Finite Group Databasebeta

← #7715476

Subgroups — #7715476

Order 512.

6744 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3550C211yesmaximal, characteristic, complemented
2C2×#3551C211yesmaximal, characteristic
3#52079C214yesmaximal, complemented
4#52064C214yesmaximal, complemented
5#51589C214yesmaximal, complemented
6#51586C214yesmaximal, complemented
7#47203C218yesmaximal, complemented
8#46825C218yesmaximal, complemented
9#38094C212yesmaximal, complemented
10#38091C212yesmaximal, complemented
11#38085C212yesmaximal, complemented
12#38081C212yesmaximal, complemented
13#37870C212yesmaximal, complemented
14#37868C212yesmaximal, complemented
15#37676C212yesmaximal, complemented
16#37675C212yesmaximal, complemented
17#37633C212yesmaximal, complemented
18#37419C211yesmaximal, characteristic, complemented
19#37388C212yesmaximal, complemented
20#37386C211yesmaximal, characteristic, complemented
21#35327C211yesmaximal, characteristic, complemented
22#35326C212yesmaximal, complemented
23#35316C211yesmaximal, characteristic, complemented
24#35308C212yesmaximal, complemented
25#34070C211yesmaximal, characteristic, complemented
26#3551—216no—
27#3550—216no—
28C2×#563C2212yes—
29C2×#563C2212yes—
30C2×#563C2212yescomplemented
31C2×#560C2212yes—
32C2×#559C2212yes—
33C2×Q82C2212yescomplemented
34C2×#556C2212yes—
35C2×#556C2212yescomplemented
36C2×#555C2212yes—
37C2×#553C2212yes—
38C2×#552C2212yes—
39C2×#551C2212yes—
40C2×D4×Q8C2212yes—
41C2×D4×Q8C2212yescomplemented
42C2×#548C2212yes—
43C2×#546C2212yes—
44C2×#542C2214yes—
45C2×#542C2214yescomplemented
46C2×#540C2214yes—
47C2×#538C2214yes—
48C2×#537C2212yes—
49C2×#536C2211yescharacteristic
50C2×#536C2211yescharacteristic
51C2×#536C2211yescharacteristic
52C2×#536C2212yes—
53C2×#536C2212yescomplemented
54C2×#535C2211yescharacteristic
55C2×#533C2212yescomplemented
56C2×#532C2211yescharacteristic
57C22×C4⋊Q8C2211yescharacteristic, complemented
58C2×#529C2212yes—
59C22×#124C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic, complemented
62#2857C2212yes—
63#2857C2212yescomplemented
64#2857C2212yescomplemented
65#2857C2212yescomplemented
66#2850C2212yes—
67#2850C2212yes—
68#2850C2212yes—
69#2850C2212yes—
70#2814C2218yescomplemented
71#2734C2214yescomplemented
72#2731C2214yes—
73#2729C2218yescomplemented
74#2724C2214yes—
75#2722C2218yes—
76#2717C2214yes—
77#2717C2218yes—
78#2717C2214yescomplemented
79#2716C2218yescomplemented
80#2715C2218yescomplemented
81#2713C2218yescomplemented
82#2709C2214yes—
83#2708C2218yescomplemented
84#2701C2218yescomplemented
85#2697C2214yes—
86#2695C2218yescomplemented
87#2691C2218yes—
88#2689C2218yes—
89#2687C2218yescomplemented
90#2686C2218yescomplemented
91#2686C2218yescomplemented
92#2686C2218yescomplemented
93#2684C2214yes—
94#2684C2218yes—
95#2677C2218yescomplemented
96#2674C2218yes—
97#2674C2218yescomplemented
98#2672C2218yes—
99#2660C2212yescomplemented
100#2658C2212yes—
101#2642C2212yescomplemented
102#2640C2212yes—
103#2637C2218yescomplemented
104#2629C2218yescomplemented
105#2621C2212yes—
106#2621C2212yescomplemented
107#2621C2212yescomplemented
108#2621C2212yescomplemented
109#2620C2212yes—
110#2620C2212yes—
111#2620C2212yes—
112#2620C2212yes—
113#2611C2218yescomplemented
114#2604C2218yescomplemented
115#2567C2212yescomplemented
116#2565C2212yescomplemented
117#2565C2212yescomplemented
118#2564C2218yescomplemented
119#2563C2212yes—
120#2547C2212yes—
121#2547C2214yes—
122#2546C2212yescomplemented
123#2546C2214yescomplemented
124#2545C2212yes—
125#2545C2212yes—
126#2545C2214yes—
127#2544C2214yes—
128#2534C2214yes—
129#2534C2214yes—
130#2503C2212yescomplemented
131#2502C2212yescomplemented
132#2500C2212yes—
133#2500C2212yes—
134#2499C2212yes—
135#2499C2212yes—
136#2499C2212yescomplemented
137#2499C2212yescomplemented
138#2498C2218yescomplemented
139#2486C2214yes—
140#2486C2214yescomplemented
141#2485C2218yescomplemented
142#2480C2218yes—
143#2478C2218yescomplemented
144#2469C2218yescomplemented
145#2468C2218yescomplemented
146#2466C2218yescomplemented
147#2465C2218yescomplemented
148#2462C2218yescomplemented
149#2458C2218yes—
150#2450C2218yescomplemented
151#2449C2218yescomplemented
152#2444C2218yescomplemented
153#2443C2218yescomplemented
154#2438C2218yescomplemented
155#2437C2218yes—
156#2436C2212yes—
157#2436C2212yes—
158#2435C2212yes—
159#2434C2212yes—
160#2434C2212yescomplemented
161#2434C2212yescomplemented
162#2432C2212yes—
163#2432C2212yes—
164#2429C2218yescomplemented
165#2427C2218yescomplemented
166#2425C2218yescomplemented
167#2425C2218yescomplemented
168#2419C2218yes—
169#2418C2218yes—
170#2328C2212yes—
171#2327C2212yescomplemented
172#2327C2212yescomplemented
173#2327C2212yescomplemented
174#2326C2212yes—
175#2326C2212yes—
176#2326C2212yes—
177#2326C2212yescomplemented
178#2325C2214yes—
179#2325C2214yescomplemented
180#2317C2212yescomplemented
181#2310C2211yescharacteristic
182#2310C2211yescharacteristic, complemented
183#2310C2211yescharacteristic, complemented
184#2309C2211yescharacteristic
185#2297C2211yescharacteristic
186#2297C2212yes—
187#2297C2211yescharacteristic, complemented
188C2×#391C2212yescomplemented
189#2290C2212yes—
190#2290C2212yes—
191#2290C2212yescomplemented
192#2290C2212yescomplemented
193#2285C2211yescharacteristic
194#2285C2211yescharacteristic, complemented
195#2285C2211yescharacteristic, complemented
196C2×#376C2211yescharacteristic, complemented
197C22×#41C2312yes—
198C22×#41C2311yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2312yes—
204C23×D4C2311yescharacteristic
205#563—216no—
206#563—216no—
207#563—216no—
208#560—216no—
209#559—216no—
210Q82—216no—
211#556—216no—
212#556—216no—
213#555—216no—
214#553—216no—
215#552—216no—
216#551—216no—
217D4×Q8—216no—
218D4×Q8—216no—
219#548—216no—
220#546—216no—
221#542—232no—
222#542—232no—
223#540—232no—
224#538—232no—
225#537—216no—
226#536—28no—
227#536—28no—
228#536—28no—
229#536—216no—
230#536—48no—
231#535—28no—
232#533—216no—
233#532D4116yes—
234C2×C4⋊Q8—44no—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2312yes—
250C2×#127C2311yescharacteristic
251#529—216no—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#124—44no—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2311yescharacteristic
278C2×#124C2311yescharacteristic
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2318yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2318yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#120C2314yes—
321C2×#120C2312yes—
322C2×#120C2312yes—
323C4×#41—44no—
324C4×#41—44no—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×Q8C2314yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×#117C2311yescharacteristic
347C2×#117C2311yescharacteristic
348C2×#117C2311yescharacteristic
349C2×#117C2311yescharacteristic
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2311yescharacteristic
356C2×#117C2311yescharacteristic
357C2×#117C2311yescharacteristic
358C2×#117C2311yescharacteristic
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2314yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2314yes—
363C22×C42C2311yescharacteristic
364C22×C42C2311yescharacteristic
365C22×C42C2311yescharacteristic
366C22×C42C2311yescharacteristic
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369#400C2318yes—
370#400C2318yes—
371#400C2318yes—
372#399C2318yes—
373#399C2318yes—
374#398C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#397C2318yes—
384#397C2318yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#396C2318yes—
399#395C2318yes—
400#395C2318yes—
401#395C2318yes—
402#395C2318yes—
403#395C2318yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2318yes—
413#393C2318yes—
414#393C2318yes—
415#393C2318yes—
416#393C2318yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2318yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#389C2318yes—
443#389C2318yes—
444#389C2318yes—
445#389C2318yes—
446#389C2318yes—
447#389C2318yes—
448#389C2318yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#387C2318yes—
464#387C2318yes—
465#387C2318yes—
466#387C2318yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2312yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2312yes—
484#386C2314yes—
485#386C2314yes—
486#386C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#385C2318yes—
492#385C2318yes—
493#385C2318yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#384C2312yes—
505#384C2312yes—
506#384C2312yes—
507#384C2312yes—
508#384C2312yes—
509#382C2312yes—
510#382C2312yes—
511#382C2312yes—
512#382C2312yes—
513#382C2312yes—
514#381C2314yes—
515#381C2314yes—
516#381C2314yes—
517#381C2318yes—
518#380C2318yes—
519#380C2318yes—
520#380C2318yes—
521#380C2314yes—
522#380C2318yes—
523#380C2318yes—
524#380C2318yes—
525#380C2314yes—
526#380C2314yes—
527#379C2314yes—
528#379C2318yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C22⋊C4C2318yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536C4×C22⋊C4C2312yes—
537C4×C22⋊C4C2312yes—
538#376C2312yes—
539#376C2312yes—
540#376C2312yes—
541#376C2312yes—
542C2×#95C2314yes—
543C2×#95C2318yes—
544C25C2412yes—
545C2×#41—28no—
546C2×#41—42no—
547C2×#41—42no—
548C2×#41—42no—
549C2×#41—42no—
550C2×#41—44no—
551C2×#41—44no—
552C2×#41C2×D418yes—
553C2×#41C2×D418yes—
554C22×Q8—24no—
555C22×Q8—28no—
556C22×Q8—24no—
557C22×Q8—24no—
558C22×Q8—42no—
559C22×Q8—42no—
560C22×Q8—42no—
561C22×Q8—44no—
562C22×Q8—42no—
563C22×Q8—42no—
564C22×Q8—42no—
565C22×Q8—44no—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2414yes—
570C22×Q8C2414yes—
571C22×Q8C2412yes—
572C22×Q8C2412yes—
573C22×Q8C2412yes—
574C22×Q8C2411yescharacteristic
575C22×Q8C2411yescharacteristic
576C22×D4—24no—
577C22×D4—42no—
578C22×D4—42no—
579C22×D4C2412yes—
580C22×D4C2414yes—
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2411yescharacteristic
589C22×D4C2412yes—
590C22×D4C2411yescharacteristic
591C22×D4C2411yescharacteristic
592C23×C4C2412yes—
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2414yes—
604C23×C4C2412yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C4⋊Q8—28no—
610C4⋊Q8—216no—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—216no—
614C4⋊Q8—216no—
615C4⋊Q8—28no—
616C4⋊Q8—28no—
617C4⋊Q8—28no—
618C4⋊Q8—48no—
619C4⋊Q8—44no—
620C4⋊Q8—44no—
621C4⋊Q8—44no—
622C4⋊Q8C2×D418yes—
623#127—28no—
624#127C2×D418yes—
625#126—216no—
626#126—216no—
627#126—216no—
628#126—216no—
629#126—216no—
630#126—216no—
631#126—216no—
632#125—216no—
633#125—28no—
634#125—216no—
635#124—28no—
636#124—28no—
637#124—28no—
638#124—216no—
639#124—28no—
640#124—216no—
641#124—216no—
642#124—216no—
643#124—28no—
644#124—28no—
645#124—48no—
646#124—44no—
647#124—44no—
648#124—44no—
649#124C2×D418yes—
650#124C2×D418yes—
651#123—28no—
652#123—28no—
653#123—216no—
654#123—28no—
655#123—28no—
656#123—28no—
657#123—28no—
658#123—216no—
659#123—216no—
660#123—216no—
661#123—216no—
662#123—216no—
663#123—416no—
664C22⋊Q8—216no—
665C22⋊Q8—28no—
666C22⋊Q8—28no—
667C22⋊Q8—28no—
668C22⋊Q8—216no—
669C22⋊Q8—28no—
670C22⋊Q8—28no—
671C22⋊Q8—28no—
672C22⋊Q8—28no—
673C22⋊Q8—28no—
674C22⋊Q8—28no—
675C22⋊Q8—216no—
676C22⋊Q8—216no—
677C22⋊Q8—216no—
678C22⋊Q8—216no—
679C22⋊Q8—216no—
680C22⋊Q8—416no—
681#121—216no—
682#121—216no—
683#121—216no—
684#121—216no—
685#121—216no—
686#121—28no—
687#121—28no—
688#121—28no—
689#121—216no—
690#121C2×D4116yes—
691#121C2×D4116yes—
692#120—28no—
693#120—28no—
694#120—216no—
695C4×Q8—216no—
696C4×Q8—216no—
697C4×Q8—28no—
698C4×Q8—28no—
699C4×Q8—28no—
700C4×Q8—216no—
701C4×Q8—44no—
702C4×Q8—44no—
703C4×D4—216no—
704C4×D4—216no—
705C4×D4—216no—
706C4×D4—216no—
707C4×D4—216no—
708C4×D4—28no—
709C4×D4—44no—
710C4×D4—44no—
711C4×D4—44no—
712C4×D4—44no—
713C4×D4—48no—
714C4×D4C2×D4116yes—
715C4×D4C2×D4116yes—
716#117—216no—
717#117—24no—
718#117—24no—
719#117—28no—
720#117—24no—
721#117—24no—
722#117—216no—
723#117—216no—
724#117—28no—
725#117—42no—
726#117—42no—
727#117—42no—
728#117—42no—
729C2×C4⋊C4—28no—
730C2×C4⋊C4—48no—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C22⋊C4—216no—
771C2×C22⋊C4—48no—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C42—24no—
814C2×C42—24no—
815C2×C42—24no—
816C2×C42—44no—
817C2×C42—42no—
818C2×C42C2×D418yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2414yes—
858#95C2414yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867C24—24no—
868C24—42no—
869C24—48no—
870C24—42no—
871C24C2514yes—
872C24C2511yescharacteristic
873C24C2512yes—
874C24C2511yescharacteristic
875C24C2511yescharacteristic
876#41—416no—
877#41—416no—
878#41—816no—
879C2×Q8—28no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—24no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—24no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8—48no—
896C2×Q8—41no—
897C2×Q8—41no—
898C2×Q8—44no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—44no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—88no—
907C2×Q8—88no—
908C2×Q8—88no—
909C2×Q8—816no—
910C2×Q8C22×D414yes—
911C2×Q8C22×D414yes—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—41no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—41no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—41no—
928C2×D4—41no—
929C2×D4—42no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—48no—
936C2×D4—48no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—88no—
940C2×D4C22×D418yes—
941C2×D4C22×D418yes—
942C2×D4C22×D414yes—
943C2×D4C22×D414yes—
944C2×D4C22×D418yes—
945C2×D4C22×D414yes—
946C2×D4C22×D414yes—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—24no—
961C22×C4—28no—
962C22×C4—28no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—48no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—48no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4C22×D414yes—
987C22×C4C22×D418yes—
988C22×C4C22×D414yes—
989C22×C4C22×D414yes—
990C22×C4C22×D418yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2511yescharacteristic
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—216no—
1034C4⋊C4—28no—
1035C4⋊C4—48no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—48no—
1039C4⋊C4—48no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—48no—
1047C4⋊C4—48no—
1048C4⋊C4C22×D418yes—
1049C4⋊C4C22×D418yes—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—216no—
1071C22⋊C4—28no—
1072C22⋊C4—48no—
1073C22⋊C4—44no—
1074C22⋊C4—48no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—44no—
1080C22⋊C4—48no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4C22×D418yes—
1088C22⋊C4C22×D418yes—
1089C22⋊C4C22×D418yes—
1090C22⋊C4C22×D418yes—
1091C42—24no—
1092C42—28no—
1093C42—24no—
1094C42—28no—
1095C42—28no—
1096C42—24no—
1097C42—24no—
1098C42—28no—
1099C42—22no—
1100C42—22no—
1101C42—22no—
1102C42—24no—
1103C42—24no—
1104C42—24no—
1105C42—24no—
1106C42—24no—
1107C42—42no—
1108C42—44no—
1109C42C22×D414yes—
1110C42C22×D418yes—
1111C42C22×D414yes—
1112C42H(5,𝔽2)14yes—
1113C23—22no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—28no—
1130C23—28no—
1131C23—84no—
1132C23—88no—
1133C23—88no—
1134C23—164no—
1135C23C23×D412yes—
1136C23C23×D412yes—
1137C23C23×D412yes—
1138C23C23×D414yes—
1139C23C2611yescharacteristic
1140Q8—44no—
1141Q8—44no—
1142Q8—416no—
1143Q8—48no—
1144Q8—48no—
1145Q8—48no—
1146Q8—88no—
1147Q8—84no—
1148Q8—84no—
1149Q8—84no—
1150D4—48no—
1151D4—48no—
1152D4—48no—
1153D4—44no—
1154D4—44no—
1155D4—44no—
1156D4—44no—
1157D4—48no—
1158D4—84no—
1159D4—88no—
1160D4—88no—
1161D4—88no—
1162D4—88no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—28no—
1175C2×C4—28no—
1176C2×C4—216no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—28no—
1201C2×C4—28no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—28no—
1206C2×C4—28no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—88no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—88no—
1217C2×C4—84no—
1218C2×C4—88no—
1219C2×C4—84no—
1220C2×C4C23×D414yes—
1221C2×C4C23×D412yes—
1222C2×C4C23×D412yes—
1223C2×C4C23×D414yes—
1224C2×C4C23×D414yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D412yes—
1227C2×C4C2×H(5,𝔽2)14yes—
1228C2×C4C2×H(5,𝔽2)12yes—
1229C2×C4#58512yes—
1230C22—22no—
1231C22—24no—
1232C22—22no—
1233C22—22no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—48no—
1251C22—48no—
1252C22—168no—
1253C22C24×D411yescharacteristic
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C2×#58511yescharacteristic
1256C222−1+614yes—
1257C4—24no—
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—24no—
1262C4—24no—
1263C4—24no—
1264C4—44no—
1265C4—44no—
1266C4—44no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C4—42no—
1272C4—42no—
1273C4—44no—
1274C4—42no—
1275C4—44no—
1276C4#349614yes—
1277C2—42no—
1278C2—44no—
1279C2—42no—
1280C2—42no—
1281C2—84no—
1282C2C2×#349611yescharacteristic
1283C2#6285912yes—
1284C2#6288612yes—
1285C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3551C2
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. #52079C2semidirect
4. #52064C2semidirect
5. #51589C2semidirect
6. #51586C2semidirect
7. #47203C2semidirect
8. #46825C2semidirect
9. #38094C2semidirect
10. #38091C2semidirect
11. #38085C2semidirect
12. #38081C2semidirect
13. #37870C2semidirect
14. #37868C2semidirect
15. #37676C2semidirect
16. #37675C2semidirect
17. #37633C2semidirect
18. #37419C2semidirect
19. #37388C2semidirect
20. #37386C2semidirect
21. #35327C2semidirect
22. #35326C2semidirect
23. #35316C2semidirect
24. #35308C2semidirect
25. #34070C2semidirect
30. C2×#563C22semidirect
33. C2×Q82C22semidirect
35. C2×#556C22semidirect
41. C2×D4×Q8C22semidirect
45. C2×#542C22semidirect
53. C2×#536C22semidirect
55. C2×#533C22semidirect
57. C22×C4⋊Q8C22semidirect
61. C2×C4×#41C22semidirect
63. #2857C22semidirect
64. #2857C22semidirect
65. #2857C22semidirect
70. #2814C22semidirect
71. #2734C22semidirect
73. #2729C22semidirect
78. #2717C22semidirect
79. #2716C22semidirect
80. #2715C22semidirect
81. #2713C22semidirect
83. #2708C22semidirect
84. #2701C22semidirect
86. #2695C22semidirect
89. #2687C22semidirect
90. #2686C22semidirect
91. #2686C22semidirect
92. #2686C22semidirect
95. #2677C22semidirect
97. #2674C22semidirect
99. #2660C22semidirect
101. #2642C22semidirect
103. #2637C22semidirect
104. #2629C22semidirect
106. #2621C22semidirect
107. #2621C22semidirect
108. #2621C22semidirect
113. #2611C22semidirect
114. #2604C22semidirect
115. #2567C22semidirect
116. #2565C22semidirect
117. #2565C22semidirect
118. #2564C22semidirect
122. #2546C22semidirect
123. #2546C22semidirect
130. #2503C22semidirect
131. #2502C22semidirect
136. #2499C22semidirect
137. #2499C22semidirect
138. #2498C22semidirect
140. #2486C22semidirect
141. #2485C22semidirect
143. #2478C22semidirect
144. #2469C22semidirect
145. #2468C22semidirect
146. #2466C22semidirect
147. #2465C22semidirect
148. #2462C22semidirect
150. #2450C22semidirect
151. #2449C22semidirect
152. #2444C22semidirect
153. #2443C22semidirect
154. #2438C22semidirect
160. #2434C22semidirect
161. #2434C22semidirect
164. #2429C22semidirect
165. #2427C22semidirect
166. #2425C22semidirect
167. #2425C22semidirect
171. #2327C22semidirect
172. #2327C22semidirect
173. #2327C22semidirect
177. #2326C22semidirect
179. #2325C22semidirect
180. #2317C22semidirect
182. #2310C22semidirect
183. #2310C22semidirect
187. #2297C22semidirect
188. C2×#391C22semidirect
191. #2290C22semidirect
192. #2290C22semidirect
194. #2285C22semidirect
195. #2285C22semidirect
196. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35502
C2×#35512
#520792
#520642
#515892
#515862
#472032
#468252
#380942
#380912
#380852
#380812
#378702
#378682
#376762
#376752
#376332
#374192
#373882
#373862
#353272
#353262
#353162
#353082
#340702