Finite Group Databasebeta

← #6831850

Subgroups — #6831850

Order 512.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42694C211yesmaximal, characteristic, complemented
2#42680C211yesmaximal, characteristic, complemented
3#33229C211yesmaximal, characteristic, complemented
4#31865C211yesmaximal, characteristic, complemented
5#31852C211yesmaximal, characteristic, complemented
6#31315C211yesmaximal, characteristic, complemented
7#31306C211yesmaximal, characteristic, complemented
8#30642C211yesmaximal, characteristic, complemented
9#30634C211yesmaximal, characteristic, complemented
10#30528C211yesmaximal, characteristic, complemented
11#30523C211yesmaximal, characteristic, complemented
12#29990C211yesmaximal, characteristic, complemented
13#29804C211yesmaximal, characteristic, complemented
14#29066C211yesmaximal, characteristic, complemented
15#29042C211yesmaximal, characteristic, complemented
16#28933C211yesmaximal, characteristic, complemented
17#28918C211yesmaximal, characteristic, complemented
18#28357C211yesmaximal, characteristic, complemented
19#28339C211yesmaximal, characteristic, complemented
20#27281C211yesmaximal, characteristic, complemented
21#27267C211yesmaximal, characteristic, complemented
22#26326C211yesmaximal, characteristic, complemented
23#26231C211yesmaximal, characteristic, complemented
24#25400C211yesmaximal, characteristic, complemented
25#25309C211yesmaximal, characteristic, complemented
26#24245C211yesmaximal, characteristic
27#24185C211yesmaximal, characteristic, complemented
28#22548C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#21637C211yesmaximal, characteristic, complemented
31#21282C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#487C2211yescharacteristic, complemented
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic, complemented
40C2×#468C2211yescharacteristic
41C2×#465C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#461C2211yescharacteristic, complemented
44C2×#449C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#446C2211yescharacteristic, complemented
47C2×C4×D8C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×#416C2211yescharacteristic
51#2829—21no—
52#2816—21no—
53#2741—21no—
54#2737—21no—
55#2718—21no—
56#2718—21no—
57#2702—21no—
58#2700—21no—
59#2685—21no—
60#2685—21no—
61#2662—21no—
62#2660C2211yescharacteristic, complemented
63#2658C2211yescharacteristic
64#2650—21no—
65#2626—21no—
66#2624—21no—
67#2592C2211yescharacteristic
68#2542C2211yescharacteristic
69#2538C2211yescharacteristic, complemented
70#2535C2211yescharacteristic
71#2525—21no—
72#2500C2211yescharacteristic
73#2500C2211yescharacteristic, complemented
74#2496C2211yescharacteristic
75#2495C2211yescharacteristic, complemented
76#2491C2211yescharacteristic, complemented
77#2490C2211yescharacteristic
78#2482—21no—
79#2441C2211yescharacteristic, complemented
80#2439C2211yescharacteristic
81#2435C2211yescharacteristic
82#2435C2211yescharacteristic
83#2432C2211yescharacteristic
84#2432C2211yescharacteristic
85#2429C2211yescharacteristic
86#2429C2211yescharacteristic
87#2426C2211yescharacteristic
88#2426C2211yescharacteristic
89#2398C2211yescharacteristic
90#2355C2211yescharacteristic, complemented
91#2354C2211yescharacteristic
92#2319C2211yescharacteristic
93#2319C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2099C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2094C2211yescharacteristic
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2058C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2043C2211yescharacteristic, complemented
109#2043C2211yescharacteristic, complemented
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#2013C2211yescharacteristic, complemented
125#2013C2211yescharacteristic, complemented
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic, complemented
133#1999C2211yescharacteristic
134#1984C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1981C2211yescharacteristic, complemented
139#1972C2211yescharacteristic
140#1970C2211yescharacteristic
141#1970C2211yescharacteristic
142#1968C2211yescharacteristic, complemented
143#1960C2211yescharacteristic, complemented
144#1960C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1959C2211yescharacteristic
147#1959C2211yescharacteristic
148#1958C2211yescharacteristic
149#1958C2211yescharacteristic
150#1958C2211yescharacteristic
151#1956C2211yescharacteristic, complemented
152#1956C2211yescharacteristic, complemented
153#1954C2211yescharacteristic
154#1949C2211yescharacteristic, complemented
155#1948C2211yescharacteristic, complemented
156#1942C2211yescharacteristic, complemented
157#1942C2211yescharacteristic, complemented
158#1936C2211yescharacteristic
159#1936C2211yescharacteristic
160#1936C2211yescharacteristic, complemented
161#1936C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1934C2211yescharacteristic
164#1928C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic, complemented
170#1923C2211yescharacteristic
171#1923C2211yescharacteristic, complemented
172#1894C2211yescharacteristic
173#1894C2211yescharacteristic
174#1893C2211yescharacteristic
175#1892C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1880C2211yescharacteristic, complemented
178#1875C2211yescharacteristic
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1832C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193C4×#107C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1726C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—24no—
213#556—42no—
214#546—24no—
215#546—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C22⋊C4—21no—
253#491—42no—
254#489—42no—
255#488—42no—
256#487—42no—
257#485—42no—
258#485—42no—
259#468—42no—
260#465—42no—
261#463—42no—
262#461—42no—
263#449—42no—
264#447—42no—
265#446—42no—
266C4×D8—24no—
267#435—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#418—42no—
280#416—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400D411yescharacteristic
336#400D411yescharacteristic
337#399—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397D411yescharacteristic
354#397D411yescharacteristic
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#395—21no—
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394D411yescharacteristic
382#394D411yescharacteristic
383#393—21no—
384#393—21no—
385#393—21no—
386#393D411yescharacteristic
387#393D411yescharacteristic
388#392—21no—
389#391—21no—
390#391—21no—
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390—21no—
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#384—21no—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#383—21no—
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#381—21no—
454#381—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#379—21no—
463#379—21no—
464#379—21no—
465#379—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476#376C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
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—22no—
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#126—44no—
569#126—44no—
570#126—82no—
571#125—41no—
572#125—41no—
573#124—22no—
574#124—22no—
575#124—22no—
576#124—22no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—82no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—44no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—82no—
597#121—22no—
598#121—44no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#120—44no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4#4114yes—
617#117—44no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
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—21no—
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⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
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—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—44no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—41no—
733#107—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785#97—22no—
786#97—22no—
787#97—41no—
788#97—41no—
789C4×C8—22no—
790C4×C8—22no—
791C4×C8—41no—
792C4×C8—41no—
793#95—21no—
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#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
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
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—44no—
842#41—82no—
843#41—82no—
844#41—82no—
845C2×Q8—22no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—41no—
865C2×Q8—41no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×D4—22no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—44no—
892C2×D4—42no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
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×D4C2×#4112yes—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—24no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
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—21no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956SD16—82no—
957SD16—82no—
958SD16—82no—
959D8—44no—
960D8—82no—
961M16—82no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
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—82no—
985C2×C8H(5,𝔽2)12yes—
986C2×C8H(5,𝔽2)12yes—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4C2×#4112yes—
1039C22⋊C4—24no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
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—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42C2×#4112yes—
1108C42H(5,𝔽2)12yes—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
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—84no—
1145C23—84no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23C23×D411yescharacteristic
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—82no—
1165Q8—162no—
1166D4—22no—
1167D4—22no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—82no—
1179D4—84no—
1180D4—84no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
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—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
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—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—162no—
1268C2×C4#54612yes—
1269C2×C4#54612yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—22no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C22—42no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
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—168no—
1320C22C2×#54611yescharacteristic
1321C22#349811yescharacteristic
1322C22#350011yescharacteristic
1323C22#358411yescharacteristic
1324C22#358411yescharacteristic
1325C22#358511yescharacteristic
1326C22#358611yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—41no—
1330C4—41no—
1331C4—42no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#346011yescharacteristic
1353C4#349411yescharacteristic
1354C4#354611yescharacteristic
1355C4#355811yescharacteristic
1356C2—81no—
1357C2—81no—
1358C2—82no—
1359C2—161no—
1360C2—161no—
1361C2#3941911yescharacteristic
1362C2#6118711yescharacteristic
1363C2#6119811yescharacteristic
1364C2#6243411yescharacteristic
1365C2#6244611yescharacteristic
1366C2#6260111yescharacteristic
1367C2#6261511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24245C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42694C2semidirect
2. #42680C2semidirect
3. #33229C2semidirect
4. #31865C2semidirect
5. #31852C2semidirect
6. #31315C2semidirect
7. #31306C2semidirect
8. #30642C2semidirect
9. #30634C2semidirect
10. #30528C2semidirect
11. #30523C2semidirect
12. #29990C2semidirect
13. #29804C2semidirect
14. #29066C2semidirect
15. #29042C2semidirect
16. #28933C2semidirect
17. #28918C2semidirect
18. #28357C2semidirect
19. #28339C2semidirect
20. #27281C2semidirect
21. #27267C2semidirect
22. #26326C2semidirect
23. #26231C2semidirect
24. #25400C2semidirect
25. #25309C2semidirect
27. #24185C2semidirect
28. #22548C2semidirect
29. #22424C2semidirect
30. #21637C2semidirect
31. #21282C2semidirect
34. C2×#491C22semidirect
37. C2×#487C22semidirect
39. C2×#485C22semidirect
41. C2×#465C22semidirect
43. C2×#461C22semidirect
46. C2×#446C22semidirect
62. #2660C22semidirect
69. #2538C22semidirect
73. #2500C22semidirect
75. #2495C22semidirect
76. #2491C22semidirect
79. #2441C22semidirect
90. #2355C22semidirect
93. #2319C22semidirect
94. #2101C22semidirect
95. #2099C22semidirect
96. #2097C22semidirect
101. #2072C22semidirect
102. #2066C22semidirect
104. #2059C22semidirect
105. #2058C22semidirect
106. #2055C22semidirect
108. #2043C22semidirect
109. #2043C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
120. #2035C22semidirect
124. #2013C22semidirect
125. #2013C22semidirect
132. #2000C22semidirect
134. #1984C22semidirect
138. #1981C22semidirect
142. #1968C22semidirect
143. #1960C22semidirect
144. #1960C22semidirect
151. #1956C22semidirect
152. #1956C22semidirect
154. #1949C22semidirect
155. #1948C22semidirect
156. #1942C22semidirect
157. #1942C22semidirect
160. #1936C22semidirect
161. #1936C22semidirect
162. #1935C22semidirect
164. #1928C22semidirect
165. #1928C22semidirect
169. #1924C22semidirect
171. #1923C22semidirect
175. #1892C22semidirect
176. #1880C22semidirect
177. #1880C22semidirect
181. #1873C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1832C22semidirect
185. #1805C22semidirect
187. #1803C22semidirect
193. C4×#107C22semidirect
194. #1763C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
200. #1752C22semidirect
201. C8×C22⋊C4C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#426942
#426802
#332292
#318652
#318522
#313152
#313062
#306422
#306342
#305282
#305232
#299902
#298042
#290662
#290422
#289332
#289182
#283572
#283392
#272812
#272672
#263262
#262312
#254002
#253092
#242452
#241852
#225482
#224242
#216372
#212822