Finite Group Databasebeta

← #7658535

Subgroups — #7658535

Order 512.

7186 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic, complemented
2C2×#3506C211yesmaximal, characteristic, complemented
3#42682C212yesmaximal, complemented
4#42646C212yesmaximal, complemented
5#42480C212yesmaximal, complemented
6#42424C212yesmaximal, complemented
7#42420C214yesmaximal, complemented
8#41424C214yesmaximal, complemented
9#41380C214yesmaximal, complemented
10#40602C214yesmaximal, complemented
11#40524C218yesmaximal, complemented
12#40501C214yesmaximal, complemented
13#37634C211yesmaximal, characteristic, complemented
14#37618C211yesmaximal, characteristic, complemented
15#37560C211yesmaximal, characteristic, complemented
16#37454C212yesmaximal, complemented
17#37446C212yesmaximal, complemented
18#37437C212yesmaximal, complemented
19#36687C211yesmaximal, characteristic, complemented
20#36652C212yesmaximal, complemented
21#36062C212yesmaximal, complemented
22#36022C212yesmaximal, complemented
23#35941C212yesmaximal, complemented
24#35752C214yesmaximal, complemented
25#35730C212yesmaximal, complemented
26#34190C211yesmaximal, characteristic, complemented
27#3519—216no—
28#3506—216no—
29C2×#559C2214yescomplemented
30C2×#556C2212yescomplemented
31C2×#555C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×#555C2211yescharacteristic, complemented
34C2×#554C2211yescharacteristic
35C2×#553C2212yes—
36C2×#553C2212yes—
37C2×#553C2212yes—
38C2×#553C2212yescomplemented
39C2×#550C2211yescharacteristic
40C2×#550C2212yescomplemented
41C2×#547C2211yescharacteristic
42C2×#547C2211yescharacteristic, complemented
43C2×#546C2214yes—
44C2×#546C2212yes—
45C2×D42C2212yes—
46C2×D42C2211yescharacteristic
47C2×#540C2212yes—
48C2×#538C2214yes—
49C2×#538C2214yescomplemented
50C2×#535C2212yes—
51C2×#533C2211yescharacteristic, complemented
52C2×#532C2211yescharacteristic
53C2×#532C2211yescharacteristic, complemented
54C2×#529C2211yescharacteristic
55C2×#525C2212yes—
56C2×#525C2212yescomplemented
57C2×#525C2212yescomplemented
58C22×#121C2212yes—
59C2×#520C2212yescomplemented
60C2×#518C2212yes—
61C22×C4×D4C2211yescharacteristic
62#2821C2212yescomplemented
63#2820C2212yescomplemented
64#2819C2212yescomplemented
65#2818C2212yescomplemented
66#2817C2212yescomplemented
67#2816C2212yes—
68#2816C2212yescomplemented
69#2816C2212yescomplemented
70#2816C2211yescharacteristic, complemented
71#2816C2211yescharacteristic, complemented
72#2815C2211yescharacteristic
73#2815C2211yescharacteristic
74#2815C2212yescomplemented
75#2815C2212yescomplemented
76#2814C2214yescomplemented
77#2814C2214yescomplemented
78#2813C2214yescomplemented
79#2813C2214yescomplemented
80#2813C2214yescomplemented
81#2812C2218yescomplemented
82#2693C2218yescomplemented
83#2689C2218yescomplemented
84#2686C2218yescomplemented
85#2685C2218yescomplemented
86#2684C2218yescomplemented
87#2676C2218yescomplemented
88#2673C2218yescomplemented
89#2672C2218yescomplemented
90#2672C2218yescomplemented
91#2671C2218yescomplemented
92#2669C2218yescomplemented
93#2669C2218yescomplemented
94#2663C2214yescomplemented
95#2661C2214yescomplemented
96#2661C2214yescomplemented
97#2660C2212yescomplemented
98#2657C2212yescomplemented
99#2656C2214yescomplemented
100#2641C2212yescomplemented
101#2640C2212yescomplemented
102#2639C2214yescomplemented
103#2638C2214yescomplemented
104#2638C2214yescomplemented
105#2635C2214yescomplemented
106#2635C2218yescomplemented
107#2635C2214yescomplemented
108#2634C2212yescomplemented
109#2632C2214yescomplemented
110#2632C2212yescomplemented
111#2631C2214yescomplemented
112#2628C2212yescomplemented
113#2628C2212yescomplemented
114#2624C2214yescomplemented
115#2623C2214yescomplemented
116#2617C2218yescomplemented
117#2616C2214yescomplemented
118#2615C2214yescomplemented
119#2615C2214yescomplemented
120#2613C2218yescomplemented
121#2613C2214yescomplemented
122#2604C2214yescomplemented
123#2600C2218yescomplemented
124#2584C2212yescomplemented
125#2563C2212yescomplemented
126#2562C2212yescomplemented
127#2561C2214yescomplemented
128#2559C2218yescomplemented
129#2555C2218yescomplemented
130#2547C2212yescomplemented
131#2543C2214yescomplemented
132#2543C2214yescomplemented
133#2542C2212yescomplemented
134#2541C2212yescomplemented
135#2539C2214yescomplemented
136#2537C2214yescomplemented
137#2536C2214yescomplemented
138#2535C2212yescomplemented
139#2535C2214yescomplemented
140#2535C2212yescomplemented
141#2521C2218yescomplemented
142#2500C2214yescomplemented
143#2498C2214yescomplemented
144#2498C2214yescomplemented
145#2486C2214yescomplemented
146#2485C2214yescomplemented
147#2482C2214yescomplemented
148#2472C2218yescomplemented
149#2469C2218yescomplemented
150#2467C2218yescomplemented
151#2461C2218yescomplemented
152#2458C2218yescomplemented
153#2457C2218yescomplemented
154#2456C2218yescomplemented
155#2442C2214yescomplemented
156#2441C2214yescomplemented
157#2431C2214yescomplemented
158#2430C2214yescomplemented
159#2430C2214yescomplemented
160#2428C2218yescomplemented
161#2428C2214yescomplemented
162#2428C2214yescomplemented
163#2422C2214yes—
164#2420C2214yes—
165#2418C2218yescomplemented
166#2416C2214yescomplemented
167#2414C2218yescomplemented
168#2414C2214yescomplemented
169#2410C2218yescomplemented
170#2408C2214yes—
171#2408C2214yes—
172#2408C2214yescomplemented
173#2404C2214yescomplemented
174#2398C2212yescomplemented
175#2397C2212yescomplemented
176#2395C2214yescomplemented
177#2395C2214yescomplemented
178#2392C2218yescomplemented
179#2392C2212yescomplemented
180#2392C2212yescomplemented
181#2388C2214yescomplemented
182#2388C2214yescomplemented
183#2388C2214yescomplemented
184#2363C2214yescomplemented
185#2361C2214yescomplemented
186#2357C2212yes—
187#2354C2214yescomplemented
188#2353C2214yescomplemented
189#2352C2214yescomplemented
190#2349C2212yescomplemented
191#2344C2212yescomplemented
192#2342C2214yescomplemented
193D4×C22⋊C4C2212yes—
194#2319C2212yes—
195#2318C2214yescomplemented
196#2283C2211yescharacteristic, complemented
197#2283C2211yescharacteristic, complemented
198#2280C2212yescomplemented
199C2×#381C2212yescomplemented
200#2275C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C23×D4C2312yes—
207C23×D4C2312yes—
208C23×D4C2314yes—
209C23×D4C2311yescharacteristic
210C24×C4C2312yes—
211#559—232no—
212#556—216no—
213#555—28no—
214#555—28no—
215#555—28no—
216#554—28no—
217#553—216no—
218#553—216no—
219#553—216no—
220#553—216no—
221#550—28no—
222#550—216no—
223#547—28no—
224#547—28no—
225#546—216no—
226#546—232no—
227D42—216no—
228D42—28no—
229#540—216no—
230#538—232no—
231#538—232no—
232#535—216no—
233#533—28no—
234#532—28no—
235#532—28no—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2314yes—
243C2×#127C2312yes—
244C2×#127C2314yes—
245#529—28no—
246C2×#126C2312yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#124C2311yescharacteristic
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261#525—216no—
262#525—216no—
263#525—216no—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2312yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2318yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2311yescharacteristic
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2318yes—
281C2×#121—216no—
282C2×#121C2311yescharacteristic
283C2×#121C2312yes—
284C2×#121C2311yescharacteristic
285C2×#121C2311yescharacteristic
286C2×#121C2312yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2318yes—
309C2×#121C2318yes—
310C2×#121C2318yes—
311C2×#121C2318yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×#120C2314yes—
317C2×#120C2318yes—
318C2×#120C2318yes—
319#520—216no—
320#518—216no—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×D4D4116yescomplemented
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2318yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2314yes—
362C22×C4⋊C4C2312yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2312yes—
365C22×C4⋊C4C2311yescharacteristic
366C22×C22⋊C4C2314yes—
367C22×C22⋊C4C2314yes—
368C22×C22⋊C4C2314yes—
369C22×C22⋊C4C2312yes—
370C22×C42C2311yescharacteristic
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2318yes—
375#400C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2318yes—
383#399C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2318yes—
390#397C2312yes—
391#397C2314yes—
392#397C2318yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2318yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2318yes—
401#397C2318yes—
402#396C2314yes—
403#396C2314yes—
404#396C2318yes—
405#396C2318yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2318yes—
410#395C2314yes—
411#394C2314yes—
412#394C2318yes—
413#394C2312yes—
414#394C2312yes—
415#394C2314yes—
416#394C2318yes—
417#394C2318yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2312yes—
440#393C2312yes—
441#393C2314yes—
442#393C2318yes—
443#393C2314yes—
444#392C2314yes—
445#392C2312yes—
446#392C2312yes—
447#392C2314yes—
448#392C2312yes—
449#392C2312yes—
450#392C2318yes—
451#392C2314yes—
452#392C2318yes—
453#392C2318yes—
454#392C2314yes—
455#392C2318yes—
456#392C2318yes—
457#392C2318yes—
458#392C2314yes—
459#392C2318yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2318yes—
464#392C2318yes—
465#391C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2318yes—
469#390C2314yes—
470#390C2318yes—
471#390C2318yes—
472#390C2314yes—
473#389C2314yes—
474#389C2318yes—
475#389C2314yes—
476#389C2314yes—
477#389C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#384C2314yes—
511#383C2312yes—
512#383C2312yes—
513#382C2314yes—
514#382C2312yes—
515#382C2312yes—
516#381C2312yes—
517#381C2311yescharacteristic
518#381C2311yescharacteristic
519#381C2318yes—
520#381C2314yes—
521#381C2314yes—
522#381C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2318yes—
526#380C2314yes—
527#380C2312yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2318yes—
533#380C2318yes—
534#379C2318yes—
535#379C2314yes—
536#379C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C22⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2312yes—
551#376C2312yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C25C2414yes—
555C25C2412yes—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—28no—
561C2×#41—48no—
562C2×#41—84no—
563C2×#41—84no—
564C2×#41—84no—
565C2×#41—84no—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×D4—216no—
572C22×D4—28no—
573C22×D4—28no—
574C22×D4—44no—
575C22×D4—44no—
576C22×D4—44no—
577C22×D4—84no—
578C22×D4—88no—
579C22×D4C2×D418yes—
580C22×D4C2412yes—
581C22×D4C2411yescharacteristic
582C22×D4C2411yescharacteristic
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2411yescharacteristic
593C22×D4C2412yes—
594C22×D4C2411yescharacteristic
595C22×D4C2411yescharacteristic
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2412yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2414yes—
604C22×D4C2414yes—
605C22×D4C2418yes—
606C22×D4C2418yes—
607C22×D4C2412yes—
608C23×C4—84no—
609C23×C4C2×D4116yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2411yescharacteristic
614C23×C4C2414yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C23×C4C2418yes—
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2412yes—
623C23×C4C2412yes—
624C23×C4C2412yes—
625C23×C4C2412yes—
626C23×C4C2411yescharacteristic
627C4⋊Q8—24no—
628C4⋊Q8—24no—
629C4⋊Q8—24no—
630C4⋊Q8—24no—
631#127—216no—
632#127—28no—
633#127—24no—
634#127—24no—
635#127—84no—
636#126—216no—
637#126—216no—
638#126—216no—
639#126—28no—
640#125—28no—
641#125—24no—
642#125—28no—
643#124—216no—
644#124—216no—
645#124—216no—
646#124—216no—
647#124—24no—
648#124—28no—
649#124—28no—
650#124—84no—
651#123—216no—
652#123—216no—
653#123—216no—
654#123—28no—
655#123—216no—
656#123—216no—
657#123—216no—
658#123—216no—
659#123—88no—
660C22⋊Q8—24no—
661C22⋊Q8—28no—
662C22⋊Q8—28no—
663C22⋊Q8—28no—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C22⋊Q8—216no—
667C22⋊Q8—88no—
668#121—28no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—28no—
674#121—24no—
675#121—28no—
676#121—216no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—24no—
681#121—24no—
682#121—28no—
683#121—28no—
684#121—28no—
685#121—28no—
686#121—28no—
687#121—28no—
688#121—216no—
689#121—216no—
690#121—216no—
691#121—216no—
692#121—48no—
693#121—48no—
694#121—88no—
695#121—88no—
696#121—88no—
697#121—88no—
698#120—216no—
699#120—216no—
700#120—216no—
701#120—216no—
702#120—216no—
703#120—88no—
704#120—88no—
705C4×Q8—216no—
706C4×Q8—24no—
707C4×Q8—28no—
708C4×Q8—28no—
709C4×D4—28no—
710C4×D4—216no—
711C4×D4—216no—
712C4×D4—216no—
713C4×D4—216no—
714C4×D4—216no—
715C4×D4—216no—
716C4×D4—28no—
717C4×D4—28no—
718C4×D4—216no—
719C4×D4—216no—
720C4×D4—28no—
721C4×D4—24no—
722C4×D4—28no—
723C4×D4—24no—
724C4×D4—24no—
725C4×D4—28no—
726C4×D4—48no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—88no—
730C4×D4C2×D418yes—
731C4×D4C2×D4116yes—
732C4×D4C2×D418yes—
733C4×D4C2×D418yes—
734C4×D4C2×D4116yes—
735C4×D4C2×D418yes—
736#117—28no—
737#117—28no—
738#117—28no—
739#117—28no—
740#117—28no—
741#117—28no—
742#117—28no—
743#117—28no—
744#117—84no—
745C2×C4⋊C4—28no—
746C2×C4⋊C4—28no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4C2×D418yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2418yes—
776C2×C4⋊C4C2418yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2418yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C22⋊C4—216no—
783C2×C22⋊C4—216no—
784C2×C22⋊C4—84no—
785C2×C22⋊C4C2×D4116yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2418yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2418yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2418yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2418yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C42C2×D418yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2418yes—
845C2×C42C2414yes—
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850#95C2412yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2418yes—
862#95C2418yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872#95C2418yes—
873#95C2418yes—
874C24—28no—
875C24—44no—
876C24—44no—
877C24—44no—
878C24—44no—
879C24—44no—
880C24—48no—
881C24—48no—
882C24C22×D418yes—
883C24C2512yes—
884C24C2514yes—
885C24C2512yes—
886C24C2512yes—
887C24C2512yes—
888C24C2511yescharacteristic
889C24C2512yes—
890#41—432no—
891#41—816no—
892#41—816no—
893#41—816no—
894#41—816no—
895C2×Q8—24no—
896C2×Q8—22no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—24no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—28no—
909C2×D4—24no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—22no—
920C2×D4—24no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—28no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—416no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—48no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—48no—
950C2×D4—48no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—48no—
956C2×D4—48no—
957C2×D4—48no—
958C2×D4—48no—
959C2×D4—48no—
960C2×D4—48no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—44no—
965C2×D4—48no—
966C2×D4—48no—
967C2×D4—48no—
968C2×D4—432no—
969C2×D4—816no—
970C2×D4—832no—
971C2×D4C22×D414yes—
972C2×D4C22×D414yes—
973C2×D4C22×D418yes—
974C22×C4—24no—
975C22×C4—28no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—28no—
987C22×C4—44no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—48no—
995C22×C4—48no—
996C22×C4—48no—
997C22×C4—48no—
998C22×C4—48no—
999C22×C4—48no—
1000C22×C4—48no—
1001C22×C4—48no—
1002C22×C4—816no—
1003C22×C4C22×D414yes—
1004C22×C4C22×D414yes—
1005C22×C4C22×D414yes—
1006C22×C4C22×D418yes—
1007C22×C4C22×D418yes—
1008C22×C4C22×D418yes—
1009C22×C4C22×D418yes—
1010C22×C4C22×D418yes—
1011C22×C4C2518yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2511yescharacteristic
1030C4⋊C4—24no—
1031C4⋊C4—22no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—28no—
1052C4⋊C4—48no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—48no—
1056C4⋊C4—48no—
1057C4⋊C4—48no—
1058C4⋊C4—44no—
1059C4⋊C4—48no—
1060C4⋊C4C22×D414yes—
1061C4⋊C4C22×D414yes—
1062C4⋊C4C22×D418yes—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—28no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—48no—
1089C22⋊C4—42no—
1090C22⋊C4—48no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—48no—
1097C22⋊C4—48no—
1098C22⋊C4—48no—
1099C22⋊C4—48no—
1100C22⋊C4—48no—
1101C22⋊C4—48no—
1102C22⋊C4—48no—
1103C22⋊C4—48no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—48no—
1107C22⋊C4—48no—
1108C22⋊C4—44no—
1109C22⋊C4—48no—
1110C22⋊C4C22×D418yes—
1111C22⋊C4C22×D418yes—
1112C22⋊C4C22×D418yes—
1113C22⋊C4C22×D418yes—
1114C42—28no—
1115C42—28no—
1116C42—28no—
1117C42—24no—
1118C42—28no—
1119C42—28no—
1120C42—48no—
1121C42—44no—
1122C42C22×D414yes—
1123C42C22×D414yes—
1124C42C22×D414yes—
1125C42C22×D414yes—
1126C23—24no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—24no—
1139C23—22no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—22no—
1147C23—28no—
1148C23—28no—
1149C23—22no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—22no—
1155C23—48no—
1156C23—48no—
1157C23—48no—
1158C23—416no—
1159C23—88no—
1160C23—88no—
1161C23—816no—
1162C23—168no—
1163C23—168no—
1164C23C23×D414yes—
1165C23C23×D414yes—
1166C23C23×D412yes—
1167C23C2611yescharacteristic
1168Q8—48no—
1169Q8—44no—
1170Q8—48no—
1171Q8—84no—
1172Q8—84no—
1173D4—28no—
1174D4—28no—
1175D4—48no—
1176D4—44no—
1177D4—48no—
1178D4—48no—
1179D4—44no—
1180D4—44no—
1181D4—416no—
1182D4—48no—
1183D4—416no—
1184D4—48no—
1185D4—48no—
1186D4—48no—
1187D4—84no—
1188D4—88no—
1189D4—84no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—88no—
1194D4—88no—
1195D4—88no—
1196D4—88no—
1197D4—88no—
1198D4—816no—
1199D4—88no—
1200D4—168no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—28no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—28no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—28no—
1226C2×C4—28no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—28no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—28no—
1236C2×C4—44no—
1237C2×C4—48no—
1238C2×C4—48no—
1239C2×C4—48no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—44no—
1243C2×C4—48no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C2×C4—88no—
1249C2×C4—88no—
1250C2×C4—88no—
1251C2×C4—168no—
1252C2×C4C23×D412yes—
1253C2×C4C23×D414yes—
1254C2×C4C23×D414yes—
1255C2×C4C23×D412yes—
1256C2×C4C23×D412yes—
1257C2×C4C23×D412yes—
1258C2×C4C23×D412yes—
1259C2×C4C23×D412yes—
1260C2×C4#58514yes—
1261C22—22no—
1262C22—24no—
1263C22—24no—
1264C22—22no—
1265C22—24no—
1266C22—24no—
1267C22—22no—
1268C22—24no—
1269C22—24no—
1270C22—48no—
1271C22—44no—
1272C22—48no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—48no—
1277C22—44no—
1278C22—44no—
1279C22—48no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—816no—
1294C22—1616no—
1295C22C24×D411yescharacteristic
1296C22C2×#58512yes—
1297C22H(7,𝔽2)12yes—
1298C22H(7,𝔽2)12yes—
1299C4—22no—
1300C4—22no—
1301C4—24no—
1302C4—24no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—44no—
1307C4—48no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4#344914yes—
1318C2—44no—
1319C2—42no—
1320C2—44no—
1321C2—82no—
1322C2—82no—
1323C2—84no—
1324C2—82no—
1325C2C2×#344911yescharacteristic
1326C2#6284211yescharacteristic
1327C2#6285211yescharacteristic
1328C2#6305114yes—
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×#3519C2semidirect
2. C2×#3506C2semidirect
3. #42682C2semidirect
4. #42646C2semidirect
5. #42480C2semidirect
6. #42424C2semidirect
7. #42420C2semidirect
8. #41424C2semidirect
9. #41380C2semidirect
10. #40602C2semidirect
11. #40524C2semidirect
12. #40501C2semidirect
13. #37634C2semidirect
14. #37618C2semidirect
15. #37560C2semidirect
16. #37454C2semidirect
17. #37446C2semidirect
18. #37437C2semidirect
19. #36687C2semidirect
20. #36652C2semidirect
21. #36062C2semidirect
22. #36022C2semidirect
23. #35941C2semidirect
24. #35752C2semidirect
25. #35730C2semidirect
26. #34190C2semidirect
29. C2×#559C22semidirect
30. C2×#556C22semidirect
33. C2×#555C22semidirect
38. C2×#553C22semidirect
40. C2×#550C22semidirect
42. C2×#547C22semidirect
49. C2×#538C22semidirect
51. C2×#533C22semidirect
53. C2×#532C22semidirect
56. C2×#525C22semidirect
57. C2×#525C22semidirect
59. C2×#520C22semidirect
62. #2821C22semidirect
63. #2820C22semidirect
64. #2819C22semidirect
65. #2818C22semidirect
66. #2817C22semidirect
68. #2816C22semidirect
69. #2816C22semidirect
70. #2816C22semidirect
71. #2816C22semidirect
74. #2815C22semidirect
75. #2815C22semidirect
76. #2814C22semidirect
77. #2814C22semidirect
78. #2813C22semidirect
79. #2813C22semidirect
80. #2813C22semidirect
81. #2812C22semidirect
82. #2693C22semidirect
83. #2689C22semidirect
84. #2686C22semidirect
85. #2685C22semidirect
86. #2684C22semidirect
87. #2676C22semidirect
88. #2673C22semidirect
89. #2672C22semidirect
90. #2672C22semidirect
91. #2671C22semidirect
92. #2669C22semidirect
93. #2669C22semidirect
94. #2663C22semidirect
95. #2661C22semidirect
96. #2661C22semidirect
97. #2660C22semidirect
98. #2657C22semidirect
99. #2656C22semidirect
100. #2641C22semidirect
101. #2640C22semidirect
102. #2639C22semidirect
103. #2638C22semidirect
104. #2638C22semidirect
105. #2635C22semidirect
106. #2635C22semidirect
107. #2635C22semidirect
108. #2634C22semidirect
109. #2632C22semidirect
110. #2632C22semidirect
111. #2631C22semidirect
112. #2628C22semidirect
113. #2628C22semidirect
114. #2624C22semidirect
115. #2623C22semidirect
116. #2617C22semidirect
117. #2616C22semidirect
118. #2615C22semidirect
119. #2615C22semidirect
120. #2613C22semidirect
121. #2613C22semidirect
122. #2604C22semidirect
123. #2600C22semidirect
124. #2584C22semidirect
125. #2563C22semidirect
126. #2562C22semidirect
127. #2561C22semidirect
128. #2559C22semidirect
129. #2555C22semidirect
130. #2547C22semidirect
131. #2543C22semidirect
132. #2543C22semidirect
133. #2542C22semidirect
134. #2541C22semidirect
135. #2539C22semidirect
136. #2537C22semidirect
137. #2536C22semidirect
138. #2535C22semidirect
139. #2535C22semidirect
140. #2535C22semidirect
141. #2521C22semidirect
142. #2500C22semidirect
143. #2498C22semidirect
144. #2498C22semidirect
145. #2486C22semidirect
146. #2485C22semidirect
147. #2482C22semidirect
148. #2472C22semidirect
149. #2469C22semidirect
150. #2467C22semidirect
151. #2461C22semidirect
152. #2458C22semidirect
153. #2457C22semidirect
154. #2456C22semidirect
155. #2442C22semidirect
156. #2441C22semidirect
157. #2431C22semidirect
158. #2430C22semidirect
159. #2430C22semidirect
160. #2428C22semidirect
161. #2428C22semidirect
162. #2428C22semidirect
165. #2418C22semidirect
166. #2416C22semidirect
167. #2414C22semidirect
168. #2414C22semidirect
169. #2410C22semidirect
172. #2408C22semidirect
173. #2404C22semidirect
174. #2398C22semidirect
175. #2397C22semidirect
176. #2395C22semidirect
177. #2395C22semidirect
178. #2392C22semidirect
179. #2392C22semidirect
180. #2392C22semidirect
181. #2388C22semidirect
182. #2388C22semidirect
183. #2388C22semidirect
184. #2363C22semidirect
185. #2361C22semidirect
187. #2354C22semidirect
188. #2353C22semidirect
189. #2352C22semidirect
190. #2349C22semidirect
191. #2344C22semidirect
192. #2342C22semidirect
195. #2318C22semidirect
196. #2283C22semidirect
197. #2283C22semidirect
198. #2280C22semidirect
199. C2×#381C22semidirect
200. #2275C22semidirect
325. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
C2×#35062
#426822
#426462
#424802
#424242
#424202
#414242
#413802
#406022
#405242
#405012
#376342
#376182
#375602
#374542
#374462
#374372
#366872
#366522
#360622
#360222
#359412
#357522
#357302
#341902