Finite Group Databasebeta

← #7739339

Subgroups — #7739339

Order 512.

7676 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3548C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59815C212yesmaximal, complemented
4#59655C212yesmaximal, complemented
5#59652C212yesmaximal, complemented
6#59419C212yesmaximal, complemented
7#51590C218yesmaximal, complemented
8#44889C214yesmaximal, complemented
9#44888C214yesmaximal, complemented
10#44885C214yesmaximal, complemented
11#44884C214yesmaximal, complemented
12#39471C212yesmaximal, complemented
13#39470C212yesmaximal, complemented
14#39341C212yesmaximal, complemented
15#39340C212yesmaximal, complemented
16#37272C214yesmaximal, complemented
17#36410C212yesmaximal, complemented
18#36404C212yesmaximal, complemented
19#36275C212yesmaximal, complemented
20#36259C212yesmaximal, complemented
21#35564C214yesmaximal, complemented
22#35280C211yesmaximal, characteristic, complemented
23#35273C211yesmaximal, characteristic, complemented
24#34979C211yesmaximal, characteristic, complemented
25#34977C211yesmaximal, characteristic, complemented
26#34207C211yesmaximal, characteristic, complemented
27#3548—216no—
28C2×#562C2214yes—
29#3483—216no—
30C2×Q82C2211yescharacteristic
31C2×#555C2211yescharacteristic
32C2×#555C2212yes—
33C2×#555C2212yes—
34C2×#555C2214yes—
35C2×#554C2212yes—
36C2×#554C2212yes—
37C2×#550C2211yescharacteristic
38C2×#550C2212yes—
39C2×#550C2212yes—
40C2×#550C2212yes—
41C2×#550C2212yes—
42C2×#550C2211yescharacteristic
43C2×#547C2212yes—
44C2×#547C2212yes—
45C2×#547C2214yes—
46C2×#540C2214yes—
47C2×#537C2214yes—
48C2×#537C2214yes—
49C2×#537C2212yes—
50C2×#537C2214yes—
51C2×#533C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#532C2212yes—
54C2×#532C2212yes—
55C2×#532C2214yes—
56C2×#532C2211yescharacteristic
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2212yes—
60C2×C4×#41C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2857C2212yes—
65#2856C2212yes—
66#2855C2214yes—
67#2854C2214yes—
68#2730C2218yes—
69#2729C2218yes—
70#2710C2218yes—
71#2703C2218yes—
72#2700C2218yes—
73#2699C2218yes—
74#2688C2218yes—
75#2686C2218yes—
76#2682C2218yes—
77#2681C2218yes—
78#2676C2218yes—
79#2675C2218yes—
80#2673C2218yes—
81#2672C2218yes—
82#2671C2218yes—
83#2671C2218yes—
84#2629C2214yes—
85#2620C2214yes—
86#2616C2214yes—
87#2615C2214yes—
88#2611C2214yes—
89#2610C2214yes—
90#2582C2212yes—
91#2582C2212yes—
92#2568C2211yescharacteristic
93#2567C2211yescharacteristic
94#2563C2211yescharacteristic
95#2550C2214yes—
96#2548C2211yescharacteristic
97#2547C2211yescharacteristic
98#2546C2211yescharacteristic
99#2543C2218yes—
100#2543C2218yes—
101#2542C2211yescharacteristic
102#2541C2214yes—
103#2541C2211yescharacteristic
104#2540C2214yes—
105#2538C2212yes—
106#2538C2212yes—
107#2538C2212yes—
108#2538C2212yes—
109#2537C2212yes—
110#2537C2212yes—
111#2537C2214yes—
112#2500C2212yes—
113#2499C2212yes—
114#2492C2214yes—
115#2490C2214yes—
116#2487C2214yes—
117#2486C2214yes—
118#2476C2218yes—
119#2470C2218yes—
120#2464C2218yes—
121#2457C2218yes—
122#2453C2214yes—
123#2452C2214yes—
124#2449C2218yes—
125#2445C2214yes—
126#2445C2214yes—
127#2441C2214yes—
128#2440C2214yes—
129#2438C2218yes—
130#2432C2212yes—
131#2431C2214yes—
132#2431C2214yes—
133#2431C2212yes—
134#2429C2214yes—
135#2429C2218yes—
136#2428C2214yes—
137#2428C2214yes—
138#2428C2214yes—
139#2428C2218yes—
140#2427C2218yes—
141#2426C2218yes—
142#2425C2218yes—
143#2420C2214yes—
144#2420C2214yes—
145#2417C2214yes—
146#2417C2214yes—
147#2417C2214yes—
148#2416C2214yes—
149#2416C2218yes—
150#2416C2214yes—
151#2416C2218yes—
152#2416C2214yes—
153#2416C2214yes—
154#2415C2214yes—
155#2415C2214yes—
156#2415C2212yes—
157#2415C2212yes—
158#2414C2214yes—
159#2414C2212yes—
160#2414C2212yes—
161#2413C2218yes—
162#2407C2214yes—
163#2407C2214yes—
164#2407C2214yes—
165#2407C2214yes—
166#2395C2214yes—
167#2388C2214yes—
168#2367C2214yes—
169#2363C2214yes—
170#2361C2214yes—
171#2361C2214yes—
172#2360C2214yes—
173#2354C2212yes—
174#2354C2212yes—
175#2352C2214yes—
176D4×C4⋊C4C2214yes—
177D4×C4⋊C4C2212yes—
178D4×C4⋊C4C2212yes—
179#2339C2214yes—
180#2339C2214yes—
181#2326C2214yes—
182#2316C2212yes—
183#2311C2214yes—
184#2311C2212yes—
185#2311C2212yes—
186#2311C2212yes—
187C4×C4⋊Q8C2212yes—
188C4×C4⋊Q8C2212yes—
189C4×#127C2212yes—
190C4×#127C2212yes—
191C4×#124C2212yes—
192C4×#124C2212yes—
193C4×C22⋊Q8C2212yes—
194C4×C22⋊Q8C2212yes—
195C4×#121C2212yes—
196C4×#121C2212yes—
197#2297C2214yes—
198C2×#389C2214yes—
199C2×#384C2211yescharacteristic
200C4×#117C2211yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2311yescharacteristic
205C22×#41C2314yes—
206C22×#41C2312yes—
207C22×#41C2314yes—
208C22×#41C2314yes—
209C22×#41C2312yes—
210#562—232no—
211Q82—28no—
212#555—28no—
213#555—232no—
214#555—216no—
215#555—216no—
216#554—216no—
217#554—216no—
218#550—28no—
219#550—28no—
220#550—216no—
221#550—216no—
222#550—216no—
223#550—216no—
224#547—216no—
225#547—216no—
226#547—416no—
227#540—232no—
228#537—232no—
229#537—232no—
230#537—416no—
231#537—48no—
232#533—28no—
233#532—232no—
234#532—216no—
235#532—216no—
236#532—28no—
237#532D4116yescomplemented
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#127C2314yes—
248C2×#127C2312yes—
249C2×#127C2312yes—
250C2×#127C2314yes—
251C2×#127C2312yes—
252C2×#127C2311yescharacteristic
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#123C2318yes—
264C2×#123C2318yes—
265C2×#123C2318yes—
266C2×#123C2318yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2318yes—
274C2×C22⋊Q8C2318yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2318yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2318yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2318yes—
292C2×#121C2318yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2318yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2318yes—
304C2×#121C2318yes—
305C2×#121C2318yes—
306C2×#121C2318yes—
307C2×#121C2318yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311#520—48no—
312C4×#41—216no—
313C4×#41—216no—
314C4×#41—28no—
315C4×#41—28no—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2318yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2312yes—
353C2×#117C2311yescharacteristic
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2314yes—
359C2×#117C2314yes—
360C2×#117C2311yescharacteristic
361C2×#117C2311yescharacteristic
362C2×#117C2314yes—
363C22×C4⋊C4C2314yes—
364C22×C4⋊C4C2314yes—
365C22×C4⋊C4C2314yes—
366C22×C4⋊C4C2312yes—
367C22×C4⋊C4C2312yes—
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2318yes—
370C22×C42C2314yes—
371C22×C42C2312yes—
372C22×C42C2312yes—
373C22×C42C2311yescharacteristic
374#400C2314yes—
375#400C2318yes—
376#399C2314yes—
377#399C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2318yes—
387#397C2318yes—
388#396C2318yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#396C2318yes—
394#395C2314yes—
395#395C2318yes—
396#394C2314yes—
397#394C2318yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#393C2314yes—
412#393C2318yes—
413#392C2314yes—
414#392C2318yes—
415#392C2318yes—
416#392C2318yes—
417#392C2314yes—
418#392C2314yes—
419#392C2318yes—
420#392C2318yes—
421#392C2318yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2318yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#390C2312yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2314yes—
442#390C2318yes—
443#390C2314yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2318yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2318yes—
467#389C2318yes—
468#389C2312yes—
469#389C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2314yes—
485#387C2314yes—
486#386C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2314yes—
497#386C2314yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2314yes—
506#385C2314yes—
507#385C2318yes—
508#385C2318yes—
509#384C2312yes—
510#384C2312yes—
511#384C2312yes—
512#384C2312yes—
513#384C2312yes—
514#384C2312yes—
515#382C2312yes—
516#382C2312yes—
517#381C2318yes—
518#381C2318yes—
519#380C2312yes—
520#380C2312yes—
521#380C2312yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2318yes—
531#380C2314yes—
532#380C2314yes—
533#380C2318yes—
534#380C2312yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2311yescharacteristic
540C4×C4⋊C4C2311yescharacteristic
541C4×C4⋊C4C2311yescharacteristic
542C4×C4⋊C4C2311yescharacteristic
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2312yes—
550C4×C22⋊C4C2314yes—
551#376C2312yes—
552C2×#95C2318yes—
553C43C2312yes—
554C2×#41—24no—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—216no—
561C2×#41—24no—
562C2×#41—24no—
563C2×#41—216no—
564C2×#41—28no—
565C2×#41—216no—
566C2×#41—44no—
567C2×#41—44no—
568C2×#41—48no—
569C2×#41—44no—
570C2×#41—44no—
571C2×#41—48no—
572C2×#41—42no—
573C2×#41—42no—
574C2×#41—44no—
575C2×#41—44no—
576C2×#41—48no—
577C2×#41—48no—
578C2×#41—48no—
579C2×#41—48no—
580C2×#41C2×D4116yes—
581C22×Q8C2412yes—
582C22×Q8C2412yes—
583C22×Q8C2411yescharacteristic
584C22×Q8C2411yescharacteristic
585C22×Q8C2412yes—
586C22×Q8C2414yes—
587C22×Q8C2412yes—
588C22×D4C2412yes—
589C22×D4C2411yescharacteristic
590C22×D4C2411yescharacteristic
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2412yes—
595C22×D4C2414yes—
596C22×D4C2412yes—
597C22×D4C2412yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2418yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2414yes—
604C22×D4C2412yes—
605C22×D4C2418yes—
606C22×D4C2414yes—
607C22×D4C2418yes—
608C22×D4C2414yes—
609C22×D4C2412yes—
610C23×C4C2414yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2414yes—
616C23×C4C2412yes—
617C23×C4C2414yes—
618C23×C4C2412yes—
619C23×C4C2411yescharacteristic
620C23×C4C2411yescharacteristic
621C23×C4C2414yes—
622C23×C4C2411yescharacteristic
623C23×C4C2418yes—
624C23×C4C2418yes—
625C23×C4C2418yes—
626C23×C4C2414yes—
627C4⋊Q8—216no—
628C4⋊Q8—28no—
629C4⋊Q8—28no—
630C4⋊Q8—28no—
631C4⋊Q8—24no—
632C4⋊Q8—24no—
633C4⋊Q8—24no—
634C4⋊Q8C2×D418yes—
635#127—216no—
636#127—28no—
637#127—28no—
638#127—216no—
639#127—24no—
640#127—44no—
641#127C2×D418yes—
642#125—216no—
643#125—28no—
644#124—216no—
645#124—28no—
646#124—216no—
647#124—216no—
648#124—216no—
649#124—28no—
650#124—44no—
651#124C2×D4116yes—
652#123—232no—
653#123—232no—
654#123—416no—
655#123—416no—
656C22⋊Q8—232no—
657C22⋊Q8—216no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—28no—
663C22⋊Q8—232no—
664C22⋊Q8—416no—
665C22⋊Q8—48no—
666C22⋊Q8—44no—
667C22⋊Q8—48no—
668C22⋊Q8—48no—
669#121—28no—
670#121—28no—
671#121—216no—
672#121—216no—
673#121—216no—
674#121—216no—
675#121—232no—
676#121—232no—
677#121—216no—
678#121—232no—
679#121—28no—
680#121—28no—
681#121—216no—
682#121—28no—
683#121—28no—
684#121—28no—
685#121—216no—
686#121—216no—
687#121—232no—
688#121—416no—
689#121—48no—
690#121—416no—
691#121—416no—
692#121—416no—
693#121—48no—
694#121—44no—
695#121—48no—
696#121—48no—
697#121—416no—
698#121C2×D4116yes—
699#121C2×D4116yes—
700C4×Q8—28no—
701C4×Q8—28no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—28no—
707C4×Q8—28no—
708C4×Q8—48no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—216no—
712C4×D4—216no—
713C4×D4—216no—
714C4×D4—28no—
715C4×D4—28no—
716C4×D4—28no—
717C4×D4—28no—
718C4×D4—216no—
719C4×D4—216no—
720C4×D4—216no—
721C4×D4—24no—
722C4×D4—24no—
723C4×D4—24no—
724C4×D4—24no—
725C4×D4—28no—
726C4×D4—28no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—48no—
732C4×D4—416no—
733C4×D4C2×D4116yes—
734C4×D4C2×D4116yes—
735#117—24no—
736#117—24no—
737#117—28no—
738#117—28no—
739#117—28no—
740#117—24no—
741#117—216no—
742#117—216no—
743#117—28no—
744#117—28no—
745#117—42no—
746#117—48no—
747C2×C4⋊C4—216no—
748C2×C4⋊C4—216no—
749C2×C4⋊C4—216no—
750C2×C4⋊C4—44no—
751C2×C4⋊C4—44no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—416no—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2418yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2418yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2418yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2418yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C42—216no—
837C2×C42—28no—
838C2×C42—28no—
839C2×C42C2×D418yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2418yes—
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860#95C2414yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2418yes—
871#95C2414yes—
872#95C2418yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2418yes—
878#95C2418yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2418yes—
883#95C2418yes—
884C24C2514yes—
885C24C2512yes—
886C24C2512yes—
887C24C2511yescharacteristic
888C24C2514yes—
889#41—432no—
890#41—416no—
891#41—416no—
892#41—432no—
893#41—432no—
894#41—816no—
895#41—832no—
896#41—832no—
897#41—832no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—28no—
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—22no—
907C2×Q8—22no—
908C2×Q8—24no—
909C2×Q8—24no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—44no—
913C2×Q8—42no—
914C2×Q8—44no—
915C2×Q8—42no—
916C2×Q8C22×D418yes—
917C2×Q8H(5,𝔽2)14yes—
918C2×Q82−1+414yes—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—28no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—216no—
925C2×D4—216no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—24no—
937C2×D4—22no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—24no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—22no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—24no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—48no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—48no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—44no—
974C2×D4—48no—
975C2×D4—44no—
976C2×D4—48no—
977C2×D4—44no—
978C2×D4—48no—
979C2×D4—48no—
980C2×D4—48no—
981C2×D4C22×D418yes—
982C2×D4C22×D418yes—
983C2×D4C22×D418yes—
984C2×D4C22×D4116yes—
985C22×C4—28no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—28no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—216no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—24no—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—216no—
1018C22×C4—216no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—48no—
1024C22×C4—48no—
1025C22×C4—48no—
1026C22×C4—48no—
1027C22×C4—48no—
1028C22×C4—48no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4C22×D4116yes—
1033C22×C4C22×D414yes—
1034C22×C4C22×D414yes—
1035C22×C4C22×D414yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2518yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—216no—
1061C4⋊C4—216no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—216no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—216no—
1082C4⋊C4—22no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—48no—
1093C4⋊C4—44no—
1094C4⋊C4—48no—
1095C4⋊C4—44no—
1096C4⋊C4C22×D418yes—
1097C4⋊C4C22×D418yes—
1098C4⋊C4H(5,𝔽2)14yes—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—216no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—216no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—216no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—42no—
1121C22⋊C4—48no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—48no—
1125C22⋊C4—48no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—48no—
1130C22⋊C4—48no—
1131C22⋊C4—48no—
1132C22⋊C4—48no—
1133C22⋊C4—48no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4C22×D4116yes—
1138C22⋊C4C22×D4116yes—
1139C42—24no—
1140C42—24no—
1141C42—28no—
1142C42—24no—
1143C42—24no—
1144C42—28no—
1145C42—24no—
1146C42—24no—
1147C42—28no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—24no—
1153C42—42no—
1154C42—48no—
1155C42C22×D414yes—
1156C42C22×D414yes—
1157C42C22×D414yes—
1158C42C22×D414yes—
1159C23—21no—
1160C23—24no—
1161C23—24no—
1162C23—21no—
1163C23—21no—
1164C23—24no—
1165C23—21no—
1166C23—24no—
1167C23—21no—
1168C23—24no—
1169C23—21no—
1170C23—24no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—22no—
1176C23—24no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23C23×D412yes—
1193C23C23×D418yes—
1194C23C2611yescharacteristic
1195Q8—28no—
1196Q8—28no—
1197Q8—48no—
1198Q8—48no—
1199Q8—48no—
1200Q8—88no—
1201Q8—84no—
1202D4—216no—
1203D4—216no—
1204D4—416no—
1205D4—48no—
1206D4—48no—
1207D4—416no—
1208D4—48no—
1209D4—416no—
1210D4—44no—
1211D4—48no—
1212D4—44no—
1213D4—48no—
1214D4—88no—
1215D4—88no—
1216D4—84no—
1217D4—88no—
1218D4—88no—
1219D4—816no—
1220D4—88no—
1221D4—816no—
1222D4—88no—
1223D4—168no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—24no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—28no—
1239C2×C4—28no—
1240C2×C4—28no—
1241C2×C4—232no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—28no—
1252C2×C4—22no—
1253C2×C4—28no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—28no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—416no—
1278C2×C4—416no—
1279C2×C4—48no—
1280C2×C4—416no—
1281C2×C4—48no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—816no—
1285C2×C4—816no—
1286C2×C4—816no—
1287C2×C4—164no—
1288C2×C4C23×D412yes—
1289C2×C4C23×D412yes—
1290C2×C4C23×D418yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D412yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D412yes—
1295C2×C4C2×H(5,𝔽2)14yes—
1296C2×C4C2×H(5,𝔽2)14yes—
1297C2×C4C2×H(5,𝔽2)12yes—
1298C2×C4C2×H(5,𝔽2)12yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4#58512yes—
1302C2×C4#58512yes—
1303C2×C4#58512yes—
1304C22—22no—
1305C22—28no—
1306C22—22no—
1307C22—28no—
1308C22—22no—
1309C22—28no—
1310C22—44no—
1311C22—41no—
1312C22—41no—
1313C22—44no—
1314C22—41no—
1315C22—44no—
1316C22—44no—
1317C22—41no—
1318C22—42no—
1319C22—44no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—44no—
1324C22—42no—
1325C22—44no—
1326C22—42no—
1327C22—44no—
1328C22—42no—
1329C22—44no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—44no—
1336C22—42no—
1337C22—42no—
1338C22—44no—
1339C22C24×D411yescharacteristic
1340C22C22×H(5,𝔽2)11yescharacteristic
1341C22C22×H(5,𝔽2)11yescharacteristic
1342C22C22×2−1+411yescharacteristic
1343C22C2×#58511yescharacteristic
1344C22C2×#58511yescharacteristic
1345C22C2×#58511yescharacteristic
1346C4—24no—
1347C4—28no—
1348C4—22no—
1349C4—22no—
1350C4—24no—
1351C4—22no—
1352C4—24no—
1353C4—48no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4#348814yes—
1365C4#348914yes—
1366C4#349614yes—
1367C2—42no—
1368C2—48no—
1369C2—82no—
1370C2—84no—
1371C2—82no—
1372C2C2×#349611yescharacteristic
1373C2C2×#348811yescharacteristic
1374C2C2×#348911yescharacteristic
1375C2#6301411yescharacteristic
1376C2#6303111yescharacteristic
1377C2#6303911yescharacteristic
1378C2#6303911yescharacteristic
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×#3548C2semidirect
2. C2×#3483C2semidirect
3. #59815C2semidirect
4. #59655C2semidirect
5. #59652C2semidirect
6. #59419C2semidirect
7. #51590C2semidirect
8. #44889C2semidirect
9. #44888C2semidirect
10. #44885C2semidirect
11. #44884C2semidirect
12. #39471C2semidirect
13. #39470C2semidirect
14. #39341C2semidirect
15. #39340C2semidirect
16. #37272C2semidirect
17. #36410C2semidirect
18. #36404C2semidirect
19. #36275C2semidirect
20. #36259C2semidirect
21. #35564C2semidirect
22. #35280C2semidirect
23. #35273C2semidirect
24. #34979C2semidirect
25. #34977C2semidirect
26. #34207C2semidirect
237. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35482
C2×#34832
#598152
#596552
#596522
#594192
#515902
#448892
#448882
#448852
#448842
#394712
#394702
#393412
#393402
#372722
#364102
#364042
#362752
#362592
#355642
#352802
#352732
#349792
#349772
#342072