Finite Group Databasebeta

← #46830914

Subgroups — #46830914

Order 34624.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#31772624C211yesmaximal, characteristic, complemented
2#31772621C212yesmaximal, complemented
3#31772610C212yesmaximal, complemented
4#31772609C211yesmaximal, characteristic, complemented
5#31772601C212yesmaximal, complemented
6#31772600C212yesmaximal, complemented
7#31772599C212yesmaximal, complemented
8#31772597C212yesmaximal, complemented
9#120×C541C211yesmaximal, characteristic, complemented
10C2×D2164C2211yescharacteristic, complemented
11C2×C22⋊D541C2212yes—
12C2×C22⋊D541C2212yes—
13C2×C22⋊D541C2212yes—
14C2×C22⋊D541C2212yescomplemented
15C22×Dic541C2211yescharacteristic, complemented
16C2×C4×D541C2212yescomplemented
17C4⋊Dic541C2212yescomplemented
18#22575815C2212yescomplemented
19#22575815C2212yescomplemented
20C22⋊Dic541C2212yes—
21C22⋊Dic541C2212yes—
22C22⋊Dic541C2212yes—
23C22⋊Dic541C2211yescharacteristic, complemented
24#22575813C2212yescomplemented
25C4×Dic541C2211yescharacteristic, complemented
26C24×C541C2211yescharacteristic
27C2×D4×C541C2212yes—
28C2×D4×C541C2211yescharacteristic
29C22⋊C4×C541C2212yes—
30C22⋊C4×C541C2211yescharacteristic
31C22×D541C2312yes—
32D2164—41no—
33C22⋊D541—42no—
34C22⋊D541—42no—
35C22⋊D541—42no—
36C22⋊D541—42no—
37C2×Dic541—41no—
38C2×Dic541C2312yes—
39C2×Dic541C2312yes—
40C2×Dic541C2312yes—
41C4×D541—42no—
42C23×C541—42no—
43C23×C541—41no—
44C23×C541C2312yes—
45C23×C541C2311yescharacteristic
46C23×C541C2311yescharacteristic
47D4×C541—42no—
48D4×C541—41no—
49C2×C4×C541C2311yescharacteristic
50C2×C4×C541C2312yes—
51C22×C541—22no—
52C22×C541—22no—
53C22×C541—22no—
54C22×C541—22no—
55C22×C541—21no—
56C22×C541—21no—
57C22×C541—22no—
58C22×C541—44no—
59C22×C541C2411yescharacteristic
60C2×D541—22no—
61C2×D541—22no—
62C2×D541—22no—
63C4×C541—22no—
64C4×C541—21no—
65Dic541—22no—
66Dic541—22no—
67Dic541—22no—
68C2×C541—41no—
69C2×C541—42no—
70C2×C541—41no—
71C2×C541H(5,𝔽2)12yes—
72C2×C541H(5,𝔽2)11yescharacteristic
73D541—42no—
74C541#56011yescharacteristic, complemented, Sylow
75#560—5411nomaximal, Sylow
76#127—5411no—
77#126—5412no—
78#123—5411no—
79#123—5412no—
80#121—5412no—
81#121—5412no—
82#121—5412no—
83#120—5412no—
84#120D54111yescharacteristic, complemented
85C24C2×D54111yescharacteristic
86C2×D4—5412no—
87C2×D4—5412no—
88C2×D4—5412no—
89C2×D4—5412no—
90C2×D4—5411no—
91C2×D4C2×D54112yes—
92C2×D4C2×D54111yescharacteristic
93C22×C4—5411no—
94C22×C4—5412no—
95C4⋊C4—5412no—
96C4⋊C4—5412no—
97C4⋊C4—5412no—
98C22⋊C4—5412no—
99C22⋊C4—5412no—
100C22⋊C4—5412no—
101C22⋊C4—5411no—
102C22⋊C4—5412no—
103C22⋊C4C2×D54112yes—
104C22⋊C4C2×D54111yescharacteristic
105C42—5411no—
106C23—42no—
107C23—41no—
108C23—5412no—
109C23C22×D54112yes—
110C23C22×D54111yescharacteristic
111C23C22×D54111yescharacteristic
112D4—42no—
113D4—41no—
114D4—21641no—
115D4—21642no—
116D4—21642no—
117D4—21642no—
118D4—21642no—
119C2×C4—5412no—
120C2×C4—5412no—
121C2×C4—5412no—
122C2×C4—21642no—
123C2×C4—21641no—
124C2×C4C22×D54111yescharacteristic
125C2×C4C22×D54112yes—
126C22—21no—
127C22—22no—
128C22—22no—
129C22—21no—
130C22—22no—
131C22—22no—
132C22—22no—
133C22—44no—
134C22—10822no—
135C22—10822no—
136C22—10822no—
137C22C23×D54111yescharacteristic
138C4—22no—
139C4—21no—
140C4—10822no—
141C4—10822no—
142C4—10822no—
143C2—42no—
144C2—41no—
145C2—41no—
146C2—21642no—
147C2#3177267312yes—
148C2#3177267311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D541
commutator, socle, cosocleC22×C541C24
Fitting#120×C541C2
hypercenter#120D541
hypocenterC541#560
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #31772624C2semidirect
2. #31772621C2semidirect
3. #31772610C2semidirect
4. #31772609C2semidirect
5. #31772601C2semidirect
6. #31772600C2semidirect
7. #31772599C2semidirect
8. #31772597C2semidirect
9. #120×C541C2semidirect
10. C2×D2164C22semidirect
14. C2×C22⋊D541C22semidirect
15. C22×Dic541C22semidirect
16. C2×C4×D541C22semidirect
17. C4⋊Dic541C22semidirect
18. #22575815C22semidirect
19. #22575815C22semidirect
23. C22⋊Dic541C22semidirect
24. #22575813C22semidirect
25. C4×Dic541C22semidirect
74. C541#560semidirect
84. #120D541semidirect

Maximal subgroups

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

subgroupindex
#317726242
#317726212
#317726102
#317726092
#317726012
#317726002
#317725992
#317725972
#120×C5412
#560541