Finite Group Databasebeta

← #7658923

Subgroups — #7658923

Order 512.

6852 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#42969C212yesmaximal, complemented
4#42913C212yesmaximal, complemented
5#42889C212yesmaximal, complemented
6#42884C212yesmaximal, complemented
7#42444C214yesmaximal, complemented
8#42393C214yesmaximal, complemented
9#41959C214yesmaximal, complemented
10#41940C218yesmaximal, complemented
11#40604C214yesmaximal, complemented
12#40601C214yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37608C212yesmaximal, complemented
15#37554C212yesmaximal, complemented
16#37546C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37536C211yesmaximal, characteristic, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36687C212yesmaximal, complemented
21#35995C212yesmaximal, complemented
22#35985C212yesmaximal, complemented
23#35930C212yesmaximal, complemented
24#35912C212yesmaximal, complemented
25#35787C214yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3517—216no—
28#3510—216no—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×#557C2211yescharacteristic, complemented
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#553C2212yes—
35C2×#553C2214yescomplemented
36C2×#551C2214yes—
37C2×#551C2214yes—
38C2×#550C2212yes—
39C2×#550C2212yes—
40C2×#550C2211yescharacteristic, complemented
41C2×#550C2211yescharacteristic, complemented
42C2×#547C2212yes—
43C2×#547C2211yescharacteristic, complemented
44C2×#542C2212yes—
45C2×#542C2212yes—
46C2×#540C2214yes—
47C2×#540C2212yescomplemented
48C2×#536C2211yescharacteristic
49C2×#535C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#532C2212yescomplemented
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×#529C2212yescomplemented
57C22×#124C2211yescharacteristic
58C2×#520C2212yescomplemented
59C2×#519C2211yescharacteristic
60C2×#518C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62#2822C2211yescharacteristic, complemented
63#2822C2211yescharacteristic, complemented
64#2821C2214yescomplemented
65#2821C2212yescomplemented
66#2821C2212yescomplemented
67#2820C2212yes—
68#2820C2212yescomplemented
69#2820C2212yescomplemented
70#2820C2211yescharacteristic, complemented
71#2820C2211yescharacteristic, complemented
72#2819C2212yes—
73#2819C2212yes—
74#2819C2212yes—
75#2818C2214yescomplemented
76#2817C2212yes—
77#2816C2212yes—
78#2816C2214yescomplemented
79#2815C2214yes—
80#2814C2214yes—
81#2813C2218yescomplemented
82#2721C2218yescomplemented
83#2714C2218yescomplemented
84#2709C2218yes—
85#2708C2218yes—
86#2693C2218yescomplemented
87#2690C2218yescomplemented
88#2676C2218yescomplemented
89#2676C2218yescomplemented
90#2672C2218yescomplemented
91#2671C2218yescomplemented
92#2669C2218yes—
93#2668C2218yes—
94#2663C2214yescomplemented
95#2662C2214yes—
96#2661C2214yescomplemented
97#2657C2212yes—
98#2656C2214yes—
99#2640C2212yes—
100#2639C2214yescomplemented
101#2638C2214yescomplemented
102#2637C2214yescomplemented
103#2637C2214yescomplemented
104#2636C2214yes—
105#2636C2214yescomplemented
106#2636C2218yescomplemented
107#2635C2214yes—
108#2631C2214yes—
109#2630C2218yescomplemented
110#2628C2214yescomplemented
111#2626C2212yes—
112#2624C2212yes—
113#2624C2212yes—
114#2620C2214yes—
115#2620C2214yes—
116#2619C2214yescomplemented
117#2618C2218yescomplemented
118#2617C2212yes—
119#2617C2214yes—
120#2616C2214yes—
121#2609C2218yescomplemented
122#2604C2214yescomplemented
123#2603C2214yes—
124#2601C2218yescomplemented
125#2599C2214yescomplemented
126#2598C2214yescomplemented
127#2592C2212yes—
128#2580C2214yescomplemented
129#2567C2212yescomplemented
130#2564C2214yescomplemented
131#2564C2214yescomplemented
132#2557C2218yescomplemented
133#2555C2218yescomplemented
134#2548C2212yescomplemented
135#2547C2212yescomplemented
136#2544C2214yes—
137#2544C2214yescomplemented
138#2543C2214yes—
139#2543C2214yescomplemented
140#2542C2212yescomplemented
141#2541C2214yes—
142#2540C2212yes—
143#2538C2214yescomplemented
144#2535C2214yes—
145#2481C2218yescomplemented
146#2476C2218yes—
147#2470C2218yes—
148#2467C2218yescomplemented
149#2464C2218yescomplemented
150#2463C2218yescomplemented
151#2454C2214yes—
152#2453C2214yescomplemented
153#2449C2218yescomplemented
154#2448C2214yes—
155#2446C2214yescomplemented
156#2436C2212yes—
157#2433C2212yes—
158#2432C2214yescomplemented
159#2431C2214yes—
160#2430C2214yescomplemented
161#2430C2214yescomplemented
162#2428C2214yes—
163#2428C2214yes—
164#2427C2214yescomplemented
165#2426C2214yescomplemented
166#2424C2218yes—
167#2422C2218yescomplemented
168#2418C2218yes—
169#2416C2218yescomplemented
170#2411C2214yes—
171#2409C2212yes—
172#2408C2212yes—
173#2404C2214yes—
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2398C2214yescomplemented
177#2397C2214yes—
178#2396C2214yescomplemented
179#2395C2212yes—
180#2395C2212yes—
181#2392C2218yescomplemented
182#2388C2214yescomplemented
183#2388C2214yescomplemented
184#2367C2214yescomplemented
185#2366C2214yes—
186#2361C2214yes—
187#2360C2214yescomplemented
188#2355C2212yescomplemented
189#2352C2214yes—
190D4×C4⋊C4C2212yescomplemented
191#2346C2212yes—
192#2343C2214yescomplemented
193#2339C2212yes—
194#2320C2212yescomplemented
195#2318C2214yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yescomplemented
199C2×#382C2212yescomplemented
200#2275C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×D4C2311yescharacteristic
208#559—216no—
209#559—216no—
210#557—28no—
211#556—216no—
212#556—216no—
213#553—216no—
214#553—232no—
215#551—232no—
216#551—232no—
217#550—216no—
218#550—28no—
219#550—216no—
220#550—28no—
221#547—216no—
222#547—28no—
223#542—216no—
224#542—216no—
225#540—232no—
226#540—216no—
227#536—28no—
228#535—28no—
229#533—28no—
230#532—28no—
231#532—216no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2312yes—
237C2×#127C2312yes—
238C2×#127C2311yescharacteristic
239C2×#127C2314yes—
240C2×#127C2312yes—
241C2×#127C2312yes—
242C2×#127C2314yes—
243#529—216no—
244#529—216no—
245#529—28no—
246#529—216no—
247C2×#126C2314yes—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2311yescharacteristic
254C2×#125C2311yescharacteristic
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#124—28no—
259C2×#124C2312yes—
260C2×#124C2311yescharacteristic
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2318yes—
291C2×#121C2311yescharacteristic
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#121C2318yes—
310C2×#121C2318yes—
311C2×#120C2314yes—
312C2×#120C2318yes—
313C2×#120C2314yes—
314#520—216no—
315#519—28no—
316#518—28no—
317C4×#41D4116yescomplemented
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2318yes—
347C2×C4×D4C2318yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×#117C2314yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2311yescharacteristic
357C2×#117C2311yescharacteristic
358C2×#117C2314yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2311yescharacteristic
362C22×C4⋊C4C2312yes—
363C22×C4⋊C4C2314yes—
364C22×C4⋊C4C2314yes—
365C22×C22⋊C4C2312yes—
366C22×C22⋊C4C2312yes—
367C22×C22⋊C4C2314yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2312yes—
373#400C2312yes—
374#400C2312yes—
375#400C2318yes—
376#400C2318yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2312yes—
382#399C2314yes—
383#399C2318yes—
384#399C2318yes—
385#398C2312yes—
386#398C2312yes—
387#398C2318yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2318yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2318yes—
402#397C2314yes—
403#397C2318yes—
404#397C2318yes—
405#396C2318yes—
406#396C2318yes—
407#396C2318yes—
408#396C2314yes—
409#396C2314yes—
410#396C2318yes—
411#396C2318yes—
412#396C2318yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#394C2312yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#394C2314yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2314yes—
433#394C2314yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2318yes—
452#392C2318yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2318yes—
458#392C2318yes—
459#392C2318yes—
460#392C2318yes—
461#392C2318yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#390C2318yes—
467#390C2314yes—
468#390C2318yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2318yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2318yes—
478#389C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2314yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#386C2318yes—
507#386C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2318yes—
514#385C2318yes—
515#385C2314yes—
516#384C2314yes—
517#384C2312yes—
518#383C2314yes—
519#383C2312yes—
520#382C2311yescharacteristic
521#382C2311yescharacteristic
522#382C2312yes—
523#382C2314yes—
524#382C2314yes—
525#382C2314yes—
526#381C2312yes—
527#381C2314yes—
528#380C2318yes—
529#380C2312yes—
530#380C2312yes—
531#380C2314yes—
532#380C2312yes—
533#380C2318yes—
534#380C2318yes—
535#379C2314yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—44no—
560C2×#41—48no—
561C2×#41—84no—
562C2×#41—84no—
563C2×#41—84no—
564C2×#41C2×D418yes—
565C22×Q8—24no—
566C22×Q8—44no—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2412yes—
574C22×D4—24no—
575C22×D4—44no—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2411yescharacteristic
579C22×D4C2412yes—
580C22×D4C2414yes—
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2412yes—
588C22×D4C2411yescharacteristic
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2418yes—
593C22×D4C2418yes—
594C22×D4C2418yes—
595C22×D4C2412yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2412yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2418yes—
606C23×C4C2411yescharacteristic
607C23×C4C2411yescharacteristic
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616#127—28no—
617#127—28no—
618#127—216no—
619#127—28no—
620#127—24no—
621#127—48no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126—216no—
626#126—216no—
627#126—28no—
628#125—28no—
629#125—216no—
630#125—24no—
631#125—24no—
632#125—24no—
633#124—28no—
634#124—28no—
635#124—216no—
636#124—216no—
637#124—28no—
638#124—28no—
639#124—28no—
640#124—28no—
641#124—24no—
642#124—28no—
643#124—48no—
644#124—84no—
645#123—216no—
646#123—28no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—216no—
653#123—216no—
654#123—216no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—24no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—48no—
664C22⋊Q8—88no—
665#121—28no—
666#121—216no—
667#121—28no—
668#121—28no—
669#121—24no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—28no—
674#121—216no—
675#121—28no—
676#121—216no—
677#121—216no—
678#121—216no—
679#121—216no—
680#121—48no—
681#121—88no—
682#121—88no—
683#121—88no—
684#121—88no—
685#120—216no—
686#120—84no—
687#120—88no—
688C4×Q8—28no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—28no—
692C4×Q8—28no—
693C4×Q8—28no—
694C4×Q8—24no—
695C4×Q8—28no—
696C4×Q8—28no—
697C4×Q8C2×D418yes—
698C4×Q8C2×D418yes—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—216no—
702C4×D4—216no—
703C4×D4—28no—
704C4×D4—28no—
705C4×D4—28no—
706C4×D4—216no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—216no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—24no—
713C4×D4—216no—
714C4×D4—28no—
715C4×D4—48no—
716C4×D4—88no—
717C4×D4—88no—
718C4×D4C2×D4116yes—
719C4×D4C2×D418yes—
720C4×D4C2×D4116yes—
721C4×D4C2×D418yes—
722#117—24no—
723#117—24no—
724#117—216no—
725#117—216no—
726#117—28no—
727#117—216no—
728#117—216no—
729#117—82no—
730#117C2×D418yes—
731#117C2×D4116yes—
732C2×C4⋊C4—28no—
733C2×C4⋊C4—216no—
734C2×C4⋊C4—84no—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C22⋊C4—28no—
779C2×C22⋊C4—28no—
780C2×C22⋊C4—216no—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C42C2×D418yes—
826C2×C42C2×D4116yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2418yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843#95C2412yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2412yes—
850#95C2414yes—
851#95C2412yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2414yes—
857#95C2418yes—
858#95C2414yes—
859#95C2418yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2418yes—
864#95C2414yes—
865#95C2414yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—24no—
870C24—44no—
871C24—42no—
872C24—44no—
873C24—42no—
874C24C2514yes—
875C24C2512yes—
876C24C2514yes—
877C24C2511yescharacteristic
878C24C2512yes—
879#41—416no—
880#41—432no—
881#41—816no—
882#41—816no—
883#41—816no—
884C2×Q8—24no—
885C2×Q8—24no—
886C2×Q8—24no—
887C2×Q8—22no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—28no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—416no—
899C2×Q8C22×D414yes—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—24no—
908C2×D4—28no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—22no—
913C2×D4—28no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—48no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—416no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—42no—
927C2×D4—48no—
928C2×D4—48no—
929C2×D4—48no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—48no—
934C2×D4—48no—
935C2×D4—48no—
936C2×D4—42no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—48no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—48no—
945C2×D4—48no—
946C2×D4—48no—
947C2×D4C22×D414yes—
948C2×D4C22×D418yes—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—28no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—28no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—42no—
962C22×C4—41no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—48no—
966C22×C4—44no—
967C22×C4—42no—
968C22×C4—48no—
969C22×C4—48no—
970C22×C4—48no—
971C22×C4—44no—
972C22×C4—48no—
973C22×C4—44no—
974C22×C4—48no—
975C22×C4—48no—
976C22×C4—48no—
977C22×C4C22×D414yes—
978C22×C4C22×D414yes—
979C22×C4C22×D414yes—
980C22×C4C22×D418yes—
981C22×C4C22×D418yes—
982C22×C4C22×D418yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2518yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—22no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—22no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—48no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—48no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4—44no—
1043C4⋊C4C22×D414yes—
1044C4⋊C4C22×D418yes—
1045C4⋊C4C22×D414yes—
1046C4⋊C4C22×D418yes—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—24no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—24no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—48no—
1072C22⋊C4—44no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—48no—
1076C22⋊C4—44no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
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⋊C4C22×D418yes—
1089C22⋊C4C22×D418yes—
1090C22⋊C4C22×D418yes—
1091C42—28no—
1092C42—28no—
1093C42—24no—
1094C42—28no—
1095C42—24no—
1096C42—24no—
1097C42—28no—
1098C42—44no—
1099C42—48no—
1100C42C22×D414yes—
1101C42C22×D418yes—
1102C42C22×D414yes—
1103C42C22×D418yes—
1104C42C22×D418yes—
1105C42C22×D414yes—
1106C42C22×D414yes—
1107C23—24no—
1108C23—22no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—24no—
1113C23—22no—
1114C23—21no—
1115C23—24no—
1116C23—24no—
1117C23—22no—
1118C23—24no—
1119C23—28no—
1120C23—28no—
1121C23—24no—
1122C23—28no—
1123C23—28no—
1124C23—24no—
1125C23—24no—
1126C23—22no—
1127C23—22no—
1128C23—24no—
1129C23—24no—
1130C23—48no—
1131C23—84no—
1132C23—84no—
1133C23—164no—
1134C23—164no—
1135C23C23×D412yes—
1136C23C23×D414yes—
1137C23C2611yescharacteristic
1138Q8—28no—
1139Q8—48no—
1140Q8—48no—
1141Q8—44no—
1142Q8—48no—
1143Q8—84no—
1144Q8—84no—
1145D4—28no—
1146D4—48no—
1147D4—48no—
1148D4—416no—
1149D4—48no—
1150D4—44no—
1151D4—48no—
1152D4—48no—
1153D4—88no—
1154D4—84no—
1155D4—88no—
1156D4—88no—
1157D4—84no—
1158D4—88no—
1159D4—88no—
1160D4—88no—
1161D4—88no—
1162D4—816no—
1163D4—816no—
1164D4—168no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—21no—
1168C2×C4—24no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—28no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—28no—
1189C2×C4—28no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—28no—
1193C2×C4—28no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—28no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—48no—
1208C2×C4—44no—
1209C2×C4—48no—
1210C2×C4—48no—
1211C2×C4—44no—
1212C2×C4—416no—
1213C2×C4—48no—
1214C2×C4—48no—
1215C2×C4—88no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4—88no—
1220C2×C4—168no—
1221C2×C4C23×D414yes—
1222C2×C4C23×D414yes—
1223C2×C4C23×D414yes—
1224C2×C4C23×D412yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D412yes—
1227C2×C4C23×D412yes—
1228C2×C4C23×D412yes—
1229C2×C4C23×D412yes—
1230C2×C4#58514yes—
1231C22—24no—
1232C22—22no—
1233C22—24no—
1234C22—22no—
1235C22—22no—
1236C22—24no—
1237C22—44no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—48no—
1242C22—48no—
1243C22—44no—
1244C22—44no—
1245C22—48no—
1246C22—48no—
1247C22—44no—
1248C22—42no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—42no—
1255C22—44no—
1256C22—168no—
1257C22C24×D411yescharacteristic
1258C22C2×#58512yes—
1259C22H(7,𝔽2)12yes—
1260C22H(7,𝔽2)11yescharacteristic
1261C222−1+611yescharacteristic
1262C4—22no—
1263C4—24no—
1264C4—22no—
1265C4—22no—
1266C4—24no—
1267C4—22no—
1268C4—22no—
1269C4—24no—
1270C4—44no—
1271C4—44no—
1272C4—48no—
1273C4—44no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—44no—
1282C4#344914yes—
1283C2—44no—
1284C2—42no—
1285C2—84no—
1286C2—82no—
1287C2—84no—
1288C2C2×#344911yescharacteristic
1289C2#6285211yescharacteristic
1290C2#6285311yescharacteristic
1291C2#6305612yes—
1292C2#6306012yes—
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×#3510C2semidirect
2. C2×#3517C2semidirect
3. #42969C2semidirect
4. #42913C2semidirect
5. #42889C2semidirect
6. #42884C2semidirect
7. #42444C2semidirect
8. #42393C2semidirect
9. #41959C2semidirect
10. #41940C2semidirect
11. #40604C2semidirect
12. #40601C2semidirect
13. #37640C2semidirect
14. #37608C2semidirect
15. #37554C2semidirect
16. #37546C2semidirect
17. #37541C2semidirect
18. #37536C2semidirect
19. #36699C2semidirect
20. #36687C2semidirect
21. #35995C2semidirect
22. #35985C2semidirect
23. #35930C2semidirect
24. #35912C2semidirect
25. #35787C2semidirect
26. #34191C2semidirect
31. C2×#557C22semidirect
35. C2×#553C22semidirect
40. C2×#550C22semidirect
41. C2×#550C22semidirect
43. C2×#547C22semidirect
47. C2×#540C22semidirect
52. C2×#532C22semidirect
56. C2×#529C22semidirect
58. C2×#520C22semidirect
62. #2822C22semidirect
63. #2822C22semidirect
64. #2821C22semidirect
65. #2821C22semidirect
66. #2821C22semidirect
68. #2820C22semidirect
69. #2820C22semidirect
70. #2820C22semidirect
71. #2820C22semidirect
75. #2818C22semidirect
78. #2816C22semidirect
81. #2813C22semidirect
82. #2721C22semidirect
83. #2714C22semidirect
86. #2693C22semidirect
87. #2690C22semidirect
88. #2676C22semidirect
89. #2676C22semidirect
90. #2672C22semidirect
91. #2671C22semidirect
94. #2663C22semidirect
96. #2661C22semidirect
100. #2639C22semidirect
101. #2638C22semidirect
102. #2637C22semidirect
103. #2637C22semidirect
105. #2636C22semidirect
106. #2636C22semidirect
109. #2630C22semidirect
110. #2628C22semidirect
116. #2619C22semidirect
117. #2618C22semidirect
121. #2609C22semidirect
122. #2604C22semidirect
124. #2601C22semidirect
125. #2599C22semidirect
126. #2598C22semidirect
128. #2580C22semidirect
129. #2567C22semidirect
130. #2564C22semidirect
131. #2564C22semidirect
132. #2557C22semidirect
133. #2555C22semidirect
134. #2548C22semidirect
135. #2547C22semidirect
137. #2544C22semidirect
139. #2543C22semidirect
140. #2542C22semidirect
143. #2538C22semidirect
145. #2481C22semidirect
148. #2467C22semidirect
149. #2464C22semidirect
150. #2463C22semidirect
152. #2453C22semidirect
153. #2449C22semidirect
155. #2446C22semidirect
158. #2432C22semidirect
160. #2430C22semidirect
161. #2430C22semidirect
164. #2427C22semidirect
165. #2426C22semidirect
167. #2422C22semidirect
169. #2416C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2398C22semidirect
178. #2396C22semidirect
181. #2392C22semidirect
182. #2388C22semidirect
183. #2388C22semidirect
184. #2367C22semidirect
187. #2360C22semidirect
188. #2355C22semidirect
190. D4×C4⋊C4C22semidirect
192. #2343C22semidirect
194. #2320C22semidirect
198. #2283C22semidirect
199. C2×#382C22semidirect
200. #2275C22semidirect
317. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35172
#429692
#429132
#428892
#428842
#424442
#423932
#419592
#419402
#406042
#406012
#376402
#376082
#375542
#375462
#375412
#375362
#366992
#366872
#359952
#359852
#359302
#359122
#357872
#341912