Finite Group Databasebeta

← #28335762

Subgroups — #28335762

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#20292991C212yesmaximal
3#20292369C211yesmaximal, characteristic, complemented
4#20292368C212yesmaximal, complemented
5#490×C107C211yesmaximal, characteristic
6#16812101C2212yes—
7#16812100—22no—
8#16812099—22no—
9#16812099—22no—
10#16812030—22no—
11#16812030—22no—
12#16812020C2212yes—
13#127×C107C2211yescharacteristic
14#125×C107C2211yescharacteristic
15#102×C107—22no—
16#97×C107C2211yescharacteristic
17C2×C107⋊C8—22no—
18C4⋊Dic107—22no—
19C4⋊Dic107D412yes—
20C4⋊Dic107D412yes—
21Dic107⋊C4—22no—
22Dic107⋊C4—22no—
23Dic107⋊C4—22no—
24Dic107⋊C4—22no—
25C4×Dic107—22no—
26C2×D4×C107—21no—
27C2×D4×C107—22no—
28C2×C8×C107—21no—
29C4⋊C4×C107—22no—
30C4⋊C4×C107D412yes—
31C42×C107C2311yescharacteristic
32C23×C107—41no—
33D4×C107—44no—
34D4×C107—42no—
35C2×C4×C107—22no—
36C2×C4×C107C2×D412yes—
37C2×C4×C107C2×D411yescharacteristic
38C2×Dic107—22no—
39C2×Dic107—22no—
40C8×C107—41no—
41C107⋊C8—42no—
42C22×C107—82no—
43C22×C107—81no—
44C22×C107#12011yescharacteristic
45C4×C107—22no—
46C4×C107—21no—
47C4×C107—42no—
48Dic107—42no—
49Dic107—42no—
50C2×C107—161no—
51C2×C107#45412yes—
52C2×C107#45411yescharacteristic
53#1658—1071nomaximal, Sylow
54C107#165811yescharacteristic, complemented, Sylow
55#564—1071no—
56#490—1072no—
57#490D10711yescharacteristic
58#330—1071no—
59#330—1072no—
60#127C2×D10711yescharacteristic
61#125—1072no—
62#125—2142no—
63#125—2142no—
64#125—2142no—
65#125C2×D10711yescharacteristic
66#102—22no—
67#102—2142no—
68#102—2142no—
69#97—1072no—
70#97C2×D10711yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—2142no—
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⋊C4C22⋊D10712yes—
84C42—2142no—
85C42C22×D10711yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—2142no—
91C2×C4—2142no—
92C2×C4D4×D10712yes—
93C2×C4C2×C22⋊D10711yescharacteristic
94C8—41no—
95C8—4282no—
96C22—82no—
97C22—81no—
98C22#1681207711yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4282no—
103C4—4282no—
104C2—161no—
105C2#2029279812yes—
106C2#2029279911yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#490×C107C2
socleC22×C107#120
prime radical#127×C107C22
hypercenter#490D107
hypocenterC107#1658
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C107⋊#564C2semidirect
3. #20292369C2semidirect
4. #20292368C2semidirect
54. C107#1658semidirect

Maximal subgroups

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

subgroupindex
C107⋊#5642
#202929912
#202923692
#202923682
#490×C1072
#1658107