Finite Group Databasebeta

← #7648455

Subgroups — #7648455

Order 512.

7334 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#42881C212yesmaximal, complemented
4#42795C212yesmaximal, complemented
5#42645C212yesmaximal, complemented
6#42425C212yesmaximal, complemented
7#41368C214yesmaximal, complemented
8#40489C214yesmaximal, complemented
9#39882C214yesmaximal, complemented
10#39853C214yesmaximal, complemented
11#38357C218yesmaximal, complemented
12#37554C212yesmaximal, complemented
13#37553C212yesmaximal, complemented
14#37280C214yesmaximal, complemented
15#37276C214yesmaximal, complemented
16#35564C212yesmaximal, complemented
17#35533C212yesmaximal, complemented
18#35328C211yesmaximal, characteristic, complemented
19#35292C212yesmaximal, complemented
20#35257C212yesmaximal, complemented
21#35256C212yesmaximal, complemented
22#35165C211yesmaximal, characteristic, complemented
23#35130C212yesmaximal, complemented
24#34952C211yesmaximal, characteristic, complemented
25C2×#2580C211yesmaximal, characteristic, complemented
26#34184C211yesmaximal, characteristic, complemented
27#3480—216no—
28C2×#559C2211yescharacteristic, complemented
29C2×#559C2212yescomplemented
30C2×#557C2211yescharacteristic, complemented
31C2×#556C2211yescharacteristic, complemented
32C2×#556C2212yescomplemented
33C2×#553C2212yes—
34C2×#553C2214yes—
35C2×#550C2211yescharacteristic, complemented
36C2×#548C2212yes—
37#3460—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#540C2212yes—
42C2×#540C2212yes—
43C2×#538C2214yes—
44C2×#537C2211yescharacteristic
45C2×#537C2212yes—
46C2×#535C2211yescharacteristic
47C2×#535C2211yescharacteristic
48C2×#535C2212yes—
49C2×#532C2211yescharacteristic
50C2×#532C2212yes—
51C2×#532C2212yes—
52C2×#532C2212yes—
53C2×#529C2212yes—
54C2×#529C2212yes—
55C2×#529C2214yescomplemented
56C2×#529C2212yescomplemented
57C2×#525C2214yes—
58C2×#520C2212yes—
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2212yes—
61C2×C4×#41C2211yescharacteristic
62C2×C4×#41C2212yescomplemented
63C22×C4×Q8C2211yescharacteristic
64C22×C4×D4C2211yescharacteristic
65#2857C2214yescomplemented
66#2856C2214yes—
67#2851C2214yescomplemented
68#2850C2214yes—
69#2850C2214yescomplemented
70#2847C2214yes—
71#2820C2214yescomplemented
72#2819C2214yescomplemented
73#2814C2214yescomplemented
74#2813C2214yescomplemented
75#2727C2218yescomplemented
76#2712C2218yescomplemented
77#2707C2218yescomplemented
78#2705C2218yescomplemented
79#2704C2218yescomplemented
80#2702C2218yescomplemented
81#2695C2218yescomplemented
82#2691C2218yescomplemented
83#2682C2218yescomplemented
84#2681C2218yescomplemented
85#2681C2218yescomplemented
86#2676C2218yescomplemented
87#2675C2218yescomplemented
88#2672C2218yescomplemented
89#2671C2218yescomplemented
90#2671C2218yescomplemented
91#2664C2214yescomplemented
92#2662C2214yescomplemented
93#2656C2214yescomplemented
94#2639C2214yescomplemented
95#2637C2214yescomplemented
96#2636C2214yescomplemented
97#2636C2218yescomplemented
98#2630C2218yescomplemented
99#2629C2214yescomplemented
100#2628C2214yescomplemented
101#2624C2214yescomplemented
102#2621C2212yescomplemented
103#2620C2214yes—
104#2619C2214yes—
105#2619C2212yescomplemented
106#2617C2214yes—
107#2615C2214yescomplemented
108#2609C2218yescomplemented
109#2601C2218yescomplemented
110#2592C2214yescomplemented
111#2582C2212yescomplemented
112#2581C2211yescharacteristic, complemented
113#2581C2211yescharacteristic, complemented
114#2580C2212yes—
115#2580C2212yes—
116#2580C2212yes—
117#2580C2214yes—
118#2580C2214yes—
119#2580C2212yes—
120#2580C2211yescharacteristic, complemented
121#2580C2211yescharacteristic, complemented
122#2579C2214yes—
123#2548C2214yes—
124#2547C2212yes—
125#2545C2214yes—
126#2544C2214yes—
127#2544C2214yes—
128#2543C2214yes—
129#2543C2214yes—
130#2543C2218yes—
131#2541C2212yes—
132#2541C2214yes—
133#2540C2214yescomplemented
134#2538C2212yescomplemented
135#2537C2214yes—
136#2536C2212yescomplemented
137#2536C2212yescomplemented
138#2535C2212yes—
139#2535C2212yes—
140#2535C2212yescomplemented
141#2535C2212yescomplemented
142#2498C2214yescomplemented
143#2487C2212yes—
144#2454C2214yescomplemented
145#2453C2214yescomplemented
146#2452C2214yescomplemented
147#2451C2214yescomplemented
148#2450C2218yes—
149#2449C2218yes—
150#2430C2214yescomplemented
151#2430C2218yescomplemented
152#2429C2214yescomplemented
153#2428C2214yes—
154#2428C2214yes—
155#2428C2214yescomplemented
156#2427C2214yescomplemented
157#2426C2214yes—
158#2426C2214yes—
159#2426C2214yescomplemented
160#2424C2218yes—
161#2424C2218yes—
162#2424C2218yes—
163#2424C2218yes—
164#2417C2214yescomplemented
165#2416C2214yes—
166#2416C2218yes—
167#2416C2214yes—
168#2416C2214yescomplemented
169#2415C2214yescomplemented
170#2414C2214yes—
171#2414C2214yes—
172#2414C2214yescomplemented
173#2409C2212yes—
174#2407C2218yescomplemented
175#2396C2212yescomplemented
176#2396C2212yescomplemented
177C2×#399C2212yes—
178C2×#393C2212yes—
179#2351C2212yescomplemented
180#2351C2212yescomplemented
181#2349C2214yes—
182#2349C2214yes—
183#2349C2212yescomplemented
184#2349C2212yescomplemented
185#2325C2218yescomplemented
186#2324C2218yescomplemented
187#2317C2212yes—
188#2317C2214yescomplemented
189#2311C2212yes—
190#2311C2212yes—
191C4×C22⋊Q8C2214yescomplemented
192#2297C2212yes—
193#2296C2212yes—
194C2×#390C2212yes—
195C2×#389C2212yes—
196C2×#385C2214yes—
197#2285C2211yescharacteristic
198#2285C2212yescomplemented
199C2×#382C2211yescharacteristic
200C2×#382C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2312yes—
205C22×#41C2314yes—
206C23×Q8C2311yescharacteristic
207C23×D4C2311yescharacteristic
208C24×C4C2312yes—
209#559—28no—
210#559—216no—
211#557—28no—
212#556—216no—
213#556—28no—
214#553—216no—
215#553—232no—
216#550—28no—
217#548—216no—
218#544—28no—
219#542—216no—
220#542—216no—
221#540—216no—
222#540—216no—
223#538—232no—
224#537—28no—
225#537—48no—
226#535—28no—
227#535—28no—
228#535—48no—
229#532—216no—
230#532—216no—
231#532—216no—
232#532—28no—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×#127C2312yes—
238C2×#127C2311yescharacteristic
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#127C2314yes—
242#529—216no—
243#529—232no—
244#529—216no—
245#529—216no—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265#525—232no—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2318yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2318yes—
300C2×#121C2318yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2318yes—
306C2×#121C2318yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#121C2318yes—
310C2×#120C2314yes—
311C2×#120C2314yes—
312C2×#120C2318yes—
313#520—48no—
314C4×#41—216no—
315C4×#41—28no—
316C4×#41—216no—
317C4×#41D4116yescomplemented
318C2×C4×Q8—28no—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×D4—28no—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2318yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×#117C2311yescharacteristic
361C2×#117C2312yes—
362C2×#117C2314yes—
363C2×#117C2314yes—
364C2×#117C2314yes—
365C2×#117C2312yes—
366C2×#117C2312yes—
367C2×#117C2314yes—
368C2×#117C2311yescharacteristic
369C2×#117C2312yes—
370C22×C4⋊C4C2311yescharacteristic
371C22×C4⋊C4C2312yes—
372C22×C4⋊C4C2312yes—
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2314yes—
375C22×C4⋊C4C2314yes—
376C22×C22⋊C4C2312yes—
377C22×C22⋊C4C2314yes—
378C22×C22⋊C4C2314yes—
379C22×C42C2314yes—
380C22×C42C2312yes—
381C22×C42C2312yes—
382C22×C42C2311yescharacteristic
383C22×C42C2312yes—
384#400C2312yes—
385#400C2312yes—
386#400C2318yes—
387#399C2312yes—
388#399C2314yes—
389#399C2314yes—
390#399C2318yes—
391#399C2312yes—
392#399C2318yes—
393#398C2314yes—
394#398C2314yes—
395#398C2318yes—
396#398C2318yes—
397#398C2314yes—
398#398C2314yes—
399#398C2318yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2318yes—
405#396C2318yes—
406#396C2318yes—
407#396C2314yes—
408#396C2314yes—
409#396C2318yes—
410#396C2318yes—
411#396C2318yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#395C2318yes—
416#395C2312yes—
417#395C2312yes—
418#394C2318yes—
419#394C2318yes—
420#394C2318yes—
421#394C2318yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2314yes—
427#394C2314yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#393C2312yes—
434#393C2314yes—
435#393C2318yes—
436#393C2314yes—
437#393C2318yes—
438#393C2312yes—
439#392C2314yes—
440#392C2314yes—
441#392C2318yes—
442#392C2314yes—
443#392C2318yes—
444#392C2318yes—
445#392C2318yes—
446#392C2314yes—
447#392C2318yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2318yes—
454#390C2314yes—
455#390C2314yes—
456#390C2318yes—
457#390C2318yes—
458#390C2318yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2318yes—
466#390C2318yes—
467#389C2314yes—
468#389C2314yes—
469#389C2318yes—
470#389C2318yes—
471#389C2318yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#387C2314yes—
491#387C2314yes—
492#387C2318yes—
493#387C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2314yes—
497#386C2314yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#386C2318yes—
507#386C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2318yes—
516#385C2318yes—
517#385C2318yes—
518#385C2318yes—
519#385C2318yes—
520#385C2318yes—
521#384C2314yes—
522#384C2312yes—
523#382C2314yes—
524#382C2314yes—
525#382C2312yes—
526#382C2312yes—
527#382C2312yes—
528#382C2312yes—
529#382C2311yescharacteristic
530#382C2311yescharacteristic
531#382C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2312yes—
537#380C2318yes—
538#380C2318yes—
539#380C2318yes—
540#380C2312yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552C2×#95C2314yes—
553C2×#95C2312yes—
554C2×#95C2312yes—
555C2×#95C2314yes—
556C2×#95C2314yes—
557C25C2412yes—
558C2×#41—28no—
559C2×#41—24no—
560C2×#41—28no—
561C2×#41—216no—
562C2×#41—24no—
563C2×#41—28no—
564C2×#41—24no—
565C2×#41—24no—
566C2×#41—28no—
567C2×#41—24no—
568C2×#41—48no—
569C2×#41—88no—
570C2×#41C2×D418yes—
571C22×Q8—24no—
572C22×Q8—44no—
573C22×Q8C2411yescharacteristic
574C22×Q8C2411yescharacteristic
575C22×Q8C2412yes—
576C22×Q8C2412yes—
577C22×Q8C2411yescharacteristic
578C22×Q8C2411yescharacteristic
579C22×Q8C2414yes—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—24no—
583C22×D4C2412yes—
584C22×D4C2414yes—
585C22×D4C2412yes—
586C22×D4C2411yescharacteristic
587C22×D4C2412yes—
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2412yes—
591C22×D4C2411yescharacteristic
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2412yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2418yes—
601C22×D4C2418yes—
602C22×D4C2418yes—
603C23×C4—28no—
604C23×C4—84no—
605C23×C4C2414yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2414yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2414yes—
612C23×C4C2412yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2412yes—
616C23×C4C2414yes—
617C23×C4C2412yes—
618C23×C4C2418yes—
619C23×C4C2411yescharacteristic
620C23×C4C2411yescharacteristic
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2411yescharacteristic
624C4⋊Q8—28no—
625C4⋊Q8—28no—
626C4⋊Q8—28no—
627C4⋊Q8—24no—
628#127—28no—
629#127—28no—
630#127—28no—
631#127—24no—
632#127—48no—
633#126—216no—
634#126—216no—
635#126—216no—
636#126—216no—
637#126—216no—
638#125—28no—
639#125—216no—
640#125—28no—
641#125—28no—
642#124—28no—
643#124—28no—
644#124—28no—
645#124—216no—
646#124—216no—
647#124—28no—
648#124—28no—
649#124—216no—
650#124—28no—
651#124—48no—
652#123—216no—
653#123—216no—
654#123—216no—
655#123—216no—
656#123—216no—
657#123—216no—
658#123—216no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—28no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668C22⋊Q8—88no—
669#121—216no—
670#121—28no—
671#121—216no—
672#121—216no—
673#121—28no—
674#121—28no—
675#121—28no—
676#121—28no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—28no—
682#121—216no—
683#121—216no—
684#121—216no—
685#121—416no—
686#121—416no—
687#121—48no—
688#121—48no—
689#121—48no—
690#121—48no—
691#121—416no—
692#121—88no—
693#121—88no—
694#121—88no—
695#121—88no—
696#120—216no—
697#120—216no—
698#120—416no—
699C4×Q8—28no—
700C4×Q8—28no—
701C4×Q8—24no—
702C4×Q8—28no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—28no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—28no—
710C4×Q8—48no—
711C4×Q8C2×D418yes—
712C4×Q8C2×D418yes—
713C4×D4—28no—
714C4×D4—216no—
715C4×D4—28no—
716C4×D4—216no—
717C4×D4—216no—
718C4×D4—216no—
719C4×D4—28no—
720C4×D4—28no—
721C4×D4—216no—
722C4×D4—216no—
723C4×D4—28no—
724C4×D4—28no—
725C4×D4—28no—
726C4×D4—28no—
727C4×D4—28no—
728C4×D4—24no—
729C4×D4—24no—
730C4×D4—28no—
731C4×D4—216no—
732C4×D4—28no—
733C4×D4—48no—
734C4×D4—416no—
735C4×D4C2×D4116yes—
736C4×D4C2×D418yes—
737C4×D4C2×D4116yes—
738C4×D4C2×D418yes—
739#117—24no—
740#117—28no—
741#117—28no—
742#117—216no—
743#117—28no—
744#117—216no—
745#117—216no—
746#117—48no—
747#117C2×D418yes—
748#117C2×D4116yes—
749C2×C4⋊C4—24no—
750C2×C4⋊C4—28no—
751C2×C4⋊C4—24no—
752C2×C4⋊C4—28no—
753C2×C4⋊C4—48no—
754C2×C4⋊C4—84no—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2418yes—
784C2×C4⋊C4C2418yes—
785C2×C4⋊C4C2418yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2418yes—
789C2×C4⋊C4C2418yes—
790C2×C4⋊C4C2418yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C22⋊C4—28no—
799C2×C22⋊C4—48no—
800C2×C22⋊C4—84no—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2418yes—
825C2×C22⋊C4C2418yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2418yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2418yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2418yes—
834C2×C22⋊C4C2418yes—
835C2×C22⋊C4C2418yes—
836C2×C22⋊C4C2418yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C42—28no—
842C2×C42—216no—
843C2×C42—28no—
844C2×C42C2×D418yes—
845C2×C42C2×D4116yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2418yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864#95C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
868#95C2418yes—
869#95C2414yes—
870#95C2418yes—
871#95C2418yes—
872#95C2414yes—
873#95C2418yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2418yes—
885#95C2418yes—
886#95C2418yes—
887#95C2418yes—
888C24—24no—
889C24—24no—
890C24—24no—
891C24—44no—
892C24—44no—
893C24C2514yes—
894C24C2514yes—
895C24C2512yes—
896C24C2512yes—
897C24C2511yescharacteristic
898#41—232no—
899#41—432no—
900#41—432no—
901#41—416no—
902#41—832no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—22no—
906C2×Q8—22no—
907C2×Q8—24no—
908C2×Q8—28no—
909C2×Q8—22no—
910C2×Q8—22no—
911C2×Q8—24no—
912C2×Q8—22no—
913C2×Q8—22no—
914C2×Q8—24no—
915C2×Q8—24no—
916C2×Q8—24no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—48no—
920C2×Q8—416no—
921C2×Q8C22×D414yes—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—24no—
936C2×D4—24no—
937C2×D4—24no—
938C2×D4—22no—
939C2×D4—24no—
940C2×D4—28no—
941C2×D4—24no—
942C2×D4—28no—
943C2×D4—22no—
944C2×D4—24no—
945C2×D4—22no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—22no—
949C2×D4—24no—
950C2×D4—24no—
951C2×D4—22no—
952C2×D4—24no—
953C2×D4—28no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—48no—
957C2×D4—48no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—48no—
962C2×D4—48no—
963C2×D4—48no—
964C2×D4—48no—
965C2×D4—48no—
966C2×D4—48no—
967C2×D4—48no—
968C2×D4—48no—
969C2×D4—48no—
970C2×D4—48no—
971C2×D4—48no—
972C2×D4—48no—
973C2×D4—416no—
974C2×D4C22×D418yes—
975C2×D4C22×D414yes—
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—24no—
985C22×C4—24no—
986C22×C4—28no—
987C22×C4—28no—
988C22×C4—24no—
989C22×C4—28no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—28no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—42no—
997C22×C4—48no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—48no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—48no—
1014C22×C4—48no—
1015C22×C4—48no—
1016C22×C4—816no—
1017C22×C4C22×D418yes—
1018C22×C4C22×D414yes—
1019C22×C4C22×D414yes—
1020C22×C4C22×D418yes—
1021C22×C4C22×D418yes—
1022C22×C4C22×D414yes—
1023C22×C4H(5,𝔽2)14yes—
1024C22×C42−1+414yes—
1025C22×C4C2514yes—
1026C22×C4C2518yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C4⋊C4—24no—
1047C4⋊C4—22no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—22no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—48no—
1075C4⋊C4—48no—
1076C4⋊C4—48no—
1077C4⋊C4—48no—
1078C4⋊C4—48no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—48no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4C22×D414yes—
1086C4⋊C4C22×D414yes—
1087C4⋊C4C22×D418yes—
1088C4⋊C4C22×D418yes—
1089C22⋊C4—24no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—216no—
1110C22⋊C4—28no—
1111C22⋊C4—48no—
1112C22⋊C4—48no—
1113C22⋊C4—48no—
1114C22⋊C4—48no—
1115C22⋊C4—48no—
1116C22⋊C4—48no—
1117C22⋊C4—48no—
1118C22⋊C4—48no—
1119C22⋊C4—48no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—48no—
1123C22⋊C4—48no—
1124C22⋊C4—48no—
1125C22⋊C4—44no—
1126C22⋊C4C22×D418yes—
1127C22⋊C4C22×D418yes—
1128C22⋊C4C22×D418yes—
1129C42—24no—
1130C42—24no—
1131C42—24no—
1132C42—28no—
1133C42—24no—
1134C42—28no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—28no—
1139C42—48no—
1140C42C22×D418yes—
1141C42C22×D414yes—
1142C42C22×D414yes—
1143C42C22×D418yes—
1144C42C22×D414yes—
1145C42C22×D414yes—
1146C42C22×D418yes—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—22no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—28no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—28no—
1168C23—24no—
1169C23—24no—
1170C23—416no—
1171C23—48no—
1172C23—84no—
1173C23—84no—
1174C23—88no—
1175C23C23×D414yes—
1176C23C23×D412yes—
1177C23C2×H(5,𝔽2)12yes—
1178C23C2×2−1+412yes—
1179C23C2611yescharacteristic
1180Q8—28no—
1181Q8—28no—
1182Q8—48no—
1183Q8—44no—
1184Q8—44no—
1185Q8—48no—
1186Q8—88no—
1187D4—216no—
1188D4—28no—
1189D4—416no—
1190D4—48no—
1191D4—48no—
1192D4—416no—
1193D4—48no—
1194D4—48no—
1195D4—44no—
1196D4—48no—
1197D4—88no—
1198D4—84no—
1199D4—88no—
1200D4—88no—
1201D4—88no—
1202D4—88no—
1203D4—88no—
1204D4—168no—
1205D4—168no—
1206D4—168no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—216no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—28no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—28no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—28no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—28no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—44no—
1249C2×C4—44no—
1250C2×C4—48no—
1251C2×C4—48no—
1252C2×C4—416no—
1253C2×C4—48no—
1254C2×C4—416no—
1255C2×C4—48no—
1256C2×C4—416no—
1257C2×C4—48no—
1258C2×C4—84no—
1259C2×C4—88no—
1260C2×C4—88no—
1261C2×C4—84no—
1262C2×C4—88no—
1263C2×C4—84no—
1264C2×C4—168no—
1265C2×C4#537116yes—
1266C2×C4C23×D412yes—
1267C2×C4C23×D412yes—
1268C2×C4C23×D414yes—
1269C2×C4C23×D414yes—
1270C2×C4C23×D412yes—
1271C2×C4C23×D414yes—
1272C2×C4C23×D412yes—
1273C2×C4C23×D412yes—
1274C2×C4C23×D412yes—
1275C2×C4C2×H(5,𝔽2)12yes—
1276C2×C4C2×H(5,𝔽2)12yes—
1277C2×C4C2×2−1+412yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4#58514yes—
1280C22—22no—
1281C22—22no—
1282C22—24no—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—24no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—42no—
1291C22—44no—
1292C22—44no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—48no—
1299C22—44no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—48no—
1306C22—816no—
1307C22C2×#53714yes—
1308C22C24×D411yescharacteristic
1309C22C22×H(5,𝔽2)11yescharacteristic
1310C22C22×2−1+411yescharacteristic
1311C22C2×#58512yes—
1312C22H(7,𝔽2)12yes—
1313C4—22no—
1314C4—24no—
1315C4—24no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—24no—
1320C4—24no—
1321C4—42no—
1322C4—42no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—44no—
1329C4—48no—
1330C4—44no—
1331C4—44no—
1332C4C2×#53714yes—
1333C4C2×#53714yes—
1334C2—24no—
1335C2—44no—
1336C2—84no—
1337C2—82no—
1338C2—84no—
1339C2C22×#53711yescharacteristic
1340C2#6281111yescharacteristic
1341C2#6285211yescharacteristic
1342C2#6292612yes—
1343C2#6296112yes—
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×#3480C2semidirect
2. C2×#3460C2semidirect
3. #42881C2semidirect
4. #42795C2semidirect
5. #42645C2semidirect
6. #42425C2semidirect
7. #41368C2semidirect
8. #40489C2semidirect
9. #39882C2semidirect
10. #39853C2semidirect
11. #38357C2semidirect
12. #37554C2semidirect
13. #37553C2semidirect
14. #37280C2semidirect
15. #37276C2semidirect
16. #35564C2semidirect
17. #35533C2semidirect
18. #35328C2semidirect
19. #35292C2semidirect
20. #35257C2semidirect
21. #35256C2semidirect
22. #35165C2semidirect
23. #35130C2semidirect
24. #34952C2semidirect
25. C2×#2580C2semidirect
26. #34184C2semidirect
28. C2×#559C22semidirect
29. C2×#559C22semidirect
30. C2×#557C22semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
35. C2×#550C22semidirect
55. C2×#529C22semidirect
56. C2×#529C22semidirect
62. C2×C4×#41C22semidirect
65. #2857C22semidirect
67. #2851C22semidirect
69. #2850C22semidirect
71. #2820C22semidirect
72. #2819C22semidirect
73. #2814C22semidirect
74. #2813C22semidirect
75. #2727C22semidirect
76. #2712C22semidirect
77. #2707C22semidirect
78. #2705C22semidirect
79. #2704C22semidirect
80. #2702C22semidirect
81. #2695C22semidirect
82. #2691C22semidirect
83. #2682C22semidirect
84. #2681C22semidirect
85. #2681C22semidirect
86. #2676C22semidirect
87. #2675C22semidirect
88. #2672C22semidirect
89. #2671C22semidirect
90. #2671C22semidirect
91. #2664C22semidirect
92. #2662C22semidirect
93. #2656C22semidirect
94. #2639C22semidirect
95. #2637C22semidirect
96. #2636C22semidirect
97. #2636C22semidirect
98. #2630C22semidirect
99. #2629C22semidirect
100. #2628C22semidirect
101. #2624C22semidirect
102. #2621C22semidirect
105. #2619C22semidirect
107. #2615C22semidirect
108. #2609C22semidirect
109. #2601C22semidirect
110. #2592C22semidirect
111. #2582C22semidirect
112. #2581C22semidirect
113. #2581C22semidirect
120. #2580C22semidirect
121. #2580C22semidirect
133. #2540C22semidirect
134. #2538C22semidirect
136. #2536C22semidirect
137. #2536C22semidirect
140. #2535C22semidirect
141. #2535C22semidirect
142. #2498C22semidirect
144. #2454C22semidirect
145. #2453C22semidirect
146. #2452C22semidirect
147. #2451C22semidirect
150. #2430C22semidirect
151. #2430C22semidirect
152. #2429C22semidirect
155. #2428C22semidirect
156. #2427C22semidirect
159. #2426C22semidirect
164. #2417C22semidirect
168. #2416C22semidirect
169. #2415C22semidirect
172. #2414C22semidirect
174. #2407C22semidirect
175. #2396C22semidirect
176. #2396C22semidirect
179. #2351C22semidirect
180. #2351C22semidirect
183. #2349C22semidirect
184. #2349C22semidirect
185. #2325C22semidirect
186. #2324C22semidirect
188. #2317C22semidirect
191. C4×C22⋊Q8C22semidirect
198. #2285C22semidirect
200. C2×#382C22semidirect
317. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
C2×#34602
#428812
#427952
#426452
#424252
#413682
#404892
#398822
#398532
#383572
#375542
#375532
#372802
#372762
#355642
#355332
#353282
#352922
#352572
#352562
#351652
#351302
#349522
C2×#25802
#341842