Finite Group Databasebeta

← #7646714

Subgroups — #7646714

Order 512.

7066 conjugacy classes of subgroups.

The subgroup lattice has 1411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42928C214yesmaximal, complemented
4#42927C214yesmaximal, complemented
5#41996C218yesmaximal, complemented
6#39747C211yesmaximal, characteristic, complemented
7#39744C211yesmaximal, characteristic, complemented
8#39363C211yesmaximal, characteristic, complemented
9#39360C211yesmaximal, characteristic, complemented
10#39174C211yesmaximal, characteristic, complemented
11#39170C211yesmaximal, characteristic, complemented
12#38956C211yesmaximal, characteristic, complemented
13#38951C211yesmaximal, characteristic, complemented
14#38093C212yesmaximal, complemented
15#38088C212yesmaximal, complemented
16#37683C212yesmaximal, complemented
17#37680C212yesmaximal, complemented
18#37544C212yesmaximal, complemented
19#37542C212yesmaximal, complemented
20#36964C218yesmaximal, complemented
21#35526C214yesmaximal, complemented
22#35298C211yesmaximal, characteristic, complemented
23#35246C212yesmaximal, complemented
24#35241C211yesmaximal, characteristic, complemented
25#35178C212yesmaximal, complemented
26#35156C214yesmaximal, complemented
27#34937C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34060C211yesmaximal, characteristic, complemented
30#3517—216no—
31#3482—216no—
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#556C2212yes—
36C2×#553C2214yes—
37C2×#553C2212yes—
38C2×#552C2214yes—
39C2×#552C2212yes—
40C2×#550C2211yescharacteristic
41C2×#550C2211yescharacteristic
42C2×#550C2212yes—
43C2×#550C2212yes—
44C2×D4×Q8C2211yescharacteristic
45C2×#548C2212yes—
46C2×#547C2211yescharacteristic
47C2×#547C2211yescharacteristic
48C2×#547C2212yes—
49C2×#547C2212yes—
50C2×#540C2212yes—
51C2×#540C2214yes—
52C2×#536C2212yes—
53C2×#536C2212yes—
54C2×#533C2211yescharacteristic
55C2×#533C2212yes—
56C2×#532C2212yes—
57C2×#532C2211yescharacteristic
58C2×#532C2212yes—
59C2×#529C2211yescharacteristic
60C2×#529C2212yes—
61C2×#529C2214yes—
62C2×#529C2212yes—
63C2×#520C2212yes—
64C2×C4×#41C2212yes—
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C22×C4×Q8C2212yes—
68#2868C2211yescharacteristic
69#2862C2211yescharacteristic
70#2858C2211yescharacteristic
71#2858C2211yescharacteristic
72#2857C2212yes—
73#2854C2218yes—
74#2853C2218yes—
75#2850C2212yes—
76#2823C2218yes—
77#2813C2218yes—
78#2721C2218yes—
79#2719C2218yes—
80#2714C2218yes—
81#2711C2218yes—
82#2709C2218yes—
83#2708C2218yes—
84#2706C2218yes—
85#2703C2218yes—
86#2695C2218yes—
87#2691C2218yes—
88#2681C2218yes—
89#2680C2218yes—
90#2676C2218yes—
91#2673C2218yes—
92#2672C2218yes—
93#2671C2218yes—
94#2664C2214yes—
95#2658C2212yes—
96#2657C2212yes—
97#2642C2212yes—
98#2641C2212yes—
99#2637C2218yes—
100#2636C2218yes—
101#2635C2218yes—
102#2630C2218yes—
103#2630C2218yes—
104#2621C2212yes—
105#2620C2212yes—
106#2620C2212yes—
107#2620C2214yes—
108#2619C2212yes—
109#2618C2218yes—
110#2609C2218yes—
111#2602C2214yes—
112#2601C2214yes—
113#2599C2218yes—
114#2598C2218yes—
115#2579C2218yes—
116#2568C2211yescharacteristic
117#2566C2212yes—
118#2566C2214yes—
119#2566C2211yescharacteristic
120#2565C2212yes—
121#2565C2211yescharacteristic
122#2565C2212yes—
123#2548C2212yes—
124#2548C2211yescharacteristic
125#2548C2212yes—
126#2547C2211yescharacteristic
127#2547C2211yescharacteristic
128#2546C2212yes—
129#2546C2211yescharacteristic
130#2546C2212yes—
131#2546C2211yescharacteristic
132#2545C2212yes—
133#2545C2211yescharacteristic
134#2545C2212yes—
135#2545C2212yes—
136#2545C2212yes—
137#2545C2212yes—
138#2544C2212yes—
139#2544C2211yescharacteristic
140#2544C2212yes—
141#2543C2214yes—
142#2542C2211yescharacteristic
143#2541C2211yescharacteristic
144#2538C2218yes—
145#2536C2218yes—
146#2504C2212yes—
147#2502C2212yes—
148#2500C2211yescharacteristic
149#2500C2214yes—
150#2499C2211yescharacteristic
151#2498C2214yes—
152#2476C2218yes—
153#2473C2218yes—
154#2470C2218yes—
155#2463C2218yes—
156#2460C2218yes—
157#2456C2218yes—
158#2455C2218yes—
159#2453C2214yes—
160#2452C2214yes—
161#2449C2218yes—
162#2446C2214yes—
163#2445C2214yes—
164#2441C2214yes—
165#2440C2214yes—
166#2436C2212yes—
167#2434C2212yes—
168#2432C2214yes—
169#2432C2211yescharacteristic
170#2432C2212yes—
171#2432C2212yes—
172#2432C2212yes—
173#2432C2212yes—
174#2431C2212yes—
175#2431C2212yes—
176#2431C2214yes—
177#2431C2211yescharacteristic
178#2427C2214yes—
179#2426C2214yes—
180#2423C2214yes—
181#2422C2214yes—
182#2417C2214yes—
183#2417C2214yes—
184#2416C2214yes—
185#2414C2214yes—
186#2407C2214yes—
187#2407C2214yes—
188#2392C2214yes—
189#2392C2214yes—
190#2327C2212yes—
191#2327C2212yes—
192#2326C2212yes—
193#2326C2212yes—
194#2326C2214yes—
195#2323C2214yes—
196#2320C2212yes—
197#2319C2212yes—
198#2318C2214yes—
199#2317C2212yes—
200#2314C2214yes—
201#2311C2212yes—
202#2311C2212yes—
203#2311C2212yes—
204C4×C4⋊Q8C2211yescharacteristic
205C4×#127C2211yescharacteristic
206C4×#124C2211yescharacteristic
207C4×#124C2211yescharacteristic
208C4×#121C2214yes—
209#2297C2212yes—
210#2295C2211yescharacteristic
211#2295C2211yescharacteristic
212#2293C2211yescharacteristic
213#2293C2211yescharacteristic
214#2290C2212yes—
215#2290C2212yes—
216#2290C2214yes—
217#2285C2212yes—
218#2283C2212yes—
219C4×#117C2211yescharacteristic
220C2×C4×C4⋊C4C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C22×#41C2311yescharacteristic
228C23×Q8C2312yes—
229#557—28no—
230#557—28no—
231#556—28no—
232#556—216no—
233#553—232no—
234#553—216no—
235#552—216no—
236#552—232no—
237#550—216no—
238#550—28no—
239#550—28no—
240#550—216no—
241D4×Q8—28no—
242#548—216no—
243#547—216no—
244#547—28no—
245#547—28no—
246#547—216no—
247#540—216no—
248#540—232no—
249#536—48no—
250#536—48no—
251#533—216no—
252#533—28no—
253#532—216no—
254#532—28no—
255#532—48no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×#127C2311yescharacteristic
268C2×#127C2312yes—
269C2×#127C2314yes—
270C2×#127C2312yes—
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273#529—232no—
274#529—216no—
275#529—216no—
276#529—28no—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2312yes—
294C2×#124C2311yescharacteristic
295C2×#124C2314yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#123C2314yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2318yes—
310C2×#123C2318yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2318yes—
322C2×C22⋊Q8C2318yes—
323C2×#121C2311yescharacteristic
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2318yes—
340#520—216no—
341C4×#41—216no—
342C4×#41—28no—
343C4×#41D4116yescomplemented
344C2×C4×Q8—216no—
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2314yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2318yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×#117C2312yes—
383C2×#117C2314yes—
384C2×#117C2314yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2314yes—
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2311yescharacteristic
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2314yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2314yes—
399C22×C4⋊C4C2312yes—
400C22×C42C2314yes—
401C22×C42C2312yes—
402C22×C42C2312yes—
403C22×C42C2312yes—
404C22×C42C2311yescharacteristic
405#400C2314yes—
406#400C2318yes—
407#400C2318yes—
408#399C2318yes—
409#399C2318yes—
410#399C2314yes—
411#398C2318yes—
412#398C2318yes—
413#398C2314yes—
414#398C2318yes—
415#398C2318yes—
416#398C2318yes—
417#398C2318yes—
418#398C2314yes—
419#398C2314yes—
420#397C2318yes—
421#397C2314yes—
422#397C2318yes—
423#397C2314yes—
424#397C2314yes—
425#396C2314yes—
426#396C2318yes—
427#396C2318yes—
428#396C2318yes—
429#396C2318yes—
430#396C2318yes—
431#396C2318yes—
432#396C2318yes—
433#396C2314yes—
434#396C2318yes—
435#395C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2318yes—
444#394C2318yes—
445#394C2318yes—
446#394C2318yes—
447#394C2318yes—
448#394C2318yes—
449#394C2318yes—
450#394C2318yes—
451#394C2318yes—
452#394C2314yes—
453#393C2318yes—
454#392C2318yes—
455#392C2314yes—
456#392C2318yes—
457#392C2318yes—
458#392C2318yes—
459#392C2318yes—
460#392C2314yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#391C2312yes—
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2311yescharacteristic
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#390C2311yescharacteristic
477#390C2311yescharacteristic
478#390C2314yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2311yescharacteristic
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2318yes—
491#390C2318yes—
492#390C2311yescharacteristic
493#390C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2318yes—
500#389C2314yes—
501#389C2318yes—
502#389C2318yes—
503#389C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2318yes—
509#388C2318yes—
510#388C2318yes—
511#388C2318yes—
512#388C2318yes—
513#388C2318yes—
514#388C2318yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2318yes—
520#387C2318yes—
521#387C2314yes—
522#387C2318yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2318yes—
528#387C2318yes—
529#387C2318yes—
530#387C2318yes—
531#387C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2318yes—
535#386C2318yes—
536#386C2318yes—
537#386C2318yes—
538#386C2318yes—
539#386C2314yes—
540#386C2318yes—
541#386C2318yes—
542#386C2318yes—
543#386C2314yes—
544#386C2318yes—
545#386C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2314yes—
549#385C2318yes—
550#385C2314yes—
551#385C2314yes—
552#385C2318yes—
553#385C2318yes—
554#385C2318yes—
555#385C2318yes—
556#385C2318yes—
557#385C2318yes—
558#385C2314yes—
559#384C2311yescharacteristic
560#384C2311yescharacteristic
561#384C2312yes—
562#384C2314yes—
563#384C2314yes—
564#384C2314yes—
565#383C2314yes—
566#382C2312yes—
567#382C2311yescharacteristic
568#382C2311yescharacteristic
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#381C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2318yes—
576#380C2318yes—
577#380C2314yes—
578#380C2314yes—
579#380C2318yes—
580#380C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2311yescharacteristic
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2311yescharacteristic
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2311yescharacteristic
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2311yescharacteristic
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2318yes—
596C4×C22⋊C4C2311yescharacteristic
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2311yescharacteristic
600#376C2312yes—
601#376C2312yes—
602#376C2312yes—
603C2×#95C2312yes—
604C43C2311yescharacteristic
605C43C2311yescharacteristic
606C2×#41—28no—
607C2×#41—24no—
608C2×#41—28no—
609C2×#41—24no—
610C2×#41—28no—
611C2×#41—28no—
612C2×#41—28no—
613C2×#41—44no—
614C2×#41—42no—
615C2×#41—48no—
616C2×#41—48no—
617C2×#41—44no—
618C2×#41—44no—
619C2×#41—44no—
620C2×#41—44no—
621C2×#41—44no—
622C2×#41—44no—
623C2×#41C2×D418yes—
624C22×Q8—28no—
625C22×Q8—28no—
626C22×Q8—44no—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2411yescharacteristic
631C22×Q8C2414yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2411yescharacteristic
634C22×D4C2412yes—
635C22×D4C2411yescharacteristic
636C22×D4C2411yescharacteristic
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2411yescharacteristic
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2418yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2412yes—
665C23×C4C2414yes—
666C23×C4C2412yes—
667C23×C4C2411yescharacteristic
668C23×C4C2412yes—
669C4⋊Q8—28no—
670C4⋊Q8—28no—
671C4⋊Q8—24no—
672C4⋊Q8—28no—
673C4⋊Q8—24no—
674C4⋊Q8—28no—
675C4⋊Q8—24no—
676C4⋊Q8—24no—
677C4⋊Q8—44no—
678C4⋊Q8—44no—
679C4⋊Q8—44no—
680#127—28no—
681#127—216no—
682#127—24no—
683#127—28no—
684#127—42no—
685#127—44no—
686#126—216no—
687#126—216no—
688#126—216no—
689#126—28no—
690#126—216no—
691#125—216no—
692#125—216no—
693#125—28no—
694#125—216no—
695#125—24no—
696#125—28no—
697#125—28no—
698#124—28no—
699#124—24no—
700#124—216no—
701#124—24no—
702#124—28no—
703#124—28no—
704#124—48no—
705#124—44no—
706#124—42no—
707#124—44no—
708#124—44no—
709#124—44no—
710#123—216no—
711#123—216no—
712#123—28no—
713#123—216no—
714#123—216no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—416no—
719#123—416no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—24no—
723C22⋊Q8—28no—
724C22⋊Q8—28no—
725C22⋊Q8—28no—
726C22⋊Q8—28no—
727C22⋊Q8—216no—
728C22⋊Q8—216no—
729C22⋊Q8—416no—
730C22⋊Q8—416no—
731C22⋊Q8—48no—
732#121—216no—
733#121—28no—
734#121—216no—
735#121—28no—
736#121—28no—
737#121—24no—
738#121—216no—
739#121—28no—
740#121—28no—
741#121—216no—
742#121—28no—
743#121—216no—
744#121—216no—
745#121—216no—
746#121—216no—
747#121—416no—
748#121—48no—
749C4×Q8—28no—
750C4×Q8—28no—
751C4×Q8—24no—
752C4×Q8—216no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—216no—
757C4×Q8—28no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—28no—
761C4×Q8C2×D418yes—
762C4×Q8C2×D418yes—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—216no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—216no—
769C4×D4—216no—
770C4×D4—28no—
771C4×D4—216no—
772C4×D4—24no—
773C4×D4—24no—
774C4×D4—28no—
775C4×D4—216no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—216no—
780C4×D4—48no—
781C4×D4—416no—
782C4×D4C2×D418yes—
783C4×D4C2×D4116yes—
784C4×D4C2×D418yes—
785C4×D4C2×D4116yes—
786#117—24no—
787#117—28no—
788#117—28no—
789#117—216no—
790#117—28no—
791#117—28no—
792#117—216no—
793#117—216no—
794#117—44no—
795#117—44no—
796#117—44no—
797#117C2×D4116yes—
798#117C2×D418yes—
799C2×C4⋊C4—28no—
800C2×C4⋊C4—216no—
801C2×C4⋊C4—216no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2418yes—
843C2×C4⋊C4C2418yes—
844C2×C4⋊C4C2418yes—
845C2×C4⋊C4C2418yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2418yes—
882C2×C22⋊C4C2418yes—
883C2×C22⋊C4C2418yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2418yes—
886C2×C22⋊C4C2418yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2418yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C42—216no—
897C2×C42—28no—
898C2×C42—44no—
899C2×C42C2×D4116yes—
900C2×C42C2×D418yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2418yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2418yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2418yes—
951#95C2418yes—
952#95C2418yes—
953#95C2418yes—
954#95C2418yes—
955#95C2418yes—
956C24C2512yes—
957C24C2512yes—
958C24C2514yes—
959C24C2512yes—
960C24C2511yescharacteristic
961#41—416no—
962#41—416no—
963#41—432no—
964#41—432no—
965#41—816no—
966#41—816no—
967#41—816no—
968C2×Q8—22no—
969C2×Q8—28no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—22no—
974C2×Q8—28no—
975C2×Q8—24no—
976C2×Q8—24no—
977C2×Q8—22no—
978C2×Q8—22no—
979C2×Q8—24no—
980C2×Q8—28no—
981C2×Q8—24no—
982C2×Q8—22no—
983C2×Q8—24no—
984C2×Q8—44no—
985C2×Q8—432no—
986C2×Q8C22×D414yes—
987C2×Q8H(5,𝔽2)14yes—
988C2×D4—28no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—22no—
996C2×D4—28no—
997C2×D4—24no—
998C2×D4—22no—
999C2×D4—24no—
1000C2×D4—28no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—22no—
1004C2×D4—24no—
1005C2×D4—22no—
1006C2×D4—24no—
1007C2×D4—28no—
1008C2×D4—22no—
1009C2×D4—24no—
1010C2×D4—22no—
1011C2×D4—44no—
1012C2×D4—48no—
1013C2×D4—42no—
1014C2×D4—48no—
1015C2×D4—48no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—48no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—48no—
1024C2×D4—44no—
1025C2×D4—48no—
1026C2×D4—48no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4C22×D414yes—
1032C2×D4C22×D418yes—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—28no—
1047C22×C4—28no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—28no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—48no—
1059C22×C4—48no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4C22×D418yes—
1070C22×C4C22×D414yes—
1071C22×C4C22×D414yes—
1072C22×C4C22×D418yes—
1073C22×C4C22×D418yes—
1074C22×C4C22×D414yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—22no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—22no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—216no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—48no—
1141C4⋊C4—48no—
1142C4⋊C4—48no—
1143C4⋊C4—48no—
1144C4⋊C4C22×D418yes—
1145C4⋊C4C22×D414yes—
1146C4⋊C4C22×D414yes—
1147C4⋊C4C22×D418yes—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—24no—
1154C22⋊C4—28no—
1155C22⋊C4—24no—
1156C22⋊C4—28no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—216no—
1167C22⋊C4—28no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—48no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—48no—
1180C22⋊C4—48no—
1181C22⋊C4—48no—
1182C22⋊C4—48no—
1183C22⋊C4—48no—
1184C22⋊C4—48no—
1185C22⋊C4—48no—
1186C22⋊C4—48no—
1187C22⋊C4—44no—
1188C22⋊C4C22×D418yes—
1189C22⋊C4C22×D418yes—
1190C22⋊C4C22×D418yes—
1191C42—24no—
1192C42—24no—
1193C42—28no—
1194C42—28no—
1195C42—24no—
1196C42—28no—
1197C42—28no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—22no—
1203C42—24no—
1204C42—24no—
1205C42—22no—
1206C42—22no—
1207C42—44no—
1208C42—42no—
1209C42—42no—
1210C42C22×D414yes—
1211C42C22×D414yes—
1212C42C22×D418yes—
1213C42C22×D414yes—
1214C42C22×D418yes—
1215C42C22×D414yes—
1216C42C22×D418yes—
1217C23—22no—
1218C23—21no—
1219C23—22no—
1220C23—22no—
1221C23—21no—
1222C23—24no—
1223C23—24no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—24no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—24no—
1232C23—28no—
1233C23—24no—
1234C23—22no—
1235C23—24no—
1236C23—22no—
1237C23—24no—
1238C23—28no—
1239C23—24no—
1240C23C23×D412yes—
1241C23C23×D414yes—
1242C23C2611yescharacteristic
1243Q8—28no—
1244Q8—28no—
1245Q8—416no—
1246Q8—48no—
1247Q8—48no—
1248Q8—48no—
1249Q8—44no—
1250D4—28no—
1251D4—48no—
1252D4—48no—
1253D4—416no—
1254D4—416no—
1255D4—48no—
1256D4—44no—
1257D4—44no—
1258D4—48no—
1259D4—84no—
1260D4—88no—
1261D4—88no—
1262D4—84no—
1263D4—88no—
1264D4—88no—
1265D4—88no—
1266D4—816no—
1267D4—88no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—28no—
1280C2×C4—216no—
1281C2×C4—28no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—28no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—48no—
1320C2×C4—44no—
1321C2×C4—48no—
1322C2×C4—48no—
1323C2×C4—416no—
1324C2×C4—48no—
1325C2×C4—416no—
1326C2×C4—416no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—88no—
1332C2×C4—88no—
1333C2×C4C23×D412yes—
1334C2×C4C23×D414yes—
1335C2×C4C23×D412yes—
1336C2×C4C23×D414yes—
1337C2×C4C23×D412yes—
1338C2×C4C23×D412yes—
1339C2×C4C23×D414yes—
1340C2×C4C23×D412yes—
1341C2×C4C23×D412yes—
1342C2×C4C2×H(5,𝔽2)14yes—
1343C2×C4C2×H(5,𝔽2)12yes—
1344C2×C4#58514yes—
1345C2×C4#58512yes—
1346C22—24no—
1347C22—22no—
1348C22—24no—
1349C22—22no—
1350C22—22no—
1351C22—24no—
1352C22—42no—
1353C22—44no—
1354C22—42no—
1355C22—44no—
1356C22—42no—
1357C22—42no—
1358C22—44no—
1359C22—42no—
1360C22—44no—
1361C22—42no—
1362C22—44no—
1363C22—48no—
1364C22—44no—
1365C22—44no—
1366C22—42no—
1367C22—42no—
1368C22—44no—
1369C22—44no—
1370C22—48no—
1371C22C24×D411yescharacteristic
1372C22C22×H(5,𝔽2)11yescharacteristic
1373C22C2×#58511yescharacteristic
1374C22C2×#58512yes—
1375C222−1+612yes—
1376C4—22no—
1377C4—24no—
1378C4—24no—
1379C4—22no—
1380C4—22no—
1381C4—24no—
1382C4—22no—
1383C4—24no—
1384C4—44no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—44no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4#344914yes—
1399C4#348814yes—
1400C2—44no—
1401C2—42no—
1402C2—82no—
1403C2—84no—
1404C2—82no—
1405C2C2×#344911yescharacteristic
1406C2C2×#348811yescharacteristic
1407C2#6285911yescharacteristic
1408C2#6292212yes—
1409C2#6296712yes—
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×#3517C2semidirect
2. C2×#3482C2semidirect
3. #42928C2semidirect
4. #42927C2semidirect
5. #41996C2semidirect
6. #39747C2semidirect
7. #39744C2semidirect
8. #39363C2semidirect
9. #39360C2semidirect
10. #39174C2semidirect
11. #39170C2semidirect
12. #38956C2semidirect
13. #38951C2semidirect
14. #38093C2semidirect
15. #38088C2semidirect
16. #37683C2semidirect
17. #37680C2semidirect
18. #37544C2semidirect
19. #37542C2semidirect
20. #36964C2semidirect
21. #35526C2semidirect
22. #35298C2semidirect
23. #35246C2semidirect
24. #35241C2semidirect
25. #35178C2semidirect
26. #35156C2semidirect
27. #34937C2semidirect
28. #34910C2semidirect
29. #34060C2semidirect
343. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34822
#429282
#429272
#419962
#397472
#397442
#393632
#393602
#391742
#391702
#389562
#389512
#380932
#380882
#376832
#376802
#375442
#375422
#369642
#355262
#352982
#352462
#352412
#351782
#351562
#349372
#349102
#340602