Finite Group Databasebeta

← #7658624

Subgroups — #7658624

Order 512.

7034 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic
2C2×#3501C211yesmaximal, characteristic, complemented
3#42681C212yesmaximal, complemented
4#42651C212yesmaximal, complemented
5#42479C212yesmaximal, complemented
6#42437C214yesmaximal, complemented
7#42431C212yesmaximal, complemented
8#41406C214yesmaximal, complemented
9#41370C214yesmaximal, complemented
10#40592C214yesmaximal, complemented
11#40491C214yesmaximal, complemented
12#40487C218yesmaximal, complemented
13#37634C211yesmaximal, characteristic, complemented
14#37619C211yesmaximal, characteristic, complemented
15#37560C211yesmaximal, characteristic, complemented
16#37451C212yesmaximal, complemented
17#37447C212yesmaximal, complemented
18#37438C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20C2×#2816C212yesmaximal, complemented
21#35950C212yesmaximal, complemented
22#35903C212yesmaximal, complemented
23#35836C212yesmaximal, complemented
24#35713C214yesmaximal, complemented
25#35702C212yesmaximal, complemented
26#34190C211yesmaximal, characteristic, complemented
27#3519—216no—
28#3501—216no—
29C2×#555C2211yescharacteristic
30C2×#554C2212yes—
31C2×#554C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×#554C2214yescomplemented
34C2×#554C2212yescomplemented
35C2×#554C2211yescharacteristic, complemented
36C2×#554C2212yescomplemented
37C2×#553C2212yes—
38C2×#553C2212yes—
39C2×#550C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2212yescomplemented
42C2×D4×Q8C2211yescharacteristic, complemented
43C2×#546C2214yes—
44C2×#546C2212yes—
45C2×D42C2211yescharacteristic
46C2×D42C2212yes—
47C2×#544C2212yescomplemented
48C2×#543C2214yescomplemented
49C2×#540C2212yes—
50C2×#538C2214yes—
51C2×#533C2211yescharacteristic, complemented
52C2×#533C2211yescharacteristic, complemented
53C2×#532C2211yescharacteristic
54C2×#529C2211yescharacteristic
55C2×#525C2212yes—
56C22×C22⋊Q8C2212yescomplemented
57C22×C22⋊Q8C2212yescomplemented
58C22×#121C2212yes—
59C2×#518C2212yes—
60C2×#518C2212yes—
61C22×C4×D4C2211yescharacteristic
62#2822C2212yescomplemented
63#2821C2212yescomplemented
64#2821C2212yescomplemented
65#2820C2212yescomplemented
66#2817C2211yescharacteristic, complemented
67#2817C2212yescomplemented
68#2817C2211yescharacteristic, complemented
69#2816C2211yescharacteristic
70#2816C2212yes—
71#2816C2211yescharacteristic
72#2816C2212yescomplemented
73#2816C2212yescomplemented
74#2816C2218yescomplemented
75#2816C2214yescomplemented
76#2816C2212yescomplemented
77#2816C2214yescomplemented
78#2816C2214yescomplemented
79#2816C2214yescomplemented
80#2816C2212yescomplemented
81#2814C2214yescomplemented
82#2721C2218yescomplemented
83#2716C2218yescomplemented
84#2700C2218yescomplemented
85#2694C2218yescomplemented
86#2687C2218yescomplemented
87#2681C2218yescomplemented
88#2681C2218yescomplemented
89#2680C2218yescomplemented
90#2674C2218yescomplemented
91#2674C2218yescomplemented
92#2672C2218yescomplemented
93#2672C2218yescomplemented
94#2663C2214yescomplemented
95#2663C2214yescomplemented
96#2663C2214yescomplemented
97#2660C2212yescomplemented
98#2659C2214yescomplemented
99#2658C2212yescomplemented
100#2641C2212yescomplemented
101#2640C2212yescomplemented
102#2639C2214yescomplemented
103#2638C2218yescomplemented
104#2634C2212yescomplemented
105#2633C2214yescomplemented
106#2632C2214yescomplemented
107#2632C2212yescomplemented
108#2628C2212yescomplemented
109#2628C2212yescomplemented
110#2626C2214yescomplemented
111#2626C2214yescomplemented
112#2625C2214yescomplemented
113#2624C2214yescomplemented
114#2623C2214yescomplemented
115#2622C2218yescomplemented
116#2620C2218yescomplemented
117#2618C2214yescomplemented
118#2618C2214yescomplemented
119#2616C2214yescomplemented
120#2616C2214yescomplemented
121#2614C2214yescomplemented
122#2604C2214yescomplemented
123#2591C2214yescomplemented
124#2584C2212yescomplemented
125#2583C2214yescomplemented
126#2580C2212yescomplemented
127#2580C2212yescomplemented
128#2564C2214yescomplemented
129#2564C2214yescomplemented
130#2563C2212yescomplemented
131#2562C2212yescomplemented
132#2552C2214yescomplemented
133#2550C2214yescomplemented
134#2549C2218yescomplemented
135#2548C2212yescomplemented
136#2546C2212yescomplemented
137#2542C2212yescomplemented
138#2536C2214yescomplemented
139#2502C2214yescomplemented
140#2501C2214yescomplemented
141#2500C2214yescomplemented
142#2491C2214yescomplemented
143#2490C2214yescomplemented
144#2487C2214yescomplemented
145#2485C2214yescomplemented
146#2484C2214yescomplemented
147#2472C2218yescomplemented
148#2472C2218yescomplemented
149#2454C2214yescomplemented
150#2452C2214yescomplemented
151#2450C2218yescomplemented
152#2449C2218yescomplemented
153#2445C2214yescomplemented
154#2445C2214yescomplemented
155#2444C2218yescomplemented
156#2443C2218yescomplemented
157#2441C2214yescomplemented
158#2440C2218yescomplemented
159#2439C2214yescomplemented
160#2437C2218yescomplemented
161#2437C2218yescomplemented
162#2436C2214yescomplemented
163#2435C2214yescomplemented
164#2432C2214yescomplemented
165#2422C2214yescomplemented
166#2420C2214yescomplemented
167#2418C2218yescomplemented
168#2418C2218yescomplemented
169#2415C2218yescomplemented
170#2412C2218yescomplemented
171#2409C2214yescomplemented
172#2406C2214yescomplemented
173#2405C2218yescomplemented
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2396C2212yescomplemented
177#2396C2212yescomplemented
178#2395C2214yescomplemented
179C2×#399C2214yescomplemented
180C2×#398C2214yescomplemented
181C2×#394C2218yescomplemented
182C2×#394C2214yescomplemented
183C2×#393C2214yescomplemented
184#2357C2212yescomplemented
185#2353C2214yescomplemented
186#2349C2214yes—
187#2349C2212yes—
188D4×C4⋊C4C2214yes—
189#2344C2212yescomplemented
190#2342C2214yescomplemented
191D4×C22⋊C4C2214yes—
192D4×C22⋊C4C2214yes—
193D4×C22⋊C4C2212yes—
194#2319C2212yescomplemented
195#2318C2214yescomplemented
196#2283C2211yescharacteristic, complemented
197#2283C2211yescharacteristic, complemented
198#2280C2212yescomplemented
199C2×#381C2212yescomplemented
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2312yes—
204C23×Q8C2312yes—
205C23×D4C2312yes—
206C23×D4C2311yescharacteristic
207C23×D4C2314yes—
208C23×D4C2312yes—
209C24×C4C2312yes—
210#555—28no—
211#554—216no—
212#554—28no—
213#554—28no—
214#554—232no—
215#554—216no—
216#554—216no—
217#554—28no—
218#553—216no—
219#553—216no—
220#550—28no—
221D4×Q8—28no—
222D4×Q8—216no—
223D4×Q8—28no—
224#546—216no—
225#546—232no—
226D42—216no—
227D42—28no—
228#544—216no—
229#543—232no—
230#540—216no—
231#538—232no—
232#533—28no—
233#533—28no—
234#532—28no—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×#127C2311yescharacteristic
245C2×#127C2312yes—
246#529—28no—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#124C2311yescharacteristic
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2318yes—
260C2×#124C2314yes—
261#525—216no—
262C2×#123C2314yes—
263C2×#123C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2318yes—
267C2×#123C2318yes—
268C2×#123C2318yes—
269C2×C22⋊Q8—216no—
270C2×C22⋊Q8—216no—
271C2×C22⋊Q8C2311yescharacteristic
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yes—
297C2×#121—216no—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#120C2314yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314#518—216no—
315#518—216no—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×D4D4116yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2311yescharacteristic
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2314yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2318yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C22⋊C4C2314yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2314yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2314yes—
363C22×C22⋊C4C2318yes—
364C22×C22⋊C4C2318yes—
365C22×C22⋊C4C2312yes—
366C22×C42C2311yescharacteristic
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#399C2312yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#399C2318yes—
381#399C2318yes—
382#399C2314yes—
383#399C2314yes—
384#399C2314yes—
385#399C2318yes—
386#399C2314yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2318yes—
393#398C2318yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2318yes—
401#397C2314yes—
402#397C2318yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#396C2314yes—
411#396C2314yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#395C2312yes—
417#395C2314yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2314yes—
422#395C2314yes—
423#395C2318yes—
424#395C2318yes—
425#395C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2318yes—
430#394C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2318yes—
434#394C2318yes—
435#394C2314yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2314yes—
443#394C2318yes—
444#394C2314yes—
445#394C2318yes—
446#394C2318yes—
447#394C2318yes—
448#394C2318yes—
449#393C2312yes—
450#393C2314yes—
451#393C2312yes—
452#393C2314yes—
453#393C2314yes—
454#393C2318yes—
455#393C2318yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2318yes—
460#393C2314yes—
461#391C2318yes—
462#391C2318yes—
463#391C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2318yes—
470#390C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2318yes—
475#389C2318yes—
476#389C2314yes—
477#389C2318yes—
478#389C2314yes—
479#389C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#384C2314yes—
511#384C2318yes—
512#383C2312yes—
513#383C2312yes—
514#382C2314yes—
515#382C2312yes—
516#382C2312yes—
517#381C2311yescharacteristic
518#381C2312yes—
519#381C2311yescharacteristic
520#381C2314yes—
521#381C2314yes—
522#381C2314yes—
523#381C2318yes—
524#380C2314yes—
525#380C2314yes—
526#380C2318yes—
527#380C2318yes—
528#380C2318yes—
529#380C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2314yes—
533#380C2318yes—
534#379C2314yes—
535#379C2318yes—
536#379C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2314yes—
549#376C2312yes—
550#376C2312yes—
551C2×#95C2314yes—
552C2×#95C2314yes—
553C2×#95C2318yes—
554C25C2414yes—
555C25C2412yes—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—84no—
559C2×#41—84no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—84no—
563C22×Q8—84no—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2414yes—
571C22×Q8C2414yes—
572C22×Q8C2412yes—
573C22×D4—28no—
574C22×D4—216no—
575C22×D4—28no—
576C22×D4—216no—
577C22×D4—28no—
578C22×D4—84no—
579C22×D4—88no—
580C22×D4C2×D418yes—
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2412yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2411yescharacteristic
595C23×C4—84no—
596C23×C4C2×D4116yes—
597C23×C4C2412yes—
598C23×C4C2411yescharacteristic
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2418yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2412yes—
608C23×C4C2411yescharacteristic
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2411yescharacteristic
614C4⋊Q8—28no—
615C4⋊Q8—28no—
616C4⋊Q8—216no—
617C4⋊Q8—24no—
618C4⋊Q8—24no—
619C4⋊Q8—24no—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622C4⋊Q8—84no—
623#127—28no—
624#127—24no—
625#126—216no—
626#126—28no—
627#125—28no—
628#125—28no—
629#125—28no—
630#125—216no—
631#125—24no—
632#125—28no—
633#125—28no—
634#124—216no—
635#124—24no—
636#124—28no—
637#124—88no—
638#124—84no—
639#123—216no—
640#123—28no—
641#123—216no—
642#123—216no—
643#123—88no—
644#123—88no—
645#123—88no—
646C22⋊Q8—24no—
647C22⋊Q8—28no—
648C22⋊Q8—24no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—24no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—216no—
666C22⋊Q8—216no—
667C22⋊Q8—216no—
668C22⋊Q8—216no—
669C22⋊Q8—216no—
670C22⋊Q8—88no—
671C22⋊Q8—88no—
672#121—216no—
673#121—28no—
674#121—24no—
675#121—28no—
676#121—216no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—28no—
682#121—28no—
683#121—216no—
684#121—216no—
685#120—216no—
686#120—216no—
687#120—216no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—28no—
692C4×Q8—28no—
693C4×Q8—28no—
694C4×D4—28no—
695C4×D4—216no—
696C4×D4—28no—
697C4×D4—28no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—28no—
701C4×D4—216no—
702C4×D4—216no—
703C4×D4—216no—
704C4×D4—28no—
705C4×D4—28no—
706C4×D4—216no—
707C4×D4—28no—
708C4×D4—24no—
709C4×D4—28no—
710C4×D4C2×D418yes—
711C4×D4C2×D4116yes—
712C4×D4C2×D418yes—
713C4×D4C2×D418yes—
714C4×D4C2×D4116yes—
715C4×D4C2×D418yes—
716#117—28no—
717#117—28no—
718#117—28no—
719#117—28no—
720#117—28no—
721#117—84no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—216no—
724C2×C4⋊C4—216no—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—88no—
728C2×C4⋊C4C2×D418yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C22⋊C4—216no—
777C2×C22⋊C4—216no—
778C2×C22⋊C4—216no—
779C2×C22⋊C4—216no—
780C2×C22⋊C4—84no—
781C2×C22⋊C4—88no—
782C2×C22⋊C4—88no—
783C2×C22⋊C4C2×D4116yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C42C2×D418yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2418yes—
835C2×C42C2414yes—
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840#95C2412yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868C24—28no—
869C24—28no—
870C24—216no—
871C24—44no—
872C24—44no—
873C24—48no—
874C24—48no—
875C24C22×D418yes—
876C24C2512yes—
877C24C2514yes—
878C24C2511yescharacteristic
879C24C2512yes—
880C24C2512yes—
881#41—816no—
882#41—816no—
883C2×Q8—22no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—28no—
890C2×Q8—28no—
891C2×Q8—24no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—44no—
897C2×Q8—48no—
898C2×Q8—42no—
899C2×Q8—48no—
900C2×Q8—42no—
901C2×Q8—44no—
902C2×Q8—816no—
903C2×Q8—816no—
904C2×D4—28no—
905C2×D4—232no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—216no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—24no—
914C2×D4—22no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—28no—
918C2×D4—24no—
919C2×D4—28no—
920C2×D4—42no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—48no—
927C2×D4—48no—
928C2×D4—44no—
929C2×D4—432no—
930C2×D4—816no—
931C2×D4—832no—
932C2×D4C22×D418yes—
933C2×D4C22×D414yes—
934C2×D4C22×D414yes—
935C2×D42−1+418yes—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—28no—
940C22×C4—28no—
941C22×C4—28no—
942C22×C4—216no—
943C22×C4—24no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—28no—
947C22×C4—44no—
948C22×C4—42no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—42no—
954C22×C4—48no—
955C22×C4—44no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—44no—
959C22×C4—48no—
960C22×C4—48no—
961C22×C4—48no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—48no—
965C22×C4—816no—
966C22×C4C22×D414yes—
967C22×C4C22×D414yes—
968C22×C4C22×D414yes—
969C22×C4C22×D418yes—
970C22×C4C22×D418yes—
971C22×C4C22×D418yes—
972C22×C4C22×D418yes—
973C22×C4C22×D418yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2518yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—22no—
1000C4⋊C4—24no—
1001C4⋊C4—22no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—44no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4—48no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—48no—
1035C4⋊C4—48no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—48no—
1039C4⋊C4C22×D414yes—
1040C4⋊C4C22×D414yes—
1041C4⋊C4C22×D418yes—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—216no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—42no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—48no—
1067C22⋊C4—48no—
1068C22⋊C4—48no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—42no—
1074C22⋊C4—48no—
1075C22⋊C4—48no—
1076C22⋊C4—48no—
1077C22⋊C4—44no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—44no—
1081C22⋊C4C22×D418yes—
1082C22⋊C4C22×D418yes—
1083C22⋊C4C22×D418yes—
1084C22⋊C4C22×D418yes—
1085C42—28no—
1086C42—24no—
1087C42—28no—
1088C42—24no—
1089C42—24no—
1090C42—28no—
1091C42—48no—
1092C42—44no—
1093C42C22×D414yes—
1094C42C22×D414yes—
1095C42C22×D414yes—
1096C42C22×D414yes—
1097C23—24no—
1098C23—24no—
1099C23—22no—
1100C23—24no—
1101C23—22no—
1102C23—24no—
1103C23—24no—
1104C23—22no—
1105C23—216no—
1106C23—22no—
1107C23—24no—
1108C23—24no—
1109C23—28no—
1110C23—28no—
1111C23—28no—
1112C23—24no—
1113C23—24no—
1114C23—48no—
1115C23—48no—
1116C23—416no—
1117C23—816no—
1118C23—88no—
1119C23—88no—
1120C23—832no—
1121C23C23×D412yes—
1122C23C23×D414yes—
1123C23C23×D414yes—
1124C23C2×2−1+418yes—
1125C23C2611yescharacteristic
1126Q8—44no—
1127Q8—48no—
1128Q8—44no—
1129Q8—44no—
1130Q8—84no—
1131Q8—84no—
1132Q8—88no—
1133Q8—88no—
1134Q8—84no—
1135D4—216no—
1136D4—28no—
1137D4—44no—
1138D4—48no—
1139D4—48no—
1140D4—416no—
1141D4—416no—
1142D4—48no—
1143D4—88no—
1144D4—84no—
1145D4—88no—
1146D4—88no—
1147D4—88no—
1148D4#536116yes—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—28no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—28no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—28no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—28no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—28no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—48no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—44no—
1196C2×C4—48no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—816no—
1200C2×C4—88no—
1201C2×C4—88no—
1202C2×C4—88no—
1203C2×C4—88no—
1204C2×C4—88no—
1205C2×C4C23×D412yes—
1206C2×C4C23×D414yes—
1207C2×C4C23×D412yes—
1208C2×C4C23×D412yes—
1209C2×C4C23×D412yes—
1210C2×C4C23×D412yes—
1211C2×C4C23×D414yes—
1212C2×C4C23×D412yes—
1213C2×C4C2×2−1+414yes—
1214C22—216no—
1215C22—24no—
1216C22—24no—
1217C22—22no—
1218C22—24no—
1219C22—22no—
1220C22—24no—
1221C22—22no—
1222C22—24no—
1223C22—48no—
1224C22—44no—
1225C22—416no—
1226C22—48no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22—816no—
1234C22—1616no—
1235C22C2×#53618yes—
1236C22C24×D411yescharacteristic
1237C22C22×2−1+412yes—
1238C22H(7,𝔽2)12yes—
1239C22H(7,𝔽2)12yes—
1240C4—22no—
1241C4—22no—
1242C4—24no—
1243C4—24no—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—44no—
1248C4—48no—
1249C4—44no—
1250C4—42no—
1251C4—42no—
1252C4—44no—
1253C4—42no—
1254C4—42no—
1255C4—44no—
1256C4—42no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4C2×#53614yes—
1261C2—28no—
1262C2—44no—
1263C2—42no—
1264C2—84no—
1265C2—82no—
1266C2C22×#53611yescharacteristic
1267C2#6284211yescharacteristic
1268C2#6285211yescharacteristic
1269C2#6305414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3519C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3501C2semidirect
3. #42681C2semidirect
4. #42651C2semidirect
5. #42479C2semidirect
6. #42437C2semidirect
7. #42431C2semidirect
8. #41406C2semidirect
9. #41370C2semidirect
10. #40592C2semidirect
11. #40491C2semidirect
12. #40487C2semidirect
13. #37634C2semidirect
14. #37619C2semidirect
15. #37560C2semidirect
16. #37451C2semidirect
17. #37447C2semidirect
18. #37438C2semidirect
19. #36699C2semidirect
20. C2×#2816C2semidirect
21. #35950C2semidirect
22. #35903C2semidirect
23. #35836C2semidirect
24. #35713C2semidirect
25. #35702C2semidirect
26. #34190C2semidirect
33. C2×#554C22semidirect
34. C2×#554C22semidirect
35. C2×#554C22semidirect
36. C2×#554C22semidirect
41. C2×D4×Q8C22semidirect
42. C2×D4×Q8C22semidirect
47. C2×#544C22semidirect
48. C2×#543C22semidirect
51. C2×#533C22semidirect
52. C2×#533C22semidirect
56. C22×C22⋊Q8C22semidirect
57. C22×C22⋊Q8C22semidirect
62. #2822C22semidirect
63. #2821C22semidirect
64. #2821C22semidirect
65. #2820C22semidirect
66. #2817C22semidirect
67. #2817C22semidirect
68. #2817C22semidirect
72. #2816C22semidirect
73. #2816C22semidirect
74. #2816C22semidirect
75. #2816C22semidirect
76. #2816C22semidirect
77. #2816C22semidirect
78. #2816C22semidirect
79. #2816C22semidirect
80. #2816C22semidirect
81. #2814C22semidirect
82. #2721C22semidirect
83. #2716C22semidirect
84. #2700C22semidirect
85. #2694C22semidirect
86. #2687C22semidirect
87. #2681C22semidirect
88. #2681C22semidirect
89. #2680C22semidirect
90. #2674C22semidirect
91. #2674C22semidirect
92. #2672C22semidirect
93. #2672C22semidirect
94. #2663C22semidirect
95. #2663C22semidirect
96. #2663C22semidirect
97. #2660C22semidirect
98. #2659C22semidirect
99. #2658C22semidirect
100. #2641C22semidirect
101. #2640C22semidirect
102. #2639C22semidirect
103. #2638C22semidirect
104. #2634C22semidirect
105. #2633C22semidirect
106. #2632C22semidirect
107. #2632C22semidirect
108. #2628C22semidirect
109. #2628C22semidirect
110. #2626C22semidirect
111. #2626C22semidirect
112. #2625C22semidirect
113. #2624C22semidirect
114. #2623C22semidirect
115. #2622C22semidirect
116. #2620C22semidirect
117. #2618C22semidirect
118. #2618C22semidirect
119. #2616C22semidirect
120. #2616C22semidirect
121. #2614C22semidirect
122. #2604C22semidirect
123. #2591C22semidirect
124. #2584C22semidirect
125. #2583C22semidirect
126. #2580C22semidirect
127. #2580C22semidirect
128. #2564C22semidirect
129. #2564C22semidirect
130. #2563C22semidirect
131. #2562C22semidirect
132. #2552C22semidirect
133. #2550C22semidirect
134. #2549C22semidirect
135. #2548C22semidirect
136. #2546C22semidirect
137. #2542C22semidirect
138. #2536C22semidirect
139. #2502C22semidirect
140. #2501C22semidirect
141. #2500C22semidirect
142. #2491C22semidirect
143. #2490C22semidirect
144. #2487C22semidirect
145. #2485C22semidirect
146. #2484C22semidirect
147. #2472C22semidirect
148. #2472C22semidirect
149. #2454C22semidirect
150. #2452C22semidirect
151. #2450C22semidirect
152. #2449C22semidirect
153. #2445C22semidirect
154. #2445C22semidirect
155. #2444C22semidirect
156. #2443C22semidirect
157. #2441C22semidirect
158. #2440C22semidirect
159. #2439C22semidirect
160. #2437C22semidirect
161. #2437C22semidirect
162. #2436C22semidirect
163. #2435C22semidirect
164. #2432C22semidirect
165. #2422C22semidirect
166. #2420C22semidirect
167. #2418C22semidirect
168. #2418C22semidirect
169. #2415C22semidirect
170. #2412C22semidirect
171. #2409C22semidirect
172. #2406C22semidirect
173. #2405C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
178. #2395C22semidirect
179. C2×#399C22semidirect
180. C2×#398C22semidirect
181. C2×#394C22semidirect
182. C2×#394C22semidirect
183. C2×#393C22semidirect
184. #2357C22semidirect
185. #2353C22semidirect
189. #2344C22semidirect
190. #2342C22semidirect
194. #2319C22semidirect
195. #2318C22semidirect
196. #2283C22semidirect
197. #2283C22semidirect
198. #2280C22semidirect
199. C2×#381C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
C2×#35012
#426812
#426512
#424792
#424372
#424312
#414062
#413702
#405922
#404912
#404872
#376342
#376192
#375602
#374512
#374472
#374382
#366992
C2×#28162
#359502
#359032
#358362
#357132
#357022
#341902