Finite Group Databasebeta

← #28335756

Subgroups — #28335756

Order 13696.

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

normal subgroups only

This group has 230 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
1#20293375C211yesmaximal, characteristic, complemented
2#20293016C212yesmaximal, complemented
3#20292993C211yesmaximal, characteristic, complemented
4#20292366C212yesmaximal, complemented
5#330×C107C211yesmaximal, characteristic, complemented
6C2×#13133807—22no—
7C2×D856—22no—
8#16812106C2211yescharacteristic
9#16812097C2212yes—
10#16812094—22no—
11#16812087—22no—
12#16812084—22no—
13#16812029—22no—
14#16812020C2211yescharacteristic
15#125×C107C2211yescharacteristic
16#97×C107C2212yes—
17C2×Dic214D412yes—
18C2×D428—22no—
19C2×D428—21no—
20C2×D428—22no—
21C2×D428D412yes—
22C2×C4×D107—22no—
23#13133807—44no—
24D856—44no—
25C2×C107⋊C8—21no—
26Dic107⋊C4—22no—
27(C2×D107)⋊C4—22no—
28(C2×D107)⋊C4—22no—
29(C2×D107)⋊C4—22no—
30C2×C8×C107—22no—
31C4⋊C4×C107—22no—
32C4⋊C4×C107D412yes—
33C42×C107C2311yescharacteristic
34C22×D107—22no—
35C22×D107—41no—
36C2×C4×C107—22no—
37C2×C4×C107C2×D412yes—
38C2×C4×C107C2×D411yescharacteristic
39C2×Dic107—22no—
40D428—42no—
41D428—42no—
42D428—42no—
43D428—42no—
44D428—82no—
45C4×D107—82no—
46Dic214—42no—
47C8×C107—24no—
48C107⋊C8—41no—
49C22×C107#12011yescharacteristic
50C2×D107—42no—
51C2×D107—42no—
52C2×D107—42no—
53C2×D107—82no—
54C2×D107—81no—
55C4×C107—22no—
56C4×C107—21no—
57C4×C107—42no—
58Dic107—42no—
59C2×C107#45312yes—
60C2×C107#45411yescharacteristic
61D107—82no—
62D107—161no—
63#1656—1071nomaximal, Sylow
64C107#165611yescharacteristic, complemented, Sylow
65#562—1071no—
66#496—1072no—
67#490—1071no—
68#330D10711yescharacteristic, complemented
69#329—1072no—
70C2×SD16—2142no—
71C2×D8—2142no—
72#127—1071no—
73#125C2×D10711yescharacteristic
74#124—1072no—
75#123—2142no—
76C22⋊Q8—2142no—
77#121—2142no—
78#102—2142no—
79#97—1071no—
80#97C2×D10712yes—
81C2×Q8—1072no—
82C2×D4—1072no—
83C2×D4—2142no—
84C2×D4—2142no—
85C2×D4—2141no—
86C22×C4—2142no—
87SD16—4284no—
88D8—4284no—
89C2×C8—22no—
90C2×C8—2141no—
91C4⋊C4—22no—
92C4⋊C4—2142no—
93C4⋊C4D42812yes—
94C22⋊C4—2142no—
95C22⋊C4—2142no—
96C22⋊C4—2142no—
97C42C22×D10711yescharacteristic
98C23—4281no—
99C23—2142no—
100Q8—4282no—
101D4—8562no—
102D4—4282no—
103D4—4282no—
104D4—4282no—
105D4—4282no—
106C2×C4—22no—
107C2×C4—8562no—
108C2×C4—2142no—
109C2×C4D4×D10712yes—
110C2×C4C2×D42811yescharacteristic
111C8—24no—
112C8—4281no—
113C22—8562no—
114C22—8561no—
115C22—4282no—
116C22—4282no—
117C22—4282no—
118C22#1681207911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—4282no—
123C2—8562no—
124C2—17121no—
125C2#2029279612yes—
126C2#2029280211yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107#120
hypercenter#330D107
hypocenterC107#1656
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. #20293375C2semidirect
2. #20293016C2semidirect
3. #20292993C2semidirect
4. #20292366C2semidirect
5. #330×C107C2semidirect
64. C107#1656semidirect
68. #330D107semidirect

Maximal subgroups

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

subgroupindex
#202933752
#202930162
#202929932
#202923662
#330×C1072
#1656107