Finite Group Databasebeta

← #7720512

Subgroups — #7720512

Order 512.

6332 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C211yesmaximal, characteristic, complemented
2C2×#3552C211yesmaximal, characteristic
3#51331C218yesmaximal, complemented
4#50869C218yesmaximal, complemented
5#45343C214yesmaximal, complemented
6#45322C214yesmaximal, complemented
7#45144C214yesmaximal, complemented
8#45095C214yesmaximal, complemented
9#39619C211yesmaximal, characteristic, complemented
10#39616C211yesmaximal, characteristic, complemented
11#39490C211yesmaximal, characteristic, complemented
12#39490C212yesmaximal, complemented
13#39488C211yesmaximal, characteristic, complemented
14#39485C212yesmaximal, complemented
15#37870C212yesmaximal, complemented
16#37865C212yesmaximal, complemented
17#37423C212yesmaximal, complemented
18#37392C212yesmaximal, complemented
19#36560C211yesmaximal, characteristic, complemented
20Q8×#124C211yesmaximal, characteristic, complemented
21#36188C211yesmaximal, characteristic, complemented
22#36164C211yesmaximal, characteristic, complemented
23#35330C212yesmaximal, complemented
24#35320C211yesmaximal, characteristic, complemented
25#35318C212yesmaximal, complemented
26#35281C211yesmaximal, characteristic, complemented
27#35201C211yesmaximal, characteristic, complemented
28#34631C211yesmaximal, characteristic, complemented
29#34151C211yesmaximal, characteristic, complemented
30#3555—216no—
31#3552—216no—
32C2×#563C2214yes—
33C2×#563C2214yes—
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2212yes—
37C2×#557C2211yescharacteristic
38C2×#556C2211yescharacteristic
39C2×#556C2211yescharacteristic
40C2×#556C2212yes—
41C2×#556C2212yes—
42C2×#554C2212yes—
43C2×#554C2211yescharacteristic
44C2×#553C2212yes—
45C2×#552C2212yes—
46C2×D4×Q8C2212yes—
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2212yes—
49C2×#547C2211yescharacteristic
50C2×#544C2212yes—
51C2×#544C2212yes—
52C2×#542C2212yes—
53C2×#542C2212yes—
54C2×#541C2212yes—
55C2×#541C2212yes—
56C2×#541C2212yes—
57C2×#541C2214yes—
58C2×#539C2214yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C22×C4⋊Q8C2211yescharacteristic
63C2×#529C2211yescharacteristic
64C2×#529C2211yescharacteristic
65#2868C2211yescharacteristic
66#2868C2211yescharacteristic
67#2862C2212yes—
68#2862C2212yes—
69#2862C2212yes—
70#2862C2211yescharacteristic
71#2862C2211yescharacteristic
72#2861C2212yes—
73#2859C2212yes—
74#2859C2212yes—
75#2857C2212yes—
76#2850C2212yes—
77#2725C2218yes—
78#2720C2218yes—
79#2719C2218yes—
80#2719C2218yes—
81#2718C2218yes—
82#2716C2218yes—
83#2713C2218yes—
84#2713C2218yes—
85#2701C2218yes—
86#2700C2218yes—
87#2698C2218yes—
88#2698C2218yes—
89#2695C2218yes—
90#2690C2218yes—
91#2689C2218yes—
92#2689C2218yes—
93#2689C2218yes—
94#2689C2218yes—
95#2687C2218yes—
96#2686C2218yes—
97#2664C2214yes—
98#2663C2214yes—
99#2663C2214yes—
100#2660C2211yescharacteristic
101#2660C2212yes—
102#2660C2212yes—
103#2660C2212yes—
104#2660C2212yes—
105#2658C2211yescharacteristic
106#2642C2211yescharacteristic
107#2642C2214yes—
108#2640C2211yescharacteristic
109#2621C2211yescharacteristic
110#2621C2212yes—
111#2621C2211yescharacteristic
112#2620C2211yescharacteristic
113#2620C2212yes—
114#2620C2211yescharacteristic
115#2604C2214yes—
116#2568C2212yes—
117#2568C2214yes—
118#2568C2212yes—
119#2568C2211yescharacteristic
120#2568C2211yescharacteristic
121#2568C2211yescharacteristic
122#2568C2211yescharacteristic
123#2568C2211yescharacteristic
124#2567C2212yes—
125#2567C2211yescharacteristic
126#2567C2214yes—
127#2566C2212yes—
128#2565C2212yes—
129#2565C2212yes—
130#2565C2212yes—
131#2563C2212yes—
132#2563C2211yescharacteristic
133#2556C2218yes—
134#2553C2218yes—
135#2550C2218yes—
136#2550C2218yes—
137#2549C2218yes—
138#2549C2218yes—
139#2547C2214yes—
140#2546C2214yes—
141#2546C2214yes—
142#2542C2211yescharacteristic
143#2521C2218yes—
144#2519C2218yes—
145#2506C2218yes—
146#2504C2212yes—
147#2503C2212yes—
148#2503C2212yes—
149#2503C2212yes—
150#2503C2212yes—
151#2503C2214yes—
152#2502C2212yes—
153#2502C2214yes—
154#2500C2212yes—
155#2500C2212yes—
156#2499C2212yes—
157#2499C2212yes—
158#2499C2212yes—
159#2499C2212yes—
160#2496C2218yes—
161#2492C2214yes—
162#2492C2218yes—
163#2489C2214yes—
164#2488C2218yes—
165#2470C2218yes—
166#2469C2218yes—
167#2468C2218yes—
168#2466C2218yes—
169#2453C2214yes—
170#2453C2218yes—
171#2451C2214yes—
172#2447C2214yes—
173#2447C2218yes—
174#2446C2214yes—
175#2438C2218yes—
176#2434C2214yes—
177#2434C2214yes—
178#2432C2214yes—
179#2429C2214yes—
180#2429C2214yes—
181#2419C2218yes—
182#2415C2214yes—
183#2396C2214yes—
184#2395C2214yes—
185#2374C2214yes—
186#2373C2214yes—
187#2370C2212yes—
188#2367C2212yes—
189#2365C2214yes—
190#2365C2214yes—
191#2363C2212yes—
192#2362C2212yes—
193Q8×C22⋊C4C2214yes—
194#2339C2214yes—
195#2327C2212yes—
196#2326C2212yes—
197#2323C2214yes—
198#2317C2212yes—
199#2317C2212yes—
200#2317C2212yes—
201#2317C2212yes—
202#2310C2214yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×C4⋊Q8C2212yes—
205C4×C4⋊Q8C2211yescharacteristic
206C4×#124C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2211yescharacteristic
209#2298C2212yes—
210#2295C2211yescharacteristic
211#2293C2212yes—
212#2293C2211yescharacteristic
213#2290C2212yes—
214#2285C2212yes—
215C2×#382C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2212yes—
219C4×#117C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C23×Q8C2312yes—
223C23×Q8C2312yes—
224#563—232no—
225#563—232no—
226Q82—28no—
227#557—216no—
228#557—28no—
229#557—28no—
230#556—216no—
231#556—28no—
232#556—216no—
233#556—28no—
234#554—216no—
235#554—28no—
236#553—216no—
237#552—216no—
238D4×Q8—216no—
239D4×Q8—28no—
240#548—216no—
241#547—28no—
242#544—216no—
243#544—216no—
244#542—216no—
245#542—216no—
246#541—232no—
247#541—216no—
248#541—216no—
249#541—216no—
250#539—232no—
251#536—216no—
252#533—28no—
253#533—28no—
254C2×C4⋊Q8—28no—
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276#529—28no—
277#529D4116yes—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#126C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2311yescharacteristic
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#125C2314yes—
298C2×#125C2314yes—
299C2×#125C2312yes—
300C2×#125C2314yes—
301C2×#125C2314yes—
302C2×#125C2314yes—
303C2×#125C2311yescharacteristic
304C2×#124C2311yescharacteristic
305C2×#124C2311yescharacteristic
306C2×#124C2311yescharacteristic
307C2×#124C2312yes—
308C2×#124C2314yes—
309C2×#124C2312yes—
310C2×#124C2314yes—
311C2×#124C2311yescharacteristic
312C2×#123C2312yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2311yescharacteristic
340C2×#121C2312yes—
341C2×#121C2311yescharacteristic
342C2×#121C2314yes—
343C2×#121C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2314yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×#117C2312yes—
371C2×#117C2311yescharacteristic
372C2×#117C2312yes—
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C42C2312yes—
386C22×C42C2311yescharacteristic
387#400C2314yes—
388#400C2314yes—
389#400C2318yes—
390#400C2318yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2318yes—
395#400C2318yes—
396#400C2314yes—
397#400C2314yes—
398#400C2318yes—
399#400C2318yes—
400#399C2314yes—
401#399C2314yes—
402#399C2314yes—
403#398C2318yes—
404#398C2318yes—
405#398C2318yes—
406#398C2314yes—
407#398C2314yes—
408#398C2318yes—
409#398C2314yes—
410#398C2318yes—
411#398C2318yes—
412#398C2318yes—
413#398C2318yes—
414#398C2318yes—
415#397C2314yes—
416#397C2314yes—
417#397C2318yes—
418#397C2314yes—
419#397C2318yes—
420#397C2318yes—
421#397C2318yes—
422#397C2318yes—
423#397C2318yes—
424#396C2318yes—
425#396C2314yes—
426#396C2314yes—
427#396C2318yes—
428#395C2314yes—
429#395C2318yes—
430#395C2318yes—
431#395C2318yes—
432#395C2314yes—
433#395C2318yes—
434#395C2318yes—
435#394C2314yes—
436#394C2314yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#393C2314yes—
441#393C2318yes—
442#393C2314yes—
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2318yes—
455#391C2318yes—
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2314yes—
464#391C2318yes—
465#391C2318yes—
466#391C2318yes—
467#391C2314yes—
468#391C2318yes—
469#391C2314yes—
470#391C2318yes—
471#391C2312yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2318yes—
481#389C2318yes—
482#389C2318yes—
483#389C2314yes—
484#389C2318yes—
485#389C2318yes—
486#389C2318yes—
487#389C2318yes—
488#389C2318yes—
489#389C2318yes—
490#389C2318yes—
491#389C2318yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2318yes—
509#388C2318yes—
510#387C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2318yes—
514#387C2318yes—
515#387C2318yes—
516#387C2314yes—
517#387C2318yes—
518#387C2318yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2318yes—
523#386C2318yes—
524#386C2318yes—
525#386C2314yes—
526#385C2318yes—
527#385C2318yes—
528#385C2318yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2314yes—
533#385C2318yes—
534#384C2311yescharacteristic
535#384C2312yes—
536#384C2311yescharacteristic
537#384C2312yes—
538#384C2312yes—
539#384C2312yes—
540#384C2312yes—
541#384C2314yes—
542#384C2314yes—
543#384C2312yes—
544#382C2312yes—
545#382C2312yes—
546#382C2312yes—
547#382C2312yes—
548#382C2312yes—
549#382C2312yes—
550#382C2312yes—
551#382C2312yes—
552#382C2318yes—
553#382C2311yescharacteristic
554#382C2312yes—
555#382C2312yes—
556#382C2311yescharacteristic
557#382C2318yes—
558#381C2318yes—
559#381C2318yes—
560#381C2318yes—
561#381C2318yes—
562#380C2314yes—
563#380C2318yes—
564#380C2318yes—
565#380C2318yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2318yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2311yescharacteristic
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2311yescharacteristic
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2318yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2318yes—
585C4×C22⋊C4C2312yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594#376C2312yes—
595#376C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598C2×#95C2318yes—
599C43C2312yes—
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—28no—
604C2×#41—48no—
605C22×Q8—28no—
606C22×Q8—28no—
607C22×Q8—48no—
608C22×Q8—48no—
609C22×Q8C2412yes—
610C22×Q8C2411yescharacteristic
611C22×Q8C2411yescharacteristic
612C22×Q8C2411yescharacteristic
613C22×Q8C2412yes—
614C22×Q8C2412yes—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2414yes—
619C22×Q8C2414yes—
620C22×Q8C2414yes—
621C22×D4C2411yescharacteristic
622C22×D4C2411yescharacteristic
623C22×D4C2412yes—
624C22×D4C2414yes—
625C22×D4C2412yes—
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2411yescharacteristic
629C23×C4C2411yescharacteristic
630C23×C4C2414yes—
631C23×C4C2414yes—
632C23×C4C2414yes—
633C23×C4C2414yes—
634C23×C4C2414yes—
635C23×C4C2411yescharacteristic
636C4⋊Q8—28no—
637C4⋊Q8—28no—
638C4⋊Q8—216no—
639C4⋊Q8—28no—
640C4⋊Q8—216no—
641C4⋊Q8—216no—
642C4⋊Q8—28no—
643C4⋊Q8—28no—
644C4⋊Q8—24no—
645C4⋊Q8—24no—
646C4⋊Q8—28no—
647C4⋊Q8—24no—
648C4⋊Q8—24no—
649C4⋊Q8—24no—
650C4⋊Q8—24no—
651C4⋊Q8—28no—
652C4⋊Q8—28no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655C4⋊Q8—48no—
656C4⋊Q8—48no—
657#126—216no—
658#126—216no—
659#126—216no—
660#126—216no—
661#126—216no—
662#126—216no—
663#126—216no—
664#126—216no—
665#126—216no—
666#126—28no—
667#126C2×D4116yes—
668#125—216no—
669#125—216no—
670#125—216no—
671#125—216no—
672#125—216no—
673#125—28no—
674#125—216no—
675#125—216no—
676#125—216no—
677#125—24no—
678#125—28no—
679#125—28no—
680#125—28no—
681#125—28no—
682#125C2×D418yes—
683#124—28no—
684#124—28no—
685#124—216no—
686#124—216no—
687#124—24no—
688#124—24no—
689#124—24no—
690#124C2×D418yes—
691#123—216no—
692#123—28no—
693#123—216no—
694#123—216no—
695#123—216no—
696#123C2×D4116yes—
697C22⋊Q8—24no—
698C22⋊Q8—28no—
699C22⋊Q8—24no—
700C22⋊Q8—24no—
701C22⋊Q8—28no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—28no—
705C22⋊Q8—28no—
706C22⋊Q8—216no—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—216no—
715C22⋊Q8—216no—
716C22⋊Q8—216no—
717C22⋊Q8—48no—
718C22⋊Q8C2×D418yes—
719#121—216no—
720#121—24no—
721#121—28no—
722#121C2×D418yes—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—216no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—24no—
730C4×Q8—28no—
731C4×Q8—24no—
732C4×Q8—28no—
733C4×Q8—28no—
734C4×Q8—24no—
735C4×Q8—28no—
736C4×Q8—28no—
737C4×Q8—28no—
738C4×Q8—44no—
739C4×Q8C2×D418yes—
740C4×D4—216no—
741C4×D4—28no—
742C4×D4—28no—
743C4×D4—216no—
744C4×D4—24no—
745C4×D4—28no—
746C4×D4—44no—
747C4×D4C2×D418yes—
748C4×D4C2×D4116yes—
749#117—28no—
750#117—28no—
751#117—28no—
752#117—28no—
753#117—216no—
754#117—28no—
755#117—24no—
756#117—28no—
757#117—24no—
758#117—44no—
759#117C2×D4116yes—
760C2×C4⋊C4—28no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—28no—
763C2×C4⋊C4—28no—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2418yes—
814C2×C4⋊C4C2418yes—
815C2×C4⋊C4C2418yes—
816C2×C4⋊C4C2418yes—
817C2×C4⋊C4C2418yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2418yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2418yes—
851C2×C22⋊C4C2418yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C42—28no—
861C2×C42C2×D418yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891#95C2414yes—
892#95C2418yes—
893#95C2418yes—
894#95C2418yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2418yes—
906#95C2414yes—
907#95C2414yes—
908#95C2418yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2418yes—
913#95C2418yes—
914#95C2418yes—
915#95C2418yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2418yes—
922#95C2418yes—
923#95C2418yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2418yes—
928C24C2512yes—
929C24C2511yescharacteristic
930C24C2512yes—
931#41—816no—
932C2×Q8—22no—
933C2×Q8—22no—
934C2×Q8—22no—
935C2×Q8—24no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—28no—
941C2×Q8—28no—
942C2×Q8—28no—
943C2×Q8—22no—
944C2×Q8—22no—
945C2×Q8—22no—
946C2×Q8—22no—
947C2×Q8—22no—
948C2×Q8—22no—
949C2×Q8—24no—
950C2×Q8—28no—
951C2×Q8—28no—
952C2×Q8—28no—
953C2×Q8—48no—
954C2×Q8—48no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—48no—
958C2×Q8—816no—
959C2×Q8—816no—
960C2×Q8C22×D414yes—
961C2×D4—24no—
962C2×D4—28no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—22no—
966C2×D4—24no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—48no—
970C2×D4C22×D414yes—
971C2×D4C22×D418yes—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—24no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—48no—
988C22×C4—48no—
989C22×C4—48no—
990C22×C4—48no—
991C22×C4C22×D414yes—
992C22×C4C22×D414yes—
993C22×C4C22×D418yes—
994C22×C4C22×D414yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—22no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—22no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—22no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—48no—
1073C4⋊C4—44no—
1074C4⋊C4—48no—
1075C4⋊C4—48no—
1076C4⋊C4—48no—
1077C4⋊C4—48no—
1078C4⋊C4—48no—
1079C4⋊C4C22×D418yes—
1080C4⋊C4C22×D418yes—
1081C4⋊C4C22×D414yes—
1082C4⋊C4C22×D418yes—
1083C4⋊C4C22×D414yes—
1084C4⋊C4C22×D418yes—
1085C22⋊C4—28no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—24no—
1090C22⋊C4—28no—
1091C22⋊C4—24no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—48no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—48no—
1112C22⋊C4C22×D418yes—
1113C22⋊C4C22×D418yes—
1114C22⋊C4C22×D418yes—
1115C22⋊C4C22×D418yes—
1116C22⋊C4C22×D418yes—
1117C42—28no—
1118C42—24no—
1119C42—24no—
1120C42—28no—
1121C42—24no—
1122C42—28no—
1123C42—28no—
1124C42—28no—
1125C42—28no—
1126C42—28no—
1127C42—24no—
1128C42—22no—
1129C42—24no—
1130C42—22no—
1131C42—24no—
1132C42—24no—
1133C42—42no—
1134C42—44no—
1135C42—42no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42C22×D414yes—
1140C42C22×D414yes—
1141C42C22×D414yes—
1142C42C22×D414yes—
1143C42C22×D418yes—
1144C422−1+414yes—
1145C422−1+414yes—
1146C23—21no—
1147C23—22no—
1148C23—21no—
1149C23—22no—
1150C23—22no—
1151C23—24no—
1152C23—24no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23C23×D414yes—
1160C23C23×D412yes—
1161C23C2611yescharacteristic
1162Q8—28no—
1163Q8—44no—
1164Q8—44no—
1165Q8—44no—
1166Q8—48no—
1167Q8—48no—
1168Q8—48no—
1169Q8—84no—
1170Q8—84no—
1171Q8—88no—
1172Q8—88no—
1173Q8—88no—
1174D4—28no—
1175D4—48no—
1176D4—48no—
1177D4—44no—
1178D4—88no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—216no—
1193C2×C4—28no—
1194C2×C4—28no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—28no—
1221C2×C4—24no—
1222C2×C4—28no—
1223C2×C4—28no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—28no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—44no—
1233C2×C4—48no—
1234C2×C4—88no—
1235C2×C4—88no—
1236C2×C4—88no—
1237C2×C4—88no—
1238C2×C4—88no—
1239C2×C4C23×D412yes—
1240C2×C4C23×D414yes—
1241C2×C4C23×D414yes—
1242C2×C4C23×D414yes—
1243C2×C4C23×D412yes—
1244C2×C4C23×D412yes—
1245C2×C4C23×D412yes—
1246C2×C4C23×D412yes—
1247C2×C4C23×D412yes—
1248C2×C4C2×2−1+414yes—
1249C2×C4C2×2−1+414yes—
1250C2×C4C2×2−1+412yes—
1251C2×C4C2×2−1+412yes—
1252C2×C4#58514yes—
1253C22—22no—
1254C22—24no—
1255C22—22no—
1256C22—24no—
1257C22—22no—
1258C22—24no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22C24×D411yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58512yes—
1272C222−1+612yes—
1273C4—24no—
1274C4—22no—
1275C4—22no—
1276C4—24no—
1277C4—22no—
1278C4—22no—
1279C4—24no—
1280C4—24no—
1281C4—24no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—44no—
1295C4—42no—
1296C4—44no—
1297C4#349914yes—
1298C4#350014yes—
1299C2—42no—
1300C2—44no—
1301C2—82no—
1302C2C2×#349911yescharacteristic
1303C2C2×#350011yescharacteristic
1304C2#6285911yescharacteristic
1305C2#6295612yes—
1306C2#6295912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3552C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3555C2semidirect
3. #51331C2semidirect
4. #50869C2semidirect
5. #45343C2semidirect
6. #45322C2semidirect
7. #45144C2semidirect
8. #45095C2semidirect
9. #39619C2semidirect
10. #39616C2semidirect
11. #39490C2semidirect
12. #39490C2semidirect
13. #39488C2semidirect
14. #39485C2semidirect
15. #37870C2semidirect
16. #37865C2semidirect
17. #37423C2semidirect
18. #37392C2semidirect
19. #36560C2semidirect
20. Q8×#124C2semidirect
21. #36188C2semidirect
22. #36164C2semidirect
23. #35330C2semidirect
24. #35320C2semidirect
25. #35318C2semidirect
26. #35281C2semidirect
27. #35201C2semidirect
28. #34631C2semidirect
29. #34151C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
C2×#35522
#513312
#508692
#453432
#453222
#451442
#450952
#396192
#396162
#394902
#394882
#394852
#378702
#378652
#374232
#373922
#365602
Q8×#1242
#361882
#361642
#353302
#353202
#353182
#352812
#352012
#346312
#341512