Finite Group Databasebeta

← #46855182

Subgroups — #46855182

Order 35008.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#31776049C211yesmaximal, characteristic
2#31776033C211yesmaximal, characteristic, complemented
3#31776000C211yesmaximal, characteristic, complemented
4#31775929C211yesmaximal, characteristic, complemented
5#31775928C211yesmaximal, characteristic, complemented
6#31775920C211yesmaximal, characteristic, complemented
7#137×C547C211yesmaximal, characteristic, complemented
8#22576776—21no—
9#22576776C2211yescharacteristic
10#22576775—22no—
11#22576775—21no—
12C2×Dic1094—21no—
13C2×Dic1094C2211yescharacteristic
14Q8×D547—21no—
15#22576766—21no—
16#22576763—21no—
17#22576760C2211yescharacteristic
18Dic547⋊C4—22no—
19C4×Dic547C2211yescharacteristic
20#41×C547C2211yescharacteristic
21C2×Q8×C547C2211yescharacteristic
22Q16×C547—21no—
23SD16×C547—21no—
24M16×C547C2211yescharacteristic
25Dic1094—22no—
26Dic1094—21no—
27Dic1094—21no—
28Dic1094D411yescharacteristic
29D2188D411yescharacteristic
30C22⋊D547—22no—
31C22⋊D547—21no—
32C2×Dic547—22no—
33C2×Dic547—21no—
34C2×Dic547D412yes—
35C4×D547—22no—
36C4×D547—21no—
37C547⋊C8—21no—
38Q8×C547—21no—
39Q8×C547—21no—
40Q8×C547D411yescharacteristic
41D4×C547—21no—
42D4×C547D411yescharacteristic
43C2×C4×C547—21no—
44C2×C4×C547—21no—
45C2×C4×C547C2311yescharacteristic
46C8×C547—21no—
47C22×C547—21no—
48C22×C547C2×D411yescharacteristic
49C2×D547—21no—
50C4×C547—21no—
51C4×C547—41no—
52C4×C547C2×D411yescharacteristic
53C4×C547C2×D411yescharacteristic
54Dic547—22no—
55Dic547—21no—
56Dic547—22no—
57C2×C547—21no—
58C2×C547—41no—
59C2×C547#12011yescharacteristic
60D547—41no—
61C547#45611yescharacteristic, complemented, Sylow
62#456—5471nomaximal, Sylow
632−1+4—5471no—
64#137—5471no—
65#137D54711yescharacteristic, complemented
66C4⋊Q8—5471no—
67#104—5471no—
68#104—5471no—
69#101—5471no—
70#41—5471no—
71#41—10941no—
72#41—10942no—
73#41—10941no—
74#41C2×D54711yescharacteristic
75C2×Q8—5471no—
76C2×Q8—10941no—
77C2×Q8—10941no—
78C2×Q8C2×D54711yescharacteristic
79Q16—21no—
80Q16—10941no—
81SD16—21no—
82SD16—10941no—
83M16—5471no—
84M16C2×D54711yescharacteristic
85C4⋊C4—10942no—
86C42—5471no—
87Q8—21no—
88Q8—21no—
89Q8—5471no—
90Q8—10942no—
91Q8—10941no—
92Q8—10941no—
93Q8C22⋊D54711yescharacteristic
94D4—21no—
95D4—5471no—
96D4—10942no—
97D4—10941no—
98D4C22⋊D54711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—5472no—
102C2×C4—10942no—
103C2×C4—10942no—
104C2×C4—10941no—
105C2×C4—10941no—
106C2×C4C22×D54711yescharacteristic
107C8—21no—
108C8—10941no—
109C22—21no—
110C22—10941no—
111C22D4×D54711yescharacteristic
112C4—21no—
113C4—41no—
114C4—10942no—
115C4—10942no—
116C4—10941no—
117C4D4×D54711yescharacteristic
118C4C2×C22⋊D54711yescharacteristic
119C2—21no—
120C2—41no—
121C2—21881no—
122C2#3177597011yescharacteristic
subgroupG/H
centerC2#31775970
commutator, cosocleC2×C4×C547C23
FrattiniC2×C4C22×D547
Fitting#137×C547C2
socleC2×C547#120
prime radical#31776049C2
hypercenter#137D547
hypocenterC547#456
LCSG ▷ C2×C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #31776033C2semidirect
3. #31776000C2semidirect
4. #31775929C2semidirect
5. #31775928C2semidirect
6. #31775920C2semidirect
7. #137×C547C2semidirect
61. C547#456semidirect
65. #137D547semidirect

Maximal subgroups

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

subgroupindex
#317760492
#317760332
#317760002
#317759292
#317759282
#317759202
#137×C5472
#456547