Finite Group Databasebeta

← #7681214

Subgroups — #7681214

Order 512.

7076 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59153C214yesmaximal, complemented
4#59118C214yesmaximal, complemented
5#59115C214yesmaximal, complemented
6#59072C214yesmaximal, complemented
7#44846C218yesmaximal, complemented
8#43899C218yesmaximal, complemented
9#39489C211yesmaximal, characteristic, complemented
10#39488C212yesmaximal, complemented
11#39363C211yesmaximal, characteristic, complemented
12#39356C212yesmaximal, complemented
13#39172C211yesmaximal, characteristic, complemented
14#39168C211yesmaximal, characteristic, complemented
15#38091C212yesmaximal, complemented
16#38079C212yesmaximal, complemented
17#36597C211yesmaximal, characteristic, complemented
18Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
19#36412C211yesmaximal, characteristic, complemented
20#36276C211yesmaximal, characteristic, complemented
21#35669C212yesmaximal, complemented
22#35535C212yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35277C212yesmaximal, complemented
25#34977C211yesmaximal, characteristic, complemented
26#34953C211yesmaximal, characteristic, complemented
27#34276C212yesmaximal, complemented
28#34151C211yesmaximal, characteristic, complemented
29C4×#536C211yesmaximal, characteristic, complemented
30#3522—216no—
31#3518—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2212yes—
34C2×Q82C2211yescharacteristic
35C2×Q82C2211yescharacteristic
36C2×#556C2211yescharacteristic
37C2×#556C2214yes—
38C2×#556C2212yes—
39C2×#556C2212yes—
40C2×#555C2211yescharacteristic
41C2×#555C2212yes—
42C2×#554C2212yes—
43C2×#554C2211yescharacteristic
44C2×#550C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2212yes—
48C2×#547C2212yes—
49C2×#547C2214yes—
50C2×#542C2214yes—
51C2×#542C2212yes—
52C2×#542C2214yes—
53C2×#542C2212yes—
54C2×#536C2211yescharacteristic
55C2×#536C2212yes—
56C2×#533C2212yes—
57C2×#533C2211yescharacteristic
58C2×#532C2211yescharacteristic
59C2×#532C2212yes—
60C2×#529C2212yes—
61C2×#529C2212yes—
62C2×#529C2211yescharacteristic
63C2×#520C2212yes—
64C2×#519C2212yes—
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2868C2212yes—
68#2868C2211yescharacteristic
69#2862C2211yescharacteristic
70#2858C2211yescharacteristic
71#2858C2212yes—
72#2858C2211yescharacteristic
73#2857C2212yes—
74#2856C2212yes—
75#2718C2218yes—
76#2718C2218yes—
77#2716C2218yes—
78#2715C2218yes—
79#2710C2218yes—
80#2692C2218yes—
81#2686C2218yes—
82#2683C2218yes—
83#2682C2218yes—
84#2681C2218yes—
85#2674C2218yes—
86#2674C2218yes—
87#2640C2212yes—
88#2640C2212yes—
89#2620C2212yes—
90#2620C2212yes—
91#2620C2212yes—
92#2620C2212yes—
93#2610C2214yes—
94#2584C2214yes—
95#2583C2214yes—
96#2568C2212yes—
97#2567C2211yescharacteristic
98#2567C2211yescharacteristic
99#2567C2212yes—
100#2567C2211yescharacteristic
101#2567C2212yes—
102#2566C2214yes—
103#2563C2211yescharacteristic
104#2555C2218yes—
105#2554C2218yes—
106#2551C2214yes—
107#2551C2218yes—
108#2550C2214yes—
109#2549C2218yes—
110#2548C2211yescharacteristic
111#2546C2211yescharacteristic
112#2546C2211yescharacteristic
113#2545C2212yes—
114#2545C2212yes—
115#2545C2214yes—
116#2545C2212yes—
117#2544C2212yes—
118#2542C2212yes—
119#2541C2211yescharacteristic
120#2512C2218yes—
121#2502C2212yes—
122#2502C2212yes—
123#2501C2212yes—
124#2500C2212yes—
125#2500C2212yes—
126#2500C2214yes—
127#2499C2212yes—
128#2491C2218yes—
129#2479C2218yes—
130#2474C2218yes—
131#2470C2218yes—
132#2469C2218yes—
133#2466C2218yes—
134#2465C2218yes—
135#2465C2218yes—
136#2461C2218yes—
137#2461C2218yes—
138#2461C2218yes—
139#2455C2218yes—
140#2452C2214yes—
141#2452C2218yes—
142#2452C2214yes—
143#2449C2218yes—
144#2448C2214yes—
145#2445C2214yes—
146#2441C2214yes—
147#2439C2214yes—
148#2436C2212yes—
149#2434C2212yes—
150#2434C2212yes—
151#2432C2218yes—
152#2432C2214yes—
153#2432C2212yes—
154#2431C2212yes—
155#2431C2212yes—
156#2430C2218yes—
157#2429C2218yes—
158#2428C2214yes—
159#2426C2214yes—
160#2425C2218yes—
161#2422C2214yes—
162#2422C2218yes—
163#2421C2214yes—
164#2414C2214yes—
165#2399C2214yes—
166#2388C2214yes—
167#2374C2214yes—
168#2373C2214yes—
169#2370C2212yes—
170#2367C2212yes—
171#2363C2214yes—
172#2363C2214yes—
173#2363C2212yes—
174#2362C2218yes—
175#2362C2212yes—
176#2360C2218yes—
177#2359C2218yes—
178#2359C2218yes—
179Q8×C4⋊C4C2214yes—
180#2349C2214yes—
181#2327C2212yes—
182#2327C2211yescharacteristic
183#2327C2211yescharacteristic
184#2326C2212yes—
185#2326C2211yescharacteristic
186#2326C2211yescharacteristic
187#2326C2212yes—
188#2326C2212yes—
189#2323C2214yes—
190#2322C2214yes—
191#2317C2211yescharacteristic
192#2317C2212yes—
193#2311C2211yescharacteristic
194#2310C2211yescharacteristic
195C4×C4⋊Q8C2211yescharacteristic
196C4×C4⋊Q8C2211yescharacteristic
197C4×C4⋊Q8C2212yes—
198C4×C4⋊Q8C2212yes—
199C4×C4⋊Q8C2212yes—
200C4×#127C2212yes—
201C4×#124C2211yescharacteristic
202C4×#124C2211yescharacteristic
203C4×#124C2212yes—
204C4×#124C2212yes—
205C4×C22⋊Q8C2214yes—
206C4×#123C2214yes—
207C4×#121C2214yes—
208#2298C2212yes—
209#2297C2212yes—
210#2296C2214yes—
211#2295C2211yescharacteristic
212C2×#391C2212yes—
213#2293C2212yes—
214#2293C2211yescharacteristic
215#2290C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C4×#117C2211yescharacteristic
220C4×#117C2212yes—
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2314yes—
225C23×Q8C2311yescharacteristic
226C23×Q8C2312yes—
227#559—216no—
228#559—28no—
229Q82—28no—
230Q82—28no—
231#556—232no—
232#556—216no—
233#556—28no—
234#556—216no—
235#555—216no—
236#555—28no—
237#554—216no—
238#554—28no—
239#550—28no—
240D4×Q8—28no—
241#548—216no—
242#548—216no—
243#547—232no—
244#547—216no—
245#542—232no—
246#542—232no—
247#542—216no—
248#542—216no—
249#536—28no—
250#536—216no—
251#533—216no—
252#533—28no—
253#532—216no—
254#532—28no—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2318yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#127C2312yes—
274#529—216no—
275#529—216no—
276#529D4116yescomplemented
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2311yescharacteristic
303C2×#123C2314yes—
304C2×#123C2318yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2318yes—
311C2×#123C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2318yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2318yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2318yes—
338C2×#121C2311yescharacteristic
339#520—216no—
340#519—216no—
341C4×#41—28no—
342C2×C4×Q8—28no—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2314yes—
359C2×C4×Q8C2314yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2314yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2318yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2314yes—
388C2×#117C2314yes—
389C2×#117C2314yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2311yescharacteristic
395C2×#117C2312yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2314yes—
400C22×C42C2312yes—
401C22×C42C2312yes—
402C22×C42C2312yes—
403C22×C42C2311yescharacteristic
404#400C2318yes—
405#399C2318yes—
406#399C2318yes—
407#398C2314yes—
408#398C2314yes—
409#398C2318yes—
410#398C2318yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2318yes—
425#395C2318yes—
426#395C2318yes—
427#395C2318yes—
428#394C2314yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#393C2314yes—
438#393C2318yes—
439#393C2318yes—
440#393C2318yes—
441#392C2314yes—
442#392C2318yes—
443#392C2318yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2318yes—
458#391C2312yes—
459#391C2314yes—
460#391C2318yes—
461#391C2312yes—
462#390C2312yes—
463#390C2318yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2311yescharacteristic
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2312yes—
471#390C2318yes—
472#390C2318yes—
473#390C2318yes—
474#390C2314yes—
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2318yes—
482#389C2318yes—
483#389C2318yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2318yes—
488#389C2318yes—
489#389C2314yes—
490#389C2318yes—
491#389C2314yes—
492#389C2314yes—
493#389C2318yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2318yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2318yes—
511#388C2318yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2318yes—
516#388C2318yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2318yes—
522#387C2318yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2318yes—
528#386C2314yes—
529#386C2318yes—
530#386C2318yes—
531#386C2314yes—
532#386C2318yes—
533#386C2318yes—
534#386C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2314yes—
538#385C2318yes—
539#385C2314yes—
540#385C2314yes—
541#385C2318yes—
542#385C2318yes—
543#385C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2314yes—
547#385C2318yes—
548#384C2312yes—
549#384C2312yes—
550#384C2312yes—
551#384C2312yes—
552#384C2311yescharacteristic
553#384C2311yescharacteristic
554#384C2314yes—
555#384C2312yes—
556#384C2318yes—
557#382C2312yes—
558#382C2314yes—
559#382C2311yescharacteristic
560#382C2311yescharacteristic
561#381C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2318yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2318yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2318yes—
569C4×C4⋊C4C2318yes—
570C4×C4⋊C4C2311yescharacteristic
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2311yescharacteristic
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C22⋊C4C2312yes—
583C4×C22⋊C4C2312yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2318yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2318yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598#376C2312yes—
599#376C2312yes—
600C2×#95C2318yes—
601C43C2312yes—
602C43C2311yescharacteristic
603C43C2311yescharacteristic
604C43C2312yes—
605C2×#41—24no—
606C2×#41—28no—
607C2×#41—216no—
608C2×#41—24no—
609C2×#41—28no—
610C2×#41—28no—
611C2×#41—44no—
612C2×#41—42no—
613C2×#41—84no—
614C2×#41—88no—
615C22×Q8—28no—
616C22×Q8—24no—
617C22×Q8—24no—
618C22×Q8—28no—
619C22×Q8—44no—
620C22×Q8—42no—
621C22×Q8C2411yescharacteristic
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2411yescharacteristic
627C22×Q8C2411yescharacteristic
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2411yescharacteristic
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2418yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C23×C4C2412yes—
645C23×C4C2414yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2411yescharacteristic
659C4⋊Q8—24no—
660C4⋊Q8—28no—
661C4⋊Q8—28no—
662C4⋊Q8—28no—
663C4⋊Q8—28no—
664C4⋊Q8—216no—
665C4⋊Q8—216no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—24no—
669C4⋊Q8—28no—
670C4⋊Q8—28no—
671C4⋊Q8—44no—
672C4⋊Q8—88no—
673C4⋊Q8—84no—
674C4⋊Q8#4118yescomplemented
675#127—28no—
676#127—24no—
677#127—44no—
678#126—216no—
679#126—216no—
680#126—216no—
681#126—216no—
682#126—216no—
683#126C2×D4116yes—
684#125—28no—
685#125—28no—
686#125C2×D418yes—
687#124—28no—
688#124—28no—
689#124—24no—
690#124—216no—
691#124—216no—
692#124—216no—
693#124—216no—
694#124—216no—
695#124—216no—
696#124—28no—
697#124—28no—
698#124—28no—
699#124—24no—
700#124—28no—
701#124—44no—
702#124—84no—
703#124C2×D418yes—
704#123—216no—
705#123—216no—
706#123—232no—
707#123—216no—
708#123—216no—
709#123—216no—
710#123—216no—
711#123—88no—
712#123C2×D4116yes—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—232no—
725C22⋊Q8—216no—
726C22⋊Q8—216no—
727C22⋊Q8—88no—
728C22⋊Q8C2×D418yes—
729#121—28no—
730#121—216no—
731#121—216no—
732#121—28no—
733#121—28no—
734#121—28no—
735#121—28no—
736#121—216no—
737#121—216no—
738#121—88no—
739#121C2×D418yes—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—216no—
743C4×Q8—216no—
744C4×Q8—216no—
745C4×Q8—28no—
746C4×Q8—24no—
747C4×Q8—28no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—24no—
751C4×Q8—28no—
752C4×Q8—24no—
753C4×Q8—24no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—28no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8C2×D418yes—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—216no—
768C4×D4—216no—
769C4×D4—216no—
770C4×D4—216no—
771C4×D4—24no—
772C4×D4—24no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—88no—
777C4×D4C2×D4116yes—
778C4×D4C2×D418yes—
779#117—24no—
780#117—28no—
781#117—28no—
782#117—216no—
783#117—28no—
784#117—28no—
785#117—28no—
786#117—216no—
787#117—216no—
788#117—28no—
789#117—24no—
790#117—28no—
791#117—42no—
792#117C2×D4116yes—
793C2×C4⋊C4—24no—
794C2×C4⋊C4—28no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—216no—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2418yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2418yes—
836C2×C4⋊C4C2418yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2418yes—
839C2×C4⋊C4C2418yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2418yes—
875C2×C22⋊C4C2418yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2418yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C42—28no—
888C2×C42—28no—
889C2×C42—44no—
890C2×C42C2×D418yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923#95C2414yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2418yes—
940#95C2418yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2418yes—
949#95C2418yes—
950#95C2414yes—
951#95C2418yes—
952C24C2512yes—
953C24C2514yes—
954C24C2511yescharacteristic
955C24C2512yes—
956#41—416no—
957#41—432no—
958#41—816no—
959#41—832no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—22no—
964C2×Q8—28no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—28no—
968C2×Q8—28no—
969C2×Q8—24no—
970C2×Q8—28no—
971C2×Q8—24no—
972C2×Q8—22no—
973C2×Q8—24no—
974C2×Q8—24no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—24no—
978C2×Q8—22no—
979C2×Q8—44no—
980C2×Q8—42no—
981C2×Q8—48no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—48no—
985C2×Q8—432no—
986C2×Q8—416no—
987C2×Q8C22×D414yes—
988C2×Q8C2×#4114yes—
989C2×Q8C2×#4114yes—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—28no—
1001C2×D4—22no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—28no—
1005C2×D4—216no—
1006C2×D4—24no—
1007C2×D4—22no—
1008C2×D4—44no—
1009C2×D4—42no—
1010C2×D4—44no—
1011C2×D4—48no—
1012C2×D4—48no—
1013C2×D4—48no—
1014C2×D4—48no—
1015C2×D4—44no—
1016C2×D4—48no—
1017C2×D4C22×D414yes—
1018C2×D4C22×D418yes—
1019C22×C4—24no—
1020C22×C4—22no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—28no—
1031C22×C4—24no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—48no—
1049C22×C4—44no—
1050C22×C4—48no—
1051C22×C4—48no—
1052C22×C4C22×D414yes—
1053C22×C4C22×D414yes—
1054C22×C4C22×D418yes—
1055C22×C4C22×D414yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—22no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—22no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—22no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—216no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—42no—
1115C4⋊C4—48no—
1116C4⋊C4—48no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—48no—
1120C4⋊C4—48no—
1121C4⋊C4—48no—
1122C4⋊C4—44no—
1123C4⋊C4—48no—
1124C4⋊C4C22×D418yes—
1125C4⋊C4C22×D418yes—
1126C4⋊C4C22×D414yes—
1127C4⋊C4C22×D414yes—
1128C4⋊C4C22×D418yes—
1129C4⋊C4C22×D418yes—
1130C4⋊C4C2×#41116yes—
1131C4⋊C42−1+418yes—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—28no—
1150C22⋊C4—216no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—216no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—216no—
1157C22⋊C4—42no—
1158C22⋊C4—48no—
1159C22⋊C4—48no—
1160C22⋊C4—44no—
1161C22⋊C4—48no—
1162C22⋊C4—48no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—48no—
1166C22⋊C4C22×D418yes—
1167C22⋊C4C22×D418yes—
1168C22⋊C4C22×D418yes—
1169C22⋊C4C22×D418yes—
1170C22⋊C4C22×D418yes—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—28no—
1179C42—28no—
1180C42—28no—
1181C42—28no—
1182C42—28no—
1183C42—22no—
1184C42—24no—
1185C42—28no—
1186C42—24no—
1187C42—28no—
1188C42—24no—
1189C42—22no—
1190C42—24no—
1191C42—22no—
1192C42—44no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—42no—
1197C42C22×D414yes—
1198C42C22×D414yes—
1199C42C22×D414yes—
1200C42C22×D414yes—
1201C42C22×D418yes—
1202C42C2×#4114yes—
1203C23—21no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—21no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—22no—
1215C23—28no—
1216C23—24no—
1217C23—24no—
1218C23—22no—
1219C23—24no—
1220C23—28no—
1221C23C23×D414yes—
1222C23C23×D412yes—
1223C23C2611yescharacteristic
1224Q8—28no—
1225Q8—28no—
1226Q8—28no—
1227Q8—48no—
1228Q8—416no—
1229Q8—44no—
1230Q8—48no—
1231Q8—84no—
1232Q8—88no—
1233Q8—84no—
1234Q8—88no—
1235D4—28no—
1236D4—48no—
1237D4—416no—
1238D4—48no—
1239D4—416no—
1240D4—44no—
1241D4—48no—
1242D4—48no—
1243D4—816no—
1244D4—84no—
1245D4—88no—
1246D4—88no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—216no—
1265C2×C4—28no—
1266C2×C4—28no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—28no—
1294C2×C4—24no—
1295C2×C4—28no—
1296C2×C4—24no—
1297C2×C4—44no—
1298C2×C4—416no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—416no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—84no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4—88no—
1308C2×C4—88no—
1309C2×C4C23×D412yes—
1310C2×C4C23×D414yes—
1311C2×C4C23×D412yes—
1312C2×C4C23×D412yes—
1313C2×C4C23×D414yes—
1314C2×C4C23×D414yes—
1315C2×C4C23×D412yes—
1316C2×C4C23×D412yes—
1317C2×C4C23×D412yes—
1318C2×C4C22×#4114yes—
1319C2×C4C22×#4114yes—
1320C2×C4C22×#4114yes—
1321C2×C4C22×#4112yes—
1322C2×C4C2×2−1+418yes—
1323C2×C4C2×2−1+414yes—
1324C2×C4#58512yes—
1325C22—22no—
1326C22—24no—
1327C22—22no—
1328C22—24no—
1329C22—22no—
1330C22—24no—
1331C22—42no—
1332C22—44no—
1333C22—44no—
1334C22—42no—
1335C22—48no—
1336C22—44no—
1337C22—42no—
1338C22—44no—
1339C22—44no—
1340C22—42no—
1341C22—44no—
1342C22—48no—
1343C22—42no—
1344C22—44no—
1345C22C24×D411yescharacteristic
1346C22C23×#4111yescharacteristic
1347C22C22×2−1+412yes—
1348C22C2×#58511yescharacteristic
1349C22H(7,𝔽2)12yes—
1350C4—24no—
1351C4—22no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—28no—
1357C4—24no—
1358C4—22no—
1359C4—24no—
1360C4—24no—
1361C4—42no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4D4×#4114yes—
1374C4#349914yes—
1375C2—42no—
1376C2—44no—
1377C2—82no—
1378C2—84no—
1379C2C2×D4×#4111yescharacteristic
1380C2C2×#349911yescharacteristic
1381C2#6285211yescharacteristic
1382C2#6295112yes—
1383C2#6299912yes—
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×#3518C2semidirect
2. C2×#3522C2semidirect
3. #59153C2semidirect
4. #59118C2semidirect
5. #59115C2semidirect
6. #59072C2semidirect
7. #44846C2semidirect
8. #43899C2semidirect
9. #39489C2semidirect
10. #39488C2semidirect
11. #39363C2semidirect
12. #39356C2semidirect
13. #39172C2semidirect
14. #39168C2semidirect
15. #38091C2semidirect
16. #38079C2semidirect
17. #36597C2semidirect
18. Q8×C4⋊Q8C2semidirect
19. #36412C2semidirect
20. #36276C2semidirect
21. #35669C2semidirect
22. #35535C2semidirect
23. #35298C2semidirect
24. #35277C2semidirect
25. #34977C2semidirect
26. #34953C2semidirect
27. #34276C2semidirect
28. #34151C2semidirect
29. C4×#536C2semidirect
276. #529D4semidirect
674. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#35222
#591532
#591182
#591152
#590722
#448462
#438992
#394892
#394882
#393632
#393562
#391722
#391682
#380912
#380792
#365972
Q8×C4⋊Q82
#364122
#362762
#356692
#355352
#352982
#352772
#349772
#349532
#342762
#341512
C4×#5362