Finite Group Databasebeta

← #7712255

Subgroups — #7712255

Order 512.

6540 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C211yesmaximal, characteristic, complemented
2C2×#3554C211yesmaximal, characteristic
3#59833C214yesmaximal, complemented
4#59829C214yesmaximal, complemented
5#45790C218yesmaximal, complemented
6#39442C218yesmaximal, complemented
7#39347C214yesmaximal, complemented
8#39346C214yesmaximal, complemented
9#39170C211yesmaximal, characteristic, complemented
10#39168C211yesmaximal, characteristic, complemented
11#38954C211yesmaximal, characteristic, complemented
12#38952C211yesmaximal, characteristic, complemented
13#38091C212yesmaximal, complemented
14#38088C212yesmaximal, complemented
15#37635C211yesmaximal, characteristic, complemented
16#37619C211yesmaximal, characteristic, complemented
17#37390C212yesmaximal, complemented
18#37303C212yesmaximal, complemented
19#36645C211yesmaximal, characteristic, complemented
20#36639C211yesmaximal, characteristic, complemented
21#36538C211yesmaximal, characteristic, complemented
22#36474C211yesmaximal, characteristic, complemented
23#36419C211yesmaximal, characteristic, complemented
24#36406C212yesmaximal, complemented
25#36376C212yesmaximal, complemented
26#36276C211yesmaximal, characteristic, complemented
27#35318C212yesmaximal, complemented
28#35312C212yesmaximal, complemented
29C4×#529C211yesmaximal, characteristic, complemented
30#3555—216no—
31#3554—216no—
32C2×#563C2214yes—
33C2×#562C2214yes—
34C2×#559C2211yescharacteristic
35C2×#559C2212yes—
36C2×Q82C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2211yescharacteristic
39C2×#557C2212yes—
40C2×#556C2211yescharacteristic
41C2×#556C2212yes—
42C2×#556C2212yes—
43C2×#554C2212yes—
44C2×#554C2211yescharacteristic
45C2×#552C2212yes—
46C2×#550C2211yescharacteristic
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2212yes—
49C2×#547C2212yes—
50C2×#544C2212yes—
51C2×#542C2212yes—
52C2×#542C2212yes—
53C2×#542C2212yes—
54C2×#541C2212yes—
55C2×#541C2214yes—
56C2×#541C2212yes—
57C2×#540C2212yes—
58C2×#539C2214yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#529C2211yescharacteristic
65#2868C2211yescharacteristic
66#2868C2211yescharacteristic
67#2862C2211yescharacteristic
68#2862C2211yescharacteristic
69#2862C2211yescharacteristic
70#2862C2211yescharacteristic
71#2862C2212yes—
72#2861C2212yes—
73#2861C2212yes—
74#2861C2212yes—
75#2859C2214yes—
76#2858C2211yescharacteristic
77#2858C2211yescharacteristic
78#2857C2211yescharacteristic
79#2857C2211yescharacteristic
80#2857C2211yescharacteristic
81#2857C2211yescharacteristic
82#2857C2214yes—
83#2857C2212yes—
84#2850C2212yes—
85#2850C2214yes—
86#2850C2214yes—
87#2817C2214yes—
88#2816C2214yes—
89#2721C2218yes—
90#2720C2218yes—
91#2720C2218yes—
92#2719C2218yes—
93#2718C2218yes—
94#2718C2218yes—
95#2715C2218yes—
96#2708C2218yes—
97#2698C2218yes—
98#2695C2218yes—
99#2686C2218yes—
100#2680C2218yes—
101#2677C2218yes—
102#2674C2218yes—
103#2674C2218yes—
104#2672C2218yes—
105#2660C2212yes—
106#2658C2212yes—
107#2642C2212yes—
108#2642C2212yes—
109#2640C2212yes—
110#2640C2212yes—
111#2634C2214yes—
112#2633C2214yes—
113#2625C2214yes—
114#2624C2214yes—
115#2621C2212yes—
116#2620C2212yes—
117#2581C2214yes—
118#2580C2214yes—
119#2568C2211yescharacteristic
120#2568C2211yescharacteristic
121#2567C2211yescharacteristic
122#2567C2211yescharacteristic
123#2567C2212yes—
124#2566C2212yes—
125#2565C2212yes—
126#2559C2218yes—
127#2558C2218yes—
128#2556C2218yes—
129#2556C2218yes—
130#2553C2218yes—
131#2553C2218yes—
132#2553C2218yes—
133#2550C2218yes—
134#2550C2214yes—
135#2550C2214yes—
136#2549C2218yes—
137#2548C2211yescharacteristic
138#2548C2211yescharacteristic
139#2546C2212yes—
140#2546C2211yescharacteristic
141#2546C2212yes—
142#2546C2211yescharacteristic
143#2545C2212yes—
144#2545C2212yes—
145#2545C2214yes—
146#2544C2214yes—
147#2542C2212yes—
148#2521C2218yes—
149#2521C2218yes—
150#2519C2218yes—
151#2502C2212yes—
152#2501C2212yes—
153#2500C2212yes—
154#2499C2212yes—
155#2499C2212yes—
156#2499C2212yes—
157#2492C2218yes—
158#2489C2218yes—
159#2488C2218yes—
160#2488C2218yes—
161#2473C2218yes—
162#2470C2218yes—
163#2466C2218yes—
164#2465C2218yes—
165#2454C2214yes—
166#2453C2214yes—
167#2452C2214yes—
168#2451C2214yes—
169#2448C2214yes—
170#2447C2214yes—
171#2446C2214yes—
172#2445C2214yes—
173#2434C2212yes—
174#2434C2212yes—
175#2432C2212yes—
176#2432C2212yes—
177#2432C2212yes—
178#2432C2212yes—
179#2427C2218yes—
180#2425C2218yes—
181#2367C2214yes—
182#2367C2214yes—
183#2360C2218yes—
184#2359C2218yes—
185#2351C2214yes—
186#2349C2214yes—
187#2327C2212yes—
188#2326C2212yes—
189#2311C2212yes—
190#2310C2212yes—
191C4×C4⋊Q8C2211yescharacteristic
192C4×C4⋊Q8C2211yescharacteristic
193C4×C4⋊Q8C2212yes—
194C4×C4⋊Q8C2211yescharacteristic
195C4×C4⋊Q8C2211yescharacteristic
196C4×C4⋊Q8C2214yes—
197C4×#125C2212yes—
198C4×#126C2214yes—
199C4×#124C2214yes—
200C4×#124C2214yes—
201C4×#124C2212yes—
202C4×#124C2212yes—
203C4×C22⋊Q8C2212yes—
204C4×#123C2214yes—
205C4×#121C2212yes—
206#2298C2212yes—
207#2297C2212yes—
208#2297C2212yes—
209#2297C2212yes—
210#2295C2211yescharacteristic
211C2×#391C2212yes—
212#2293C2211yescharacteristic
213#2290C2212yes—
214#2285C2214yes—
215#2283C2211yescharacteristic
216C42×Q8C2211yescharacteristic
217C42×D4C2212yes—
218C42×D4C2211yescharacteristic
219C4×#117C2212yes—
220C2×C43C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C23×Q8C2312yes—
224#563—232no—
225#562—232no—
226#559—216no—
227#559—28no—
228Q82—28no—
229#557—216no—
230#557—28no—
231#557—28no—
232#556—216no—
233#556—216no—
234#556—28no—
235#554—216no—
236#554—28no—
237#552—216no—
238#550—28no—
239D4×Q8—28no—
240#548—216no—
241#547—216no—
242#544—216no—
243#542—216no—
244#542—216no—
245#542—216no—
246#541—232no—
247#541—216no—
248#541—216no—
249#540—216no—
250#539—232no—
251#536—216no—
252#533—28no—
253#533—28no—
254#533—28no—
255#532—28no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279#529D4116yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2312yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#125C2312yes—
298C2×#125C2314yes—
299C2×#125C2314yes—
300C2×#125C2311yescharacteristic
301C2×#124C2314yes—
302C2×#124C2312yes—
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2314yes—
306C2×#124C2314yes—
307C2×#124C2312yes—
308C2×#124C2312yes—
309C2×#124C2312yes—
310C2×#124C2314yes—
311C2×#124C2312yes—
312C2×#124C2311yescharacteristic
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2318yes—
321C2×#123C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×C22⋊Q8C2311yescharacteristic
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2318yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2314yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2314yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2314yes—
389C22×C42C2312yes—
390C22×C42C2312yes—
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393C22×C42C2311yescharacteristic
394C22×C42C2311yescharacteristic
395#400C2314yes—
396#400C2314yes—
397#400C2318yes—
398#400C2318yes—
399#400C2318yes—
400#400C2318yes—
401#399C2318yes—
402#399C2318yes—
403#399C2318yes—
404#399C2318yes—
405#398C2314yes—
406#398C2314yes—
407#398C2318yes—
408#398C2318yes—
409#398C2318yes—
410#398C2318yes—
411#398C2318yes—
412#398C2318yes—
413#397C2318yes—
414#397C2318yes—
415#397C2318yes—
416#397C2318yes—
417#397C2318yes—
418#397C2318yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#396C2318yes—
423#395C2314yes—
424#395C2314yes—
425#395C2318yes—
426#395C2318yes—
427#395C2318yes—
428#395C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2314yes—
432#394C2314yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#393C2318yes—
438#393C2318yes—
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2318yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2318yes—
465#391C2312yes—
466#391C2318yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2318yes—
489#389C2314yes—
490#389C2314yes—
491#389C2318yes—
492#389C2314yes—
493#389C2314yes—
494#389C2318yes—
495#389C2318yes—
496#389C2318yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2318yes—
507#388C2318yes—
508#388C2318yes—
509#388C2318yes—
510#388C2318yes—
511#388C2314yes—
512#388C2318yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2318yes—
518#387C2318yes—
519#387C2318yes—
520#387C2318yes—
521#387C2318yes—
522#387C2318yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2318yes—
527#386C2318yes—
528#386C2314yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2318yes—
538#385C2314yes—
539#384C2311yescharacteristic
540#384C2311yescharacteristic
541#384C2311yescharacteristic
542#384C2312yes—
543#384C2314yes—
544#384C2311yescharacteristic
545#384C2312yes—
546#384C2314yes—
547#384C2314yes—
548#383C2312yes—
549#382C2312yes—
550#382C2312yes—
551#382C2312yes—
552#382C2314yes—
553#382C2314yes—
554#382C2314yes—
555#382C2314yes—
556#382C2318yes—
557#381C2312yes—
558#381C2318yes—
559#380C2318yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2318yes—
565#380C2312yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2318yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2311yescharacteristic
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2318yes—
585C4×C22⋊C4C2318yes—
586C4×C22⋊C4C2318yes—
587C4×C22⋊C4C2312yes—
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2318yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593#376C2312yes—
594#376C2312yes—
595C2×#95C2318yes—
596C43C2312yes—
597C43C2312yes—
598C43C2311yescharacteristic
599C43C2311yescharacteristic
600C43C2312yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—44no—
606C2×#41—44no—
607C2×#41—44no—
608C2×#41—44no—
609C22×Q8—28no—
610C22×Q8—44no—
611C22×Q8—44no—
612C22×Q8C2411yescharacteristic
613C22×Q8C2411yescharacteristic
614C22×Q8C2412yes—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2411yescharacteristic
618C22×Q8C2411yescharacteristic
619C22×Q8C2412yes—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×D4C2412yes—
625C22×D4C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2414yes—
628C22×D4C2412yes—
629C22×D4C2414yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2414yes—
637C23×C4C2414yes—
638C23×C4C2414yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2414yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C4⋊Q8—28no—
645C4⋊Q8—216no—
646C4⋊Q8—28no—
647C4⋊Q8—28no—
648C4⋊Q8—216no—
649C4⋊Q8—24no—
650C4⋊Q8—24no—
651C4⋊Q8—24no—
652C4⋊Q8—24no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655C4⋊Q8—24no—
656C4⋊Q8—28no—
657C4⋊Q8—28no—
658C4⋊Q8—48no—
659C4⋊Q8—44no—
660C4⋊Q8—42no—
661C4⋊Q8—42no—
662C4⋊Q8—42no—
663C4⋊Q8—42no—
664C4⋊Q8—44no—
665#127—28no—
666#127—24no—
667#126—216no—
668#126—216no—
669#126—216no—
670#126—216no—
671#126—216no—
672#126—216no—
673#126—216no—
674#126C2×D4116yes—
675#125—216no—
676#125—28no—
677#125—216no—
678#125—216no—
679#125—216no—
680#125—28no—
681#125—216no—
682#125—216no—
683#125—28no—
684#125—28no—
685#125—28no—
686#125—28no—
687#125C2×D418yes—
688#124—28no—
689#124—28no—
690#124—216no—
691#124—216no—
692#124—216no—
693#124—28no—
694#124—28no—
695#124—216no—
696#124—48no—
697#124—44no—
698#124—44no—
699#124C2×D418yes—
700#123—216no—
701#123—216no—
702#123—216no—
703#123—216no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—416no—
708#123C2×D4116yes—
709C22⋊Q8—28no—
710C22⋊Q8—24no—
711C22⋊Q8—24no—
712C22⋊Q8—24no—
713C22⋊Q8—24no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—216no—
726C22⋊Q8—216no—
727C22⋊Q8—216no—
728C22⋊Q8—416no—
729C22⋊Q8C2×D418yes—
730#121—216no—
731#121—216no—
732#121—28no—
733#121—28no—
734#121—28no—
735#121—216no—
736#121C2×D418yes—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—216no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×Q8—24no—
744C4×Q8—24no—
745C4×Q8—24no—
746C4×Q8—28no—
747C4×Q8—28no—
748C4×Q8—28no—
749C4×Q8—24no—
750C4×Q8—28no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8C2×D418yes—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—216no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—48no—
765C4×D4C2×D4116yes—
766C4×D4C2×D418yes—
767#117—28no—
768#117—28no—
769#117—28no—
770#117—28no—
771#117—216no—
772#117—44no—
773#117C2×D4116yes—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—216no—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2418yes—
822C2×C4⋊C4C2418yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2418yes—
855C2×C22⋊C4C2418yes—
856C2×C22⋊C4C2418yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2418yes—
862C2×C22⋊C4C2418yes—
863C2×C22⋊C4C2418yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C42—28no—
870C2×C42—44no—
871C2×C42—42no—
872C2×C42—42no—
873C2×C42—44no—
874C2×C42C2×D418yes—
875C2×C42C2414yes—
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908#95C2414yes—
909#95C2418yes—
910#95C2418yes—
911#95C2418yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2418yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2418yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2418yes—
936#95C2418yes—
937#95C2418yes—
938#95C2418yes—
939C24C2514yes—
940C24C2512yes—
941C24C2511yescharacteristic
942#41—816no—
943#41—816no—
944C2×Q8—22no—
945C2×Q8—22no—
946C2×Q8—24no—
947C2×Q8—22no—
948C2×Q8—24no—
949C2×Q8—22no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—28no—
954C2×Q8—28no—
955C2×Q8—24no—
956C2×Q8—28no—
957C2×Q8—22no—
958C2×Q8—22no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—22no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—22no—
966C2×Q8—22no—
967C2×Q8—48no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×Q8—816no—
974C2×Q8C22×D414yes—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—44no—
986C2×D4—48no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4C22×D414yes—
993C2×D4C22×D418yes—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—24no—
999C22×C4—28no—
1000C22×C4—28no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—28no—
1007C22×C4—28no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—48no—
1015C22×C4—48no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4C22×D414yes—
1023C22×C4C22×D414yes—
1024C22×C4C22×D418yes—
1025C22×C4C22×D414yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C4⋊C4—24no—
1053C4⋊C4—22no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—22no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—44no—
1097C4⋊C4—48no—
1098C4⋊C4—48no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—48no—
1106C4⋊C4—48no—
1107C4⋊C4C22×D418yes—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D418yes—
1110C4⋊C4C22×D414yes—
1111C4⋊C4C22×D414yes—
1112C4⋊C4C22×D418yes—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—216no—
1130C22⋊C4—216no—
1131C22⋊C4—28no—
1132C22⋊C4—216no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—48no—
1136C22⋊C4—48no—
1137C22⋊C4—48no—
1138C22⋊C4—48no—
1139C22⋊C4—48no—
1140C22⋊C4C22×D418yes—
1141C22⋊C4C22×D418yes—
1142C22⋊C4C22×D418yes—
1143C22⋊C4C22×D418yes—
1144C22⋊C4C22×D418yes—
1145C42—28no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—28no—
1151C42—28no—
1152C42—28no—
1153C42—28no—
1154C42—24no—
1155C42—24no—
1156C42—24no—
1157C42—28no—
1158C42—22no—
1159C42—22no—
1160C42—24no—
1161C42—24no—
1162C42—22no—
1163C42—22no—
1164C42—24no—
1165C42—24no—
1166C42—42no—
1167C42—44no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—44no—
1172C42C22×D414yes—
1173C42C22×D414yes—
1174C42C22×D414yes—
1175C42C22×D414yes—
1176C42C22×D418yes—
1177C422−1+418yes—
1178C23—24no—
1179C23—22no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—21no—
1185C23—21no—
1186C23—24no—
1187C23—28no—
1188C23—28no—
1189C23—24no—
1190C23—24no—
1191C23C23×D412yes—
1192C23C23×D414yes—
1193C23C2611yescharacteristic
1194Q8—28no—
1195Q8—48no—
1196Q8—44no—
1197Q8—44no—
1198Q8—44no—
1199Q8—48no—
1200Q8—44no—
1201Q8—84no—
1202Q8—84no—
1203Q8—84no—
1204Q8—88no—
1205Q8—88no—
1206D4—28no—
1207D4—48no—
1208D4—48no—
1209D4—48no—
1210D4—84no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—28no—
1230C2×C4—216no—
1231C2×C4—28no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—28no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—28no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—44no—
1269C2×C4—48no—
1270C2×C4—48no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4—88no—
1276C2×C4—88no—
1277C2×C4C23×D412yes—
1278C2×C4C23×D414yes—
1279C2×C4C23×D414yes—
1280C2×C4C23×D414yes—
1281C2×C4C23×D412yes—
1282C2×C4C23×D412yes—
1283C2×C4C23×D412yes—
1284C2×C4C23×D412yes—
1285C2×C4C23×D412yes—
1286C2×C4C2×2−1+414yes—
1287C2×C4C2×2−1+414yes—
1288C2×C4C2×2−1+414yes—
1289C2×C4#58514yes—
1290C2×C4#58512yes—
1291C2×C4#58512yes—
1292C22—22no—
1293C22—24no—
1294C22—24no—
1295C22—22no—
1296C22—22no—
1297C22—24no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—44no—
1302C22—48no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—48no—
1307C22C24×D411yescharacteristic
1308C22C22×2−1+412yes—
1309C22C2×#58511yescharacteristic
1310C22C2×#58512yes—
1311C22C2×#58511yescharacteristic
1312C4—24no—
1313C4—22no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—22no—
1318C4—22no—
1319C4—24no—
1320C4—24no—
1321C4—24no—
1322C4—44no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4#349914yes—
1337C4#350014yes—
1338C2—42no—
1339C2—44no—
1340C2—84no—
1341C2#6276112yes—
1342C2C2×#349911yescharacteristic
1343C2C2×#350011yescharacteristic
1344C2#6281211yescharacteristic
1345C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3554C2
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×#3555C2semidirect
3. #59833C2semidirect
4. #59829C2semidirect
5. #45790C2semidirect
6. #39442C2semidirect
7. #39347C2semidirect
8. #39346C2semidirect
9. #39170C2semidirect
10. #39168C2semidirect
11. #38954C2semidirect
12. #38952C2semidirect
13. #38091C2semidirect
14. #38088C2semidirect
15. #37635C2semidirect
16. #37619C2semidirect
17. #37390C2semidirect
18. #37303C2semidirect
19. #36645C2semidirect
20. #36639C2semidirect
21. #36538C2semidirect
22. #36474C2semidirect
23. #36419C2semidirect
24. #36406C2semidirect
25. #36376C2semidirect
26. #36276C2semidirect
27. #35318C2semidirect
28. #35312C2semidirect
29. C4×#529C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
C2×#35542
#598332
#598292
#457902
#394422
#393472
#393462
#391702
#391682
#389542
#389522
#380912
#380882
#376352
#376192
#373902
#373032
#366452
#366392
#365382
#364742
#364192
#364062
#363762
#362762
#353182
#353122
C4×#5292