Finite Group Databasebeta

← #7658630

Subgroups — #7658630

Order 512.

6794 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic, complemented
2C2×#3506C211yesmaximal, characteristic, complemented
3#42683C212yesmaximal, complemented
4#42649C212yesmaximal, complemented
5#42481C212yesmaximal, complemented
6#42435C214yesmaximal, complemented
7#42429C212yesmaximal, complemented
8#41425C214yesmaximal, complemented
9#41385C214yesmaximal, complemented
10#40603C214yesmaximal, complemented
11#40520C218yesmaximal, complemented
12#40504C214yesmaximal, complemented
13#37635C211yesmaximal, characteristic, complemented
14#37619C211yesmaximal, characteristic, complemented
15#37559C211yesmaximal, characteristic, complemented
16#37454C212yesmaximal, complemented
17#37447C212yesmaximal, complemented
18#37438C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36652C212yesmaximal, complemented
21#35959C212yesmaximal, complemented
22#35912C212yesmaximal, complemented
23#35846C212yesmaximal, complemented
24#35724C214yesmaximal, complemented
25#35704C212yesmaximal, complemented
26#34190C211yesmaximal, characteristic, complemented
27#3520—216no—
28#3506—216no—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×#556C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#555C2212yes—
35C2×#554C2212yes—
36C2×#553C2214yes—
37C2×#552C2212yes—
38C2×#551C2214yes—
39C2×#550C2211yescharacteristic
40C2×#550C2211yescharacteristic
41C2×D4×Q8C2211yescharacteristic
42C2×#548C2212yes—
43C2×#547C2212yes—
44C2×#547C2211yescharacteristic
45C2×#547C2211yescharacteristic
46C2×#546C2212yes—
47C2×#542C2212yes—
48C2×#539C2214yes—
49C2×#538C2214yes—
50C2×#535C2212yes—
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#532C2211yescharacteristic
54C2×#529C2211yescharacteristic
55C2×#525C2212yes—
56C2×#525C2212yes—
57C2×#525C2212yes—
58C22×C22⋊Q8C2212yes—
59C2×#520C2212yes—
60C2×#520C2212yes—
61C22×C4×D4C2211yescharacteristic
62#2822C2212yescomplemented
63#2821C2212yescomplemented
64#2821C2212yescomplemented
65#2820C2212yescomplemented
66#2817C2212yes—
67#2817C2212yes—
68#2817C2211yescharacteristic
69#2817C2211yescharacteristic
70#2816C2211yescharacteristic
71#2816C2212yes—
72#2816C2212yes—
73#2816C2212yes—
74#2816C2211yescharacteristic
75#2815C2212yes—
76#2814C2214yes—
77#2814C2214yescomplemented
78#2814C2214yescomplemented
79#2813C2214yescomplemented
80#2813C2214yescomplemented
81#2812C2218yes—
82#2722C2218yescomplemented
83#2715C2218yescomplemented
84#2710C2218yescomplemented
85#2708C2218yes—
86#2708C2218yes—
87#2706C2218yescomplemented
88#2700C2218yescomplemented
89#2691C2218yescomplemented
90#2688C2218yes—
91#2680C2218yescomplemented
92#2676C2218yescomplemented
93#2671C2218yes—
94#2663C2214yescomplemented
95#2663C2214yescomplemented
96#2661C2214yes—
97#2660C2212yescomplemented
98#2659C2214yescomplemented
99#2658C2212yescomplemented
100#2642C2212yescomplemented
101#2640C2212yescomplemented
102#2639C2214yescomplemented
103#2638C2218yes—
104#2638C2214yescomplemented
105#2638C2214yescomplemented
106#2635C2214yescomplemented
107#2635C2214yescomplemented
108#2634C2214yescomplemented
109#2633C2214yescomplemented
110#2633C2212yescomplemented
111#2631C2212yescomplemented
112#2625C2214yes—
113#2625C2214yescomplemented
114#2624C2214yes—
115#2623C2214yescomplemented
116#2622C2218yes—
117#2621C2212yescomplemented
118#2619C2212yescomplemented
119#2617C2218yes—
120#2616C2214yescomplemented
121#2614C2214yescomplemented
122#2603C2214yescomplemented
123#2600C2218yes—
124#2592C2212yescomplemented
125#2591C2214yescomplemented
126#2583C2214yescomplemented
127#2581C2212yescomplemented
128#2581C2212yescomplemented
129#2580C2214yescomplemented
130#2568C2212yescomplemented
131#2567C2212yescomplemented
132#2564C2214yescomplemented
133#2564C2214yescomplemented
134#2557C2218yescomplemented
135#2553C2218yescomplemented
136#2548C2212yescomplemented
137#2547C2214yes—
138#2546C2212yescomplemented
139#2544C2214yes—
140#2540C2212yescomplemented
141#2521C2218yescomplemented
142#2499C2214yes—
143#2498C2214yescomplemented
144#2498C2214yescomplemented
145#2487C2214yescomplemented
146#2484C2214yescomplemented
147#2478C2218yescomplemented
148#2477C2218yescomplemented
149#2476C2218yescomplemented
150#2475C2218yescomplemented
151#2473C2218yescomplemented
152#2466C2218yescomplemented
153#2456C2218yescomplemented
154#2452C2214yescomplemented
155#2451C2214yescomplemented
156#2449C2218yescomplemented
157#2447C2214yes—
158#2445C2214yes—
159#2432C2214yes—
160#2432C2214yes—
161#2431C2214yes—
162#2430C2214yescomplemented
163#2430C2214yescomplemented
164#2429C2214yescomplemented
165#2428C2214yes—
166#2427C2214yes—
167#2427C2214yescomplemented
168#2422C2218yescomplemented
169#2415C2218yes—
170#2412C2218yes—
171#2409C2214yescomplemented
172#2407C2214yes—
173#2406C2214yescomplemented
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2396C2212yescomplemented
177#2396C2212yescomplemented
178#2395C2214yes—
179#2395C2214yescomplemented
180#2395C2214yescomplemented
181#2392C2218yes—
182#2388C2214yescomplemented
183#2388C2214yescomplemented
184#2367C2214yescomplemented
185#2365C2214yescomplemented
186#2361C2214yescomplemented
187#2360C2214yescomplemented
188#2357C2212yes—
189#2353C2214yes—
190#2349C2212yes—
191#2344C2212yes—
192#2342C2214yes—
193D4×C22⋊C4C2212yes—
194#2319C2212yes—
195#2318C2214yes—
196#2283C2211yescharacteristic
197#2283C2211yescharacteristic
198#2280C2212yes—
199C2×#381C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C23×Q8C2312yes—
207C23×D4C2311yescharacteristic
208C24×C4C2312yes—
209#559—216no—
210#559—216no—
211#556—28no—
212#556—28no—
213#556—28no—
214#555—216no—
215#554—216no—
216#553—232no—
217#552—216no—
218#551—232no—
219#550—28no—
220#550—28no—
221D4×Q8—28no—
222#548—216no—
223#547—216no—
224#547—28no—
225#547—28no—
226#546—216no—
227#542—216no—
228#539—232no—
229#538—232no—
230#535—216no—
231#533—28no—
232#533—28no—
233#532—28no—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#127C2312yes—
244#529—28no—
245C2×#126C2312yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#124C2311yescharacteristic
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263#525—216no—
264#525—216no—
265#525—216no—
266C2×#123C2314yes—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2318yes—
276C2×C22⋊Q8—216no—
277C2×C22⋊Q8C2311yescharacteristic
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2318yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2318yes—
309C2×#120C2314yes—
310C2×#120C2314yes—
311C2×#120C2314yes—
312#520—216no—
313#520—216no—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4D4116yescomplemented
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2318yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2314yes—
359C22×C4⋊C4C2311yescharacteristic
360C22×C22⋊C4C2314yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2312yes—
363C22×C42C2311yescharacteristic
364#400C2312yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2318yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#399C2318yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2318yes—
392#398C2318yes—
393#398C2318yes—
394#397C2318yes—
395#397C2314yes—
396#397C2318yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2318yes—
403#397C2314yes—
404#397C2318yes—
405#397C2318yes—
406#397C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#396C2314yes—
411#396C2314yes—
412#396C2318yes—
413#396C2318yes—
414#395C2312yes—
415#395C2314yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2318yes—
424#394C2312yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2314yes—
433#394C2314yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2314yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2318yes—
443#394C2318yes—
444#393C2314yes—
445#393C2314yes—
446#393C2312yes—
447#393C2312yes—
448#393C2314yes—
449#393C2314yes—
450#393C2318yes—
451#392C2318yes—
452#392C2314yes—
453#392C2318yes—
454#392C2314yes—
455#392C2314yes—
456#392C2318yes—
457#392C2318yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2318yes—
465#390C2314yes—
466#390C2318yes—
467#390C2314yes—
468#390C2318yes—
469#390C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2318yes—
474#389C2318yes—
475#389C2318yes—
476#389C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#384C2314yes—
514#383C2312yes—
515#383C2312yes—
516#382C2312yes—
517#382C2314yes—
518#382C2312yes—
519#381C2311yescharacteristic
520#381C2311yescharacteristic
521#381C2312yes—
522#381C2314yes—
523#381C2314yes—
524#381C2314yes—
525#381C2318yes—
526#380C2318yes—
527#380C2318yes—
528#380C2314yes—
529#380C2312yes—
530#380C2312yes—
531#380C2314yes—
532#380C2318yes—
533#380C2318yes—
534#379C2314yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2318yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C22⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2312yes—
551#376C2312yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—48no—
561C2×#41—44no—
562C2×#41—44no—
563C2×#41—84no—
564C2×#41—84no—
565C2×#41—84no—
566C22×Q8—28no—
567C22×Q8—84no—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2411yescharacteristic
574C22×Q8C2412yes—
575C22×Q8C2414yes—
576C22×D4—44no—
577C22×D4C2×D418yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2411yescharacteristic
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2418yes—
593C22×D4C2412yes—
594C23×C4—84no—
595C23×C4C2×D4116yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2418yes—
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616C4⋊Q8—24no—
617C4⋊Q8—24no—
618C4⋊Q8—48no—
619#127—28no—
620#127—28no—
621#127—24no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126—216no—
626#126—28no—
627#125—216no—
628#125—24no—
629#125—28no—
630#125—28no—
631#124—28no—
632#124—28no—
633#124—28no—
634#124—216no—
635#124—216no—
636#124—216no—
637#124—24no—
638#124—28no—
639#124—48no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—28no—
645#123—216no—
646#123—216no—
647#123—216no—
648#123—216no—
649#123—88no—
650C22⋊Q8—24no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—24no—
657C22⋊Q8—24no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—28no—
662C22⋊Q8—28no—
663C22⋊Q8—216no—
664C22⋊Q8—28no—
665C22⋊Q8—216no—
666C22⋊Q8—48no—
667C22⋊Q8—88no—
668#121—216no—
669#121—216no—
670#121—216no—
671#121—28no—
672#121—24no—
673#121—28no—
674#121—28no—
675#121—28no—
676#121—28no—
677#121—28no—
678#121—216no—
679#121—216no—
680#121—48no—
681#121—88no—
682#120—216no—
683#120—216no—
684#120—216no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8—28no—
689C4×Q8—24no—
690C4×Q8—28no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—28no—
694C4×D4—28no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—216no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—216no—
705C4×D4—24no—
706C4×D4—28no—
707C4×D4—28no—
708C4×D4—48no—
709C4×D4—88no—
710C4×D4C2×D418yes—
711C4×D4C2×D4116yes—
712C4×D4C2×D418yes—
713C4×D4C2×D418yes—
714C4×D4C2×D418yes—
715C4×D4C2×D4116yes—
716#117—28no—
717#117—28no—
718#117—28no—
719#117—28no—
720#117—28no—
721#117—216no—
722#117—216no—
723#117—28no—
724#117—84no—
725C2×C4⋊C4—216no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—216no—
728C2×C4⋊C4—28no—
729C2×C4⋊C4C2×D418yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C22⋊C4—216no—
775C2×C22⋊C4—84no—
776C2×C22⋊C4C2×D4116yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C42C2×D418yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2418yes—
830C2×C42C2414yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2418yes—
840#95C2418yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2418yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2418yes—
854#95C2414yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2414yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865C24—44no—
866C24—44no—
867C24—44no—
868C24C22×D418yes—
869C24C2512yes—
870C24C2514yes—
871C24C2511yescharacteristic
872C24C2512yes—
873C24C2512yes—
874#41—432no—
875#41—432no—
876#41—816no—
877#41—816no—
878#41—816no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—22no—
882C2×Q8—24no—
883C2×Q8—22no—
884C2×Q8—22no—
885C2×Q8—24no—
886C2×Q8—28no—
887C2×Q8—28no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—48no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—816no—
898C2×D4—24no—
899C2×D4—28no—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—22no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—416no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—48no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—48no—
922C2×D4—48no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—44no—
927C2×D4—48no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4C22×D414yes—
933C2×D4C22×D414yes—
934C2×D4C22×D418yes—
935C22×C4—24no—
936C22×C4—28no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—44no—
946C22×C4—42no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—42no—
952C22×C4—48no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—48no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—48no—
959C22×C4—48no—
960C22×C4—48no—
961C22×C4—48no—
962C22×C4—816no—
963C22×C4C22×D414yes—
964C22×C4C22×D414yes—
965C22×C4C22×D414yes—
966C22×C4C22×D418yes—
967C22×C4C22×D418yes—
968C22×C4C22×D418yes—
969C22×C4C22×D418yes—
970C22×C4C22×D418yes—
971C22×C4C2518yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—48no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—48no—
1032C4⋊C4—48no—
1033C4⋊C4C22×D418yes—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D414yes—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—24no—
1057C22⋊C4—42no—
1058C22⋊C4—44no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—42no—
1065C22⋊C4—48no—
1066C22⋊C4—44no—
1067C22⋊C4—48no—
1068C22⋊C4—48no—
1069C22⋊C4—44no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4C22×D418yes—
1076C22⋊C4C22×D418yes—
1077C22⋊C4C22×D418yes—
1078C22⋊C4C22×D418yes—
1079C42—28no—
1080C42—28no—
1081C42—28no—
1082C42—28no—
1083C42—24no—
1084C42—24no—
1085C42—24no—
1086C42—28no—
1087C42—44no—
1088C42—48no—
1089C42C22×D414yes—
1090C42C22×D414yes—
1091C42C22×D414yes—
1092C42C22×D414yes—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—22no—
1097C23—24no—
1098C23—24no—
1099C23—24no—
1100C23—24no—
1101C23—22no—
1102C23—22no—
1103C23—24no—
1104C23—22no—
1105C23—28no—
1106C23—22no—
1107C23—28no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—48no—
1113C23—48no—
1114C23—48no—
1115C23—816no—
1116C23C23×D414yes—
1117C23C23×D412yes—
1118C23C23×D414yes—
1119C23C2611yescharacteristic
1120Q8—44no—
1121Q8—48no—
1122Q8—44no—
1123Q8—44no—
1124Q8—48no—
1125Q8—48no—
1126Q8—84no—
1127Q8—88no—
1128D4—28no—
1129D4—28no—
1130D4—48no—
1131D4—48no—
1132D4—44no—
1133D4—48no—
1134D4—416no—
1135D4—416no—
1136D4—48no—
1137D4—84no—
1138D4—88no—
1139D4—88no—
1140D4—88no—
1141D4—88no—
1142D4—88no—
1143D4—816no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—28no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—28no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—28no—
1172C2×C4—24no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—44no—
1186C2×C4—48no—
1187C2×C4—48no—
1188C2×C4—48no—
1189C2×C4—48no—
1190C2×C4—48no—
1191C2×C4—44no—
1192C2×C4—416no—
1193C2×C4—416no—
1194C2×C4—48no—
1195C2×C4—88no—
1196C2×C4—88no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—168no—
1200C2×C4C23×D412yes—
1201C2×C4C23×D414yes—
1202C2×C4C23×D414yes—
1203C2×C4C23×D412yes—
1204C2×C4C23×D412yes—
1205C2×C4C23×D412yes—
1206C2×C4C23×D412yes—
1207C2×C4C23×D412yes—
1208C2×C4#58514yes—
1209C22—22no—
1210C22—24no—
1211C22—24no—
1212C22—22no—
1213C22—24no—
1214C22—24no—
1215C22—22no—
1216C22—24no—
1217C22—24no—
1218C22—48no—
1219C22—48no—
1220C22—44no—
1221C22—44no—
1222C22—48no—
1223C22—44no—
1224C22—48no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—816no—
1232C22C24×D411yescharacteristic
1233C22C2×#58512yes—
1234C22H(7,𝔽2)12yes—
1235C222−1+612yes—
1236C4—22no—
1237C4—22no—
1238C4—24no—
1239C4—24no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—44no—
1244C4—44no—
1245C4—48no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4#344914yes—
1257C2—44no—
1258C2—44no—
1259C2—42no—
1260C2—82no—
1261C2—84no—
1262C2C2×#344911yescharacteristic
1263C2#6284211yescharacteristic
1264C2#6285911yescharacteristic
1265C2#6305614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3520C2semidirect
2. C2×#3506C2semidirect
3. #42683C2semidirect
4. #42649C2semidirect
5. #42481C2semidirect
6. #42435C2semidirect
7. #42429C2semidirect
8. #41425C2semidirect
9. #41385C2semidirect
10. #40603C2semidirect
11. #40520C2semidirect
12. #40504C2semidirect
13. #37635C2semidirect
14. #37619C2semidirect
15. #37559C2semidirect
16. #37454C2semidirect
17. #37447C2semidirect
18. #37438C2semidirect
19. #36699C2semidirect
20. #36652C2semidirect
21. #35959C2semidirect
22. #35912C2semidirect
23. #35846C2semidirect
24. #35724C2semidirect
25. #35704C2semidirect
26. #34190C2semidirect
62. #2822C22semidirect
63. #2821C22semidirect
64. #2821C22semidirect
65. #2820C22semidirect
77. #2814C22semidirect
78. #2814C22semidirect
79. #2813C22semidirect
80. #2813C22semidirect
82. #2722C22semidirect
83. #2715C22semidirect
84. #2710C22semidirect
87. #2706C22semidirect
88. #2700C22semidirect
89. #2691C22semidirect
91. #2680C22semidirect
92. #2676C22semidirect
94. #2663C22semidirect
95. #2663C22semidirect
97. #2660C22semidirect
98. #2659C22semidirect
99. #2658C22semidirect
100. #2642C22semidirect
101. #2640C22semidirect
102. #2639C22semidirect
104. #2638C22semidirect
105. #2638C22semidirect
106. #2635C22semidirect
107. #2635C22semidirect
108. #2634C22semidirect
109. #2633C22semidirect
110. #2633C22semidirect
111. #2631C22semidirect
113. #2625C22semidirect
115. #2623C22semidirect
117. #2621C22semidirect
118. #2619C22semidirect
120. #2616C22semidirect
121. #2614C22semidirect
122. #2603C22semidirect
124. #2592C22semidirect
125. #2591C22semidirect
126. #2583C22semidirect
127. #2581C22semidirect
128. #2581C22semidirect
129. #2580C22semidirect
130. #2568C22semidirect
131. #2567C22semidirect
132. #2564C22semidirect
133. #2564C22semidirect
134. #2557C22semidirect
135. #2553C22semidirect
136. #2548C22semidirect
138. #2546C22semidirect
140. #2540C22semidirect
141. #2521C22semidirect
143. #2498C22semidirect
144. #2498C22semidirect
145. #2487C22semidirect
146. #2484C22semidirect
147. #2478C22semidirect
148. #2477C22semidirect
149. #2476C22semidirect
150. #2475C22semidirect
151. #2473C22semidirect
152. #2466C22semidirect
153. #2456C22semidirect
154. #2452C22semidirect
155. #2451C22semidirect
156. #2449C22semidirect
162. #2430C22semidirect
163. #2430C22semidirect
164. #2429C22semidirect
167. #2427C22semidirect
168. #2422C22semidirect
171. #2409C22semidirect
173. #2406C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
179. #2395C22semidirect
180. #2395C22semidirect
182. #2388C22semidirect
183. #2388C22semidirect
184. #2367C22semidirect
185. #2365C22semidirect
186. #2361C22semidirect
187. #2360C22semidirect
323. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#35062
#426832
#426492
#424812
#424352
#424292
#414252
#413852
#406032
#405202
#405042
#376352
#376192
#375592
#374542
#374472
#374382
#366992
#366522
#359592
#359122
#358462
#357242
#357042
#341902