Finite Group Databasebeta

← #7598010

Subgroups — #7598010

Order 512.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45269C211yesmaximal, characteristic
2#44983C211yesmaximal, characteristic, complemented
3#31365C211yesmaximal, characteristic, complemented
4#31363C211yesmaximal, characteristic, complemented
5#31293C211yesmaximal, characteristic, complemented
6#31289C211yesmaximal, characteristic, complemented
7#29266C211yesmaximal, characteristic, complemented
8#29054C211yesmaximal, characteristic, complemented
9#29050C211yesmaximal, characteristic, complemented
10#28856C211yesmaximal, characteristic, complemented
11#28852C211yesmaximal, characteristic, complemented
12#28214C211yesmaximal, characteristic, complemented
13#27529C211yesmaximal, characteristic, complemented
14#27527C211yesmaximal, characteristic, complemented
15#27404C211yesmaximal, characteristic, complemented
16#27400C211yesmaximal, characteristic, complemented
17#27263C211yesmaximal, characteristic, complemented
18#27263C211yesmaximal, characteristic, complemented
19#25892C211yesmaximal, characteristic, complemented
20#25656C211yesmaximal, characteristic, complemented
21#25475C211yesmaximal, characteristic, complemented
22#25342C211yesmaximal, characteristic, complemented
23#25002C211yesmaximal, characteristic, complemented
24#24978C211yesmaximal, characteristic, complemented
25#22569C211yesmaximal, characteristic, complemented
26#22565C211yesmaximal, characteristic, complemented
27#22544C211yesmaximal, characteristic, complemented
28#22417C211yesmaximal, characteristic, complemented
29#21653C211yesmaximal, characteristic, complemented
30#21652C211yesmaximal, characteristic, complemented
31#21638C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#446C2211yescharacteristic
39C2×C8×D4C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C2×#416C2211yescharacteristic
42#2800—21no—
43#2783—21no—
44#2777—21no—
45#2727—21no—
46#2714—21no—
47#2714—21no—
48#2696—21no—
49#2696—21no—
50#2604—21no—
51#2584C2211yescharacteristic
52#2580C2211yescharacteristic
53#2562C2211yescharacteristic
54#2535C2211yescharacteristic
55#2533—21no—
56#2509—21no—
57#2497C2211yescharacteristic
58#2497C2211yescharacteristic
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2481—21no—
62#2481—21no—
63#2471—21no—
64#2471—21no—
65#2469—21no—
66#2441C2211yescharacteristic
67#2441C2211yescharacteristic
68#2431C2211yescharacteristic
69#2431C2211yescharacteristic
70#2426C2211yescharacteristic
71#2426C2211yescharacteristic
72#2421C2211yescharacteristic
73#2421C2211yescharacteristic
74#2398C2211yescharacteristic
75#2354C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2347C2211yescharacteristic
78#2346C2211yescharacteristic
79#2341C2211yescharacteristic
80#2341C2211yescharacteristic
81#2330C2211yescharacteristic
82#2330C2211yescharacteristic
83#2328C2211yescharacteristic
84#2327C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2096C2211yescharacteristic
88#2095C2211yescharacteristic
89#2088C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2075C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2035C2211yescharacteristic
110#2035C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1985C2211yescharacteristic
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic
122#1981C2211yescharacteristic
123#1981C2211yescharacteristic
124#1959C2211yescharacteristic
125#1959C2211yescharacteristic
126#1957C2211yescharacteristic
127#1956C2211yescharacteristic
128#1955C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1944C2211yescharacteristic
132#1943C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic
142#1933C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic
161#1873C2211yescharacteristic
162#1873C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1836C2211yescharacteristic
172#1836C2211yescharacteristic
173#1832C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1808C2211yescharacteristic
177#1807C2211yescharacteristic
178#1803C2211yescharacteristic
179#1803C2211yescharacteristic
180#1802C2211yescharacteristic
181#1802C2211yescharacteristic
182#1788C2211yescharacteristic
183#1788C2211yescharacteristic
184#1788C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#556—24no—
208#556—42no—
209#547—24no—
210#547—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4—21no—
242#491—24no—
243#490—24no—
244#478—42no—
245#478—42no—
246#446—42no—
247C8×D4—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#416—24no—
261#416—24no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400D411yescharacteristic
316#400D411yescharacteristic
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397D411yescharacteristic
327#397D411yescharacteristic
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394D411yescharacteristic
339#394D411yescharacteristic
340#393—21no—
341#393D411yescharacteristic
342#393D411yescharacteristic
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457#376C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C22×Q8C2×D411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C22×C8—22no—
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—22no—
535C4⋊Q8#4114yes—
536#127—22no—
537#127—41no—
538#126—44no—
539#126—44no—
540#126—82no—
541#126—82no—
542#125—22no—
543#125—22no—
544#125—22no—
545#125—41no—
546#124—22no—
547#124—22no—
548#124—41no—
549#124—41no—
550#123—44no—
551#123—44no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—44no—
557#121—44no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—82no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—22no—
581#117—41no—
582#117—41no—
583#117—44no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102#4114yes—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736#97—22no—
737#97—22no—
738#97—41no—
739#97—41no—
740#97—41no—
741C4×C8—22no—
742C4×C8—41no—
743C4×C8—41no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792#41—44no—
793#41—44no—
794#41—82no—
795#41—82no—
796#41—82no—
797#41—82no—
798#41—82no—
799#41—82no—
800C2×Q8—22no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—41no—
812C2×Q8—41no—
813C2×Q8C2×#4112yes—
814C2×Q8C2×#4112yes—
815C2×D4—22no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4C2×#4112yes—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—82no—
923C2×C8—82no—
924C2×C8C2×#4112yes—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4C2×#4112yes—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—42no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42C2×#4112yes—
1042C42H(5,𝔽2)12yes—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—21no—
1057C23—21no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23C23×D411yescharacteristic
1072Q8—22no—
1073Q8—22no—
1074Q8—22no—
1075Q8—22no—
1076Q8—44no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081D4—22no—
1082D4—22no—
1083D4—44no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—84no—
1091D4—84no—
1092D4—162no—
1093D4—162no—
1094D4—162no—
1095D4—162no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4#54612yes—
1185C2×C4#54612yes—
1186C2×C4C22×#4111yescharacteristic
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C2×H(5,𝔽2)11yescharacteristic
1189C2×C4#58511yescharacteristic
1190C2×C4#58511yescharacteristic
1191C2×C4#58511yescharacteristic
1192C8—22no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C22—41no—
1201C22—41no—
1202C22—42no—
1203C22—42no—
1204C22—41no—
1205C22—41no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22C2×#54611yescharacteristic
1229C22D4×#4111yescharacteristic
1230C22#350011yescharacteristic
1231C22#358411yescharacteristic
1232C22#358411yescharacteristic
1233C22#358511yescharacteristic
1234C22#358611yescharacteristic
1235C4—22no—
1236C4—22no—
1237C4—41no—
1238C4—41no—
1239C4—42no—
1240C4—42no—
1241C4—41no—
1242C4—41no—
1243C4—42no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4#347511yescharacteristic
1262C4#351411yescharacteristic
1263C4#352111yescharacteristic
1264C4#356211yescharacteristic
1265C2—81no—
1266C2—81no—
1267C2—82no—
1268C2—161no—
1269C2#5941611yescharacteristic
1270C2#6117011yescharacteristic
1271C2#6117811yescharacteristic
1272C2#6153111yescharacteristic
1273C2#6153211yescharacteristic
1274C2#6260011yescharacteristic
1275C2#6260111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45269C2
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
2. #44983C2semidirect
3. #31365C2semidirect
4. #31363C2semidirect
5. #31293C2semidirect
6. #31289C2semidirect
7. #29266C2semidirect
8. #29054C2semidirect
9. #29050C2semidirect
10. #28856C2semidirect
11. #28852C2semidirect
12. #28214C2semidirect
13. #27529C2semidirect
14. #27527C2semidirect
15. #27404C2semidirect
16. #27400C2semidirect
17. #27263C2semidirect
18. #27263C2semidirect
19. #25892C2semidirect
20. #25656C2semidirect
21. #25475C2semidirect
22. #25342C2semidirect
23. #25002C2semidirect
24. #24978C2semidirect
25. #22569C2semidirect
26. #22565C2semidirect
27. #22544C2semidirect
28. #22417C2semidirect
29. #21653C2semidirect
30. #21652C2semidirect
31. #21638C2semidirect

Maximal subgroups

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

subgroupindex
#452692
#449832
#313652
#313632
#312932
#312892
#292662
#290542
#290502
#288562
#288522
#282142
#275292
#275272
#274042
#274002
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