Finite Group Databasebeta

← #7720817

Subgroups — #7720817

Order 512.

7176 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3550C211yesmaximal, characteristic, complemented
2C2×#3554C211yesmaximal, characteristic, complemented
3#51900C218yesmaximal, complemented
4#50657C218yesmaximal, complemented
5#45248C214yesmaximal, complemented
6#45245C214yesmaximal, complemented
7#45101C214yesmaximal, complemented
8#45091C214yesmaximal, complemented
9#39747C211yesmaximal, characteristic, complemented
10#39739C212yesmaximal, complemented
11#39617C212yesmaximal, complemented
12#39616C211yesmaximal, characteristic, complemented
13#39171C211yesmaximal, characteristic, complemented
14#39168C212yesmaximal, complemented
15#39167C211yesmaximal, characteristic, complemented
16#39161C212yesmaximal, complemented
17#37301C212yesmaximal, complemented
18#37299C212yesmaximal, complemented
19#36597C211yesmaximal, characteristic, complemented
20Q8×#127C211yesmaximal, characteristic, complemented
21#36508C211yesmaximal, characteristic, complemented
22#36465C211yesmaximal, characteristic, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35277C212yesmaximal, complemented
25#35276C212yesmaximal, complemented
26#35241C211yesmaximal, characteristic, complemented
27#35166C211yesmaximal, characteristic, complemented
28#34624C211yesmaximal, characteristic, complemented
29#34145C211yesmaximal, characteristic, complemented
30#3554—216no—
31#3550—216no—
32C2×#563C2214yes—
33C2×#562C2214yes—
34C2×#559C2212yes—
35C2×#559C2211yescharacteristic
36C2×#559C2212yes—
37C2×Q82C2212yes—
38C2×#557C2211yescharacteristic
39C2×#556C2212yes—
40C2×#556C2211yescharacteristic
41C2×#556C2211yescharacteristic
42C2×#554C2212yes—
43C2×#550C2211yescharacteristic
44C2×D4×Q8C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×D4×Q8C2211yescharacteristic
47C2×D4×Q8C2212yes—
48C2×D4×Q8C2214yes—
49C2×#548C2212yes—
50C2×#548C2214yes—
51C2×#547C2212yes—
52C2×#542C2212yes—
53C2×#542C2212yes—
54C2×#542C2212yes—
55C2×#542C2212yes—
56C2×#542C2214yes—
57C2×#540C2212yes—
58C2×#539C2214yes—
59C2×#537C2214yes—
60C2×#536C2212yes—
61C2×#536C2212yes—
62C2×#536C2212yes—
63C2×#533C2211yescharacteristic
64C2×#533C2211yescharacteristic
65C2×#532C2211yescharacteristic
66C2×#532C2211yescharacteristic
67C2×#529C2211yescharacteristic
68#2868C2211yescharacteristic
69#2868C2212yes—
70#2862C2211yescharacteristic
71#2861C2212yes—
72#2858C2212yes—
73#2858C2211yescharacteristic
74#2858C2212yes—
75#2858C2211yescharacteristic
76#2857C2212yes—
77#2856C2212yes—
78#2856C2212yes—
79#2850C2212yes—
80#2733C2218yes—
81#2730C2218yes—
82#2727C2218yes—
83#2723C2218yes—
84#2720C2218yes—
85#2714C2218yes—
86#2705C2218yes—
87#2696C2218yes—
88#2683C2218yes—
89#2682C2218yes—
90#2681C2218yes—
91#2681C2218yes—
92#2677C2218yes—
93#2677C2218yes—
94#2676C2218yes—
95#2674C2218yes—
96#2674C2218yes—
97#2672C2218yes—
98#2672C2218yes—
99#2671C2218yes—
100#2664C2214yes—
101#2662C2214yes—
102#2661C2214yes—
103#2660C2211yescharacteristic
104#2660C2212yes—
105#2657C2211yescharacteristic
106#2657C2212yes—
107#2656C2214yes—
108#2641C2211yescharacteristic
109#2640C2211yescharacteristic
110#2640C2212yes—
111#2640C2212yes—
112#2620C2211yescharacteristic
113#2620C2211yescharacteristic
114#2620C2212yes—
115#2620C2212yes—
116#2619C2211yescharacteristic
117#2619C2211yescharacteristic
118#2568C2211yescharacteristic
119#2567C2212yes—
120#2567C2212yes—
121#2566C2212yes—
122#2566C2214yes—
123#2565C2212yes—
124#2565C2212yes—
125#2563C2212yes—
126#2555C2218yes—
127#2554C2218yes—
128#2554C2218yes—
129#2548C2212yes—
130#2547C2211yescharacteristic
131#2546C2211yescharacteristic
132#2545C2212yes—
133#2545C2212yes—
134#2545C2214yes—
135#2545C2212yes—
136#2544C2212yes—
137#2544C2212yes—
138#2544C2212yes—
139#2544C2212yes—
140#2542C2212yes—
141#2542C2212yes—
142#2542C2214yes—
143#2542C2211yescharacteristic
144#2542C2211yescharacteristic
145#2542C2211yescharacteristic
146#2542C2212yes—
147#2542C2212yes—
148#2542C2218yes—
149#2541C2211yescharacteristic
150#2541C2212yes—
151#2541C2212yes—
152#2541C2211yescharacteristic
153#2540C2214yes—
154#2540C2214yes—
155#2540C2214yes—
156#2540C2218yes—
157#2519C2218yes—
158#2512C2218yes—
159#2500C2214yes—
160#2498C2214yes—
161#2491C2218yes—
162#2464C2218yes—
163#2463C2218yes—
164#2461C2218yes—
165#2456C2218yes—
166#2456C2218yes—
167#2452C2218yes—
168#2452C2218yes—
169#2448C2218yes—
170#2443C2218yes—
171#2440C2218yes—
172#2436C2214yes—
173#2434C2214yes—
174#2432C2214yes—
175#2429C2214yes—
176#2429C2214yes—
177#2427C2214yes—
178#2426C2214yes—
179#2423C2218yes—
180#2422C2218yes—
181#2417C2214yes—
182#2415C2214yes—
183#2414C2214yes—
184#2409C2214yes—
185#2407C2214yes—
186#2392C2214yes—
187#2388C2214yes—
188#2370C2214yes—
189#2369C2212yes—
190#2368C2214yes—
191#2365C2212yes—
192#2363C2214yes—
193#2362C2214yes—
194#2360C2212yes—
195#2360C2212yes—
196#2328C2212yes—
197#2326C2212yes—
198#2326C2212yes—
199#2326C2212yes—
200#2326C2212yes—
201#2326C2212yes—
202#2323C2214yes—
203C4×C4⋊Q8C2212yes—
204C4×#127C2212yes—
205C4×#127C2211yescharacteristic
206C4×#127C2211yescharacteristic
207C4×#127C2212yes—
208C4×#124C2211yescharacteristic
209C4×#124C2211yescharacteristic
210C4×#124C2212yes—
211#2296C2212yes—
212#2295C2212yes—
213#2295C2211yescharacteristic
214#2295C2212yes—
215#2295C2211yescharacteristic
216C42×Q8C2211yescharacteristic
217C42×Q8C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C4×#117C2212yes—
220C2×C4×C4⋊C4C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227#563—232no—
228#562—232no—
229#559—216no—
230#559—216no—
231#559—28no—
232Q82—216no—
233#557—28no—
234#556—216no—
235#556—28no—
236#556—28no—
237#554—216no—
238#550—28no—
239D4×Q8—216no—
240D4×Q8—28no—
241D4×Q8—28no—
242D4×Q8—28no—
243D4×Q8—416no—
244#548—216no—
245#548—416no—
246#547—216no—
247#542—216no—
248#542—232no—
249#542—216no—
250#542—216no—
251#542—216no—
252#540—216no—
253#539—232no—
254#537—416no—
255#536—216no—
256#536—216no—
257#536—216no—
258#533—28no—
259#533D4116yescomplemented
260#532—28no—
261#532—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2318yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282C2×#127C2312yes—
283C2×#127C2311yescharacteristic
284C2×#127C2312yes—
285#529—28no—
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#126C2314yes—
292C2×#125C2311yescharacteristic
293C2×#125C2312yes—
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#125C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2311yescharacteristic
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2314yes—
306C2×#124C2312yes—
307C2×#124C2314yes—
308C2×#124C2312yes—
309C2×#124C2314yes—
310C2×#124C2314yes—
311C2×#124C2312yes—
312C2×#124C2312yes—
313C2×#124C2318yes—
314C2×#124C2314yes—
315C2×#124C2311yescharacteristic
316C2×#123C2312yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×#123C2314yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2318yes—
348C2×C22⋊Q8C2318yes—
349C2×C22⋊Q8C2318yes—
350C2×C22⋊Q8C2318yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2311yescharacteristic
356C2×#121C2311yescharacteristic
357C2×#121C2312yes—
358C2×#121C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#121C2314yes—
364C2×#121C2314yes—
365C2×#121C2318yes—
366C2×#121C2318yes—
367C2×#121C2314yes—
368C2×#121C2318yes—
369C2×#121C2318yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2314yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2314yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2314yes—
400C2×C4×D4C2318yes—
401C2×C4×D4C2318yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2311yescharacteristic
406C2×#117C2312yes—
407C2×#117C2311yescharacteristic
408C2×#117C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C4⋊C4C2314yes—
411C22×C42C2312yes—
412C22×C42C2311yescharacteristic
413#400C2314yes—
414#399C2318yes—
415#399C2314yes—
416#399C2314yes—
417#399C2314yes—
418#399C2318yes—
419#399C2318yes—
420#399C2318yes—
421#398C2318yes—
422#398C2318yes—
423#398C2314yes—
424#398C2318yes—
425#398C2314yes—
426#397C2314yes—
427#397C2318yes—
428#397C2318yes—
429#397C2314yes—
430#396C2318yes—
431#396C2318yes—
432#396C2318yes—
433#396C2314yes—
434#396C2314yes—
435#396C2318yes—
436#396C2318yes—
437#396C2318yes—
438#395C2318yes—
439#395C2318yes—
440#395C2314yes—
441#395C2318yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2318yes—
447#394C2318yes—
448#394C2314yes—
449#394C2314yes—
450#394C2318yes—
451#394C2318yes—
452#394C2318yes—
453#394C2318yes—
454#394C2318yes—
455#393C2318yes—
456#393C2314yes—
457#393C2318yes—
458#393C2318yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2318yes—
465#392C2314yes—
466#392C2318yes—
467#392C2318yes—
468#392C2318yes—
469#391C2311yescharacteristic
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#390C2311yescharacteristic
483#390C2311yescharacteristic
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2311yescharacteristic
488#390C2311yescharacteristic
489#390C2314yes—
490#390C2314yes—
491#390C2318yes—
492#390C2318yes—
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2311yescharacteristic
500#390C2312yes—
501#390C2318yes—
502#390C2318yes—
503#390C2314yes—
504#390C2318yes—
505#390C2318yes—
506#390C2318yes—
507#390C2318yes—
508#389C2318yes—
509#389C2318yes—
510#389C2318yes—
511#389C2318yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#388C2318yes—
520#388C2318yes—
521#388C2318yes—
522#388C2318yes—
523#388C2318yes—
524#388C2318yes—
525#388C2318yes—
526#388C2318yes—
527#388C2318yes—
528#388C2318yes—
529#388C2318yes—
530#388C2314yes—
531#388C2314yes—
532#388C2318yes—
533#387C2318yes—
534#387C2318yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#386C2318yes—
542#386C2318yes—
543#386C2318yes—
544#386C2318yes—
545#386C2318yes—
546#386C2318yes—
547#386C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#385C2318yes—
552#385C2318yes—
553#385C2318yes—
554#385C2314yes—
555#385C2314yes—
556#384C2312yes—
557#384C2311yescharacteristic
558#384C2311yescharacteristic
559#384C2312yes—
560#384C2312yes—
561#384C2312yes—
562#384C2314yes—
563#384C2312yes—
564#384C2318yes—
565#382C2311yescharacteristic
566#382C2312yes—
567#382C2314yes—
568#382C2311yescharacteristic
569#380C2318yes—
570#380C2314yes—
571#380C2318yes—
572C4×C4⋊C4C2318yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2311yescharacteristic
589C4×C4⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2318yes—
596C4×C22⋊C4C2312yes—
597#376C2311yescharacteristic
598#376C2311yescharacteristic
599#376C2312yes—
600#376C2312yes—
601C2×#95C2312yes—
602C43C2312yes—
603C43C2311yescharacteristic
604C43C2311yescharacteristic
605C43C2312yes—
606C2×#41—28no—
607C2×#41—28no—
608C2×#41—28no—
609C2×#41—48no—
610C2×#41—48no—
611C2×#41—48no—
612C22×Q8—28no—
613C22×Q8—28no—
614C22×Q8—28no—
615C22×Q8—48no—
616C22×Q8—48no—
617C22×Q8—48no—
618C22×Q8C2411yescharacteristic
619C22×Q8C2412yes—
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2411yescharacteristic
624C22×Q8C2414yes—
625C22×Q8C2414yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2412yes—
632C22×D4C2411yescharacteristic
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2418yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2418yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2411yescharacteristic
660C4⋊Q8—28no—
661C4⋊Q8—216no—
662C4⋊Q8—216no—
663C4⋊Q8—216no—
664C4⋊Q8—24no—
665C4⋊Q8—24no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—28no—
669C4⋊Q8—28no—
670C4⋊Q8—28no—
671C4⋊Q8—416no—
672C4⋊Q8—44no—
673C4⋊Q8—48no—
674C4⋊Q8C2×D418yes—
675C4⋊Q8C2×D418yes—
676#127—24no—
677#127—24no—
678#127—28no—
679#127—24no—
680#127—44no—
681#127—44no—
682#127—42no—
683#126—216no—
684#126—216no—
685#126—216no—
686#126—216no—
687#126—216no—
688#126—28no—
689#125—216no—
690#125—24no—
691#125—28no—
692#125—28no—
693#125C2×D4116yes—
694#124—28no—
695#124—216no—
696#124—216no—
697#124—216no—
698#124—216no—
699#124—216no—
700#124—24no—
701#124—28no—
702#124—28no—
703#124—28no—
704#124—28no—
705#124—28no—
706#124—24no—
707#124—28no—
708#124—416no—
709#124—44no—
710#124—44no—
711#124—42no—
712#124—48no—
713#123—28no—
714#123—216no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—216no—
719#123—216no—
720#123—216no—
721#123—216no—
722#123—216no—
723#123—216no—
724C22⋊Q8—28no—
725C22⋊Q8—28no—
726C22⋊Q8—216no—
727C22⋊Q8—24no—
728C22⋊Q8—28no—
729C22⋊Q8—28no—
730C22⋊Q8—216no—
731C22⋊Q8—28no—
732C22⋊Q8—28no—
733C22⋊Q8—216no—
734C22⋊Q8—216no—
735C22⋊Q8—216no—
736C22⋊Q8—28no—
737C22⋊Q8—216no—
738C22⋊Q8—216no—
739C22⋊Q8—216no—
740C22⋊Q8—216no—
741C22⋊Q8—216no—
742C22⋊Q8—216no—
743C22⋊Q8—416no—
744C22⋊Q8—416no—
745C22⋊Q8—416no—
746C22⋊Q8—416no—
747C22⋊Q8—48no—
748C22⋊Q8C2×D418yes—
749C22⋊Q8C2×D418yes—
750C22⋊Q8C2×D4116yes—
751#121—24no—
752#121—28no—
753#121—24no—
754#121—24no—
755#121—28no—
756#121—28no—
757#121—216no—
758#121—28no—
759#121—216no—
760#121—216no—
761#121—216no—
762#121—416no—
763#121—416no—
764#121—416no—
765#121—48no—
766#121—416no—
767C4×Q8—216no—
768C4×Q8—28no—
769C4×Q8—28no—
770C4×Q8—28no—
771C4×Q8—24no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8C2×D418yes—
778C4×Q8C2×D418yes—
779C4×Q8C2×D4116yes—
780C4×D4—28no—
781C4×D4—216no—
782C4×D4—28no—
783C4×D4—216no—
784C4×D4—24no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—24no—
788C4×D4—24no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—28no—
795C4×D4—416no—
796C4×D4—416no—
797C4×D4—48no—
798C4×D4—48no—
799#117—28no—
800#117—28no—
801#117—28no—
802#117—28no—
803#117—24no—
804#117—42no—
805#117C2×D4116yes—
806C2×C4⋊C4—216no—
807C2×C4⋊C4—28no—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2418yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2418yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2418yes—
844C2×C4⋊C4C2418yes—
845C2×C4⋊C4C2418yes—
846C2×C4⋊C4C2418yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2418yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2418yes—
894C2×C22⋊C4C2418yes—
895C2×C22⋊C4C2418yes—
896C2×C22⋊C4C2418yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2418yes—
899C2×C22⋊C4C2418yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—44no—
905C2×C42C2×D418yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2418yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2418yes—
951#95C2414yes—
952#95C2414yes—
953#95C2418yes—
954#95C2418yes—
955#95C2418yes—
956#95C2418yes—
957C24C2512yes—
958C24C2512yes—
959C24C2512yes—
960C24C2514yes—
961C24C2511yescharacteristic
962#41—816no—
963#41—816no—
964#41—816no—
965C2×Q8—22no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—28no—
970C2×Q8—28no—
971C2×Q8—28no—
972C2×Q8—24no—
973C2×Q8—24no—
974C2×Q8—24no—
975C2×Q8—28no—
976C2×Q8—28no—
977C2×Q8—22no—
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—22no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—48no—
984C2×Q8—48no—
985C2×Q8—48no—
986C2×Q8—816no—
987C2×Q8—816no—
988C2×Q8—816no—
989C2×Q8C22×D414yes—
990C2×Q8C22×D414yes—
991C2×Q8C22×D418yes—
992C2×D4—24no—
993C2×D4—28no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—24no—
1006C2×D4—28no—
1007C2×D4—216no—
1008C2×D4—22no—
1009C2×D4—24no—
1010C2×D4—28no—
1011C2×D4—22no—
1012C2×D4—22no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—24no—
1016C2×D4—22no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—48no—
1024C2×D4—44no—
1025C2×D4—48no—
1026C2×D4—48no—
1027C2×D4—44no—
1028C2×D4—48no—
1029C2×D4—44no—
1030C2×D4—48no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—48no—
1034C2×D4—48no—
1035C2×D4—48no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—28no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—28no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—28no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—48no—
1055C22×C4—48no—
1056C22×C4—48no—
1057C22×C4—48no—
1058C22×C4—48no—
1059C22×C4—44no—
1060C22×C4—48no—
1061C22×C4C22×D414yes—
1062C22×C4C22×D414yes—
1063C22×C4C22×D414yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—216no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—216no—
1119C4⋊C4—24no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—48no—
1125C4⋊C4—44no—
1126C4⋊C4—48no—
1127C4⋊C4—48no—
1128C4⋊C4—48no—
1129C4⋊C4C22×D418yes—
1130C4⋊C4C22×D414yes—
1131C4⋊C4C22×D414yes—
1132C4⋊C4C22×D418yes—
1133C4⋊C4C22×D418yes—
1134C4⋊C4C22×D418yes—
1135C4⋊C4C22×D418yes—
1136C4⋊C4C22×D418yes—
1137C4⋊C4C22×D418yes—
1138C4⋊C4H(5,𝔽2)18yes—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—216no—
1163C22⋊C4—216no—
1164C22⋊C4—216no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—216no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—48no—
1176C22⋊C4—48no—
1177C22⋊C4—48no—
1178C22⋊C4—48no—
1179C22⋊C4—48no—
1180C22⋊C4—48no—
1181C22⋊C4—44no—
1182C22⋊C4C22×D418yes—
1183C22⋊C4C22×D418yes—
1184C42—24no—
1185C42—28no—
1186C42—28no—
1187C42—28no—
1188C42—28no—
1189C42—28no—
1190C42—24no—
1191C42—28no—
1192C42—24no—
1193C42—22no—
1194C42—24no—
1195C42—24no—
1196C42—22no—
1197C42—22no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—42no—
1203C42C22×D414yes—
1204C42C22×D414yes—
1205C42C22×D414yes—
1206C42C22×D414yes—
1207C42C22×D418yes—
1208C42C22×D418yes—
1209C422−1+414yes—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—28no—
1221C23—24no—
1222C23—22no—
1223C23—24no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—24no—
1228C23—22no—
1229C23—22no—
1230C23—24no—
1231C23—24no—
1232C23—28no—
1233C23—24no—
1234C23C23×D412yes—
1235C23C2611yescharacteristic
1236Q8—28no—
1237Q8—28no—
1238Q8—48no—
1239Q8—44no—
1240Q8—48no—
1241Q8—48no—
1242Q8—48no—
1243Q8—88no—
1244Q8—88no—
1245Q8—88no—
1246Q8—84no—
1247D4—48no—
1248D4—416no—
1249D4—44no—
1250D4—44no—
1251D4—48no—
1252D4—44no—
1253D4—48no—
1254D4—84no—
1255D4—88no—
1256D4—816no—
1257D4—84no—
1258D4—88no—
1259D4—84no—
1260D4—84no—
1261D4—84no—
1262D4—88no—
1263D4—88no—
1264D4—168no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—24no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—28no—
1279C2×C4—28no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—28no—
1293C2×C4—28no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—44no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—48no—
1314C2×C4—88no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4C23×D412yes—
1322C2×C4C23×D414yes—
1323C2×C4C23×D414yes—
1324C2×C4C23×D412yes—
1325C2×C4C23×D412yes—
1326C2×C4C23×D412yes—
1327C2×C4C23×D414yes—
1328C2×C4C23×D414yes—
1329C2×C4C23×D412yes—
1330C2×C4C23×D412yes—
1331C2×C4C2×H(5,𝔽2)18yes—
1332C2×C4C2×H(5,𝔽2)14yes—
1333C2×C4C2×2−1+414yes—
1334C2×C4C2×2−1+412yes—
1335C2×C4#58512yes—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—44no—
1349C22—44no—
1350C22—42no—
1351C22—42no—
1352C22—42no—
1353C22—44no—
1354C22—44no—
1355C22—48no—
1356C22—44no—
1357C22—44no—
1358C22—48no—
1359C22—44no—
1360C22—44no—
1361C22C24×D411yescharacteristic
1362C22C22×H(5,𝔽2)12yes—
1363C22C22×2−1+411yescharacteristic
1364C22C2×#58511yescharacteristic
1365C222−1+612yes—
1366C4—22no—
1367C4—22no—
1368C4—24no—
1369C4—24no—
1370C4—22no—
1371C4—22no—
1372C4—24no—
1373C4—24no—
1374C4—24no—
1375C4—28no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—44no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4#349714yes—
1389C4#349814yes—
1390C2—42no—
1391C2—82no—
1392C2—82no—
1393C2—82no—
1394C2—84no—
1395C2C2×#349711yescharacteristic
1396C2C2×#349811yescharacteristic
1397C2#6285911yescharacteristic
1398C2#6291312yes—
1399C2#6292112yes—
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×#3550C2semidirect
2. C2×#3554C2semidirect
3. #51900C2semidirect
4. #50657C2semidirect
5. #45248C2semidirect
6. #45245C2semidirect
7. #45101C2semidirect
8. #45091C2semidirect
9. #39747C2semidirect
10. #39739C2semidirect
11. #39617C2semidirect
12. #39616C2semidirect
13. #39171C2semidirect
14. #39168C2semidirect
15. #39167C2semidirect
16. #39161C2semidirect
17. #37301C2semidirect
18. #37299C2semidirect
19. #36597C2semidirect
20. Q8×#127C2semidirect
21. #36508C2semidirect
22. #36465C2semidirect
23. #35298C2semidirect
24. #35277C2semidirect
25. #35276C2semidirect
26. #35241C2semidirect
27. #35166C2semidirect
28. #34624C2semidirect
29. #34145C2semidirect
259. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35502
C2×#35542
#519002
#506572
#452482
#452452
#451012
#450912
#397472
#397392
#396172
#396162
#391712
#391682
#391672
#391612
#373012
#372992
#365972
Q8×#1272
#365082
#364652
#352982
#352772
#352762
#352412
#351662
#346242
#341452