Finite Group Databasebeta

← #7720404

Subgroups — #7720404

Order 512.

6572 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3550C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic
3#51527C218yesmaximal, complemented
4#51212C214yesmaximal, complemented
5#50892C214yesmaximal, complemented
6#45389C212yesmaximal, complemented
7#45338C212yesmaximal, complemented
8#45141C212yesmaximal, complemented
9#45137C212yesmaximal, complemented
10#45096C214yesmaximal, complemented
11#45095C214yesmaximal, complemented
12#38923C212yesmaximal, complemented
13#38911C212yesmaximal, complemented
14#38051C214yesmaximal, complemented
15#38027C214yesmaximal, complemented
16#37376C214yesmaximal, complemented
17#36405C212yesmaximal, complemented
18#36274C212yesmaximal, complemented
19#35307C214yesmaximal, complemented
20#35297C211yesmaximal, characteristic, complemented
21#35248C211yesmaximal, characteristic, complemented
22#35179C211yesmaximal, characteristic, complemented
23#34627C211yesmaximal, characteristic, complemented
24#34367C211yesmaximal, characteristic, complemented
25#3550—216no—
26C2×#563C2214yes—
27#3480—216no—
28C2×#559C2212yes—
29C2×#559C2212yes—
30C2×#559C2211yescharacteristic
31C2×Q82C2212yes—
32C2×#557C2211yescharacteristic
33C2×#556C2212yes—
34C2×#556C2211yescharacteristic
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#553C2212yes—
38C2×#553C2214yes—
39C2×#550C2211yescharacteristic
40C2×D4×Q8C2212yes—
41C2×D4×Q8C2212yes—
42C2×#548C2212yes—
43C2×#542C2214yes—
44C2×#542C2214yes—
45C2×#536C2214yes—
46C2×#533C2211yescharacteristic
47C2×#533C2211yescharacteristic
48C2×#532C2212yes—
49C2×#532C2211yescharacteristic
50C2×#529C2212yes—
51C2×#529C2214yes—
52C2×C4×#41C2212yes—
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2212yes—
55C22×C4×Q8C2211yescharacteristic
56#2857C2212yes—
57#2857C2212yes—
58#2855C2214yes—
59#2855C2214yes—
60#2855C2214yes—
61#2855C2214yes—
62#2734C2218yes—
63#2731C2218yes—
64#2722C2218yes—
65#2718C2218yes—
66#2717C2218yes—
67#2717C2218yes—
68#2716C2218yes—
69#2713C2218yes—
70#2709C2218yes—
71#2701C2218yes—
72#2701C2218yes—
73#2700C2218yes—
74#2698C2218yes—
75#2695C2218yes—
76#2689C2218yes—
77#2689C2218yes—
78#2687C2218yes—
79#2686C2218yes—
80#2686C2218yes—
81#2686C2218yes—
82#2638C2214yes—
83#2634C2214yes—
84#2634C2212yes—
85#2633C2212yes—
86#2628C2212yes—
87#2627C2214yes—
88#2625C2214yes—
89#2625C2212yes—
90#2625C2214yes—
91#2625C2212yes—
92#2621C2212yes—
93#2616C2212yes—
94#2616C2212yes—
95#2584C2212yes—
96#2582C2212yes—
97#2582C2212yes—
98#2581C2212yes—
99#2581C2212yes—
100#2581C2212yes—
101#2581C2214yes—
102#2568C2212yes—
103#2568C2211yescharacteristic
104#2568C2211yescharacteristic
105#2567C2212yes—
106#2565C2214yes—
107#2562C2212yes—
108#2550C2214yes—
109#2549C2218yes—
110#2547C2214yes—
111#2546C2211yescharacteristic
112#2546C2211yescharacteristic
113#2536C2212yes—
114#2521C2218yes—
115#2503C2212yes—
116#2496C2218yes—
117#2492C2214yes—
118#2488C2218yes—
119#2485C2214yes—
120#2485C2214yes—
121#2485C2214yes—
122#2484C2214yes—
123#2478C2218yes—
124#2469C2218yes—
125#2468C2218yes—
126#2462C2218yes—
127#2453C2214yes—
128#2451C2214yes—
129#2450C2218yes—
130#2447C2218yes—
131#2447C2214yes—
132#2447C2214yes—
133#2447C2218yes—
134#2446C2218yes—
135#2446C2218yes—
136#2444C2218yes—
137#2439C2214yes—
138#2438C2218yes—
139#2434C2212yes—
140#2432C2214yes—
141#2429C2214yes—
142#2427C2214yes—
143#2420C2214yes—
144#2419C2218yes—
145#2419C2218yes—
146#2419C2218yes—
147#2419C2218yes—
148#2419C2218yes—
149#2417C2214yes—
150#2417C2214yes—
151#2415C2214yes—
152#2415C2214yes—
153#2415C2214yes—
154#2409C2214yes—
155#2409C2214yes—
156#2399C2212yes—
157#2398C2212yes—
158#2395C2214yes—
159#2377C2214yes—
160#2365C2214yes—
161#2363C2214yes—
162#2362C2214yes—
163#2354C2212yes—
164#2352C2214yes—
165#2349C2214yes—
166D4×C4⋊C4C2212yes—
167#2339C2214yes—
168#2337C2214yes—
169#2331C2212yes—
170#2328C2212yes—
171#2327C2212yes—
172#2327C2212yes—
173#2323C2214yes—
174#2317C2212yes—
175#2316C2214yes—
176#2311C2214yes—
177#2310C2212yes—
178#2310C2214yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181#2296C2214yes—
182C2×#391C2214yes—
183#2285C2211yescharacteristic
184#2283C2211yescharacteristic
185C22×#41C2312yes—
186C22×#41C2311yescharacteristic
187C22×#41C2312yes—
188C23×Q8C2311yescharacteristic
189C23×Q8C2314yes—
190#563—232no—
191#559—28no—
192#559—216no—
193#559—216no—
194Q82—216no—
195#557—28no—
196#556—28no—
197#556—216no—
198#556—216no—
199#556—216no—
200#553—216no—
201#553—232no—
202#550—28no—
203D4×Q8—216no—
204D4×Q8—216no—
205#548—216no—
206#542—232no—
207#542—232no—
208#536—232no—
209#533—28no—
210#533—28no—
211#532—216no—
212#532D4116yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2318yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2312yes—
225C2×#127C2311yescharacteristic
226#529—232no—
227#529—216no—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2318yes—
232C2×#126C2318yes—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×#125C2314yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2318yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2318yes—
249C2×#123C2318yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2318yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C4×#41—216no—
271C4×#41—216no—
272C4×#41—28no—
273C2×C4×Q8—28no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2314yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2314yes—
321C22×C42C2312yes—
322C22×C42C2314yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2318yes—
331#400C2314yes—
332#400C2318yes—
333#400C2318yes—
334#400C2314yes—
335#399C2314yes—
336#398C2318yes—
337#398C2318yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2318yes—
343#398C2318yes—
344#398C2314yes—
345#398C2314yes—
346#398C2318yes—
347#398C2318yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#397C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#397C2318yes—
361#396C2318yes—
362#396C2318yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2318yes—
367#395C2314yes—
368#395C2314yes—
369#395C2318yes—
370#395C2318yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#393C2314yes—
381#393C2318yes—
382#393C2318yes—
383#391C2314yes—
384#391C2314yes—
385#391C2312yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2318yes—
392#391C2318yes—
393#391C2318yes—
394#391C2314yes—
395#391C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2318yes—
403#391C2318yes—
404#390C2318yes—
405#390C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#389C2314yes—
414#389C2314yes—
415#389C2318yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2318yes—
422#389C2312yes—
423#389C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
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#387C2318yes—
445#387C2314yes—
446#387C2314yes—
447#387C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2314yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#384C2314yes—
467#384C2312yes—
468#383C2312yes—
469#382C2314yes—
470#382C2312yes—
471#382C2312yes—
472#382C2312yes—
473#382C2312yes—
474#381C2318yes—
475#381C2318yes—
476#381C2318yes—
477#381C2318yes—
478#381C2318yes—
479#381C2318yes—
480#381C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2314yes—
487#380C2318yes—
488#380C2318yes—
489#380C2314yes—
490#380C2314yes—
491#380C2318yes—
492#380C2312yes—
493#380C2312yes—
494#380C2312yes—
495#380C2318yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2318yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509#376C2312yes—
510C2×#95C2318yes—
511C2×#95C2318yes—
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—24no—
515C2×#41—48no—
516C2×#41—44no—
517C2×#41—44no—
518C2×#41C2×D4116yes—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—216no—
522C22×Q8—42no—
523C22×Q8—48no—
524C22×Q8—48no—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2418yes—
534C22×Q8C2412yes—
535C22×D4C2414yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2414yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2418yes—
554C23×C4C2418yes—
555C23×C4C2411yescharacteristic
556C4⋊Q8—28no—
557C4⋊Q8—232no—
558C4⋊Q8—28no—
559C4⋊Q8—216no—
560C4⋊Q8—216no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—24no—
565C4⋊Q8—44no—
566C4⋊Q8C2×D418yes—
567#127—28no—
568#127C2×D418yes—
569#126—216no—
570#126—216no—
571#126—216no—
572#126—232no—
573#126—232no—
574#125—216no—
575#125—28no—
576#125—28no—
577#125—28no—
578#124—28no—
579#124—28no—
580#124—28no—
581#124—232no—
582#124—216no—
583#124—216no—
584#124—216no—
585#124C2×D4116yes—
586#123—216no—
587#123—232no—
588#123—232no—
589#123—216no—
590#123—216no—
591C22⋊Q8—28no—
592C22⋊Q8—28no—
593C22⋊Q8—28no—
594C22⋊Q8—28no—
595C22⋊Q8—216no—
596C22⋊Q8—216no—
597C22⋊Q8—28no—
598C22⋊Q8—216no—
599C22⋊Q8—232no—
600C22⋊Q8—232no—
601C22⋊Q8—44no—
602C22⋊Q8—48no—
603C22⋊Q8—44no—
604C22⋊Q8—48no—
605#121—28no—
606#121—216no—
607#121—216no—
608#121—216no—
609#121C2×D4116yes—
610#121C2×D4116yes—
611C4×Q8—28no—
612C4×Q8—28no—
613C4×Q8—28no—
614C4×Q8—216no—
615C4×Q8—216no—
616C4×Q8—24no—
617C4×Q8—28no—
618C4×Q8—24no—
619C4×Q8—24no—
620C4×Q8—24no—
621C4×Q8—28no—
622C4×Q8—24no—
623C4×Q8—24no—
624C4×Q8—28no—
625C4×Q8—28no—
626C4×Q8—28no—
627C4×Q8—28no—
628C4×D4—216no—
629C4×D4—28no—
630C4×D4—216no—
631C4×D4—28no—
632C4×D4—28no—
633C4×D4—216no—
634C4×D4—216no—
635C4×D4—216no—
636C4×D4—28no—
637C4×D4—28no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—24no—
641C4×D4—24no—
642C4×D4—48no—
643C4×D4C2×D4116yes—
644C4×D4C2×D4116yes—
645#117—24no—
646#117—216no—
647#117—28no—
648#117—28no—
649#117—216no—
650#117—28no—
651#117—216no—
652#117—28no—
653#117—48no—
654#117—44no—
655C2×C4⋊C4—28no—
656C2×C4⋊C4—24no—
657C2×C4⋊C4—48no—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C42—28no—
733C2×C42—216no—
734C2×C42—28no—
735C2×C42C2×D418yes—
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2418yes—
743C2×C42C2412yes—
744C2×C42C2414yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2414yes—
751C2×C42C2418yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779#95C2418yes—
780#95C2412yes—
781#95C2412yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789C24C2512yes—
790C24C2511yescharacteristic
791C24C2514yes—
792#41—432no—
793#41—416no—
794#41—432no—
795C2×Q8—22no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—216no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—28no—
811C2×Q8—24no—
812C2×Q8—22no—
813C2×Q8—42no—
814C2×Q8—44no—
815C2×Q8—44no—
816C2×Q8—42no—
817C2×Q8—48no—
818C2×Q8—48no—
819C2×Q8—416no—
820C2×Q8—832no—
821C2×Q8C22×D418yes—
822C2×Q82−1+414yes—
823C2×D4—24no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—22no—
827C2×D4—24no—
828C2×D4—28no—
829C2×D4—24no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—42no—
835C2×D4—44no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4C22×D418yes—
841C2×D4C22×D418yes—
842C2×D4C22×D4116yes—
843C2×D4C22×D418yes—
844C22×C4—22no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—28no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—28no—
851C22×C4—24no—
852C22×C4—28no—
853C22×C4—216no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4C22×D414yes—
877C22×C4C22×D4116yes—
878C22×C4C22×D414yes—
879C22×C4C22×D414yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2518yes—
883C22×C4C2512yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2514yes—
897C22×C4C2511yescharacteristic
898C22×C4C2512yes—
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—216no—
927C4⋊C4—216no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—216no—
931C4⋊C4—24no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—48no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—48no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4C22×D418yes—
947C4⋊C4C22×D418yes—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—216no—
955C22⋊C4—28no—
956C22⋊C4—216no—
957C22⋊C4—216no—
958C22⋊C4—24no—
959C22⋊C4—28no—
960C22⋊C4—24no—
961C22⋊C4—28no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4C22×D4116yes—
974C22⋊C4C22×D4116yes—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—28no—
979C42—24no—
980C42—28no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—28no—
985C42—28no—
986C42—216no—
987C42—24no—
988C42—24no—
989C42—44no—
990C42—48no—
991C42C22×D414yes—
992C42C22×D414yes—
993C42C22×D414yes—
994C42C22×D414yes—
995C23—21no—
996C23—24no—
997C23—21no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23C23×D418yes—
1013C23C23×D412yes—
1014C23C2611yescharacteristic
1015Q8—28no—
1016Q8—48no—
1017Q8—48no—
1018Q8—48no—
1019Q8—44no—
1020Q8—48no—
1021Q8—48no—
1022Q8—48no—
1023Q8—44no—
1024Q8—816no—
1025D4—216no—
1026D4—48no—
1027D4—48no—
1028D4—416no—
1029D4—416no—
1030D4—44no—
1031D4—48no—
1032D4—88no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—232no—
1043C2×C4—28no—
1044C2×C4—28no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—28no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—44no—
1082C2×C4—48no—
1083C2×C4—416no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—84no—
1087C2×C4—88no—
1088C2×C4—84no—
1089C2×C4—816no—
1090C2×C4—168no—
1091C2×C4C23×D412yes—
1092C2×C4C23×D412yes—
1093C2×C4C23×D418yes—
1094C2×C4C23×D412yes—
1095C2×C4C23×D412yes—
1096C2×C4C23×D412yes—
1097C2×C4C23×D412yes—
1098C2×C4C2×2−1+414yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4#58514yes—
1101C2×C4#58512yes—
1102C22—28no—
1103C22—22no—
1104C22—22no—
1105C22—28no—
1106C22—22no—
1107C22—28no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—42no—
1113C22—44no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22C24×D411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58512yes—
1124C22C2×#58511yescharacteristic
1125C222−1+612yes—
1126C4—22no—
1127C4—28no—
1128C4—22no—
1129C4—24no—
1130C4—22no—
1131C4—22no—
1132C4—42no—
1133C4—44no—
1134C4—44no—
1135C4—42no—
1136C4—42no—
1137C4—44no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—44no—
1143C4—48no—
1144C4—44no—
1145C4#348514yes—
1146C4#348914yes—
1147C2—48no—
1148C2—42no—
1149C2—82no—
1150C2C2×#348511yescharacteristic
1151C2C2×#348911yescharacteristic
1152C2#6285911yescharacteristic
1153C2#6295312yes—
1154C2#6296812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3480C2
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×#3550C2semidirect
3. #51527C2semidirect
4. #51212C2semidirect
5. #50892C2semidirect
6. #45389C2semidirect
7. #45338C2semidirect
8. #45141C2semidirect
9. #45137C2semidirect
10. #45096C2semidirect
11. #45095C2semidirect
12. #38923C2semidirect
13. #38911C2semidirect
14. #38051C2semidirect
15. #38027C2semidirect
16. #37376C2semidirect
17. #36405C2semidirect
18. #36274C2semidirect
19. #35307C2semidirect
20. #35297C2semidirect
21. #35248C2semidirect
22. #35179C2semidirect
23. #34627C2semidirect
24. #34367C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35502
C2×#34802
#515272
#512122
#508922
#453892
#453382
#451412
#451372
#450962
#450952
#389232
#389112
#380512
#380272
#373762
#364052
#362742
#353072
#352972
#352482
#351792
#346272
#343672