Finite Group Databasebeta

← #7712439

Subgroups — #7712439

Order 512.

6784 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic, complemented
2C2×#3554C211yesmaximal, characteristic, complemented
3#59586C214yesmaximal, complemented
4#59417C214yesmaximal, complemented
5#45489C218yesmaximal, complemented
6#39439C214yesmaximal, complemented
7#39436C214yesmaximal, complemented
8#39394C218yesmaximal, complemented
9#39173C211yesmaximal, characteristic, complemented
10#39171C211yesmaximal, characteristic, complemented
11#38958C211yesmaximal, characteristic, complemented
12#38956C211yesmaximal, characteristic, complemented
13#38095C212yesmaximal, complemented
14#38092C212yesmaximal, complemented
15#37635C211yesmaximal, characteristic, complemented
16#37618C211yesmaximal, characteristic, complemented
17#37423C212yesmaximal, complemented
18#37422C212yesmaximal, complemented
19#36639C211yesmaximal, characteristic, complemented
20#36639C211yesmaximal, characteristic, complemented
21#36496C211yesmaximal, characteristic, complemented
22#36446C211yesmaximal, characteristic, complemented
23#36415C212yesmaximal, complemented
24#36412C211yesmaximal, characteristic, complemented
25#36396C212yesmaximal, complemented
26#36303C211yesmaximal, characteristic, complemented
27#35312C212yesmaximal, complemented
28#35276C212yesmaximal, complemented
29C4×#529C211yesmaximal, characteristic, complemented
30#3554—216no—
31#3547—216no—
32C2×#562C2214yes—
33C2×#562C2214yes—
34C2×#559C2211yescharacteristic
35C2×#559C2212yes—
36C2×#557C2211yescharacteristic
37C2×#555C2211yescharacteristic
38C2×#555C2212yes—
39C2×#554C2211yescharacteristic
40C2×#554C2212yes—
41C2×#553C2212yes—
42C2×#552C2212yes—
43C2×#550C2211yescharacteristic
44C2×D4×Q8C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2212yes—
48C2×#547C2212yes—
49C2×#547C2211yescharacteristic
50C2×#544C2212yes—
51C2×#542C2212yes—
52C2×#542C2212yes—
53C2×#542C2214yes—
54C2×#540C2212yes—
55C2×#540C2212yes—
56C2×#539C2214yes—
57C2×#537C2212yes—
58C2×#536C2212yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#532C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#529C2211yescharacteristic
65#2862C2211yescharacteristic
66#2862C2211yescharacteristic
67#2862C2211yescharacteristic
68#2862C2211yescharacteristic
69#2862C2212yes—
70#2861C2212yes—
71#2861C2212yes—
72#2861C2214yes—
73#2861C2212yes—
74#2858C2211yescharacteristic
75#2858C2211yescharacteristic
76#2858C2211yescharacteristic
77#2858C2211yescharacteristic
78#2856C2212yes—
79#2850C2214yes—
80#2850C2211yescharacteristic
81#2850C2211yescharacteristic
82#2850C2214yes—
83#2850C2214yes—
84#2850C2211yescharacteristic
85#2850C2211yescharacteristic
86#2850C2212yes—
87#2817C2214yes—
88#2815C2214yes—
89#2716C2218yes—
90#2712C2218yes—
91#2703C2218yes—
92#2703C2218yes—
93#2703C2218yes—
94#2700C2218yes—
95#2700C2218yes—
96#2696C2218yes—
97#2696C2218yes—
98#2696C2218yes—
99#2693C2218yes—
100#2690C2218yes—
101#2690C2218yes—
102#2688C2218yes—
103#2688C2218yes—
104#2687C2218yes—
105#2660C2212yes—
106#2657C2212yes—
107#2642C2212yes—
108#2642C2212yes—
109#2640C2212yes—
110#2640C2212yes—
111#2634C2214yes—
112#2631C2214yes—
113#2625C2214yes—
114#2620C2212yes—
115#2619C2212yes—
116#2615C2214yes—
117#2581C2214yes—
118#2568C2211yescharacteristic
119#2568C2211yescharacteristic
120#2568C2212yes—
121#2567C2211yescharacteristic
122#2567C2211yescharacteristic
123#2566C2212yes—
124#2565C2212yes—
125#2563C2212yes—
126#2560C2218yes—
127#2557C2218yes—
128#2557C2218yes—
129#2557C2218yes—
130#2555C2218yes—
131#2555C2218yes—
132#2554C2218yes—
133#2547C2212yes—
134#2547C2211yescharacteristic
135#2547C2212yes—
136#2547C2211yescharacteristic
137#2544C2212yes—
138#2544C2212yes—
139#2543C2218yes—
140#2541C2211yescharacteristic
141#2541C2211yescharacteristic
142#2535C2218yes—
143#2535C2214yes—
144#2504C2212yes—
145#2503C2212yes—
146#2500C2212yes—
147#2499C2212yes—
148#2499C2212yes—
149#2499C2212yes—
150#2492C2214yes—
151#2492C2218yes—
152#2489C2214yes—
153#2489C2218yes—
154#2489C2218yes—
155#2488C2218yes—
156#2488C2218yes—
157#2488C2218yes—
158#2481C2218yes—
159#2477C2218yes—
160#2464C2218yes—
161#2461C2218yes—
162#2461C2218yes—
163#2459C2218yes—
164#2457C2218yes—
165#2442C2214yes—
166#2439C2214yes—
167#2436C2214yes—
168#2436C2212yes—
169#2436C2212yes—
170#2431C2214yes—
171#2431C2212yes—
172#2431C2212yes—
173#2431C2212yes—
174#2431C2212yes—
175#2428C2214yes—
176#2427C2214yes—
177#2427C2214yes—
178#2426C2214yes—
179#2421C2214yes—
180#2420C2214yes—
181#2364C2218yes—
182#2363C2214yes—
183#2361C2214yes—
184#2352C2218yes—
185Q8×C22⋊C4C2214yes—
186#2339C2214yes—
187#2328C2212yes—
188#2326C2212yes—
189#2311C2212yes—
190#2310C2212yes—
191C4×#127C2212yes—
192C4×#125C2212yes—
193C4×#126C2214yes—
194C4×#124C2211yescharacteristic
195C4×#124C2211yescharacteristic
196C4×#124C2212yes—
197C4×#124C2214yes—
198C4×#124C2214yes—
199C4×#124C2211yescharacteristic
200C4×#124C2211yescharacteristic
201C4×#124C2214yes—
202C4×#124C2212yes—
203C4×C22⋊Q8C2212yes—
204C4×#123C2214yes—
205C4×#121C2212yes—
206#2298C2212yes—
207#2297C2214yes—
208#2297C2212yes—
209#2297C2212yes—
210#2297C2212yes—
211#2295C2211yescharacteristic
212C2×#391C2212yes—
213#2293C2211yescharacteristic
214#2290C2212yes—
215#2283C2211yescharacteristic
216C42×Q8C2211yescharacteristic
217C42×D4C2212yes—
218C42×D4C2211yescharacteristic
219C4×#117C2212yes—
220C2×C43C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227#562—232no—
228#562—232no—
229#559—216no—
230#559—28no—
231#557—28no—
232#555—216no—
233#555—28no—
234#554—216no—
235#554—28no—
236#553—216no—
237#552—216no—
238#550—28no—
239D4×Q8—28no—
240D4×Q8—28no—
241#548—216no—
242#548—216no—
243#547—28no—
244#547—216no—
245#544—216no—
246#542—232no—
247#542—216no—
248#542—216no—
249#540—216no—
250#540—216no—
251#539—232no—
252#537—216no—
253#536—216no—
254#536—216no—
255#533—28no—
256#533—28no—
257#532—28no—
258#532—28no—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2312yes—
273C2×#127C2312yes—
274#529D4116yescomplemented
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2311yescharacteristic
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2311yescharacteristic
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2311yescharacteristic
300C2×#124C2314yes—
301C2×#124C2314yes—
302C2×#124C2312yes—
303C2×#124C2311yescharacteristic
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2314yes—
314C2×#123C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2311yescharacteristic
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2311yescharacteristic
334C2×#121C2312yes—
335C2×#121C2311yescharacteristic
336C2×#121C2311yescharacteristic
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2312yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2318yes—
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2311yescharacteristic
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2318yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2314yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2314yes—
390C22×C4⋊C4C2312yes—
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393C22×C42C2311yescharacteristic
394C22×C42C2312yes—
395C22×C42C2312yes—
396C22×C42C2311yescharacteristic
397#400C2314yes—
398#400C2314yes—
399#400C2318yes—
400#400C2318yes—
401#400C2318yes—
402#400C2318yes—
403#400C2318yes—
404#400C2318yes—
405#398C2318yes—
406#398C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#397C2314yes—
411#397C2314yes—
412#397C2318yes—
413#397C2318yes—
414#397C2318yes—
415#397C2318yes—
416#397C2318yes—
417#396C2318yes—
418#396C2318yes—
419#395C2314yes—
420#395C2314yes—
421#395C2318yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#393C2318yes—
428#393C2318yes—
429#393C2318yes—
430#393C2318yes—
431#393C2318yes—
432#392C2318yes—
433#392C2318yes—
434#392C2318yes—
435#392C2318yes—
436#392C2314yes—
437#392C2314yes—
438#392C2318yes—
439#392C2318yes—
440#392C2318yes—
441#391C2318yes—
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2318yes—
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2318yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2314yes—
462#391C2314yes—
463#391C2318yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#390C2318yes—
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2318yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2311yescharacteristic
478#390C2311yescharacteristic
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2318yes—
494#388C2318yes—
495#388C2318yes—
496#388C2314yes—
497#388C2318yes—
498#388C2314yes—
499#388C2318yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2318yes—
505#388C2318yes—
506#388C2314yes—
507#388C2318yes—
508#388C2318yes—
509#388C2318yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2318yes—
515#387C2314yes—
516#387C2318yes—
517#387C2318yes—
518#387C2318yes—
519#386C2318yes—
520#386C2318yes—
521#386C2318yes—
522#386C2318yes—
523#386C2314yes—
524#386C2318yes—
525#386C2314yes—
526#386C2314yes—
527#386C2318yes—
528#386C2314yes—
529#386C2318yes—
530#386C2318yes—
531#386C2318yes—
532#386C2318yes—
533#386C2318yes—
534#386C2318yes—
535#386C2318yes—
536#386C2318yes—
537#386C2318yes—
538#386C2318yes—
539#386C2314yes—
540#385C2318yes—
541#385C2318yes—
542#385C2314yes—
543#384C2312yes—
544#384C2312yes—
545#383C2312yes—
546#382C2312yes—
547#382C2311yescharacteristic
548#382C2312yes—
549#382C2311yescharacteristic
550#382C2311yescharacteristic
551#382C2311yescharacteristic
552#382C2312yes—
553#382C2314yes—
554#382C2314yes—
555#382C2314yes—
556#382C2318yes—
557#381C2312yes—
558#381C2318yes—
559#381C2318yes—
560#380C2318yes—
561#380C2318yes—
562#380C2314yes—
563#380C2314yes—
564#380C2318yes—
565#380C2318yes—
566#380C2312yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2311yescharacteristic
577C4×C22⋊C4C2314yes—
578C4×C22⋊C4C2314yes—
579C4×C22⋊C4C2314yes—
580C4×C22⋊C4C2318yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2318yes—
584C4×C22⋊C4C2318yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
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—
598C43C2312yes—
599C43C2311yescharacteristic
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—28no—
606C2×#41—28no—
607C2×#41—48no—
608C2×#41—44no—
609C2×#41—44no—
610C2×#41—44no—
611C2×#41—44no—
612C2×#41—48no—
613C22×Q8—28no—
614C22×Q8—28no—
615C22×Q8—44no—
616C22×Q8—44no—
617C22×Q8—48no—
618C22×Q8C2412yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2411yescharacteristic
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×D4C2412yes—
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2412yes—
632C22×D4C2411yescharacteristic
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2412yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2418yes—
644C22×D4C2418yes—
645C22×D4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C4⋊Q8—216no—
663C4⋊Q8—28no—
664C4⋊Q8—24no—
665C4⋊Q8—24no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—24no—
669C4⋊Q8—24no—
670C4⋊Q8—28no—
671C4⋊Q8—28no—
672#127—28no—
673#127—24no—
674#127—24no—
675#127—44no—
676#127—44no—
677#126—216no—
678#126—216no—
679#126C2×D4116yes—
680#125—216no—
681#125—28no—
682#125—216no—
683#125—28no—
684#125—28no—
685#125—28no—
686#125C2×D418yes—
687#124—28no—
688#124—216no—
689#124—216no—
690#124—216no—
691#124—216no—
692#124—216no—
693#124—28no—
694#124—28no—
695#124—28no—
696#124—48no—
697#124—48no—
698#124—48no—
699#124—42no—
700#124—42no—
701#124—42no—
702#124—42no—
703#124—44no—
704#124—44no—
705#124C2×D418yes—
706#123—216no—
707#123—216no—
708#123—216no—
709#123—216no—
710#123—216no—
711#123—216no—
712#123—216no—
713#123—216no—
714#123—216no—
715#123—216no—
716#123C2×D4116yes—
717C22⋊Q8—28no—
718C22⋊Q8—28no—
719C22⋊Q8—24no—
720C22⋊Q8—24no—
721C22⋊Q8—28no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C22⋊Q8—216no—
725C22⋊Q8—28no—
726C22⋊Q8—216no—
727C22⋊Q8—28no—
728C22⋊Q8—216no—
729C22⋊Q8—216no—
730C22⋊Q8—216no—
731C22⋊Q8—216no—
732C22⋊Q8—216no—
733C22⋊Q8—216no—
734C22⋊Q8—216no—
735C22⋊Q8C2×D418yes—
736#121—28no—
737#121—216no—
738#121—216no—
739#121—216no—
740#121—216no—
741#121—28no—
742#121—24no—
743#121—24no—
744#121—28no—
745#121—28no—
746#121—28no—
747#121—28no—
748#121—28no—
749#121—216no—
750#121—216no—
751#121—216no—
752#121—416no—
753#121—48no—
754#121—48no—
755#121C2×D418yes—
756C4×Q8—28no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—44no—
764C4×Q8C2×D418yes—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—216no—
769C4×D4—216no—
770C4×D4—28no—
771C4×D4—24no—
772C4×D4—28no—
773C4×D4—24no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—28no—
777C4×D4—28no—
778C4×D4—416no—
779C4×D4—44no—
780C4×D4—48no—
781C4×D4C2×D4116yes—
782C4×D4C2×D418yes—
783#117—28no—
784#117—28no—
785#117—28no—
786#117—28no—
787#117—216no—
788#117—44no—
789#117C2×D4116yes—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—216no—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2418yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2418yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2418yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2418yes—
865C2×C22⋊C4C2418yes—
866C2×C22⋊C4C2418yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C42—42no—
879C2×C42—44no—
880C2×C42—42no—
881C2×C42—44no—
882C2×C42—44no—
883C2×C42C2×D418yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913#95C2414yes—
914#95C2418yes—
915#95C2418yes—
916#95C2418yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2418yes—
931#95C2418yes—
932#95C2414yes—
933#95C2414yes—
934#95C2418yes—
935#95C2414yes—
936#95C2418yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2418yes—
941#95C2418yes—
942#95C2418yes—
943#95C2418yes—
944C24C2512yes—
945C24C2514yes—
946C24C2512yes—
947C24C2511yescharacteristic
948C24C2512yes—
949#41—816no—
950#41—816no—
951#41—816no—
952#41—816no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—22no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—28no—
960C2×Q8—28no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—28no—
968C2×Q8—22no—
969C2×Q8—22no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×Q8—48no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—816no—
977C2×Q8—816no—
978C2×Q8C22×D414yes—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—28no—
983C2×D4—28no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—44no—
1002C2×D4—48no—
1003C2×D4—48no—
1004C2×D4—48no—
1005C2×D4—48no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—48no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—48no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—48no—
1018C2×D4—48no—
1019C2×D4—48no—
1020C2×D4C22×D414yes—
1021C2×D4C22×D418yes—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—48no—
1049C22×C4—48no—
1050C22×C4—48no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—48no—
1058C22×C4C22×D414yes—
1059C22×C4C22×D414yes—
1060C22×C4C22×D418yes—
1061C22×C4C22×D414yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—22no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—48no—
1119C4⋊C4—44no—
1120C4⋊C4—48no—
1121C4⋊C4C22×D418yes—
1122C4⋊C4C22×D414yes—
1123C4⋊C4C22×D414yes—
1124C4⋊C4C22×D418yes—
1125C4⋊C4C22×D418yes—
1126C4⋊C4C22×D418yes—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—24no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—216no—
1148C22⋊C4—28no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—48no—
1154C22⋊C4—48no—
1155C22⋊C4—44no—
1156C22⋊C4—48no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—48no—
1161C22⋊C4—48no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—48no—
1165C22⋊C4—48no—
1166C22⋊C4C22×D418yes—
1167C22⋊C4C22×D418yes—
1168C22⋊C4C22×D418yes—
1169C22⋊C4C22×D418yes—
1170C22⋊C4C22×D418yes—
1171C42—28no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—28no—
1176C42—22no—
1177C42—22no—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—22no—
1182C42—22no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—28no—
1187C42—42no—
1188C42—44no—
1189C42—42no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—42no—
1194C42—44no—
1195C42C22×D414yes—
1196C42C22×D414yes—
1197C42C22×D414yes—
1198C42C22×D414yes—
1199C42C22×D418yes—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—24no—
1204C23—22no—
1205C23—21no—
1206C23—22no—
1207C23—21no—
1208C23—22no—
1209C23—22no—
1210C23—24no—
1211C23—24no—
1212C23—28no—
1213C23—24no—
1214C23—22no—
1215C23—22no—
1216C23—28no—
1217C23—22no—
1218C23—22no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23C23×D412yes—
1224C23C23×D414yes—
1225C23C2611yescharacteristic
1226Q8—28no—
1227Q8—44no—
1228Q8—48no—
1229Q8—48no—
1230Q8—44no—
1231Q8—84no—
1232Q8—84no—
1233Q8—88no—
1234Q8—88no—
1235Q8—84no—
1236D4—28no—
1237D4—48no—
1238D4—44no—
1239D4—44no—
1240D4—48no—
1241D4—48no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—88no—
1246D4—88no—
1247D4—84no—
1248D4—84no—
1249D4—88no—
1250D4—88no—
1251D4—88no—
1252D4—816no—
1253D4—168no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—216no—
1266C2×C4—28no—
1267C2×C4—28no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—28no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—28no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—48no—
1307C2×C4—48no—
1308C2×C4—48no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—88no—
1312C2×C4—88no—
1313C2×C4—88no—
1314C2×C4—88no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4C23×D412yes—
1318C2×C4C23×D414yes—
1319C2×C4C23×D414yes—
1320C2×C4C23×D412yes—
1321C2×C4C23×D412yes—
1322C2×C4C23×D412yes—
1323C2×C4C23×D414yes—
1324C2×C4C23×D412yes—
1325C2×C4C23×D412yes—
1326C2×C4#58514yes—
1327C2×C4#58512yes—
1328C2×C4#58512yes—
1329C2×C4#58514yes—
1330C22—24no—
1331C22—22no—
1332C22—22no—
1333C22—24no—
1334C22—22no—
1335C22—24no—
1336C22—42no—
1337C22—44no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—48no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—42no—
1347C22—42no—
1348C22—44no—
1349C22—42no—
1350C22—44no—
1351C22—42no—
1352C22—44no—
1353C22—48no—
1354C22—44no—
1355C22C24×D411yescharacteristic
1356C22C2×#58511yescharacteristic
1357C22C2×#58512yes—
1358C22C2×#58512yes—
1359C22C2×#58511yescharacteristic
1360C4—22no—
1361C4—24no—
1362C4—22no—
1363C4—24no—
1364C4—22no—
1365C4—22no—
1366C4—24no—
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—44no—
1382C4#350014yes—
1383C4#350014yes—
1384C2—44no—
1385C2—42no—
1386C2—82no—
1387C2—84no—
1388C2—82no—
1389C2#6276212yes—
1390C2C2×#350011yescharacteristic
1391C2C2×#350011yescharacteristic
1392C2#6281211yescharacteristic
1393C2#6282712yes—
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×#3547C2semidirect
2. C2×#3554C2semidirect
3. #59586C2semidirect
4. #59417C2semidirect
5. #45489C2semidirect
6. #39439C2semidirect
7. #39436C2semidirect
8. #39394C2semidirect
9. #39173C2semidirect
10. #39171C2semidirect
11. #38958C2semidirect
12. #38956C2semidirect
13. #38095C2semidirect
14. #38092C2semidirect
15. #37635C2semidirect
16. #37618C2semidirect
17. #37423C2semidirect
18. #37422C2semidirect
19. #36639C2semidirect
20. #36639C2semidirect
21. #36496C2semidirect
22. #36446C2semidirect
23. #36415C2semidirect
24. #36412C2semidirect
25. #36396C2semidirect
26. #36303C2semidirect
27. #35312C2semidirect
28. #35276C2semidirect
29. C4×#529C2semidirect
274. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
C2×#35542
#595862
#594172
#454892
#394392
#394362
#393942
#391732
#391712
#389582
#389562
#380952
#380922
#376352
#376182
#374232
#374222
#366392
#364962
#364462
#364152
#364122
#363962
#363032
#353122
#352762
C4×#5292