Finite Group Databasebeta

← #7642994

Subgroups — #7642994

Order 512.

7004 conjugacy classes of subgroups.

The subgroup lattice has 1311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3#39594C212yesmaximal, complemented
4#39466C212yesmaximal, complemented
5#39122C212yesmaximal, complemented
6#38923C212yesmaximal, complemented
7#38920C212yesmaximal, complemented
8#38918C212yesmaximal, complemented
9#38915C214yesmaximal, complemented
10#38911C212yesmaximal, complemented
11#38908C212yesmaximal, complemented
12#38903C214yesmaximal, complemented
13#38046C214yesmaximal, complemented
14#37842C214yesmaximal, complemented
15#37121C218yesmaximal, complemented
16#36625C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic, complemented
18#35654C214yesmaximal, complemented
19#35636C214yesmaximal, complemented
20#35311C212yesmaximal, complemented
21#35263C212yesmaximal, complemented
22#35248C211yesmaximal, characteristic, complemented
23#35247C211yesmaximal, characteristic, complemented
24#35031C212yesmaximal, complemented
25#35010C212yesmaximal, complemented
26#34194C211yesmaximal, characteristic, complemented
27#3520—216no—
28C2×#556C2211yescharacteristic, complemented
29C2×#554C2212yes—
30C2×#552C2212yescomplemented
31C2×#551C2214yes—
32C2×D4×Q8C2211yescharacteristic, complemented
33C2×#548C2212yescomplemented
34C2×#547C2211yescharacteristic, complemented
35C2×#547C2211yescharacteristic, complemented
36C2×#546C2212yes—
37C2×#542C2212yescomplemented
38C2×#539C2214yescomplemented
39C2×#533C2211yescharacteristic
40C2×#529—216no—
41C2×#529C2214yes—
42C2×#529C2214yes—
43C2×#529C2212yes—
44C2×#529C2212yes—
45C2×#529C2211yescharacteristic
46C2×#529C2212yes—
47C2×#529C2212yes—
48C22×#126C2212yes—
49C22×#125C2211yescharacteristic
50C22×#124C2211yescharacteristic
51C2×#525C2212yes—
52C22×#123C2212yes—
53C22×C22⋊Q8C2212yes—
54C22×C22⋊Q8C2211yescharacteristic
55C22×#121C2211yescharacteristic
56C2×#520C2212yescomplemented
57C22×C4×Q8C2211yescharacteristic
58C22×C4×D4C2212yes—
59C22×C4×D4C2211yescharacteristic
60C22×#117C2212yes—
61C23×C42C2211yescharacteristic
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2855C2212yes—
65#2855C2211yescharacteristic
66#2855C2212yes—
67#2855C2212yes—
68#2855C2212yes—
69#2855C2212yes—
70#2854C2211yescharacteristic
71#2854C2212yes—
72#2853C2212yes—
73#2852C2214yescomplemented
74#2851C2214yescomplemented
75#2851C2212yescomplemented
76#2850C2212yescomplemented
77#2849C2212yes—
78#2848C2211yescharacteristic
79#2848C2212yes—
80#2848C2212yes—
81#2847C2211yescharacteristic
82#2722C2218yescomplemented
83#2720C2218yescomplemented
84#2719C2218yescomplemented
85#2718C2218yescomplemented
86#2717C2218yescomplemented
87#2708C2218yes—
88#2706C2218yescomplemented
89#2695C2218yescomplemented
90#2695C2218yescomplemented
91#2693C2218yescomplemented
92#2692C2218yescomplemented
93#2690C2218yescomplemented
94#2689C2218yescomplemented
95#2688C2218yes—
96#2687C2218yescomplemented
97#2686C2218yescomplemented
98#2637C2214yescomplemented
99#2634C2214yescomplemented
100#2627C2214yes—
101#2626C2214yes—
102#2625C2214yescomplemented
103#2625C2214yescomplemented
104#2625C2214yescomplemented
105#2624C2214yescomplemented
106#2622C2214yes—
107#2613C2214yes—
108#2602C2218yescomplemented
109#2600C2218yescomplemented
110#2592C2212yescomplemented
111#2584C2212yescomplemented
112#2582C2212yescomplemented
113#2581C2214yescomplemented
114#2579C2218yescomplemented
115#2568C2212yescomplemented
116#2564C2218yescomplemented
117#2557C2218yescomplemented
118#2553C2218yescomplemented
119#2550C2214yescomplemented
120#2547C2214yescomplemented
121#2546C2212yescomplemented
122#2542C2214yescomplemented
123#2538C2212yescomplemented
124#2535C2214yes—
125#2521C2218yescomplemented
126#2503C2212yes—
127#2503C2214yes—
128#2502C2214yes—
129#2499C2218yescomplemented
130#2498C2218yescomplemented
131#2496C2218yescomplemented
132#2492C2214yescomplemented
133#2489C2214yescomplemented
134#2487C2214yes—
135#2487C2214yescomplemented
136#2486C2212yes—
137#2486C2214yes—
138#2485C2218yescomplemented
139#2485C2214yescomplemented
140#2484C2214yes—
141#2484C2218yescomplemented
142#2483C2214yes—
143#2483C2214yes—
144#2478C2218yescomplemented
145#2470C2218yescomplemented
146#2468C2218yescomplemented
147#2457C2218yescomplemented
148#2453C2214yescomplemented
149#2447C2214yescomplemented
150#2442C2214yescomplemented
151#2434C2212yes—
152#2432C2214yescomplemented
153#2429C2214yescomplemented
154#2427C2214yes—
155#2427C2214yescomplemented
156#2420C2214yes—
157#2417C2214yescomplemented
158#2417C2214yescomplemented
159#2417C2214yescomplemented
160#2415C2214yescomplemented
161#2414C2214yescomplemented
162#2413C2214yes—
163#2412C2214yes—
164#2412C2214yes—
165#2409C2212yes—
166#2409C2214yescomplemented
167#2407C2214yes—
168#2407C2214yescomplemented
169#2354C2212yescomplemented
170#2352C2214yescomplemented
171D4×C4⋊C4C2212yescomplemented
172#2345C2212yes—
173#2342C2214yes—
174D4×C22⋊C4C2212yes—
175#2327C2214yescomplemented
176#2323C2214yescomplemented
177#2322C2214yes—
178#2321C2214yes—
179#2319C2212yescomplemented
180#2318C2214yescomplemented
181#2317C2214yescomplemented
182#2316C2214yescomplemented
183#2315C2214yes—
184#2311C2214yescomplemented
185#2310C2214yescomplemented
186#2308C2214yes—
187C4×C22⋊Q8C2214yescomplemented
188C4×C22⋊Q8C2212yescomplemented
189C4×C22⋊Q8C2214yescomplemented
190C4×#123C2212yes—
191C4×#121C2212yescomplemented
192C4×#120C2212yes—
193#2296C2212yes—
194#2290C2214yescomplemented
195#2285C2211yescharacteristic
196#2283C2211yescharacteristic
197#2280C2212yes—
198#2280C2212yes—
199C2×#380C2212yes—
200#2275C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2312yes—
204C23×Q8C2311yescharacteristic
205C23×D4C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2311yescharacteristic
208C24×C4C2311yescharacteristic
209C24×C4C2311yescharacteristic
210C24×C4C2312yes—
211#556—28no—
212#554—216no—
213#552—216no—
214#551—232no—
215D4×Q8—28no—
216#548—216no—
217#547—28no—
218#547—28no—
219#546—216no—
220#542—216no—
221#539—232no—
222#533—28no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2314yes—
227#529—216no—
228#529—232no—
229#529—216no—
230#529—216no—
231#529—216no—
232#529—232no—
233#529—28no—
234C2×#126—216no—
235C2×#126C2312yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125—28no—
243C2×#125C2311yescharacteristic
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#124—28no—
250C2×#124C2311yescharacteristic
251C2×#124C2312yes—
252C2×#124C2314yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256#525—216no—
257C2×#123—216no—
258C2×#123C2312yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×C22⋊Q8—216no—
270C2×C22⋊Q8—28no—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×#121—28no—
290C2×#121C2311yescharacteristic
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#120C2312yes—
299C2×#120C2314yes—
300#520—216no—
301C2×C4×Q8—28no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×D4—216no—
311C2×C4×D4D4116yescomplemented
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×#117—216no—
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2314yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2311yescharacteristic
351C22×C22⋊C4C2314yes—
352C22×C22⋊C4C2312yes—
353C22×C22⋊C4C2312yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2314yes—
357C22×C22⋊C4C2312yes—
358C22×C42—28no—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364C22×C42C2311yescharacteristic
365C22×C42C2312yes—
366C22×C42C2312yes—
367C22×C42C2311yescharacteristic
368#400C2318yes—
369#400C2318yes—
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#399C2318yes—
375#399C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2314yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#397C2314yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#397C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#395C2318yes—
398#395C2318yes—
399#395C2314yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#393C2318yes—
407#393C2314yes—
408#392C2318yes—
409#392C2318yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2318yes—
415#391C2318yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#390C2312yes—
422#390C2314yes—
423#390C2314yes—
424#390C2318yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2318yes—
430#389C2318yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2318yes—
436#389C2314yes—
437#389C2318yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2314yes—
460#387C2314yes—
461#387C2318yes—
462#387C2318yes—
463#387C2314yes—
464#387C2314yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2314yes—
473#386C2318yes—
474#386C2312yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2312yes—
480#385C2314yes—
481#385C2318yes—
482#385C2312yes—
483#385C2314yes—
484#385C2318yes—
485#385C2318yes—
486#385C2314yes—
487#385C2314yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2314yes—
492#385C2318yes—
493#385C2318yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2312yes—
499#384C2318yes—
500#384C2312yes—
501#383C2312yes—
502#382C2314yes—
503#382C2318yes—
504#382C2312yes—
505#382C2312yes—
506#381C2314yes—
507#381C2314yes—
508#381C2318yes—
509#381C2318yes—
510#381C2314yes—
511#381C2314yes—
512#381C2312yes—
513#381C2312yes—
514#381C2314yes—
515#380C2318yes—
516#380C2318yes—
517#380C2318yes—
518#380C2318yes—
519#380C2318yes—
520#380C2318yes—
521#380C2314yes—
522#380C2314yes—
523#380C2312yes—
524#380C2311yescharacteristic
525#380C2312yes—
526#380C2312yes—
527#380C2311yescharacteristic
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#379C2312yes—
537#379C2314yes—
538#379C2314yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2318yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2312yes—
553C2×#95C2314yes—
554C25C2412yes—
555C25C2411yescharacteristic
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—48no—
559C2×#41—48no—
560C22×Q8—24no—
561C22×Q8—28no—
562C22×Q8—44no—
563C22×Q8—48no—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2414yes—
570C22×D4—28no—
571C22×D4—28no—
572C22×D4—44no—
573C22×D4—44no—
574C22×D4C2×D418yes—
575C22×D4C2412yes—
576C22×D4C2411yescharacteristic
577C22×D4C2414yes—
578C22×D4C2414yes—
579C22×D4C2411yescharacteristic
580C22×D4C2411yescharacteristic
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C23×C4—24no—
586C23×C4—24no—
587C23×C4—24no—
588C23×C4—24no—
589C23×C4—48no—
590C23×C4—44no—
591C23×C4—44no—
592C23×C4—42no—
593C23×C4C2×D4116yes—
594C23×C4C2411yescharacteristic
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C23×C4C2412yes—
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2411yescharacteristic
608C23×C4C2411yescharacteristic
609C23×C4C2414yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2418yes—
615C23×C4C2412yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C4⋊Q8—28no—
619C4⋊Q8—24no—
620C4⋊Q8—24no—
621C4⋊Q8—48no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126—216no—
626#126—216no—
627#126—216no—
628#126—28no—
629#125—28no—
630#125—216no—
631#125—28no—
632#125—216no—
633#125—24no—
634#125—28no—
635#124—28no—
636#124—28no—
637#124—216no—
638#124—28no—
639#124—216no—
640#124—24no—
641#123—216no—
642#123—216no—
643#123—28no—
644#123—216no—
645#123—216no—
646#123—216no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—44no—
651#123—48no—
652C22⋊Q8—24no—
653C22⋊Q8—28no—
654C22⋊Q8—216no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—216no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—28no—
663C22⋊Q8—216no—
664C22⋊Q8—28no—
665C22⋊Q8—216no—
666C22⋊Q8—44no—
667C22⋊Q8—48no—
668C22⋊Q8—48no—
669C22⋊Q8—48no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—216no—
674#121—28no—
675#121—24no—
676#121—28no—
677#121—44no—
678#120—216no—
679#120—28no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—28no—
684C4×Q8—28no—
685C4×Q8—28no—
686C4×Q8—24no—
687C4×Q8—28no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—216no—
694C4×D4—216no—
695C4×D4—28no—
696C4×D4—216no—
697C4×D4—24no—
698C4×D4—48no—
699C4×D4—48no—
700C4×D4C2×D418yes—
701C4×D4C2×D4116yes—
702C4×D4C2×D418yes—
703C4×D4C2×D418yes—
704C4×D4C2×D418yes—
705C4×D4C2×D4116yes—
706#117—216no—
707#117—216no—
708#117—216no—
709#117—216no—
710#117—28no—
711#117—28no—
712#117—216no—
713#117—28no—
714#117—44no—
715#117—48no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—28no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—28no—
721C2×C4⋊C4—216no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—28no—
724C2×C4⋊C4—48no—
725C2×C4⋊C4C2×D418yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C22⋊C4—28no—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—216no—
774C2×C22⋊C4—28no—
775C2×C22⋊C4—48no—
776C2×C22⋊C4C2×D4116yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C42—24no—
817C2×C42—28no—
818C2×C42—24no—
819C2×C42—24no—
820C2×C42—28no—
821C2×C42—28no—
822C2×C42—28no—
823C2×C42—28no—
824C2×C42C2×D418yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2418yes—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843#95C2412yes—
844#95C2414yes—
845#95C2418yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2414yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2418yes—
857#95C2418yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872C24—22no—
873C24—22no—
874C24—24no—
875C24—24no—
876C24—42no—
877C24—42no—
878C24—44no—
879C24—44no—
880C24C22×D418yes—
881C242−1+414yes—
882C24C2512yes—
883C24C2512yes—
884C24C2512yes—
885C24C2512yes—
886C24C2511yescharacteristic
887#41—432no—
888#41—816no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—28no—
895C2×Q8—24no—
896C2×Q8—28no—
897C2×Q8—24no—
898C2×Q8—28no—
899C2×Q8—24no—
900C2×Q8—44no—
901C2×Q8—48no—
902C2×Q8—416no—
903C2×Q8—816no—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—22no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—416no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—48no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—48no—
926C2×D4—432no—
927C2×D4C22×D414yes—
928C2×D4C22×D414yes—
929C2×D4C22×D418yes—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—28no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—28no—
962C22×C4—432no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—48no—
976C22×C4—48no—
977C22×C4—48no—
978C22×C4—48no—
979C22×C4—48no—
980C22×C4—48no—
981C22×C4—416no—
982C22×C4—416no—
983C22×C4—416no—
984C22×C4C22×D414yes—
985C22×C4C22×D414yes—
986C22×C4C22×D414yes—
987C22×C4C22×D418yes—
988C22×C4C22×D418yes—
989C22×C4C22×D418yes—
990C22×C4C22×D418yes—
991C22×C4C22×D418yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2518yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—22no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—24no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—22no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—48no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—48no—
1047C4⋊C4—48no—
1048C4⋊C4—48no—
1049C4⋊C4—44no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—48no—
1053C4⋊C4—48no—
1054C4⋊C4C22×D414yes—
1055C4⋊C4C22×D418yes—
1056C4⋊C4C22×D414yes—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—24no—
1080C22⋊C4—48no—
1081C22⋊C4—48no—
1082C22⋊C4—48no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—48no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—44no—
1090C22⋊C4—48no—
1091C22⋊C4—44no—
1092C22⋊C4C22×D418yes—
1093C22⋊C4C22×D418yes—
1094C22⋊C4C22×D418yes—
1095C22⋊C4C22×D418yes—
1096C42—24no—
1097C42—24no—
1098C42—24no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—28no—
1103C42—28no—
1104C42—28no—
1105C42—28no—
1106C42—24no—
1107C42—28no—
1108C42—44no—
1109C42—48no—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C42C22×D414yes—
1113C42C22×D414yes—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—22no—
1125C23—24no—
1126C23—24no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—28no—
1131C23—216no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—24no—
1136C23—24no—
1137C23—48no—
1138C23—48no—
1139C23—48no—
1140C23—44no—
1141C23—44no—
1142C23—48no—
1143C23—88no—
1144C23—88no—
1145C23C23×D414yes—
1146C23C23×D414yes—
1147C23C23×D412yes—
1148C23C2×2−1+414yes—
1149C23C2×2−1+412yes—
1150C23#58512yes—
1151C23C2611yescharacteristic
1152Q8—48no—
1153Q8—48no—
1154Q8—48no—
1155Q8—44no—
1156Q8—48no—
1157Q8—88no—
1158D4—28no—
1159D4—28no—
1160D4—48no—
1161D4—416no—
1162D4—416no—
1163D4—416no—
1164D4—48no—
1165D4—44no—
1166D4—88no—
1167D4—88no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—24no—
1172C2×C4—21no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—28no—
1177C2×C4—28no—
1178C2×C4—28no—
1179C2×C4—216no—
1180C2×C4—216no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—24no—
1201C2×C4—28no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—28no—
1210C2×C4—28no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—48no—
1217C2×C4—48no—
1218C2×C4—48no—
1219C2×C4—48no—
1220C2×C4—48no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—48no—
1226C2×C4—416no—
1227C2×C4—44no—
1228C2×C4—48no—
1229C2×C4—48no—
1230C2×C4—48no—
1231C2×C4—48no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4—168no—
1235C2×C4C23×D412yes—
1236C2×C4C23×D412yes—
1237C2×C4C23×D412yes—
1238C2×C4C23×D412yes—
1239C2×C4C23×D414yes—
1240C2×C4C23×D414yes—
1241C2×C4C23×D412yes—
1242C2×C4C23×D412yes—
1243C2×C4#58514yes—
1244C2×C4#58514yes—
1245C22—22no—
1246C22—24no—
1247C22—24no—
1248C22—22no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—416no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—42no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—42no—
1272C22—816no—
1273C22#348914yes—
1274C22C24×D411yescharacteristic
1275C22C22×2−1+411yescharacteristic
1276C22C2×#58512yes—
1277C22C2×#58511yescharacteristic
1278C22C2×#58512yes—
1279C4—22no—
1280C4—24no—
1281C4—24no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—42no—
1286C4—44no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—44no—
1292C4—48no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—44no—
1297C4—44no—
1298C4#344914yes—
1299C4#348514yes—
1300C2—24no—
1301C2—44no—
1302C2—44no—
1303C2—44no—
1304C2—82no—
1305C2C2×#344911yescharacteristic
1306C2C2×#348511yescharacteristic
1307C2C2×#348911yescharacteristic
1308C2#6282312yes—
1309C2#6282712yes—
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×#3520C2semidirect
2. C22×#529C2semidirect
3. #39594C2semidirect
4. #39466C2semidirect
5. #39122C2semidirect
6. #38923C2semidirect
7. #38920C2semidirect
8. #38918C2semidirect
9. #38915C2semidirect
10. #38911C2semidirect
11. #38908C2semidirect
12. #38903C2semidirect
13. #38046C2semidirect
14. #37842C2semidirect
15. #37121C2semidirect
16. #36625C2semidirect
17. #36621C2semidirect
18. #35654C2semidirect
19. #35636C2semidirect
20. #35311C2semidirect
21. #35263C2semidirect
22. #35248C2semidirect
23. #35247C2semidirect
24. #35031C2semidirect
25. #35010C2semidirect
26. #34194C2semidirect
28. C2×#556C22semidirect
30. C2×#552C22semidirect
32. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
34. C2×#547C22semidirect
35. C2×#547C22semidirect
37. C2×#542C22semidirect
38. C2×#539C22semidirect
56. C2×#520C22semidirect
62. #2857C22semidirect
63. #2857C22semidirect
73. #2852C22semidirect
74. #2851C22semidirect
75. #2851C22semidirect
76. #2850C22semidirect
82. #2722C22semidirect
83. #2720C22semidirect
84. #2719C22semidirect
85. #2718C22semidirect
86. #2717C22semidirect
88. #2706C22semidirect
89. #2695C22semidirect
90. #2695C22semidirect
91. #2693C22semidirect
92. #2692C22semidirect
93. #2690C22semidirect
94. #2689C22semidirect
96. #2687C22semidirect
97. #2686C22semidirect
98. #2637C22semidirect
99. #2634C22semidirect
102. #2625C22semidirect
103. #2625C22semidirect
104. #2625C22semidirect
105. #2624C22semidirect
108. #2602C22semidirect
109. #2600C22semidirect
110. #2592C22semidirect
111. #2584C22semidirect
112. #2582C22semidirect
113. #2581C22semidirect
114. #2579C22semidirect
115. #2568C22semidirect
116. #2564C22semidirect
117. #2557C22semidirect
118. #2553C22semidirect
119. #2550C22semidirect
120. #2547C22semidirect
121. #2546C22semidirect
122. #2542C22semidirect
123. #2538C22semidirect
125. #2521C22semidirect
129. #2499C22semidirect
130. #2498C22semidirect
131. #2496C22semidirect
132. #2492C22semidirect
133. #2489C22semidirect
135. #2487C22semidirect
138. #2485C22semidirect
139. #2485C22semidirect
141. #2484C22semidirect
144. #2478C22semidirect
145. #2470C22semidirect
146. #2468C22semidirect
147. #2457C22semidirect
148. #2453C22semidirect
149. #2447C22semidirect
150. #2442C22semidirect
152. #2432C22semidirect
153. #2429C22semidirect
155. #2427C22semidirect
157. #2417C22semidirect
158. #2417C22semidirect
159. #2417C22semidirect
160. #2415C22semidirect
161. #2414C22semidirect
166. #2409C22semidirect
168. #2407C22semidirect
169. #2354C22semidirect
170. #2352C22semidirect
171. D4×C4⋊C4C22semidirect
175. #2327C22semidirect
176. #2323C22semidirect
179. #2319C22semidirect
180. #2318C22semidirect
181. #2317C22semidirect
182. #2316C22semidirect
184. #2311C22semidirect
185. #2310C22semidirect
187. C4×C22⋊Q8C22semidirect
188. C4×C22⋊Q8C22semidirect
189. C4×C22⋊Q8C22semidirect
191. C4×#121C22semidirect
194. #2290C22semidirect
200. #2275C22semidirect
311. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C22×#5292
#395942
#394662
#391222
#389232
#389202
#389182
#389152
#389112
#389082
#389032
#380462
#378422
#371212
#366252
#366212
#356542
#356362
#353112
#352632
#352482
#352472
#350312
#350102
#341942