Finite Group Databasebeta

← #7658086

Subgroups — #7658086

Order 512.

6561 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic
3#42913C212yesmaximal, complemented
4#42912C212yesmaximal, complemented
5#42815C212yesmaximal, complemented
6#42811C212yesmaximal, complemented
7#42391C214yesmaximal, complemented
8#42315C214yesmaximal, complemented
9#41425C214yesmaximal, complemented
10#41421C214yesmaximal, complemented
11#39468C212yesmaximal, complemented
12#39463C214yesmaximal, complemented
13#38923C212yesmaximal, complemented
14#38915C214yesmaximal, complemented
15#37622C211yesmaximal, characteristic, complemented
16#37617C211yesmaximal, characteristic, complemented
17#37560C212yesmaximal, complemented
18#37555C212yesmaximal, complemented
19#36545C212yesmaximal, complemented
20#36505C212yesmaximal, complemented
21#36007C212yesmaximal, complemented
22#35985C212yesmaximal, complemented
23#35959C212yesmaximal, complemented
24#35856C212yesmaximal, complemented
25#35334C212yesmaximal, complemented
26#35279C211yesmaximal, characteristic, complemented
27#34627C211yesmaximal, characteristic, complemented
28#34627C212yesmaximal, complemented
29#34191C211yesmaximal, characteristic, complemented
30#3509—216no—
31#3480—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2212yes—
34C2×#557C2211yescharacteristic
35C2×#557C2212yes—
36C2×#557C2212yes—
37C2×#556C2212yes—
38C2×#556C2212yes—
39C2×#556C2212yes—
40C2×#556C2211yescharacteristic
41C2×#553C2211yescharacteristic
42C2×#553C2211yescharacteristic
43C2×#553C2212yes—
44C2×#553C2212yes—
45C2×#552C2214yes—
46C2×#552C2214yes—
47C2×#550C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#541C2214yes—
51C2×#536C2212yes—
52C2×#533C2212yes—
53C2×#533C2212yes—
54C2×#533C2211yescharacteristic
55C2×#532C2212yes—
56C2×#532C2211yescharacteristic
57C22×C4⋊Q8C2211yescharacteristic
58C2×#529C2212yes—
59C2×#529C2211yescharacteristic
60C2×#529C2212yes—
61C2×#529C2211yescharacteristic
62C2×#519C2212yes—
63C2×C4×#41C2212yes—
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C22×C4×Q8C2211yescharacteristic
68#2857C2212yes—
69#2857C2212yes—
70#2851C2214yes—
71#2851C2214yes—
72#2822C2214yes—
73#2821C2214yes—
74#2820C2214yes—
75#2817C2214yes—
76#2816C2214yes—
77#2814C2214yes—
78#2722C2218yes—
79#2720C2218yes—
80#2719C2218yes—
81#2717C2218yes—
82#2715C2218yes—
83#2713C2218yes—
84#2711C2218yes—
85#2709C2218yes—
86#2708C2218yes—
87#2708C2218yes—
88#2695C2218yes—
89#2691C2218yes—
90#2664C2214yes—
91#2663C2214yes—
92#2663C2214yes—
93#2659C2214yes—
94#2658C2212yes—
95#2642C2212yes—
96#2639C2214yes—
97#2638C2214yes—
98#2638C2214yes—
99#2638C2212yes—
100#2638C2212yes—
101#2637C2214yes—
102#2637C2214yes—
103#2634C2214yes—
104#2634C2214yes—
105#2634C2212yes—
106#2633C2214yes—
107#2633C2212yes—
108#2632C2214yes—
109#2628C2211yescharacteristic
110#2628C2212yes—
111#2628C2212yes—
112#2628C2212yes—
113#2628C2211yescharacteristic
114#2628C2212yes—
115#2628C2212yes—
116#2625C2212yes—
117#2625C2214yes—
118#2625C2212yes—
119#2624C2212yes—
120#2623C2214yes—
121#2621C2211yescharacteristic
122#2621C2211yescharacteristic
123#2621C2212yes—
124#2616C2212yes—
125#2616C2214yes—
126#2604C2214yes—
127#2604C2214yes—
128#2592C2212yes—
129#2584C2214yes—
130#2584C2212yes—
131#2582C2212yes—
132#2581C2214yes—
133#2581C2214yes—
134#2581C2214yes—
135#2580C2214yes—
136#2580C2214yes—
137#2568C2212yes—
138#2567C2212yes—
139#2564C2214yes—
140#2564C2214yes—
141#2564C2214yes—
142#2564C2214yes—
143#2563C2212yes—
144#2562C2214yes—
145#2559C2218yes—
146#2553C2218yes—
147#2547C2214yes—
148#2547C2212yes—
149#2546C2212yes—
150#2544C2214yes—
151#2542C2212yes—
152#2538C2212yes—
153#2536C2214yes—
154#2521C2218yes—
155#2498C2214yes—
156#2498C2214yes—
157#2496C2218yes—
158#2487C2214yes—
159#2487C2212yes—
160#2487C2212yes—
161#2485C2214yes—
162#2485C2214yes—
163#2478C2218yes—
164#2476C2218yes—
165#2475C2218yes—
166#2474C2218yes—
167#2473C2218yes—
168#2470C2218yes—
169#2462C2218yes—
170#2460C2218yes—
171#2453C2214yes—
172#2451C2214yes—
173#2446C2214yes—
174#2446C2214yes—
175#2436C2212yes—
176#2434C2214yes—
177#2434C2212yes—
178#2432C2214yes—
179#2429C2214yes—
180#2427C2214yes—
181#2427C2214yes—
182#2426C2214yes—
183#2417C2214yes—
184#2417C2214yes—
185#2415C2214yes—
186#2409C2212yes—
187#2409C2212yes—
188#2399C2212yes—
189#2399C2214yes—
190#2398C2212yes—
191#2398C2214yes—
192#2395C2214yes—
193#2395C2214yes—
194#2395C2212yes—
195#2395C2212yes—
196#2367C2214yes—
197#2365C2214yes—
198#2362C2214yes—
199#2360C2214yes—
200#2355C2212yes—
201#2352C2214yes—
202D4×C4⋊C4C2212yes—
203#2346C2212yes—
204#2343C2214yes—
205#2339C2212yes—
206#2320C2212yes—
207#2318C2214yes—
208#2317C2212yes—
209#2316C2214yes—
210#2311C2214yes—
211#2311C2212yes—
212C4×C22⋊Q8C2214yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2214yes—
215C4×C22⋊Q8C2212yes—
216#2285C2211yescharacteristic
217#2283C2212yes—
218#2283C2211yescharacteristic
219C2×#382C2212yes—
220#2275C2212yes—
221C22×#41C2312yes—
222C22×#41C2311yescharacteristic
223C22×#41C2311yescharacteristic
224C22×#41C2311yescharacteristic
225C23×Q8C2311yescharacteristic
226C23×Q8C2312yes—
227#559—216no—
228#559—28no—
229#557—28no—
230#557—216no—
231#557—216no—
232#556—216no—
233#556—216no—
234#556—28no—
235#556—216no—
236#553—216no—
237#553—28no—
238#553—28no—
239#553—216no—
240#552—232no—
241#552—232no—
242#550—28no—
243#548—28no—
244#548—28no—
245#541—232no—
246#536—216no—
247#533—28no—
248#533—216no—
249#533—216no—
250#532—216no—
251#532—28no—
252C2×C4⋊Q8—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2314yes—
263C2×#127C2312yes—
264C2×#127C2311yescharacteristic
265#529—216no—
266#529—28no—
267#529—28no—
268#529—216no—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2312yes—
272C2×#126C2312yes—
273C2×#126C2312yes—
274C2×#126C2312yes—
275C2×#126C2318yes—
276C2×#126C2318yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2318yes—
285C2×#125C2318yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2312yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2312yes—
298C2×#123C2312yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×#123C2318yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×#121C2312yes—
318C2×#121C2311yescharacteristic
319C2×#121C2311yescharacteristic
320C2×#121C2312yes—
321C2×#121C2311yescharacteristic
322C2×#121C2311yescharacteristic
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328#519—216no—
329C4×#41—28no—
330C4×#41—28no—
331C4×#41—216no—
332C4×#41D4116yes—
333C2×C4×Q8—28no—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2314yes—
337C2×C4×Q8C2314yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2314yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2314yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2314yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×D4C2312yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×#117C2314yes—
379C2×#117C2312yes—
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2318yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2314yes—
397C22×C42C2312yes—
398C22×C42C2312yes—
399C22×C42C2311yescharacteristic
400C22×C42C2311yescharacteristic
401C22×C42C2311yescharacteristic
402C22×C42C2312yes—
403#400C2312yes—
404#400C2318yes—
405#400C2314yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2318yes—
410#400C2314yes—
411#400C2318yes—
412#400C2314yes—
413#400C2318yes—
414#400C2314yes—
415#399C2312yes—
416#399C2314yes—
417#399C2312yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2318yes—
422#399C2314yes—
423#398C2318yes—
424#398C2318yes—
425#398C2312yes—
426#398C2314yes—
427#398C2318yes—
428#398C2318yes—
429#398C2318yes—
430#398C2318yes—
431#398C2314yes—
432#398C2312yes—
433#398C2312yes—
434#398C2312yes—
435#398C2318yes—
436#398C2314yes—
437#397C2318yes—
438#397C2318yes—
439#397C2312yes—
440#397C2314yes—
441#397C2318yes—
442#397C2314yes—
443#397C2312yes—
444#397C2312yes—
445#397C2312yes—
446#397C2318yes—
447#397C2318yes—
448#397C2314yes—
449#397C2314yes—
450#397C2318yes—
451#396C2318yes—
452#396C2318yes—
453#396C2318yes—
454#395C2314yes—
455#395C2314yes—
456#395C2318yes—
457#395C2312yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2318yes—
462#395C2318yes—
463#395C2314yes—
464#395C2312yes—
465#394C2318yes—
466#394C2318yes—
467#394C2318yes—
468#394C2318yes—
469#394C2318yes—
470#394C2314yes—
471#394C2318yes—
472#394C2314yes—
473#394C2314yes—
474#394C2318yes—
475#394C2318yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#393C2312yes—
483#391C2314yes—
484#391C2318yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#390C2314yes—
495#390C2318yes—
496#390C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2318yes—
502#389C2318yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2318yes—
510#389C2318yes—
511#389C2314yes—
512#389C2314yes—
513#389C2318yes—
514#388C2318yes—
515#388C2318yes—
516#388C2318yes—
517#388C2318yes—
518#388C2318yes—
519#388C2318yes—
520#388C2318yes—
521#388C2318yes—
522#387C2318yes—
523#387C2318yes—
524#387C2318yes—
525#387C2318yes—
526#387C2318yes—
527#387C2318yes—
528#387C2318yes—
529#387C2318yes—
530#387C2318yes—
531#387C2318yes—
532#387C2318yes—
533#387C2318yes—
534#387C2314yes—
535#387C2314yes—
536#386C2318yes—
537#386C2318yes—
538#386C2314yes—
539#386C2314yes—
540#386C2318yes—
541#386C2318yes—
542#386C2318yes—
543#386C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2314yes—
549#385C2314yes—
550#385C2318yes—
551#385C2318yes—
552#385C2318yes—
553#385C2318yes—
554#385C2314yes—
555#385C2314yes—
556#384C2314yes—
557#384C2312yes—
558#383C2312yes—
559#383C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2311yescharacteristic
565#382C2312yes—
566#382C2311yescharacteristic
567#381C2314yes—
568#381C2312yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2318yes—
576#380C2318yes—
577#380C2312yes—
578#380C2314yes—
579#380C2314yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2312yes—
584#380C2318yes—
585#380C2318yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2318yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2318yes—
594C4×C4⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2318yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2318yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2318yes—
602#376C2312yes—
603#376C2314yes—
604C2×#95C2314yes—
605C2×#95C2314yes—
606C2×#41—24no—
607C2×#41—24no—
608C2×#41—28no—
609C2×#41—28no—
610C2×#41—24no—
611C2×#41—44no—
612C2×#41—42no—
613C2×#41—44no—
614C2×#41—44no—
615C2×#41C2×D418yes—
616C22×Q8—24no—
617C22×Q8—28no—
618C22×Q8—48no—
619C22×Q8—44no—
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2414yes—
623C22×Q8C2411yescharacteristic
624C22×Q8C2412yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2414yes—
629C22×D4C2411yescharacteristic
630C22×D4C2412yes—
631C22×D4C2411yescharacteristic
632C22×D4C2411yescharacteristic
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2411yescharacteristic
636C22×D4C2411yescharacteristic
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2414yes—
651C23×C4C2412yes—
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2418yes—
658C23×C4C2411yescharacteristic
659C23×C4C2412yes—
660C23×C4C2412yes—
661C4⋊Q8—216no—
662C4⋊Q8—24no—
663C4⋊Q8—28no—
664C4⋊Q8—28no—
665C4⋊Q8—28no—
666C4⋊Q8—28no—
667C4⋊Q8—28no—
668C4⋊Q8—24no—
669C4⋊Q8—24no—
670C4⋊Q8—48no—
671#127—24no—
672#127—28no—
673#126—28no—
674#126—28no—
675#126—28no—
676#126—232no—
677#126—232no—
678#126—28no—
679#126—28no—
680#126—28no—
681#125—24no—
682#125—28no—
683#125—232no—
684#125—232no—
685#125—28no—
686#125—24no—
687#125—28no—
688#125—216no—
689#125—216no—
690#124—24no—
691#124—28no—
692#124—216no—
693#124—28no—
694#124—28no—
695#124—28no—
696#124—28no—
697#124—24no—
698#124—48no—
699#123—232no—
700#123—28no—
701#123—28no—
702#123—28no—
703#123—28no—
704#123—28no—
705#123—28no—
706C22⋊Q8—24no—
707C22⋊Q8—28no—
708C22⋊Q8—216no—
709C22⋊Q8—216no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—28no—
715C22⋊Q8—24no—
716C22⋊Q8—28no—
717C22⋊Q8—44no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721#121—24no—
722#121—28no—
723#121—24no—
724#121—28no—
725#121—24no—
726#121—28no—
727#121—24no—
728#121—28no—
729#121—28no—
730#121—28no—
731#121—28no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—24no—
735C4×Q8—28no—
736C4×Q8—216no—
737C4×Q8—216no—
738C4×Q8—28no—
739C4×Q8—24no—
740C4×Q8—28no—
741C4×Q8—24no—
742C4×Q8—28no—
743C4×Q8—24no—
744C4×Q8—216no—
745C4×Q8—216no—
746C4×Q8—216no—
747C4×Q8—216no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8C2×D418yes—
751C4×Q8C2×D418yes—
752C4×D4—24no—
753C4×D4—28no—
754C4×D4—24no—
755C4×D4—28no—
756C4×D4—24no—
757C4×D4—28no—
758C4×D4—24no—
759C4×D4—28no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—24no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—24no—
767C4×D4—28no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—24no—
771C4×D4—48no—
772C4×D4C2×D4116yes—
773C4×D4C2×D418yes—
774C4×D4C2×D4116yes—
775C4×D4C2×D418yes—
776#117—24no—
777#117—28no—
778#117—28no—
779#117—216no—
780#117—216no—
781#117—24no—
782#117—28no—
783#117—232no—
784#117—24no—
785#117—24no—
786#117—28no—
787#117—44no—
788#117C2×D418yes—
789#117C2×D4116yes—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—24no—
793C2×C4⋊C4—28no—
794C2×C4⋊C4—48no—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2418yes—
823C2×C4⋊C4C2418yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2418yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2418yes—
837C2×C4⋊C4C2418yes—
838C2×C4⋊C4C2418yes—
839C2×C4⋊C4C2418yes—
840C2×C4⋊C4C2418yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2418yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2411yescharacteristic
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2418yes—
864C2×C22⋊C4C2418yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2418yes—
874C2×C22⋊C4C2418yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2418yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2418yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C42—28no—
888C2×C42—24no—
889C2×C42—28no—
890C2×C42—24no—
891C2×C42C2×D418yes—
892C2×C42C2×D4116yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2418yes—
899C2×C42C2418yes—
900C2×C42C2414yes—
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2418yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2418yes—
922#95C2418yes—
923#95C2412yes—
924#95C2414yes—
925#95C2412yes—
926#95C2418yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2414yes—
931#95C2414yes—
932#95C2418yes—
933#95C2418yes—
934#95C2414yes—
935#95C2418yes—
936#95C2418yes—
937#95C2414yes—
938#95C2418yes—
939#95C2414yes—
940#95C2414yes—
941#95C2418yes—
942#95C2414yes—
943#95C2418yes—
944#95C2418yes—
945#95C2418yes—
946#95C2418yes—
947#95C2418yes—
948#95C2418yes—
949C24C2511yescharacteristic
950C24C2512yes—
951C24C2511yescharacteristic
952C24C2512yes—
953C24C2511yescharacteristic
954#41—432no—
955#41—416no—
956#41—416no—
957#41—416no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—22no—
962C2×Q8—28no—
963C2×Q8—24no—
964C2×Q8—22no—
965C2×Q8—28no—
966C2×Q8—24no—
967C2×Q8—22no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—28no—
972C2×Q8—28no—
973C2×Q8—24no—
974C2×Q8—48no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—41no—
978C2×Q8—42no—
979C2×Q8—432no—
980C2×Q8—416no—
981C2×Q8C22×D414yes—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—24no—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—22no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—22no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—22no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—41no—
1002C2×D4—42no—
1003C2×D4—41no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—41no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4C22×D414yes—
1013C2×D4C22×D418yes—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—22no—
1017C22×C4—24no—
1018C22×C4—22no—
1019C22×C4—24no—
1020C22×C4—22no—
1021C22×C4—28no—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—22no—
1026C22×C4—24no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—48no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—48no—
1049C22×C4—48no—
1050C22×C4—48no—
1051C22×C4C22×D414yes—
1052C22×C4C22×D418yes—
1053C22×C4C22×D414yes—
1054C22×C4C22×D414yes—
1055C22×C4C22×D418yes—
1056C22×C4C22×D418yes—
1057C22×C42−1+414yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2518yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2518yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—216no—
1108C4⋊C4—216no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—216no—
1113C4⋊C4—216no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—48no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—48no—
1125C4⋊C4—44no—
1126C4⋊C4—48no—
1127C4⋊C4—48no—
1128C4⋊C4—48no—
1129C4⋊C4—44no—
1130C4⋊C4—48no—
1131C4⋊C4—48no—
1132C4⋊C4C22×D414yes—
1133C4⋊C4C22×D418yes—
1134C4⋊C4C22×D414yes—
1135C4⋊C4C22×D418yes—
1136C22⋊C4—28no—
1137C22⋊C4—24no—
1138C22⋊C4—22no—
1139C22⋊C4—24no—
1140C22⋊C4—22no—
1141C22⋊C4—216no—
1142C22⋊C4—216no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—22no—
1148C22⋊C4—22no—
1149C22⋊C4—22no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—22no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—48no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—48no—
1165C22⋊C4—48no—
1166C22⋊C4—48no—
1167C22⋊C4—48no—
1168C22⋊C4—44no—
1169C22⋊C4—48no—
1170C22⋊C4—48no—
1171C22⋊C4C22×D418yes—
1172C22⋊C4C22×D418yes—
1173C22⋊C4C22×D418yes—
1174C42—22no—
1175C42—24no—
1176C42—22no—
1177C42—24no—
1178C42—22no—
1179C42—24no—
1180C42—22no—
1181C42—24no—
1182C42—22no—
1183C42—24no—
1184C42—22no—
1185C42—216no—
1186C42—216no—
1187C42—28no—
1188C42—28no—
1189C42—48no—
1190C42—44no—
1191C42C22×D418yes—
1192C42C22×D414yes—
1193C42C22×D414yes—
1194C42C22×D418yes—
1195C42C22×D414yes—
1196C42C22×D418yes—
1197C42C22×D414yes—
1198C23—21no—
1199C23—21no—
1200C23—22no—
1201C23—22no—
1202C23—21no—
1203C23—24no—
1204C23—22no—
1205C23—22no—
1206C23—21no—
1207C23—22no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23—22no—
1214C23—21no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—24no—
1220C23C23×D414yes—
1221C23C23×D412yes—
1222C23C2×2−1+412yes—
1223C23C2611yescharacteristic
1224Q8—28no—
1225Q8—44no—
1226Q8—48no—
1227Q8—48no—
1228Q8—416no—
1229Q8—48no—
1230Q8—44no—
1231Q8—416no—
1232Q8—48no—
1233D4—28no—
1234D4—48no—
1235D4—44no—
1236D4—48no—
1237D4—44no—
1238D4—48no—
1239D4—48no—
1240D4—44no—
1241D4—48no—
1242D4—44no—
1243D4—84no—
1244D4—84no—
1245D4—84no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—216no—
1259C2×C4—28no—
1260C2×C4—28no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—28no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—28no—
1279C2×C4—28no—
1280C2×C4—24no—
1281C2×C4—28no—
1282C2×C4—24no—
1283C2×C4—28no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—28no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—44no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—416no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—44no—
1307C2×C4—84no—
1308C2×C4—82no—
1309C2×C4—84no—
1310C2×C4—82no—
1311C2×C4—168no—
1312C2×C4C23×D414yes—
1313C2×C4C23×D414yes—
1314C2×C4C23×D412yes—
1315C2×C4C23×D414yes—
1316C2×C4C23×D412yes—
1317C2×C4C23×D412yes—
1318C2×C4C23×D412yes—
1319C2×C4C23×D412yes—
1320C2×C4C23×D412yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4C2×2−1+412yes—
1323C2×C4#58514yes—
1324C2×C4#58512yes—
1325C22—22no—
1326C22—22no—
1327C22—24no—
1328C22—22no—
1329C22—24no—
1330C22—22no—
1331C22—24no—
1332C22—24no—
1333C22—41no—
1334C22—41no—
1335C22—44no—
1336C22—42no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—41no—
1342C22—42no—
1343C22—41no—
1344C22—42no—
1345C22—41no—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22C24×D411yescharacteristic
1351C22C22×2−1+411yescharacteristic
1352C22C2×#58511yescharacteristic
1353C22C2×#58512yes—
1354C222−1+612yes—
1355C4—22no—
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—22no—
1361C4—22no—
1362C4—24no—
1363C4—42no—
1364C4—41no—
1365C4—44no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—44no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—48no—
1374C4—44no—
1375C4—48no—
1376C4—44no—
1377C4#344914yes—
1378C4#348914yes—
1379C2—42no—
1380C2—42no—
1381C2—44no—
1382C2—82no—
1383C2—81no—
1384C2C2×#344911yescharacteristic
1385C2C2×#348911yescharacteristic
1386C2#6285911yescharacteristic
1387C2#6295612yes—
1388C2#6296812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3480C2
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×#3509C2semidirect
3. #42913C2semidirect
4. #42912C2semidirect
5. #42815C2semidirect
6. #42811C2semidirect
7. #42391C2semidirect
8. #42315C2semidirect
9. #41425C2semidirect
10. #41421C2semidirect
11. #39468C2semidirect
12. #39463C2semidirect
13. #38923C2semidirect
14. #38915C2semidirect
15. #37622C2semidirect
16. #37617C2semidirect
17. #37560C2semidirect
18. #37555C2semidirect
19. #36545C2semidirect
20. #36505C2semidirect
21. #36007C2semidirect
22. #35985C2semidirect
23. #35959C2semidirect
24. #35856C2semidirect
25. #35334C2semidirect
26. #35279C2semidirect
27. #34627C2semidirect
28. #34627C2semidirect
29. #34191C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34802
#429132
#429122
#428152
#428112
#423912
#423152
#414252
#414212
#394682
#394632
#389232
#389152
#376222
#376172
#375602
#375552
#365452
#365052
#360072
#359852
#359592
#358562
#353342
#352792
#346272
#341912