Finite Group Databasebeta

← #7681796

Subgroups — #7681796

Order 512.

6838 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3512C211yesmaximal, characteristic
2C2×#3507C211yesmaximal, characteristic, complemented
3#59073C214yesmaximal, complemented
4#59069C214yesmaximal, complemented
5#59063C218yesmaximal, complemented
6#45324C214yesmaximal, complemented
7#45100C214yesmaximal, complemented
8#43027C218yesmaximal, complemented
9#39485C212yesmaximal, complemented
10#39484C212yesmaximal, complemented
11#37870C212yesmaximal, complemented
12#37868C212yesmaximal, complemented
13#37865C212yesmaximal, complemented
14#37862C212yesmaximal, complemented
15#36184C212yesmaximal, complemented
16#36181C212yesmaximal, complemented
17#35619C211yesmaximal, characteristic, complemented
18#35619C211yesmaximal, characteristic, complemented
19#35618C211yesmaximal, characteristic, complemented
20#35530C211yesmaximal, characteristic, complemented
21#35335C211yesmaximal, characteristic, complemented
22#35308C211yesmaximal, characteristic, complemented
23#35308C211yesmaximal, characteristic, complemented
24#34947C211yesmaximal, characteristic, complemented
25C2×#2565C211yesmaximal, characteristic, complemented
26#34184C211yesmaximal, characteristic, complemented
27#34183C211yesmaximal, characteristic, complemented
28#34141C211yesmaximal, characteristic, complemented
29C4×#536C211yesmaximal, characteristic, complemented
30#3512—216no—
31#3507—216no—
32C2×#559C2212yes—
33C2×#557C2212yes—
34C2×#556C2212yes—
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#554C2212yes—
38C2×#553C2214yes—
39C2×#553C2212yes—
40C2×#553C2214yes—
41C2×#553C2212yes—
42C2×#552C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×#552C2212yes—
46C2×#541C2212yes—
47C2×#540C2212yes—
48C2×#539C2214yes—
49C2×#537C2211yescharacteristic
50C2×#537C2211yescharacteristic
51C2×#536C2211yescharacteristic
52C2×#536C2211yescharacteristic
53C2×#536C2211yescharacteristic
54C2×#533C2211yescharacteristic
55C2×#532C2211yescharacteristic
56C2×#529C2214yes—
57C2×#529C2212yes—
58C2×#529C2212yes—
59C22×#125C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#520C2211yescharacteristic
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C22×C4×Q8C2211yescharacteristic
68#2859C2212yes—
69#2859C2212yes—
70#2857C2212yes—
71#2857C2212yes—
72#2850C2212yes—
73#2850C2212yes—
74#2726C2218yes—
75#2725C2218yes—
76#2724C2218yes—
77#2722C2218yes—
78#2721C2218yes—
79#2719C2218yes—
80#2717C2218yes—
81#2701C2218yes—
82#2698C2218yes—
83#2695C2218yes—
84#2686C2218yes—
85#2680C2218yes—
86#2660C2212yes—
87#2660C2212yes—
88#2621C2212yes—
89#2621C2212yes—
90#2620C2212yes—
91#2620C2212yes—
92#2584C2214yes—
93#2584C2214yes—
94#2583C2214yes—
95#2583C2214yes—
96#2568C2211yescharacteristic
97#2567C2211yescharacteristic
98#2566C2211yescharacteristic
99#2566C2211yescharacteristic
100#2565C2214yes—
101#2565C2211yescharacteristic
102#2565C2212yes—
103#2565C2212yes—
104#2565C2214yes—
105#2565C2212yes—
106#2565C2212yes—
107#2565C2211yescharacteristic
108#2564C2214yes—
109#2563C2211yescharacteristic
110#2553C2218yes—
111#2542C2211yescharacteristic
112#2519C2218yes—
113#2506C2218yes—
114#2504C2212yes—
115#2503C2212yes—
116#2503C2212yes—
117#2503C2212yes—
118#2502C2212yes—
119#2502C2212yes—
120#2502C2212yes—
121#2501C2212yes—
122#2500C2212yes—
123#2500C2212yes—
124#2499C2212yes—
125#2499C2212yes—
126#2499C2212yes—
127#2499C2212yes—
128#2499C2212yes—
129#2499C2212yes—
130#2496C2218yes—
131#2486C2218yes—
132#2478C2218yes—
133#2478C2218yes—
134#2478C2218yes—
135#2470C2218yes—
136#2469C2218yes—
137#2468C2218yes—
138#2466C2218yes—
139#2462C2218yes—
140#2449C2218yes—
141#2447C2214yes—
142#2447C2214yes—
143#2446C2214yes—
144#2446C2214yes—
145#2444C2218yes—
146#2443C2218yes—
147#2443C2218yes—
148#2438C2218yes—
149#2429C2214yes—
150#2429C2214yes—
151#2427C2214yes—
152#2427C2214yes—
153#2425C2218yes—
154#2425C2218yes—
155#2425C2218yes—
156#2423C2214yes—
157#2422C2214yes—
158#2421C2214yes—
159#2420C2214yes—
160#2419C2218yes—
161#2419C2218yes—
162#2419C2218yes—
163#2417C2214yes—
164#2396C2214yes—
165C2×#398C2214yes—
166#2367C2212yes—
167#2367C2212yes—
168#2366C2212yes—
169#2365C2212yes—
170#2364C2214yes—
171#2361C2214yes—
172#2359C2218yes—
173#2351C2214yes—
174Q8×C4⋊C4C2214yes—
175#2349C2218yes—
176#2349C2214yes—
177D4×C4⋊C4C2218yes—
178D4×C4⋊C4C2214yes—
179#2344C2218yes—
180#2327C2212yes—
181#2326C2212yes—
182#2323C2214yes—
183#2322C2214yes—
184#2317C2211yescharacteristic
185#2317C2211yescharacteristic
186#2317C2211yescharacteristic
187#2317C2211yescharacteristic
188#2317C2211yescharacteristic
189#2317C2212yes—
190#2317C2212yes—
191#2317C2212yes—
192#2317C2212yes—
193#2311C2211yescharacteristic
194#2310C2211yescharacteristic
195C4×C4⋊Q8C2212yes—
196C4×#124C2212yes—
197C4×C22⋊Q8C2214yes—
198C4×C22⋊Q8C2214yes—
199C4×#123C2214yes—
200#2297C2211yescharacteristic
201#2297C2211yescharacteristic
202#2297C2211yescharacteristic
203#2297C2211yescharacteristic
204C2×#391C2211yescharacteristic
205C2×#391C2211yescharacteristic
206#2293C2212yes—
207#2290C2212yes—
208#2290C2212yes—
209C2×#387C2214yes—
210#2285C2211yescharacteristic
211#2285C2211yescharacteristic
212#2285C2212yes—
213#2285C2212yes—
214C2×#384C2211yescharacteristic
215C2×#384C2212yes—
216C2×#382C2211yescharacteristic
217C2×#382C2212yes—
218C42×D4C2212yes—
219C4×#117C2211yescharacteristic
220C2×C4×C4⋊C4C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2311yescharacteristic
223C22×#41C2311yescharacteristic
224C23×Q8C2311yescharacteristic
225#559—216no—
226#557—216no—
227#556—216no—
228#556—216no—
229#556—216no—
230#554—216no—
231#553—232no—
232#553—232no—
233#553—216no—
234#553—216no—
235#552—216no—
236#552—216no—
237#552—216no—
238#552—216no—
239#541—216no—
240#540—216no—
241#539—232no—
242#537—28no—
243#537—28no—
244#536—28no—
245#536—28no—
246#536—28no—
247#533—28no—
248#532D4116yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×#127C2311yescharacteristic
256#529—216no—
257#529—216no—
258#529—232no—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125—28no—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#124C2312yes—
280C2×#124C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2311yescharacteristic
284C2×#124C2311yescharacteristic
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2318yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319#520—28no—
320#520—28no—
321#520—28no—
322#520—28no—
323C4×#41—28no—
324C4×#41—28no—
325C4×#41—28no—
326C2×C4×Q8—28no—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2314yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2312yes—
367C2×#117C2312yes—
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2314yes—
376C2×#117C2314yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C2×#117C2311yescharacteristic
380C22×C4⋊C4C2311yescharacteristic
381C22×C4⋊C4C2311yescharacteristic
382C22×C4⋊C4C2311yescharacteristic
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2318yes—
391C22×C4⋊C4C2314yes—
392C22×C4⋊C4C2312yes—
393C22×C42C2312yes—
394C22×C42C2312yes—
395C22×C42C2312yes—
396C22×C42C2312yes—
397C22×C42C2311yescharacteristic
398C22×C42C2311yescharacteristic
399C22×C42C2311yescharacteristic
400#400C2314yes—
401#400C2318yes—
402#400C2318yes—
403#400C2318yes—
404#399C2314yes—
405#399C2318yes—
406#398C2318yes—
407#398C2318yes—
408#398C2318yes—
409#398C2318yes—
410#398C2314yes—
411#398C2314yes—
412#398C2318yes—
413#398C2318yes—
414#398C2318yes—
415#398C2318yes—
416#398C2318yes—
417#398C2318yes—
418#398C2318yes—
419#397C2318yes—
420#397C2318yes—
421#397C2318yes—
422#397C2318yes—
423#397C2318yes—
424#397C2318yes—
425#397C2318yes—
426#397C2318yes—
427#397C2318yes—
428#396C2314yes—
429#396C2314yes—
430#396C2318yes—
431#396C2318yes—
432#395C2314yes—
433#395C2318yes—
434#395C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#393C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2311yescharacteristic
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#390C2311yescharacteristic
458#390C2311yescharacteristic
459#390C2311yescharacteristic
460#390C2311yescharacteristic
461#390C2312yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#389C2318yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2318yes—
473#389C2318yes—
474#389C2318yes—
475#389C2318yes—
476#389C2318yes—
477#389C2318yes—
478#389C2318yes—
479#389C2318yes—
480#389C2318yes—
481#389C2318yes—
482#389C2314yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2318yes—
493#387C2314yes—
494#387C2314yes—
495#387C2318yes—
496#387C2318yes—
497#387C2318yes—
498#387C2318yes—
499#387C2318yes—
500#387C2318yes—
501#387C2318yes—
502#387C2318yes—
503#387C2318yes—
504#387C2314yes—
505#387C2314yes—
506#387C2318yes—
507#387C2318yes—
508#387C2318yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2318yes—
513#386C2318yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2318yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2318yes—
527#385C2318yes—
528#385C2318yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2314yes—
533#385C2314yes—
534#385C2318yes—
535#385C2318yes—
536#384C2312yes—
537#384C2312yes—
538#384C2314yes—
539#384C2312yes—
540#384C2311yescharacteristic
541#384C2311yescharacteristic
542#384C2311yescharacteristic
543#384C2311yescharacteristic
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#384C2312yes—
548#384C2318yes—
549#382C2311yescharacteristic
550#382C2311yescharacteristic
551#382C2312yes—
552#382C2314yes—
553#382C2312yes—
554#382C2311yescharacteristic
555#382C2311yescharacteristic
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2312yes—
560#382C2312yes—
561#382C2318yes—
562#381C2314yes—
563#381C2318yes—
564#381C2318yes—
565#381C2318yes—
566#380C2314yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2318yes—
571#380C2318yes—
572#380C2318yes—
573#380C2318yes—
574C4×C4⋊C4C2318yes—
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2311yescharacteristic
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2318yes—
584C4×C4⋊C4C2318yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599#376C2312yes—
600C2×#95C2312yes—
601C2×#95C2318yes—
602C2×#95C2314yes—
603C2×#95C2314yes—
604C2×#95C2314yes—
605C43C2312yes—
606C2×#41—24no—
607C2×#41—24no—
608C2×#41—24no—
609C2×#41—24no—
610C2×#41—24no—
611C2×#41—24no—
612C2×#41—24no—
613C2×#41C2×D418yes—
614C2×#41C2×D418yes—
615C22×Q8—24no—
616C22×Q8—24no—
617C22×Q8—24no—
618C22×Q8C2412yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2411yescharacteristic
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×D4C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2412yes—
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2414yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2412yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C4⋊Q8—28no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—24no—
659C4⋊Q8—28no—
660C4⋊Q8C2×D418yes—
661#127C2×D418yes—
662#126—216no—
663#126—216no—
664#126—216no—
665#126—216no—
666#126—216no—
667#126—216no—
668#126—216no—
669#126—216no—
670#125—216no—
671#125—216no—
672#125—216no—
673#125—216no—
674#125—216no—
675#125—28no—
676#125—28no—
677#125—28no—
678#125—28no—
679#125—24no—
680#125—24no—
681#124—216no—
682#124—28no—
683#124—28no—
684#124—28no—
685#124C2×D418yes—
686#124C2×D418yes—
687#123—216no—
688#123—216no—
689#123—216no—
690#123—216no—
691#123—216no—
692#123—216no—
693#123—216no—
694#123—216no—
695#123—216no—
696#123—416no—
697C22⋊Q8—28no—
698C22⋊Q8—28no—
699C22⋊Q8—28no—
700C22⋊Q8—28no—
701C22⋊Q8—28no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—28no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—216no—
710C22⋊Q8—48no—
711#121—28no—
712#121—28no—
713#121—216no—
714#121—216no—
715#121—216no—
716#121—216no—
717#121—28no—
718#121—28no—
719#121C2×D4116yes—
720#121C2×D4116yes—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—216no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—28no—
730C4×Q8—28no—
731C4×Q8—28no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—28no—
735C4×Q8—28no—
736C4×D4—216no—
737C4×D4—216no—
738C4×D4—28no—
739C4×D4—28no—
740C4×D4—216no—
741C4×D4—216no—
742C4×D4—28no—
743C4×D4—28no—
744C4×D4—216no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—216no—
750C4×D4—216no—
751C4×D4—216no—
752C4×D4—216no—
753C4×D4—24no—
754C4×D4—24no—
755C4×D4—48no—
756C4×D4C2×D4116yes—
757C4×D4C2×D4116yes—
758#117—24no—
759#117—24no—
760#117—24no—
761#117—28no—
762#117—28no—
763#117—28no—
764#117—28no—
765#117—24no—
766#117—216no—
767#117—216no—
768#117—216no—
769#117—216no—
770#117—28no—
771#117—28no—
772#117—28no—
773#117#4118yes—
774C2×C4⋊C4—24no—
775C2×C4⋊C4—28no—
776C2×C4⋊C4—24no—
777C2×C4⋊C4—24no—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—416no—
785C2×C4⋊C4—48no—
786C2×C4⋊C4—44no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2418yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2418yes—
835C2×C4⋊C4C2418yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2418yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2418yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2418yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C42—28no—
881C2×C42—24no—
882C2×C42—24no—
883C2×C42—28no—
884C2×C42—28no—
885C2×C42—28no—
886C2×C42C2×D418yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914#95C2418yes—
915#95C2414yes—
916#95C2412yes—
917#95C2418yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2418yes—
922#95C2418yes—
923#95C2418yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2418yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2418yes—
942#95C2418yes—
943#95C2418yes—
944#95C2418yes—
945#95C2418yes—
946C24C2512yes—
947C24C2512yes—
948C24C2512yes—
949C24C2511yescharacteristic
950#41—232no—
951#41—232no—
952#41—416no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—22no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—22no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—22no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—416no—
971C2×Q8C22×D414yes—
972C2×Q8C22×D414yes—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—28no—
981C2×D4—28no—
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—48no—
992C2×D4—48no—
993C2×D4C22×D418yes—
994C2×D4C22×D418yes—
995C2×D4C22×D414yes—
996C2×D4C22×D414yes—
997C2×D4C22×D418yes—
998C2×D4C22×D418yes—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—28no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—28no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—28no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—48no—
1031C22×C4—48no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—48no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—48no—
1040C22×C4—44no—
1041C22×C4C22×D418yes—
1042C22×C4C22×D418yes—
1043C22×C4C22×D414yes—
1044C22×C4C22×D414yes—
1045C22×C4C22×D414yes—
1046C22×C4C2×#4114yes—
1047C22×C42−1+414yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
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—216no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—42no—
1118C4⋊C4—48no—
1119C4⋊C4—48no—
1120C4⋊C4—42no—
1121C4⋊C4—48no—
1122C4⋊C4—48no—
1123C4⋊C4—44no—
1124C4⋊C4—48no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—48no—
1128C4⋊C4C22×D418yes—
1129C4⋊C4C22×D418yes—
1130C4⋊C4C2×#4118yes—
1131C22⋊C4—24no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—216no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—48no—
1161C22⋊C4C22×D418yes—
1162C22⋊C4C22×D418yes—
1163C22⋊C4C22×D418yes—
1164C22⋊C4C22×D418yes—
1165C22⋊C4C2×#4118yes—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—28no—
1170C42—28no—
1171C42—28no—
1172C42—28no—
1173C42—28no—
1174C42—28no—
1175C42—24no—
1176C42—24no—
1177C42—22no—
1178C42—22no—
1179C42—22no—
1180C42—22no—
1181C42—28no—
1182C42—24no—
1183C42—28no—
1184C42—24no—
1185C42—24no—
1186C42—44no—
1187C42—44no—
1188C42C22×D414yes—
1189C42C22×D414yes—
1190C42C22×D414yes—
1191C42C22×D414yes—
1192C42C2×#4118yes—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23C23×D414yes—
1209C23C23×D414yes—
1210C23C23×D412yes—
1211C23C22×#4112yes—
1212C23C2×2−1+412yes—
1213C23C2611yescharacteristic
1214Q8—28no—
1215Q8—28no—
1216Q8—48no—
1217Q8—48no—
1218Q8—48no—
1219Q8—44no—
1220Q8—84no—
1221D4—216no—
1222D4—216no—
1223D4—28no—
1224D4—28no—
1225D4—48no—
1226D4—48no—
1227D4—48no—
1228D4—44no—
1229D4—88no—
1230D4—88no—
1231C2×C4—22no—
1232C2×C4—22no—
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—216no—
1244C2×C4—216no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—28no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—28no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—28no—
1281C2×C4—44no—
1282C2×C4—44no—
1283C2×C4—416no—
1284C2×C4—48no—
1285C2×C4—48no—
1286C2×C4—48no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C2×C4—88no—
1295C2×C4—84no—
1296C2×C4—88no—
1297C2×C4—84no—
1298C2×C4#547116yes—
1299C2×C4C23×D412yes—
1300C2×C4C23×D412yes—
1301C2×C4C23×D414yes—
1302C2×C4C23×D414yes—
1303C2×C4C23×D412yes—
1304C2×C4C23×D412yes—
1305C2×C4C23×D412yes—
1306C2×C4C23×D412yes—
1307C2×C4C22×#4118yes—
1308C2×C4C22×#4112yes—
1309C2×C4C22×#4112yes—
1310C2×C4C2×2−1+412yes—
1311C2×C4C2×2−1+412yes—
1312C2×C4#58514yes—
1313C22—24no—
1314C22—22no—
1315C22—22no—
1316C22—24no—
1317C22—24no—
1318C22—24no—
1319C22—24no—
1320C22—24no—
1321C22—24no—
1322C22—24no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—44no—
1332C22C2×#54714yes—
1333C22C24×D411yescharacteristic
1334C22C23×#4111yescharacteristic
1335C22C22×2−1+411yescharacteristic
1336C22C2×#58512yes—
1337C222−1+612yes—
1338C4—24no—
1339C4—28no—
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—24no—
1345C4—24no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—44no—
1360C4—44no—
1361C4C2×#54714yes—
1362C4C2×#54714yes—
1363C2—24no—
1364C2—44no—
1365C2—44no—
1366C2—82no—
1367C2C22×#54711yescharacteristic
1368C2#6281211yescharacteristic
1369C2#6285911yescharacteristic
1370C2#6295612yes—
1371C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3512C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3507C2semidirect
3. #59073C2semidirect
4. #59069C2semidirect
5. #59063C2semidirect
6. #45324C2semidirect
7. #45100C2semidirect
8. #43027C2semidirect
9. #39485C2semidirect
10. #39484C2semidirect
11. #37870C2semidirect
12. #37868C2semidirect
13. #37865C2semidirect
14. #37862C2semidirect
15. #36184C2semidirect
16. #36181C2semidirect
17. #35619C2semidirect
18. #35619C2semidirect
19. #35618C2semidirect
20. #35530C2semidirect
21. #35335C2semidirect
22. #35308C2semidirect
23. #35308C2semidirect
24. #34947C2semidirect
25. C2×#2565C2semidirect
26. #34184C2semidirect
27. #34183C2semidirect
28. #34141C2semidirect
29. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
C2×#35072
#590732
#590692
#590632
#453242
#451002
#430272
#394852
#394842
#378702
#378682
#378652
#378622
#361842
#361812
#356192
#356182
#355302
#353352
#353082
#349472
C2×#25652
#341842
#341832
#341412
C4×#5362