Finite Group Databasebeta

← #28335764

Subgroups — #28335764

Order 13696.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C107⋊#564C211yesmaximal, characteristic, complemented
2#20292993C211yesmaximal, characteristic
3#20292992C212yesmaximal
4#20292368C212yesmaximal, complemented
5#330×C107C211yesmaximal, characteristic, complemented
6#16812106C2211yescharacteristic
7#16812101C2212yes—
8#16812100—22no—
9#16812099—22no—
10#16812099—22no—
11#16812031—22no—
12#16812031—22no—
13#16812029—22no—
14#16812020C2211yescharacteristic
15#125×C107C2211yescharacteristic
16#97×C107C2212yes—
17C2×D428—21no—
18C2×D428—22no—
19C2×C107⋊C8—21no—
20C4⋊Dic107—22no—
21C4⋊Dic107D412yes—
22C4⋊Dic107D412yes—
23Dic107⋊C4—22no—
24Dic107⋊C4—22no—
25Dic107⋊C4—22no—
26Dic107⋊C4—22no—
27C4×Dic107—22no—
28C2×C8×C107—22no—
29C4⋊C4×C107—22no—
30C4⋊C4×C107D412yes—
31C42×C107C2311yescharacteristic
32C22×D107—41no—
33C2×C4×C107—22no—
34C2×C4×C107C2×D412yes—
35C2×C4×C107C2×D411yescharacteristic
36C2×Dic107—22no—
37C2×Dic107—22no—
38D428—42no—
39D428—44no—
40C8×C107—42no—
41C107⋊C8—41no—
42C22×C107#12011yescharacteristic
43C2×D107—82no—
44C2×D107—81no—
45C4×C107—21no—
46C4×C107—22no—
47C4×C107—42no—
48Dic107—42no—
49Dic107—42no—
50C2×C107#45412yes—
51C2×C107#45411yescharacteristic
52D107—161no—
53#1658—1071nomaximal, Sylow
54C107#165811yescharacteristic, complemented, Sylow
55#564—1071no—
56#490—1071no—
57#490—1072no—
58#330—1072no—
59#330D10711yescharacteristic, complemented
60#127—1071no—
61#125—1072no—
62#125—2142no—
63#125—2142no—
64#125—2142no—
65#125C2×D10711yescharacteristic
66#102—2142no—
67#102—2142no—
68#102—2142no—
69#97—1071no—
70#97C2×D10712yes—
71C2×D4—2142no—
72C2×D4—2141no—
73C2×C8—22no—
74C2×C8—2141no—
75C4⋊C4—22no—
76C4⋊C4—1072no—
77C4⋊C4—1072no—
78C4⋊C4—2142no—
79C4⋊C4—2142no—
80C4⋊C4—2142no—
81C4⋊C4—2142no—
82C4⋊C4—2142no—
83C4⋊C4D42812yes—
84C42—2142no—
85C42C22×D10711yescharacteristic
86C23—4281no—
87D4—4284no—
88D4—4282no—
89C2×C4—22no—
90C2×C4—2142no—
91C2×C4—2142no—
92C2×C4D4×D10712yes—
93C2×C4C2×D42811yescharacteristic
94C8—42no—
95C8—4281no—
96C22—8562no—
97C22—8561no—
98C22#1681207911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4282no—
103C4—4282no—
104C2—17121no—
105C2#2029280112yes—
106C2#2029280211yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107#120
prime radical#16812106C22
hypercenter#330D107
hypocenterC107#1658
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C107⋊#564C2semidirect
4. #20292368C2semidirect
5. #330×C107C2semidirect
54. C107#1658semidirect
59. #330D107semidirect

Maximal subgroups

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

subgroupindex
C107⋊#5642
#202929932
#202929922
#202923682
#330×C1072
#1658107