
1120C4—24no—
1121C4—24no—
1122C4—24no—
1123C4—22no—
1124C4—22no—
1125C4—42no—
1126C4—44no—
1127C4—44no—
1128C4—42no—
1129C4—41no—
1130C4—44no—
1131C4—42no—
1132C4—48no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—42no—
1138C4#349714yes—
1139C4#349914yes—
1140C4#355514yescomplemented
1141C2—44no—
1142C2—82no—
1143C2C2×#355511yescharacteristic
1144C2C2×#349711yescharacteristic
1145C2C2×#349911yescharacteristic
1146C2#6294711yescharacteristic
1147C2#6295911yescharacteristic
1148C2#6298811yescharacteristic
1149C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3555C2semidirect
2. #59832C2semidirect
3. #59667C2semidirect
4. #59244C2semidirect
5. #59081C2semidirect
6. #51540C2semidirect
7. #45485C2semidirect
8. #45343C2semidirect
9. #45326C2semidirect
10. #42649C2semidirect
11. #42644C2semidirect
12. #39724C2semidirect
13. #39385C2semidirect
14. #39353C2semidirect
15. #39353C2semidirect
16. #38923C2semidirect
17. #36593C2semidirect
18. #36188C2semidirect
19. #36188C2semidirect
20. #36186C2semidirect
21. #36134C2semidirect
23. #35167C2semidirect
25. #34929C2semidirect
26. C4×#554C2semidirect
207. #554D4semidirect
1140. C4#3555semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
#598322
#596672
#592442
#590812
#515402
#454852
#453432
#453262
#426492
#426442
#397242
#393852
#393532
#389232
#365932
#361882
#361862
#361342
#351702
#351672
#349322
#349292
C4×#5542