Finite Group Databasebeta

← #7715417

Subgroups — #7715417

Order 512.

7020 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3546C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic, complemented
3#51072C214yesmaximal, complemented
4#50695C214yesmaximal, complemented
5#47957C218yesmaximal, complemented
6#47687C218yesmaximal, complemented
7#46428C214yesmaximal, complemented
8#46360C214yesmaximal, complemented
9#39169C212yesmaximal, complemented
10#39163C212yesmaximal, complemented
11#38956C212yesmaximal, complemented
12#38945C212yesmaximal, complemented
13#38092C212yesmaximal, complemented
14#38089C212yesmaximal, complemented
15#38082C212yesmaximal, complemented
16#38080C212yesmaximal, complemented
17#37618C211yesmaximal, characteristic, complemented
18#37539C211yesmaximal, characteristic, complemented
19#37423C212yesmaximal, complemented
20#37302C212yesmaximal, complemented
21#35341C211yesmaximal, characteristic, complemented
22#35293C211yesmaximal, characteristic, complemented
23#35276C212yesmaximal, complemented
24#35264C212yesmaximal, complemented
25#34081C211yesmaximal, characteristic, complemented
26#3559—216no—
27#3546—216no—
28C2×#563C2212yescomplemented
29C2×#562C2212yes—
30C2×#560C2214yes—
31C2×#556C2211yescharacteristic
32C2×#554C2212yescomplemented
33C2×#553C2212yes—
34C2×#553C2212yes—
35C2×#553C2212yescomplemented
36C2×#550C2211yescharacteristic
37C2×#550C2212yes—
38C2×#547C2211yescharacteristic
39C2×#547C2212yescomplemented
40C2×#547C2214yescomplemented
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic
44C2×#544C2212yescomplemented
45C2×#542C2212yes—
46C2×#540C2212yescomplemented
47C2×#539C2212yescomplemented
48C2×#539C2214yescomplemented
49C2×#538C2214yes—
50C2×#537C2212yes—
51C2×#537C2212yes—
52C2×#535C2212yes—
53C2×#535C2212yes—
54C2×#532C2211yescharacteristic
55C2×#532C2211yescharacteristic
56C2×#532C2211yescharacteristic, complemented
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic, complemented
59#2867C2211yescharacteristic
60#2862C2211yescharacteristic, complemented
61#2861C2212yes—
62#2861C2212yescomplemented
63#2861C2212yescomplemented
64#2858C2211yescharacteristic
65#2858C2212yescomplemented
66#2858C2211yescharacteristic, complemented
67#2856C2212yes—
68#2850C2212yescomplemented
69#2820C2214yescomplemented
70#2815C2214yescomplemented
71#2728C2218yescomplemented
72#2716C2218yescomplemented
73#2714C2218yes—
74#2705C2218yescomplemented
75#2703C2218yescomplemented
76#2703C2218yescomplemented
77#2703C2218yescomplemented
78#2702C2218yescomplemented
79#2700C2218yescomplemented
80#2696C2218yescomplemented
81#2693C2218yescomplemented
82#2690C2218yescomplemented
83#2688C2218yes—
84#2687C2218yescomplemented
85#2678C2218yes—
86#2678C2218yescomplemented
87#2676C2218yescomplemented
88#2676C2218yescomplemented
89#2673C2218yescomplemented
90#2673C2218yescomplemented
91#2673C2218yescomplemented
92#2671C2218yescomplemented
93#2669C2218yescomplemented
94#2669C2218yescomplemented
95#2660C2212yescomplemented
96#2657C2212yescomplemented
97#2642C2212yescomplemented
98#2641C2212yes—
99#2641C2212yes—
100#2641C2212yescomplemented
101#2640C2212yes—
102#2640C2212yescomplemented
103#2633C2214yescomplemented
104#2631C2214yescomplemented
105#2620C2212yescomplemented
106#2619C2212yes—
107#2619C2212yes—
108#2619C2212yescomplemented
109#2618C2214yescomplemented
110#2615C2214yescomplemented
111#2591C2214yescomplemented
112#2591C2214yescomplemented
113#2568C2212yescomplemented
114#2566C2212yes—
115#2566C2212yescomplemented
116#2566C2212yescomplemented
117#2565C2212yescomplemented
118#2563C2212yescomplemented
119#2562C2214yescomplemented
120#2562C2214yescomplemented
121#2555C2218yescomplemented
122#2554C2218yescomplemented
123#2547C2212yescomplemented
124#2544C2212yes—
125#2544C2212yes—
126#2544C2214yescomplemented
127#2544C2214yescomplemented
128#2541C2212yes—
129#2541C2212yescomplemented
130#2541C2212yescomplemented
131#2535C2214yescomplemented
132#2504C2212yes—
133#2504C2211yescharacteristic
134#2504C2211yescharacteristic, complemented
135#2503C2212yescomplemented
136#2501C2211yescharacteristic
137#2501C2211yescharacteristic, complemented
138#2500C2212yes—
139#2499C2212yescomplemented
140#2491C2218yescomplemented
141#2490C2218yescomplemented
142#2481C2218yescomplemented
143#2481C2218yescomplemented
144#2477C2218yescomplemented
145#2472C2218yescomplemented
146#2472C2218yescomplemented
147#2467C2218yescomplemented
148#2464C2218yescomplemented
149#2464C2218yescomplemented
150#2461C2218yescomplemented
151#2457C2218yescomplemented
152#2456C2218yescomplemented
153#2433C2212yes—
154#2433C2212yes—
155#2431C2214yescomplemented
156#2431C2212yescomplemented
157#2431C2218yescomplemented
158#2431C2212yescomplemented
159#2431C2214yescomplemented
160#2431C2212yescomplemented
161#2431C2212yescomplemented
162#2427C2218yescomplemented
163#2424C2218yes—
164#2418C2218yescomplemented
165#2416C2218yescomplemented
166#2412C2218yescomplemented
167#2410C2218yes—
168#2407C2218yescomplemented
169#2406C2214yescomplemented
170#2404C2218yescomplemented
171#2337C2212yes—
172#2336C2212yescomplemented
173#2335C2214yescomplemented
174#2334C2214yescomplemented
175#2333C2212yes—
176#2332C2212yescomplemented
177#2328C2212yes—
178#2328C2212yescomplemented
179#2328C2212yescomplemented
180#2326C2212yescomplemented
181#2311C2212yescomplemented
182#2311C2212yescomplemented
183#2311C2212yescomplemented
184#2309C2212yes—
185C4×#127C2212yescomplemented
186C4×#124C2212yescomplemented
187#2298C2212yescomplemented
188#2297C2212yescomplemented
189#2295C2212yescomplemented
190#2293C2212yescomplemented
191C2×#390C2212yes—
192#2290C2212yes—
193#2290C2212yescomplemented
194#2283C2211yescharacteristic, complemented
195C4×#117C2211yescharacteristic, complemented
196C4×#117C2212yescomplemented
197C22×#41C2312yes—
198C22×#41C2312yes—
199C22×#41C2312yes—
200C22×#41C2314yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×D4C2312yes—
204C23×D4C2312yes—
205#563—216no—
206#562—216no—
207#560—232no—
208#556—28no—
209#554—216no—
210#553—216no—
211#553—216no—
212#553—216no—
213#550—28no—
214#550—216no—
215#547—232no—
216#547—28no—
217#547—216no—
218#546—216no—
219#546—216no—
220D42—28no—
221#544—216no—
222#542—216no—
223#540—216no—
224#539—232no—
225#539—216no—
226#538—232no—
227#537—216no—
228#537—216no—
229#535—216no—
230#535—216no—
231#532—28no—
232#532—28no—
233#532—28no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2314yes—
239C2×#127C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2312yes—
242C2×#127C2311yescharacteristic
243C2×#127C2314yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2312yes—
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2314yes—
250#529D4116yescomplemented
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2312yes—
256C2×#125—28no—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2318yes—
273C2×#124C2314yes—
274C2×#124C2311yescharacteristic
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2311yescharacteristic
304C2×#121C2312yes—
305C2×#121C2311yescharacteristic
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2318yes—
321C2×#121C2318yes—
322C2×#121C2318yes—
323C2×#121C2318yes—
324C2×#121C2311yescharacteristic
325C2×#120C2314yes—
326C2×#120C2314yes—
327C2×#120C2314yes—
328C2×#120C2314yes—
329C2×#120C2318yes—
330C2×#120C2318yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2318yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C4⋊C4C2312yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2318yes—
363C22×C42C2312yes—
364C22×C42C2311yescharacteristic
365#400C2318yes—
366#400C2318yes—
367#400C2318yes—
368#400C2318yes—
369#399C2314yes—
370#399C2314yes—
371#398C2318yes—
372#398C2318yes—
373#397C2314yes—
374#397C2314yes—
375#397C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#396C2318yes—
381#396C2318yes—
382#396C2318yes—
383#396C2318yes—
384#395C2318yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2318yes—
396#394C2318yes—
397#394C2318yes—
398#393C2318yes—
399#393C2318yes—
400#393C2318yes—
401#392C2318yes—
402#392C2318yes—
403#392C2318yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#392C2318yes—
408#392C2318yes—
409#392C2318yes—
410#392C2318yes—
411#392C2318yes—
412#392C2318yes—
413#392C2318yes—
414#392C2318yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2318yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#390C2312yes—
426#390C2312yes—
427#390C2318yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2318yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2318yes—
443#390C2314yes—
444#390C2318yes—
445#390C2314yes—
446#390C2318yes—
447#389C2314yes—
448#389C2314yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#387C2318yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2314yes—
483#386C2314yes—
484#386C2318yes—
485#386C2314yes—
486#386C2314yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2314yes—
500#385C2314yes—
501#384C2312yes—
502#384C2312yes—
503#383C2312yes—
504#382C2312yes—
505#382C2312yes—
506#382C2312yes—
507#382C2312yes—
508#382C2312yes—
509#381C2312yes—
510#381C2318yes—
511#380C2318yes—
512#380C2318yes—
513#380C2318yes—
514#380C2318yes—
515#380C2312yes—
516#380C2318yes—
517#379C2318yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2318yes—
530C4×C22⋊C4C2311yescharacteristic
531C4×C22⋊C4C2311yescharacteristic
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2318yes—
535#376C2312yes—
536#376C2312yes—
537#376C2312yes—
538C43C2312yes—
539C43C2311yescharacteristic
540C43C2311yescharacteristic
541C25C2414yes—
542C2×#41—28no—
543C2×#41—216no—
544C2×#41—28no—
545C2×#41—28no—
546C2×#41—28no—
547C2×#41—28no—
548C2×#41—44no—
549C2×#41—44no—
550C2×#41—44no—
551C2×#41—44no—
552C2×#41—84no—
553C2×#41—88no—
554C2×#41—84no—
555C2×#41—84no—
556C22×Q8C2412yes—
557C22×Q8C2414yes—
558C22×Q8C2412yes—
559C22×Q8C2412yes—
560C22×Q8C2411yescharacteristic
561C22×D4—28no—
562C22×D4—28no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4—84no—
566C22×D4C2412yes—
567C22×D4C2411yescharacteristic
568C22×D4C2412yes—
569C22×D4C2411yescharacteristic
570C22×D4C2414yes—
571C22×D4C2412yes—
572C22×D4C2412yes—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2414yes—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2414yes—
580C22×D4C2412yes—
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2418yes—
588C22×D4C2418yes—
589C22×D4C2418yes—
590C22×D4C2418yes—
591C22×D4C2412yes—
592C22×D4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2412yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2412yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2412yes—
606C23×C4C2414yes—
607C23×C4C2411yescharacteristic
608C23×C4C2411yescharacteristic
609C4⋊Q8—216no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614#127—216no—
615#127—24no—
616#127—24no—
617#127—24no—
618#127—28no—
619#127—44no—
620#127—44no—
621#127—44no—
622#127—44no—
623#127—84no—
624#127—84no—
625#126—216no—
626#126—216no—
627#126—216no—
628#126—216no—
629#126C2×D4116yes—
630#125—216no—
631#125—28no—
632#125—28no—
633#125—28no—
634#125—28no—
635#125—28no—
636#125C2×D418yes—
637#124—216no—
638#124—28no—
639#124—28no—
640#124—28no—
641#124—28no—
642#124—44no—
643#124—44no—
644#124—84no—
645#124—88no—
646#124—84no—
647#124C2×D418yes—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—216no—
653#123—216no—
654#123—216no—
655#123—216no—
656#123—216no—
657#123—84no—
658#123—84no—
659#123C2×D4116yes—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—28no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—216no—
666C22⋊Q8—216no—
667C22⋊Q8—216no—
668C22⋊Q8—216no—
669C22⋊Q8C2×D418yes—
670#121—28no—
671#121—216no—
672#121—216no—
673#121—28no—
674#121—28no—
675#121—24no—
676#121—28no—
677#121—24no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—28no—
682#121—28no—
683#121—216no—
684#121—28no—
685#121—216no—
686#121—28no—
687#121—216no—
688#121—216no—
689#121—216no—
690#121—216no—
691#121—216no—
692#121—216no—
693#121—88no—
694#121—88no—
695#121—88no—
696#121—88no—
697#121C2×D418yes—
698#120—216no—
699#120—216no—
700#120—216no—
701#120—216no—
702#120—88no—
703#120—88no—
704C4×Q8—28no—
705C4×Q8C2×D418yes—
706C4×D4—216no—
707C4×D4—216no—
708C4×D4—216no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—24no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—24no—
715C4×D4—28no—
716C4×D4—28no—
717C4×D4—28no—
718C4×D4—28no—
719C4×D4—88no—
720C4×D4C2×D418yes—
721C4×D4C2×D4116yes—
722#117—28no—
723#117—28no—
724#117—44no—
725#117—44no—
726#117C2×D4116yes—
727C2×C4⋊C4—28no—
728C2×C4⋊C4—24no—
729C2×C4⋊C4—28no—
730C2×C4⋊C4—24no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4—28no—
733C2×C4⋊C4—216no—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C22⋊C4—216no—
769C2×C22⋊C4—88no—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C42—44no—
816C2×C42C2×D418yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2412yes—
845#95C2412yes—
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858C24—28no—
859C24—44no—
860C24—48no—
861C24—48no—
862C24—44no—
863C24C2512yes—
864C24C2514yes—
865C24C2514yes—
866C24C2512yes—
867C24C2512yes—
868C24C2511yescharacteristic
869#41—816no—
870#41—816no—
871#41—816no—
872#41—816no—
873#41—832no—
874#41—816no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—48no—
885C2×Q8C22×D414yes—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—24no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—22no—
897C2×D4—24no—
898C2×D4—22no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—42no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—48no—
917C2×D4—48no—
918C2×D4—48no—
919C2×D4—48no—
920C2×D4—44no—
921C2×D4—48no—
922C2×D4—48no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—48no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—48no—
945C2×D4—48no—
946C2×D4—48no—
947C2×D4—816no—
948C2×D4—816no—
949C2×D4C22×D418yes—
950C2×D4C22×D414yes—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—28no—
961C22×C4—28no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—48no—
973C22×C4—48no—
974C22×C4—48no—
975C22×C4—44no—
976C22×C4—48no—
977C22×C4—48no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4C22×D414yes—
984C22×C4C22×D418yes—
985C22×C4C22×D414yes—
986C22×C4C22×D414yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—48no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—48no—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D418yes—
1036C4⋊C4C22×D414yes—
1037C4⋊C4C22×D418yes—
1038C4⋊C4C22×D418yes—
1039C4⋊C4C22×D418yes—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—48no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4C22×D418yes—
1081C22⋊C4C22×D418yes—
1082C22⋊C4C22×D418yes—
1083C22⋊C4C22×D418yes—
1084C22⋊C4C22×D418yes—
1085C42—28no—
1086C42—28no—
1087C42—24no—
1088C42—24no—
1089C42—24no—
1090C42—24no—
1091C42—44no—
1092C42—44no—
1093C42—42no—
1094C42—42no—
1095C42—44no—
1096C42—42no—
1097C42—42no—
1098C42C22×D414yes—
1099C42C22×D414yes—
1100C42C22×D414yes—
1101C42C22×D414yes—
1102C42C22×D418yes—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—24no—
1108C23—24no—
1109C23—22no—
1110C23—24no—
1111C23—22no—
1112C23—24no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—28no—
1122C23—24no—
1123C23—24no—
1124C23—28no—
1125C23—28no—
1126C23—24no—
1127C23—28no—
1128C23—88no—
1129C23—88no—
1130C23—88no—
1131C23—816no—
1132C23—168no—
1133C23C23×D414yes—
1134C23C23×D412yes—
1135C23C2611yescharacteristic
1136Q8—44no—
1137Q8—48no—
1138Q8—84no—
1139Q8—84no—
1140Q8—88no—
1141D4—44no—
1142D4—48no—
1143D4—48no—
1144D4—416no—
1145D4—48no—
1146D4—44no—
1147D4—48no—
1148D4—44no—
1149D4—84no—
1150D4—84no—
1151D4—84no—
1152D4—88no—
1153D4—88no—
1154D4—84no—
1155D4—84no—
1156D4—88no—
1157D4—88no—
1158D4—88no—
1159D4—88no—
1160D4—88no—
1161D4—84no—
1162D4—88no—
1163D4—84no—
1164D4—816no—
1165D4—168no—
1166D4—168no—
1167D4—168no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—216no—
1178C2×C4—28no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—28no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—48no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4—88no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—84no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4C23×D414yes—
1219C2×C4C23×D414yes—
1220C2×C4C23×D412yes—
1221C2×C4C23×D412yes—
1222C2×C4C23×D412yes—
1223C2×C4C23×D412yes—
1224C2×C4C23×D412yes—
1225C2×C4C23×D414yes—
1226C2×C4C23×D412yes—
1227C2×C4#58514yes—
1228C22—22no—
1229C22—24no—
1230C22—22no—
1231C22—22no—
1232C22—24no—
1233C22—24no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—44no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—42no—
1249C22—48no—
1250C22—48no—
1251C22—48no—
1252C22—48no—
1253C22—48no—
1254C22—48no—
1255C22—1616no—
1256C22C24×D411yescharacteristic
1257C22C2×#58512yes—
1258C22H(7,𝔽2)12yes—
1259C22H(7,𝔽2)12yes—
1260C4—22no—
1261C4—24no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—24no—
1267C4—24no—
1268C4—44no—
1269C4—42no—
1270C4—44no—
1271C4—42no—
1272C4—44no—
1273C4—44no—
1274C4—44no—
1275C4—44no—
1276C4—44no—
1277C4—44no—
1278C4#350014yes—
1279C2—42no—
1280C2—44no—
1281C2—82no—
1282C2—84no—
1283C2—84no—
1284C2—82no—
1285C2C2×#350011yescharacteristic
1286C2#6285211yescharacteristic
1287C2#6285211yescharacteristic
1288C2#6288314yes—
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×#3546C2semidirect
2. C2×#3559C2semidirect
3. #51072C2semidirect
4. #50695C2semidirect
5. #47957C2semidirect
6. #47687C2semidirect
7. #46428C2semidirect
8. #46360C2semidirect
9. #39169C2semidirect
10. #39163C2semidirect
11. #38956C2semidirect
12. #38945C2semidirect
13. #38092C2semidirect
14. #38089C2semidirect
15. #38082C2semidirect
16. #38080C2semidirect
17. #37618C2semidirect
18. #37539C2semidirect
19. #37423C2semidirect
20. #37302C2semidirect
21. #35341C2semidirect
22. #35293C2semidirect
23. #35276C2semidirect
24. #35264C2semidirect
25. #34081C2semidirect
28. C2×#563C22semidirect
32. C2×#554C22semidirect
35. C2×#553C22semidirect
39. C2×#547C22semidirect
40. C2×#547C22semidirect
44. C2×#544C22semidirect
46. C2×#540C22semidirect
47. C2×#539C22semidirect
48. C2×#539C22semidirect
56. C2×#532C22semidirect
58. C22×#125C22semidirect
60. #2862C22semidirect
62. #2861C22semidirect
63. #2861C22semidirect
65. #2858C22semidirect
66. #2858C22semidirect
68. #2850C22semidirect
69. #2820C22semidirect
70. #2815C22semidirect
71. #2728C22semidirect
72. #2716C22semidirect
74. #2705C22semidirect
75. #2703C22semidirect
76. #2703C22semidirect
77. #2703C22semidirect
78. #2702C22semidirect
79. #2700C22semidirect
80. #2696C22semidirect
81. #2693C22semidirect
82. #2690C22semidirect
84. #2687C22semidirect
86. #2678C22semidirect
87. #2676C22semidirect
88. #2676C22semidirect
89. #2673C22semidirect
90. #2673C22semidirect
91. #2673C22semidirect
92. #2671C22semidirect
93. #2669C22semidirect
94. #2669C22semidirect
95. #2660C22semidirect
96. #2657C22semidirect
97. #2642C22semidirect
100. #2641C22semidirect
102. #2640C22semidirect
103. #2633C22semidirect
104. #2631C22semidirect
105. #2620C22semidirect
108. #2619C22semidirect
109. #2618C22semidirect
110. #2615C22semidirect
111. #2591C22semidirect
112. #2591C22semidirect
113. #2568C22semidirect
115. #2566C22semidirect
116. #2566C22semidirect
117. #2565C22semidirect
118. #2563C22semidirect
119. #2562C22semidirect
120. #2562C22semidirect
121. #2555C22semidirect
122. #2554C22semidirect
123. #2547C22semidirect
126. #2544C22semidirect
127. #2544C22semidirect
129. #2541C22semidirect
130. #2541C22semidirect
131. #2535C22semidirect
134. #2504C22semidirect
135. #2503C22semidirect
137. #2501C22semidirect
139. #2499C22semidirect
140. #2491C22semidirect
141. #2490C22semidirect
142. #2481C22semidirect
143. #2481C22semidirect
144. #2477C22semidirect
145. #2472C22semidirect
146. #2472C22semidirect
147. #2467C22semidirect
148. #2464C22semidirect
149. #2464C22semidirect
150. #2461C22semidirect
151. #2457C22semidirect
152. #2456C22semidirect
155. #2431C22semidirect
156. #2431C22semidirect
157. #2431C22semidirect
158. #2431C22semidirect
159. #2431C22semidirect
160. #2431C22semidirect
161. #2431C22semidirect
162. #2427C22semidirect
164. #2418C22semidirect
165. #2416C22semidirect
166. #2412C22semidirect
168. #2407C22semidirect
169. #2406C22semidirect
170. #2404C22semidirect
172. #2336C22semidirect
173. #2335C22semidirect
174. #2334C22semidirect
176. #2332C22semidirect
178. #2328C22semidirect
179. #2328C22semidirect
180. #2326C22semidirect
181. #2311C22semidirect
182. #2311C22semidirect
183. #2311C22semidirect
185. C4×#127C22semidirect
186. C4×#124C22semidirect
187. #2298C22semidirect
188. #2297C22semidirect
189. #2295C22semidirect
190. #2293C22semidirect
193. #2290C22semidirect
194. #2283C22semidirect
195. C4×#117C22semidirect
196. C4×#117C22semidirect
250. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35462
C2×#35592
#510722
#506952
#479572
#476872
#464282
#463602
#391692
#391632
#389562
#389452
#380922
#380892
#380822
#380802
#376182
#375392
#374232
#373022
#353412
#352932
#352762
#352642
#340812