Finite Group Databasebeta

← #7105590

Subgroups — #7105590

Order 512.

1508 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45264C211yesmaximal, characteristic, complemented
2#42982C211yesmaximal, characteristic
3#32241C211yesmaximal, characteristic, complemented
4#32237C211yesmaximal, characteristic, complemented
5#31947C211yesmaximal, characteristic, complemented
6#31943C211yesmaximal, characteristic, complemented
7#31766C211yesmaximal, characteristic, complemented
8#31741C211yesmaximal, characteristic, complemented
9#31400C211yesmaximal, characteristic, complemented
10#31386C211yesmaximal, characteristic, complemented
11#29170C211yesmaximal, characteristic, complemented
12#28998C211yesmaximal, characteristic, complemented
13#28981C211yesmaximal, characteristic, complemented
14#28110C211yesmaximal, characteristic, complemented
15#28097C211yesmaximal, characteristic, complemented
16#27971C211yesmaximal, characteristic, complemented
17#27725C211yesmaximal, characteristic, complemented
18#27701C211yesmaximal, characteristic, complemented
19#27564C211yesmaximal, characteristic, complemented
20#27564C211yesmaximal, characteristic, complemented
21#26219C211yesmaximal, characteristic, complemented
22#26208C211yesmaximal, characteristic, complemented
23#24952C211yesmaximal, characteristic, complemented
24#24938C211yesmaximal, characteristic, complemented
25#23982C211yesmaximal, characteristic, complemented
26#23966C211yesmaximal, characteristic, complemented
27#23632C211yesmaximal, characteristic, complemented
28#23122C211yesmaximal, characteristic, complemented
29#22499C211yesmaximal, characteristic, complemented
30#22486C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#450C2211yescharacteristic
35C2×#436C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×#418C2211yescharacteristic
38C22×#102C2211yescharacteristic
39#2830—21no—
40#2735—21no—
41#2725—21no—
42#2719—21no—
43#2718—21no—
44#2706—21no—
45#2684—21no—
46#2684—21no—
47#2668—21no—
48#2648—21no—
49#2648—21no—
50#2628C2211yescharacteristic
51#2555—21no—
52#2552C2211yescharacteristic, complemented
53#2538C2211yescharacteristic, complemented
54#2513C2211yescharacteristic
55#2513C2211yescharacteristic
56#2504C2211yescharacteristic
57#2504C2211yescharacteristic
58#2491C2211yescharacteristic
59#2491C2211yescharacteristic
60#2487C2211yescharacteristic
61#2485C2211yescharacteristic
62#2479—21no—
63#2478—21no—
64#2470—21no—
65#2442C2211yescharacteristic, complemented
66#2441—21no—
67#2441C2211yescharacteristic, complemented
68#2423C2211yescharacteristic, complemented
69#2421C2211yescharacteristic, complemented
70#2416C2211yescharacteristic
71#2416C2211yescharacteristic
72#2408C2211yescharacteristic
73#2408C2211yescharacteristic
74#2392C2211yescharacteristic
75#2352C2211yescharacteristic
76#2352C2211yescharacteristic
77#2352C2211yescharacteristic, complemented
78#2351C2211yescharacteristic, complemented
79#2323C2211yescharacteristic
80#2317C2211yescharacteristic
81#2309C2211yescharacteristic
82#2101C2211yescharacteristic, complemented
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2097C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2058C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic, complemented
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#2000C2211yescharacteristic
122#1993C2211yescharacteristic, complemented
123#1991C2211yescharacteristic, complemented
124#1991C2211yescharacteristic, complemented
125#1990C2211yescharacteristic, complemented
126#1989C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1968C2211yescharacteristic
130#1936C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1926C2211yescharacteristic
137#1925C2211yescharacteristic
138#1924C2211yescharacteristic, complemented
139#1923C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1920C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1916C2211yescharacteristic, complemented
147#1916C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic, complemented
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic, complemented
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1836C2211yescharacteristic, complemented
179#1835C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1823C2211yescharacteristic, complemented
187#1823C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1807C2211yescharacteristic
190#1805C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193C4×#103C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195#1753C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic, complemented
197#1750C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#552—24no—
211#552—24no—
212#552—42no—
213#552—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252#450—24no—
253#436—42no—
254C8×D4—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#418—42no—
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102—42no—
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398D411yescharacteristic
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397D411yescharacteristic
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396D411yescharacteristic
327#396D411yescharacteristic
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394D411yescharacteristic
337#394D411yescharacteristic
338#394D411yescharacteristic
339#393—21no—
340#393—21no—
341#393—21no—
342#392—21no—
343#392—21no—
344#392D411yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#379—21no—
428#379—21no—
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#126—44no—
542#126—44no—
543#125—22no—
544#125—22no—
545#125—41no—
546#125—41no—
547#125—44no—
548#125—44no—
549#124—82no—
550#124—82no—
551#123—44no—
552#123—44no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8#4114yes—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—82no—
568#121—82no—
569#120—82no—
570#120—82no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—44no—
589#117—44no—
590#117—41no—
591#117—41no—
592#117—41no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
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—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—41no—
708#107—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#102—22no—
722#102—22no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743#97—41no—
744C4×C8—41no—
745C4×C8—41no—
746C4×C8—41no—
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#95—21no—
777#95—21no—
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24—21no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C24C22×D411yescharacteristic
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8C2×#4112yes—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—41no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—82no—
834C2×D4—82no—
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—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
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—21no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
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×C4C2×#4112yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4C2511yescharacteristic
901SD16—82no—
902SD16—82no—
903M16—82no—
904M16—82no—
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—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—82no—
930C2×C8—82no—
931C4⋊C4—24no—
932C4⋊C4—22no—
933C4⋊C4—22no—
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—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4C2×#4112yes—
990C22⋊C4—24no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
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—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—81no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—84no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23—162no—
1094C23#54612yes—
1095C23#57712yes—
1096C23C23×D411yescharacteristic
1097Q8—22no—
1098Q8—22no—
1099Q8—41no—
1100Q8—41no—
1101Q8—162no—
1102D4—44no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—84no—
1112D4—82no—
1113D4—82no—
1114D4—162no—
1115D4—162no—
1116D4—162no—
1117D4—162no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
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—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4#54612yes—
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—168no—
1259C22C2×#54611yescharacteristic
1260C22#348511yescharacteristic
1261C22#350011yescharacteristic
1262C22C2×#57711yescharacteristic
1263C22#358411yescharacteristic
1264C22#358411yescharacteristic
1265C22#358511yescharacteristic
1266C4—22no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—42no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4#352111yescharacteristic
1292C4#352111yescharacteristic
1293C4#353311yescharacteristic
1294C4#353311yescharacteristic
1295C2—42no—
1296C2—42no—
1297C2—81no—
1298C2—161no—
1299C2—161no—
1300C2#4445011yescharacteristic
1301C2#6117411yescharacteristic
1302C2#6118911yescharacteristic
1303C2#6175611yescharacteristic
1304C2#6179011yescharacteristic
1305C2#6255611yescharacteristic
1306C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42982C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45264C2semidirect
3. #32241C2semidirect
4. #32237C2semidirect
5. #31947C2semidirect
6. #31943C2semidirect
7. #31766C2semidirect
8. #31741C2semidirect
9. #31400C2semidirect
10. #31386C2semidirect
11. #29170C2semidirect
12. #28998C2semidirect
13. #28981C2semidirect
14. #28110C2semidirect
15. #28097C2semidirect
16. #27971C2semidirect
17. #27725C2semidirect
18. #27701C2semidirect
19. #27564C2semidirect
20. #27564C2semidirect
21. #26219C2semidirect
22. #26208C2semidirect
23. #24952C2semidirect
24. #24938C2semidirect
25. #23982C2semidirect
26. #23966C2semidirect
27. #23632C2semidirect
28. #23122C2semidirect
29. #22499C2semidirect
30. #22486C2semidirect
31. #22052C2semidirect
52. #2552C22semidirect
53. #2538C22semidirect
65. #2442C22semidirect
67. #2441C22semidirect
68. #2423C22semidirect
69. #2421C22semidirect
77. #2352C22semidirect
78. #2351C22semidirect
82. #2101C22semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2097C22semidirect
90. #2085C22semidirect
91. #2085C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
94. #2077C22semidirect
95. #2076C22semidirect
108. #2058C22semidirect
117. #2024C22semidirect
122. #1993C22semidirect
123. #1991C22semidirect
124. #1991C22semidirect
125. #1990C22semidirect
126. #1989C22semidirect
127. #1989C22semidirect
138. #1924C22semidirect
139. #1923C22semidirect
140. #1921C22semidirect
141. #1920C22semidirect
142. #1920C22semidirect
143. #1919C22semidirect
144. #1919C22semidirect
145. #1918C22semidirect
146. #1916C22semidirect
147. #1916C22semidirect
151. #1894C22semidirect
155. #1892C22semidirect
167. #1872C22semidirect
168. #1872C22semidirect
170. #1870C22semidirect
172. #1869C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
176. #1853C22semidirect
177. #1852C22semidirect
178. #1836C22semidirect
179. #1835C22semidirect
182. #1825C22semidirect
184. #1824C22semidirect
186. #1823C22semidirect
187. #1823C22semidirect
190. #1805C22semidirect
191. #1805C22semidirect
193. C4×#103C22semidirect
194. C4×#103C22semidirect
195. #1753C22semidirect
196. C8×C22⋊C4C22semidirect
199. #1736C22semidirect
201. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#452642
#429822
#322412
#322372
#319472
#319432
#317662
#317412
#314002
#313862
#291702
#289982
#289812
#281102
#280972
#279712
#277252
#277012
#275642
#262192
#262082
#249522
#249382
#239822
#239662
#236322
#231222
#224992
#224862
#220522