Finite Group Databasebeta

← #46830977

Subgroups — #46830977

Order 34624.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31772674C212yesmaximal, complemented
2#31772655C214yesmaximal, complemented
3#31772653C212yesmaximal, complemented
4#31772651C212yesmaximal, complemented
5C2×D4328C211yesmaximal, characteristic, complemented
6D8×D541C212yesmaximal, complemented
7#31772634C211yesmaximal, characteristic, complemented
8#135×C541C211yesmaximal, characteristic, complemented
9#22575837C2214yescomplemented
10#22575836—22no—
11#22575836C2211yescharacteristic
12C2×D2164—22no—
13C2×D2164C2212yescomplemented
14D4×D541—24no—
15D4×D541C2214yescomplemented
16#22575823C2214yescomplemented
17D4328C2212yescomplemented
18D4328C2212yescomplemented
19#22575821C2214yescomplemented
20#22575820C2211yescharacteristic, complemented
21#22575819C2212yescomplemented
22C8×D541C2212yescomplemented
23#41×C541C2212yescomplemented
24Q16×C541C2211yescharacteristic, complemented
25SD16×C541C2212yescomplemented
26D8×C541C2211yescharacteristic, complemented
27C2×C8×C541C2211yescharacteristic, complemented
28C22×D541—22no—
29C22×D541—24no—
30Dic1082D411yescharacteristic
31D2164—24no—
32D2164—22no—
33D2164D411yescharacteristic
34D2164C2314yes—
35C22⋊D541—24no—
36C22⋊D541D412yes—
37C4×D541—24no—
38C4×D541C2312yes—
39#16864513C2312yes—
40Q8×C541C2312yes—
41D4×C541—22no—
42D4×C541C2312yes—
43C2×C4×C541—22no—
44C2×C4×C541C2311yescharacteristic
45C8×C541C2311yescharacteristic
46C8×C541C2311yescharacteristic
47C22×C541—22no—
48C22×C541C2×D411yescharacteristic
49C2×D541—24no—
50C2×D541—84no—
51C2×D541—82no—
52C2×D541C2×D412yes—
53C4×C541—22no—
54C4×C541C2×D411yescharacteristic
55C4×C541C2411yescharacteristic
56Dic541C2×D412yes—
57C2×C541—21no—
58C2×C541—42no—
59C2×C541C22×D411yescharacteristic
60D541—22no—
61D541—44no—
62C541#57611yescharacteristic, complemented, Sylow
63#576—5411nomaximal, Sylow
64H(5,𝔽2)—5412no—
65AGL(1,ℤ/8)—5412no—
66AGL(1,ℤ/8)—5414no—
67#135—5412no—
68#135D54111yescharacteristic, complemented
69C2×D8—5412no—
70C2×D8—5411no—
71#131—5411no—
72#41—5411no—
73#41—5414no—
74#41—10822no—
75#41C2×D54112yescomplemented
76C2×D4—5414no—
77C2×D4—5412no—
78C2×D4—10822no—
79C2×D4—10824no—
80Q16C2×D54111yescharacteristic, complemented
81SD16—5414no—
82SD16C2×D54112yescomplemented
83D8—5414no—
84D8—5412no—
85D8—5412no—
86D8C2×D54111yescharacteristic, complemented
87M16—5411no—
88M16—5412no—
89C2×C8—5412no—
90C2×C8C2×D54111yescharacteristic, complemented
91C23—10824no—
92C23—10822no—
93Q8—5411no—
94Q8C22×D54112yes—
95D4—22no—
96D4—5412no—
97D4—5411no—
98D4—5414no—
99D4—10824no—
100D4—10824no—
101D4—10822no—
102D4C22×D54112yes—
103C2×C4—22no—
104C2×C4—5412no—
105C2×C4—10824no—
106C2×C4C22×D54111yescharacteristic
107C8—5412no—
108C8C22×D54111yescharacteristic
109C8C22×D54111yescharacteristic
110C22—22no—
111C22—5412no—
112C22—10824no—
113C22—43282no—
114C22—43284no—
115C22D4×D54111yescharacteristic
116C4—22no—
117C4—5412no—
118C4D4×D54111yescharacteristic
119C4C23×D54111yescharacteristic
120C2—21no—
121C2—42no—
122C2—10822no—
123C2—21644no—
124C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#135×C541C2
socleC2×C541C22×D4
hypercenter#135D541
hypocenterC541#576
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #31772674C2semidirect
2. #31772655C2semidirect
3. #31772653C2semidirect
4. #31772651C2semidirect
5. C2×D4328C2semidirect
6. D8×D541C2semidirect
7. #31772634C2semidirect
8. #135×C541C2semidirect
9. #22575837C22semidirect
13. C2×D2164C22semidirect
15. D4×D541C22semidirect
16. #22575823C22semidirect
17. D4328C22semidirect
18. D4328C22semidirect
19. #22575821C22semidirect
20. #22575820C22semidirect
21. #22575819C22semidirect
22. C8×D541C22semidirect
23. #41×C541C22semidirect
24. Q16×C541C22semidirect
25. SD16×C541C22semidirect
26. D8×C541C22semidirect
27. C2×C8×C541C22semidirect
62. C541#576semidirect
68. #135D541semidirect
75. #41C2×D541semidirect
80. Q16C2×D541semidirect
82. SD16C2×D541semidirect
86. D8C2×D541semidirect
90. C2×C8C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726742
#317726552
#317726532
#317726512
C2×D43282
D8×D5412
#317726342
#135×C5412
#576541