Finite Group Databasebeta

← #7658944

Subgroups — #7658944

Order 512.

6860 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3512C211yesmaximal, characteristic, complemented
2C2×#3514C211yesmaximal, characteristic, complemented
3#42988C212yesmaximal, complemented
4#42942C212yesmaximal, complemented
5#42798C214yesmaximal, complemented
6#42485C212yesmaximal, complemented
7#42480C212yesmaximal, complemented
8#42304C214yesmaximal, complemented
9#42172C214yesmaximal, complemented
10#41986C214yesmaximal, complemented
11#41950C214yesmaximal, complemented
12#40528C218yesmaximal, complemented
13#37639C211yesmaximal, characteristic, complemented
14#37606C212yesmaximal, complemented
15#37549C211yesmaximal, characteristic, complemented
16#37546C212yesmaximal, complemented
17#37541C212yesmaximal, complemented
18#37539C211yesmaximal, characteristic, complemented
19#36687C211yesmaximal, characteristic, complemented
20#36684C212yesmaximal, complemented
21#36087C212yesmaximal, complemented
22#36065C212yesmaximal, complemented
23#35853C212yesmaximal, complemented
24#35823C214yesmaximal, complemented
25#35756C212yesmaximal, complemented
26#34193C211yesmaximal, characteristic, complemented
27#3514—216no—
28#3512—216no—
29C2×#559C2211yescharacteristic
30C2×#556C2211yescharacteristic
31C2×#555C2212yes—
32C2×#553C2212yes—
33C2×#553C2212yes—
34C2×#553C2214yescomplemented
35C2×#553C2214yescomplemented
36C2×#552C2212yescomplemented
37C2×#552C2212yescomplemented
38C2×#551C2214yes—
39C2×D4×Q8C2211yescharacteristic
40C2×#548C2212yes—
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic
44C2×#542C2212yes—
45C2×#541C2212yescomplemented
46C2×#540C2212yescomplemented
47C2×#538C2214yes—
48C2×#537C2211yescharacteristic
49C2×#537C2211yescharacteristic
50C2×#532C2211yescharacteristic
51C2×#532C2211yescharacteristic, complemented
52C2×#529C2212yes—
53C2×#529C2211yescharacteristic
54C2×#529C2212yescomplemented
55C2×#529C2212yescomplemented
56C22×#125C2211yescharacteristic, complemented
57C22×#124C2212yes—
58C2×#520C2211yescharacteristic, complemented
59C2×#520C2211yescharacteristic, complemented
60C2×#518C2212yes—
61C2×C4×#41C2211yescharacteristic
62#2823C2218yescomplemented
63#2822C2212yescomplemented
64#2821C2212yescomplemented
65#2820C2212yes—
66#2820C2211yescharacteristic, complemented
67#2820C2212yescomplemented
68#2820C2211yescharacteristic, complemented
69#2820C2212yescomplemented
70#2819C2211yescharacteristic
71#2819C2211yescharacteristic
72#2819C2212yescomplemented
73#2819C2212yescomplemented
74#2818C2212yescomplemented
75#2816C2212yescomplemented
76#2815C2212yes—
77#2814C2214yescomplemented
78#2814C2214yescomplemented
79#2813C2214yes—
80#2813C2214yescomplemented
81#2813C2214yescomplemented
82#2707C2218yescomplemented
83#2704C2218yescomplemented
84#2699C2218yescomplemented
85#2698C2218yescomplemented
86#2685C2218yes—
87#2682C2218yescomplemented
88#2682C2218yescomplemented
89#2681C2218yescomplemented
90#2681C2218yescomplemented
91#2678C2218yescomplemented
92#2678C2218yescomplemented
93#2669C2218yes—
94#2664C2214yescomplemented
95#2663C2214yescomplemented
96#2662C2214yes—
97#2662C2214yescomplemented
98#2662C2218yescomplemented
99#2661C2214yescomplemented
100#2660C2212yescomplemented
101#2641C2212yes—
102#2638C2214yescomplemented
103#2635C2214yes—
104#2633C2214yescomplemented
105#2632C2214yescomplemented
106#2631C2214yescomplemented
107#2630C2218yescomplemented
108#2629C2214yescomplemented
109#2627C2212yescomplemented
110#2626C2214yescomplemented
111#2620C2218yescomplemented
112#2619C2214yescomplemented
113#2618C2212yes—
114#2618C2214yescomplemented
115#2617C2214yescomplemented
116#2615C2214yescomplemented
117#2615C2212yescomplemented
118#2615C2212yescomplemented
119#2614C2214yescomplemented
120#2613C2214yes—
121#2610C2214yes—
122#2610C2214yescomplemented
123#2604C2214yescomplemented
124#2603C2214yescomplemented
125#2601C2218yescomplemented
126#2599C2214yescomplemented
127#2598C2214yescomplemented
128#2592C2214yescomplemented
129#2584C2212yescomplemented
130#2566C2214yescomplemented
131#2563C2212yescomplemented
132#2563C2212yescomplemented
133#2562C2212yes—
134#2561C2214yescomplemented
135#2558C2218yescomplemented
136#2554C2218yescomplemented
137#2541C2212yes—
138#2541C2212yescomplemented
139#2540C2214yescomplemented
140#2539C2214yescomplemented
141#2538C2214yescomplemented
142#2537C2214yescomplemented
143#2536C2214yescomplemented
144#2534C2218yescomplemented
145#2519C2218yescomplemented
146#2504C2212yescomplemented
147#2501C2212yescomplemented
148#2487C2212yescomplemented
149#2486C2212yescomplemented
150#2480C2218yescomplemented
151#2468C2218yescomplemented
152#2464C2218yescomplemented
153#2464C2218yescomplemented
154#2461C2218yescomplemented
155#2459C2218yescomplemented
156#2456C2218yescomplemented
157#2445C2218yescomplemented
158#2440C2214yescomplemented
159#2439C2214yescomplemented
160#2426C2214yescomplemented
161#2426C2214yescomplemented
162#2424C2218yescomplemented
163#2422C2214yes—
164#2420C2214yes—
165#2416C2214yes—
166#2414C2214yes—
167#2413C2214yescomplemented
168#2411C2218yescomplemented
169#2409C2214yescomplemented
170#2408C2214yes—
171#2408C2214yes—
172#2408C2214yes—
173#2406C2214yescomplemented
174#2398C2212yescomplemented
175#2397C2212yes—
176#2396C2214yescomplemented
177#2396C2214yescomplemented
178#2392C2214yescomplemented
179#2392C2214yescomplemented
180#2392C2218yescomplemented
181#2392C2214yescomplemented
182#2388C2212yescomplemented
183#2388C2212yescomplemented
184#2363C2214yescomplemented
185#2361C2214yescomplemented
186#2354C2212yes—
187#2354C2214yescomplemented
188#2354C2214yescomplemented
189#2352C2214yescomplemented
190Q8×C4⋊C4C2212yescomplemented
191#2347C2214yescomplemented
192#2347C2212yescomplemented
193#2341C2212yes—
194#2319C2212yes—
195#2319C2214yescomplemented
196#2285C2211yescharacteristic, complemented
197#2285C2212yescomplemented
198#2283C2211yescharacteristic, complemented
199#2283C2212yescomplemented
200#2276C2212yescomplemented
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2311yescharacteristic
205C23×Q8C2312yes—
206C23×D4C2312yes—
207C23×D4C2312yes—
208#559—28no—
209#556—28no—
210#555—216no—
211#553—216no—
212#553—216no—
213#553—232no—
214#553—232no—
215#552—216no—
216#552—216no—
217#551—232no—
218D4×Q8—28no—
219#548—216no—
220#546—216no—
221#546—216no—
222D42—28no—
223#542—216no—
224#541—216no—
225#540—216no—
226#538—232no—
227#537—28no—
228#537—28no—
229#532—28no—
230#532—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2314yes—
237#529—216no—
238#529—28no—
239#529—216no—
240#529—216no—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125—28no—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#124—216no—
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2318yes—
276C2×#123C2314yes—
277C2×#123C2318yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2318yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#120C2314yes—
310C2×#120C2314yes—
311C2×#120C2318yes—
312C2×#120C2318yes—
313#520—28no—
314#520—28no—
315#518—216no—
316C4×#41D4116yescomplemented
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2318yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×#117C2314yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2314yes—
356C2×#117C2312yes—
357C2×#117C2311yescharacteristic
358C2×#117C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2311yescharacteristic
363C22×C4⋊C4C2311yescharacteristic
364C22×C4⋊C4C2312yes—
365C22×C22⋊C4C2314yes—
366C22×C22⋊C4C2314yes—
367C22×C22⋊C4C2314yes—
368C22×C42C2312yes—
369C22×C42C2311yescharacteristic
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#398C2314yes—
380#398C2318yes—
381#398C2314yes—
382#398C2314yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2314yes—
393#397C2318yes—
394#397C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#396C2314yes—
399#396C2314yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#396C2318yes—
405#396C2318yes—
406#396C2318yes—
407#395C2314yes—
408#395C2312yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2318yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2312yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2318yes—
423#394C2318yes—
424#394C2314yes—
425#394C2314yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#393C2312yes—
437#393C2312yes—
438#393C2312yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2312yes—
444#393C2318yes—
445#392C2312yes—
446#392C2312yes—
447#392C2314yes—
448#392C2314yes—
449#392C2312yes—
450#392C2312yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2318yes—
456#392C2318yes—
457#392C2318yes—
458#392C2318yes—
459#392C2314yes—
460#392C2314yes—
461#392C2318yes—
462#391C2318yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2318yes—
469#390C2318yes—
470#390C2318yes—
471#390C2318yes—
472#390C2318yes—
473#390C2318yes—
474#390C2318yes—
475#389C2314yes—
476#389C2318yes—
477#389C2314yes—
478#389C2314yes—
479#389C2318yes—
480#389C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#388C2318yes—
491#388C2318yes—
492#388C2318yes—
493#388C2318yes—
494#388C2318yes—
495#387C2318yes—
496#387C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2314yes—
503#386C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2314yes—
510#384C2314yes—
511#384C2314yes—
512#384C2312yes—
513#383C2312yes—
514#383C2314yes—
515#382C2314yes—
516#382C2311yescharacteristic
517#382C2311yescharacteristic
518#382C2312yes—
519#382C2314yes—
520#381C2312yes—
521#381C2318yes—
522#381C2314yes—
523#381C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2318yes—
529#380C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2314yes—
533#380C2314yes—
534#380C2312yes—
535#379C2318yes—
536#379C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2318yes—
545C4×C4⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2312yes—
553#376C2314yes—
554C25C2414yes—
555C2×#41—24no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—44no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—84no—
562C2×#41C2×D418yes—
563C22×Q8—28no—
564C22×Q8—84no—
565C22×Q8C2411yescharacteristic
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2414yes—
571C22×D4—28no—
572C22×D4—28no—
573C22×D4—48no—
574C22×D4—84no—
575C22×D4C2412yes—
576C22×D4C2411yescharacteristic
577C22×D4C2414yes—
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2411yescharacteristic
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2412yes—
588C22×D4C2411yescharacteristic
589C22×D4C2412yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2418yes—
595C22×D4C2418yes—
596C22×D4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2411yescharacteristic
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2411yescharacteristic
611C23×C4C2411yescharacteristic
612C23×C4C2412yes—
613C4⋊Q8—28no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616#127—24no—
617#127—24no—
618#127—84no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—28no—
624#126—216no—
625#126—216no—
626#125—216no—
627#125—216no—
628#125—28no—
629#125—28no—
630#125—28no—
631#125—28no—
632#125—24no—
633#124—28no—
634#124—216no—
635#124—24no—
636#124—28no—
637#124—216no—
638#124—28no—
639#124—28no—
640#124—216no—
641#124—24no—
642#124—24no—
643#123—28no—
644#123—216no—
645#123—216no—
646#123—216no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—84no—
652#123—88no—
653#123—88no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—24no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—88no—
664#121—28no—
665#121—28no—
666#121—216no—
667#121—216no—
668#121—216no—
669#121—28no—
670#121—28no—
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—216no—
681#121—48no—
682#121—48no—
683#121—88no—
684#121—88no—
685#120—216no—
686#120—216no—
687#120—88no—
688#120—88no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—28no—
692C4×Q8—24no—
693C4×Q8—48no—
694C4×Q8C2×D418yes—
695C4×Q8C2×D418yes—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—28no—
699C4×D4—216no—
700C4×D4—216no—
701C4×D4—28no—
702C4×D4—216no—
703C4×D4—216no—
704C4×D4—216no—
705C4×D4—28no—
706C4×D4—28no—
707C4×D4—28no—
708C4×D4—24no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—88no—
716C4×D4C2×D418yes—
717C4×D4C2×D4116yes—
718C4×D4C2×D418yes—
719C4×D4C2×D4116yes—
720#117—28no—
721#117—28no—
722#117—28no—
723#117—28no—
724#117—216no—
725#117—216no—
726#117—216no—
727#117—84no—
728#117—82no—
729#117C2×D418yes—
730#117C2×D4116yes—
731C2×C4⋊C4—24no—
732C2×C4⋊C4—24no—
733C2×C4⋊C4—28no—
734C2×C4⋊C4—28no—
735C2×C4⋊C4—28no—
736C2×C4⋊C4—28no—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C22⋊C4—216no—
779C2×C22⋊C4—216no—
780C2×C22⋊C4—216no—
781C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C42C2×D4116yes—
831C2×C42C2×D418yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2418yes—
838C2×C42C2414yes—
839C2×C42C2418yes—
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847#95C2412yes—
848#95C2414yes—
849#95C2412yes—
850#95C2418yes—
851#95C2414yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2418yes—
857#95C2414yes—
858#95C2418yes—
859#95C2414yes—
860#95C2414yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2414yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—28no—
870C24—48no—
871C24—44no—
872C24—48no—
873C24—44no—
874C24C2512yes—
875C24C2514yes—
876C24C2512yes—
877C24C2512yes—
878C24C2512yes—
879C24C2511yescharacteristic
880#41—416no—
881#41—416no—
882#41—416no—
883#41—816no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—22no—
887C2×Q8—24no—
888C2×Q8—28no—
889C2×Q8—24no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—48no—
895C2×Q8—816no—
896C2×Q8C22×D414yes—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—48no—
916C2×D4—42no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—48no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—48no—
935C2×D4—42no—
936C2×D4—48no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—42no—
943C2×D4—44no—
944C2×D4—48no—
945C2×D4—48no—
946C2×D4—48no—
947C2×D4—432no—
948C2×D4—816no—
949C2×D4C22×D414yes—
950C2×D4C22×D418yes—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—28no—
961C22×C4—28no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—42no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—41no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—48no—
975C22×C4—48no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—48no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4C22×D414yes—
983C22×C4C22×D418yes—
984C22×C4C22×D418yes—
985C22×C4C22×D414yes—
986C22×C4C22×D414yes—
987C22×C4C22×D418yes—
988C22×C4C2514yes—
989C22×C4C2518yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2512yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—48no—
1039C4⋊C4—48no—
1040C4⋊C4—44no—
1041C4⋊C4—48no—
1042C4⋊C4—48no—
1043C4⋊C4—48no—
1044C4⋊C4—48no—
1045C4⋊C4C22×D414yes—
1046C4⋊C4C22×D414yes—
1047C4⋊C4C22×D418yes—
1048C4⋊C4C22×D418yes—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—28no—
1073C22⋊C4—48no—
1074C22⋊C4—44no—
1075C22⋊C4—48no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—48no—
1091C22⋊C4—48no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4C22×D418yes—
1096C22⋊C4C22×D418yes—
1097C22⋊C4C22×D418yes—
1098C42—28no—
1099C42—28no—
1100C42—28no—
1101C42—24no—
1102C42—28no—
1103C42—48no—
1104C42—44no—
1105C42—48no—
1106C42C22×D414yes—
1107C42C22×D418yes—
1108C42C22×D414yes—
1109C42C22×D418yes—
1110C42C22×D418yes—
1111C42C22×D414yes—
1112C42C22×D414yes—
1113C23—22no—
1114C23—24no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—21no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—24no—
1125C23—24no—
1126C23—28no—
1127C23—24no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—22no—
1133C23—24no—
1134C23—28no—
1135C23—24no—
1136C23—22no—
1137C23—24no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—416no—
1142C23—88no—
1143C23—88no—
1144C23—168no—
1145C23—168no—
1146C23C23×D414yes—
1147C23C23×D412yes—
1148C23C2611yescharacteristic
1149Q8—28no—
1150Q8—44no—
1151Q8—48no—
1152Q8—44no—
1153Q8—44no—
1154Q8—88no—
1155D4—28no—
1156D4—48no—
1157D4—44no—
1158D4—48no—
1159D4—44no—
1160D4—44no—
1161D4—416no—
1162D4—48no—
1163D4—48no—
1164D4—48no—
1165D4—84no—
1166D4—84no—
1167D4—84no—
1168D4—88no—
1169D4—88no—
1170D4—84no—
1171D4—88no—
1172D4—88no—
1173D4—88no—
1174D4—816no—
1175D4—88no—
1176D4—168no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—28no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—28no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—28no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—28no—
1208C2×C4—24no—
1209C2×C4—28no—
1210C2×C4—22no—
1211C2×C4—28no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—48no—
1217C2×C4—44no—
1218C2×C4—48no—
1219C2×C4—48no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—88no—
1227C2×C4—88no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—88no—
1231C2×C4C23×D414yes—
1232C2×C4C23×D414yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D412yes—
1235C2×C4C23×D412yes—
1236C2×C4C23×D414yes—
1237C2×C4C23×D412yes—
1238C2×C4C23×D412yes—
1239C2×C4C23×D412yes—
1240C2×C4#58514yes—
1241C22—22no—
1242C22—24no—
1243C22—22no—
1244C22—24no—
1245C22—22no—
1246C22—24no—
1247C22—42no—
1248C22—44no—
1249C22—42no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—48no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—48no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—1616no—
1272C22C24×D411yescharacteristic
1273C22C2×#58512yes—
1274C22H(7,𝔽2)11yescharacteristic
1275C22H(7,𝔽2)12yes—
1276C222−1+611yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—24no—
1280C4—22no—
1281C4—24no—
1282C4—22no—
1283C4—22no—
1284C4—24no—
1285C4—44no—
1286C4—48no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4#344914yes—
1297C2—42no—
1298C2—44no—
1299C2—82no—
1300C2—82no—
1301C2—84no—
1302C2—82no—
1303C2C2×#344911yescharacteristic
1304C2#6285211yescharacteristic
1305C2#6285311yescharacteristic
1306C2#6305112yes—
1307C2#6306512yes—
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×#3512C2semidirect
2. C2×#3514C2semidirect
3. #42988C2semidirect
4. #42942C2semidirect
5. #42798C2semidirect
6. #42485C2semidirect
7. #42480C2semidirect
8. #42304C2semidirect
9. #42172C2semidirect
10. #41986C2semidirect
11. #41950C2semidirect
12. #40528C2semidirect
13. #37639C2semidirect
14. #37606C2semidirect
15. #37549C2semidirect
16. #37546C2semidirect
17. #37541C2semidirect
18. #37539C2semidirect
19. #36687C2semidirect
20. #36684C2semidirect
21. #36087C2semidirect
22. #36065C2semidirect
23. #35853C2semidirect
24. #35823C2semidirect
25. #35756C2semidirect
26. #34193C2semidirect
34. C2×#553C22semidirect
35. C2×#553C22semidirect
36. C2×#552C22semidirect
37. C2×#552C22semidirect
45. C2×#541C22semidirect
46. C2×#540C22semidirect
51. C2×#532C22semidirect
54. C2×#529C22semidirect
55. C2×#529C22semidirect
56. C22×#125C22semidirect
58. C2×#520C22semidirect
59. C2×#520C22semidirect
62. #2823C22semidirect
63. #2822C22semidirect
64. #2821C22semidirect
66. #2820C22semidirect
67. #2820C22semidirect
68. #2820C22semidirect
69. #2820C22semidirect
72. #2819C22semidirect
73. #2819C22semidirect
74. #2818C22semidirect
75. #2816C22semidirect
77. #2814C22semidirect
78. #2814C22semidirect
80. #2813C22semidirect
81. #2813C22semidirect
82. #2707C22semidirect
83. #2704C22semidirect
84. #2699C22semidirect
85. #2698C22semidirect
87. #2682C22semidirect
88. #2682C22semidirect
89. #2681C22semidirect
90. #2681C22semidirect
91. #2678C22semidirect
92. #2678C22semidirect
94. #2664C22semidirect
95. #2663C22semidirect
97. #2662C22semidirect
98. #2662C22semidirect
99. #2661C22semidirect
100. #2660C22semidirect
102. #2638C22semidirect
104. #2633C22semidirect
105. #2632C22semidirect
106. #2631C22semidirect
107. #2630C22semidirect
108. #2629C22semidirect
109. #2627C22semidirect
110. #2626C22semidirect
111. #2620C22semidirect
112. #2619C22semidirect
114. #2618C22semidirect
115. #2617C22semidirect
116. #2615C22semidirect
117. #2615C22semidirect
118. #2615C22semidirect
119. #2614C22semidirect
122. #2610C22semidirect
123. #2604C22semidirect
124. #2603C22semidirect
125. #2601C22semidirect
126. #2599C22semidirect
127. #2598C22semidirect
128. #2592C22semidirect
129. #2584C22semidirect
130. #2566C22semidirect
131. #2563C22semidirect
132. #2563C22semidirect
134. #2561C22semidirect
135. #2558C22semidirect
136. #2554C22semidirect
138. #2541C22semidirect
139. #2540C22semidirect
140. #2539C22semidirect
141. #2538C22semidirect
142. #2537C22semidirect
143. #2536C22semidirect
144. #2534C22semidirect
145. #2519C22semidirect
146. #2504C22semidirect
147. #2501C22semidirect
148. #2487C22semidirect
149. #2486C22semidirect
150. #2480C22semidirect
151. #2468C22semidirect
152. #2464C22semidirect
153. #2464C22semidirect
154. #2461C22semidirect
155. #2459C22semidirect
156. #2456C22semidirect
157. #2445C22semidirect
158. #2440C22semidirect
159. #2439C22semidirect
160. #2426C22semidirect
161. #2426C22semidirect
162. #2424C22semidirect
167. #2413C22semidirect
168. #2411C22semidirect
169. #2409C22semidirect
173. #2406C22semidirect
174. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
178. #2392C22semidirect
179. #2392C22semidirect
180. #2392C22semidirect
181. #2392C22semidirect
182. #2388C22semidirect
183. #2388C22semidirect
184. #2363C22semidirect
185. #2361C22semidirect
187. #2354C22semidirect
188. #2354C22semidirect
189. #2352C22semidirect
190. Q8×C4⋊C4C22semidirect
191. #2347C22semidirect
192. #2347C22semidirect
195. #2319C22semidirect
196. #2285C22semidirect
197. #2285C22semidirect
198. #2283C22semidirect
199. #2283C22semidirect
200. #2276C22semidirect
316. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
C2×#35142
#429882
#429422
#427982
#424852
#424802
#423042
#421722
#419862
#419502
#405282
#376392
#376062
#375492
#375462
#375412
#375392
#366872
#366842
#360872
#360652
#358532
#358232
#357562
#341932