Finite Group Databasebeta

← #6529936

Subgroups — #6529936

Order 512.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3081C211yesmaximal, characteristic, complemented
3#35537C211yesmaximal, characteristic
4#34434C211yesmaximal, characteristic, complemented
5#28292C211yesmaximal, characteristic, complemented
6#28290C211yesmaximal, characteristic, complemented
7#28286C211yesmaximal, characteristic, complemented
8#28279C211yesmaximal, characteristic, complemented
9#28214C211yesmaximal, characteristic, complemented
10#28210C211yesmaximal, characteristic, complemented
11#28207C211yesmaximal, characteristic, complemented
12#28202C211yesmaximal, characteristic, complemented
13#25462C211yesmaximal, characteristic, complemented
14#25461C211yesmaximal, characteristic, complemented
15#25457C211yesmaximal, characteristic, complemented
16#25457C211yesmaximal, characteristic, complemented
17#25288C211yesmaximal, characteristic, complemented
18#25288C211yesmaximal, characteristic, complemented
19#25274C211yesmaximal, characteristic, complemented
20#25272C211yesmaximal, characteristic, complemented
21#24591C211yesmaximal, characteristic, complemented
22#24589C211yesmaximal, characteristic, complemented
23#24585C211yesmaximal, characteristic, complemented
24#24585C211yesmaximal, characteristic, complemented
25#24492C211yesmaximal, characteristic, complemented
26#24492C211yesmaximal, characteristic, complemented
27#24478C211yesmaximal, characteristic, complemented
28#24476C211yesmaximal, characteristic, complemented
29#21980C211yesmaximal, characteristic, complemented
30#21897C211yesmaximal, characteristic, complemented
31#20744C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#518C2211yescharacteristic
35#3241—28no—
36C2×#501C2211yescharacteristic, complemented
37C2×#499C2211yescharacteristic, complemented
38C2×#490C2211yescharacteristic, complemented
39C2×#486C2211yescharacteristic, complemented
40C2×#481C2211yescharacteristic
41C2×#482C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#480C2211yescharacteristic
44#3081—28no—
45C2×#478C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic, complemented
50C2×#478C2211yescharacteristic, complemented
51C2×#476C2211yescharacteristic
52C2×#476C2211yescharacteristic
53C2×#476C2211yescharacteristic, complemented
54C2×#474C2211yescharacteristic
55C2×#474C2211yescharacteristic
56C2×#474C2211yescharacteristic, complemented
57C2×#433C2211yescharacteristic
58C2×#428C2211yescharacteristic
59C2×#427C2211yescharacteristic
60C2×#424C2211yescharacteristic
61C2×#418C2211yescharacteristic
62C22×#102C2211yescharacteristic
63#2566C2211yescharacteristic
64#2566C2211yescharacteristic
65#2541C2211yescharacteristic
66#2541C2211yescharacteristic
67#2500C2211yescharacteristic
68#2500C2211yescharacteristic
69#2456—21no—
70#2456—21no—
71#2456—21no—
72#2456—21no—
73#2433C2211yescharacteristic
74#2433C2211yescharacteristic
75#2424—21no—
76#2424—21no—
77#2424—21no—
78#2424—21no—
79#2381—21no—
80#2378—21no—
81#2370C2211yescharacteristic, complemented
82#2370C2211yescharacteristic, complemented
83#2369C2211yescharacteristic, complemented
84#2365—21no—
85#2365C2211yescharacteristic, complemented
86#2362—21no—
87#2347C2211yescharacteristic
88#2347C2211yescharacteristic
89#2345C2211yescharacteristic
90#2344C2211yescharacteristic
91#2336—21no—
92#2336—21no—
93#2332—21no—
94#2331C2211yescharacteristic, complemented
95#2330C2211yescharacteristic, complemented
96#2328C2211yescharacteristic
97#2328C2211yescharacteristic
98#2323—21no—
99#2314C2211yescharacteristic
100C4×C4⋊Q8C2211yescharacteristic, complemented
101C4×#127C2211yescharacteristic
102C4×#127C2211yescharacteristic
103C4×#125C2211yescharacteristic, complemented
104#2298C2211yescharacteristic
105#2085C2211yescharacteristic, complemented
106#2085C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2084C2211yescharacteristic, complemented
110#2084C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2083C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic, complemented
120#2067C2211yescharacteristic, complemented
121#2067C2211yescharacteristic, complemented
122#2067C2211yescharacteristic, complemented
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic, complemented
126#2065C2211yescharacteristic, complemented
127#2065C2211yescharacteristic, complemented
128#2065C2211yescharacteristic, complemented
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic
131#2041C2211yescharacteristic
132#2041C2211yescharacteristic
133#2041C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2041C2211yescharacteristic
137#1989C2211yescharacteristic, complemented
138#1989C2211yescharacteristic, complemented
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1982C2211yescharacteristic
143#1982C2211yescharacteristic
144#1982C2211yescharacteristic
145#1982C2211yescharacteristic
146#1982C2211yescharacteristic
147#1982C2211yescharacteristic, complemented
148#1982C2211yescharacteristic, complemented
149#1949C2211yescharacteristic, complemented
150#1949C2211yescharacteristic, complemented
151#1949C2211yescharacteristic, complemented
152#1949C2211yescharacteristic, complemented
153#1948C2211yescharacteristic, complemented
154#1947C2211yescharacteristic, complemented
155#1947C2211yescharacteristic, complemented
156#1947C2211yescharacteristic, complemented
157#1940C2211yescharacteristic, complemented
158#1940C2211yescharacteristic, complemented
159#1939C2211yescharacteristic, complemented
160#1939C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic, complemented
168#1926C2211yescharacteristic, complemented
169#1926C2211yescharacteristic, complemented
170#1926C2211yescharacteristic, complemented
171#1925C2211yescharacteristic
172#1925C2211yescharacteristic
173#1925C2211yescharacteristic, complemented
174#1925C2211yescharacteristic, complemented
175#1925C2211yescharacteristic, complemented
176#1925C2211yescharacteristic, complemented
177#1895C2211yescharacteristic
178#1895C2211yescharacteristic
179#1893C2211yescharacteristic
180#1893C2211yescharacteristic
181#1851C2211yescharacteristic
182#1851C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1843C2211yescharacteristic, complemented
186#1842C2211yescharacteristic, complemented
187#1832C2211yescharacteristic, complemented
188#1831C2211yescharacteristic, complemented
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1802C2211yescharacteristic, complemented
198#1802C2211yescharacteristic, complemented
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#102C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#544—24no—
209#544D418yescomplemented
210#540—24no—
211#540—24no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240#518—24no—
241#518—24no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263#501—24no—
264#499—24no—
265#490—24no—
266#486—24no—
267#482—24no—
268#482—24no—
269#481—24no—
270#480—24no—
271#478—24no—
272#478—24no—
273#478—24no—
274#478—24no—
275#478—24no—
276#478—24no—
277#476—24no—
278#476—24no—
279#476—24no—
280#474—24no—
281#474—24no—
282#474—24no—
283#433—24no—
284#428—24no—
285#427—24no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302#424—24no—
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317#418—24no—
318C2×#102—24no—
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388D411yescharacteristic
414#388D411yescharacteristic
415#388D411yescharacteristic
416#388D411yescharacteristic
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387D411yescharacteristic
436#387D411yescharacteristic
437#387D411yescharacteristic
438#387D411yescharacteristic
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#383—21no—
455#383—21no—
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381—21no—
460#380—21no—
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C22⋊C4—21no—
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#376C2311yescharacteristic
487C43C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512C25—21no—
513C22×Q8—21no—
514C22×Q8—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—22no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2411yescharacteristic
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—28no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8C2×D414yes—
564C4⋊Q8C2×D414yes—
565#127—22no—
566#127—22no—
567#127—22no—
568#127—22no—
569#127—22no—
570#127—22no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—41no—
575#125—28no—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125C2×D414yes—
581#125C2×D414yes—
582#123—44no—
583#123—44no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—44no—
591#121—44no—
592#121—82no—
593#121—82no—
594#121—82no—
595#121—82no—
596#120—82no—
597#120—82no—
598#120—82no—
599#120—82no—
600C4×Q8—82no—
601C4×Q8—82no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—44no—
615C4×D4—44no—
616C4×D4—82no—
617C4×D4—82no—
618C4×D4—82no—
619C4×D4—82no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—82no—
624#117C2×D414yes—
625#117C2×D414yes—
626#117#4114yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D414yes—
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746C4⋊C8—22no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792#97—22no—
793C4×C8—22no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C2×Q8—24no—
845C2×Q8—24no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×D4—28no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D42−1+412yes—
916C2×D42−1+412yes—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—24no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D412yes—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C2×#4112yes—
969C22×C4C2511yescharacteristic
970M16—44no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—44no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4#12114yes—
1044C4⋊C4#12114yes—
1045C4⋊C4C22×D412yes—
1046C4⋊C4C22×D412yes—
1047C4⋊C4C22×D412yes—
1048C4⋊C4C22×D412yes—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4#12114yes—
1082C22⋊C4#12114yes—
1083C42—24no—
1084C42—22no—
1085C42—22no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—41no—
1095C42—41no—
1096C42—42no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42C22×D412yes—
1108C42C22×D412yes—
1109C42C2×#4112yes—
1110C42C2×#4112yes—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—22no—
1119C23—48no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23C2×#12112yes—
1153C23C23×D411yescharacteristic
1154Q8—84no—
1155Q8—84no—
1156D4—22no—
1157D4—22no—
1158D4—22no—
1159D4—22no—
1160D4—48no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—84no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—84no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4C2×#12112yes—
1265C2×C4C2×#12112yes—
1266C2×C4C2×#12112yes—
1267C2×C4C2×#12112yes—
1268C2×C4C2×#12112yes—
1269C2×C4#57612yes—
1270C2×C4#57712yes—
1271C2×C4C23×D411yescharacteristic
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×2−1+411yescharacteristic
1274C2×C4C2×2−1+411yescharacteristic
1275C2×C4#58511yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—168no—
1321C22C22×#12111yescharacteristic
1322C22#348911yescharacteristic
1323C22#348911yescharacteristic
1324C22C2×#57611yescharacteristic
1325C22C2×#57711yescharacteristic
1326C22#358511yescharacteristic
1327C22#358511yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4#348611yescharacteristic
1354C4#348711yescharacteristic
1355C4#349511yescharacteristic
1356C4#349511yescharacteristic
1357C2—42no—
1358C2—82no—
1359C2—82no—
1360C2—161no—
1361C2—161no—
1362C2#3566111yescharacteristic
1363C2#6042811yescharacteristic
1364C2#6043111yescharacteristic
1365C2#6216311yescharacteristic
1366C2#6218811yescharacteristic
1367C2#6219911yescharacteristic
1368C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3241C2semidirect
2. C2×#3081C2semidirect
4. #34434C2semidirect
5. #28292C2semidirect
6. #28290C2semidirect
7. #28286C2semidirect
8. #28279C2semidirect
9. #28214C2semidirect
10. #28210C2semidirect
11. #28207C2semidirect
12. #28202C2semidirect
13. #25462C2semidirect
14. #25461C2semidirect
15. #25457C2semidirect
16. #25457C2semidirect
17. #25288C2semidirect
18. #25288C2semidirect
19. #25274C2semidirect
20. #25272C2semidirect
21. #24591C2semidirect
22. #24589C2semidirect
23. #24585C2semidirect
24. #24585C2semidirect
25. #24492C2semidirect
26. #24492C2semidirect
27. #24478C2semidirect
28. #24476C2semidirect
29. #21980C2semidirect
30. #21897C2semidirect
31. #20744C2semidirect
36. C2×#501C22semidirect
37. C2×#499C22semidirect
38. C2×#490C22semidirect
39. C2×#486C22semidirect
49. C2×#478C22semidirect
50. C2×#478C22semidirect
53. C2×#476C22semidirect
56. C2×#474C22semidirect
81. #2370C22semidirect
82. #2370C22semidirect
83. #2369C22semidirect
85. #2365C22semidirect
94. #2331C22semidirect
95. #2330C22semidirect
100. C4×C4⋊Q8C22semidirect
103. C4×#125C22semidirect
105. #2085C22semidirect
106. #2085C22semidirect
107. #2085C22semidirect
108. #2085C22semidirect
109. #2084C22semidirect
110. #2084C22semidirect
111. #2084C22semidirect
112. #2083C22semidirect
119. #2067C22semidirect
120. #2067C22semidirect
121. #2067C22semidirect
122. #2067C22semidirect
125. #2065C22semidirect
126. #2065C22semidirect
127. #2065C22semidirect
128. #2065C22semidirect
137. #1989C22semidirect
138. #1989C22semidirect
147. #1982C22semidirect
148. #1982C22semidirect
149. #1949C22semidirect
150. #1949C22semidirect
151. #1949C22semidirect
152. #1949C22semidirect
153. #1948C22semidirect
154. #1947C22semidirect
155. #1947C22semidirect
156. #1947C22semidirect
157. #1940C22semidirect
158. #1940C22semidirect
159. #1939C22semidirect
160. #1939C22semidirect
167. #1926C22semidirect
168. #1926C22semidirect
169. #1926C22semidirect
170. #1926C22semidirect
173. #1925C22semidirect
174. #1925C22semidirect
175. #1925C22semidirect
176. #1925C22semidirect
185. #1843C22semidirect
186. #1842C22semidirect
187. #1832C22semidirect
188. #1831C22semidirect
193. #1804C22semidirect
194. #1804C22semidirect
197. #1802C22semidirect
198. #1802C22semidirect
209. #544D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#30812
#355372
#344342
#282922
#282902
#282862
#282792
#282142
#282102
#282072
#282022
#254622
#254612
#254572
#252882
#252742
#252722
#245912
#245892
#245852
#244922
#244782
#244762
#219802
#218972
#207442