Finite Group Databasebeta

← #28344650

Subgroups — #28344650

Order 13696.

380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 115 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#20292568C213yesmaximal, complemented
2#20292565C213yesmaximal, complemented
3#20292556C213yesmaximal
4#20292546C211yesmaximal, characteristic, complemented
5#20292538C211yesmaximal, characteristic
6#20292498C213yesmaximal
7#395×C107C211yesmaximal, characteristic, complemented
8C22×C4×D107C2211yescharacteristic
9C2×Dic107⋊C4C2213yes—
10C2×Dic107⋊C4C2213yes—
11C2×(C2×D107)⋊C4C2213yes—
12C2×(C2×D107)⋊C4C2213yes—
13C107⋊#95C2213yes—
14C107⋊#95C2213yes—
15C107⋊#95C2213yes—
16C107⋊#95C2213yes—
17C107⋊#95C2213yes—
18C22×Q8×C107C2211yescharacteristic
19C2×C4⋊C4×C107C2213yes—
20#95×C107C2213yes—
21C23×D107C2311yescharacteristic
22C22×Dic107C2313yes—
23C22×Dic107C2313yes—
24C22×Dic107C2311yescharacteristic
25C2×C4×D107—43no—
26Dic107⋊C4—43no—
27Dic107⋊C4—43no—
28(C2×D107)⋊C4—26no—
29(C2×D107)⋊C4—43no—
30C2×Q8×C107—43no—
31C22×C4×C107C2313yes—
32C22×C4×C107C2313yes—
33C22×C4×C107C2311yescharacteristic
34C4⋊C4×C107—43no—
35C23×C107C2411yescharacteristic
36C22×D107—23no—
37C22×D107—23no—
38C22×D107#4112yes—
39Q8×C107—44no—
40C2×C4×C107—23no—
41C2×C4×C107—23no—
42C2×C4×C107—23no—
43C2×C4×C107—23no—
44C2×C4×C107—23no—
45C2×C4×C107—23no—
46C2×C4×C107—23no—
47C2×Dic107—23no—
48C2×Dic107—23no—
49C2×Dic107—23no—
50C2×Dic107—23no—
51C2×Dic107—23no—
52C2×Dic107—26no—
53C4×D107—44no—
54C22×C107C2×#4111yescharacteristic
55C22×C107H(5,𝔽2)13yes—
56C22×C1072−1+413yes—
57C2×D107—26no—
58C2×D107—41no—
59C2×D107—43no—
60C4×C107—43no—
61C4×C107—41no—
62C4×C107—43no—
63Dic107—43no—
64Dic107—41no—
65Dic107—43no—
66C2×C107#53913yes—
67C2×C107H(3,𝔽4)11yescharacteristic
68C2×C107#56313yes—
69D107—42no—
70#2835—1071nomaximal, Sylow
71C107#283511yescharacteristic, complemented, Sylow
72#400—1073no—
73#400—1073no—
74#397—1073no—
75#395—1071no—
76#395D10711yescharacteristic, complemented
77#393—1071no—
78#385—1073no—
79C22×Q8C2×D10711yescharacteristic
80C23×C4—1071no—
81C2×C4⋊C4—1073no—
82C2×C4⋊C4—1073no—
83C2×C4⋊C4C2×D10713yes—
84C2×C22⋊C4—1073no—
85C2×C22⋊C4—1073no—
86#95—1073no—
87#95—1073no—
88#95—1073no—
89#95—1073no—
90#95—1073no—
91#95C2×D10713yes—
92C24—1071no—
93C2×Q8—43no—
94C22×C4—1073no—
95C22×C4—1073no—
96C22×C4—1071no—
97C22×C4—4283no—
98C22×C4C22×D10711yescharacteristic
99C22×C4C22×D10713yes—
100C22×C4C22×D10713yes—
101C4⋊C4—43no—
102C4⋊C4—4283no—
103C4⋊C4—4283no—
104C22⋊C4—4283no—
105C22⋊C4—2146no—
106C23—1072no—
107C23—2143no—
108C23—2143no—
109C23C23×D10711yescharacteristic
110Q8—44no—
111C2×C4—23no—
112C2×C4—23no—
113C2×C4—23no—
114C2×C4—23no—
115C2×C4—23no—
116C2×C4—23no—
117C2×C4—23no—
118C2×C4—4284no—
119C2×C4—2143no—
120C2×C4—2143no—
121C2×C4—2143no—
122C2×C4—2143no—
123C2×C4—2146no—
124C2×C4—2143no—
125C22—4283no—
126C22—4281no—
127C22—2146no—
128C22#41×D10711yescharacteristic
129C22#1681215413yes—
130C22#1681215713yes—
131C4—43no—
132C4—41no—
133C4—43no—
134C4—4283no—
135C4—4283no—
136C4—4281no—
137C2—4282no—
138C2#2029322313yes—
139C2#2029337011yescharacteristic
140C2#2029337613yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#395×C107C2
prime radicalC23×D107C23
hypercenter#395D107
hypocenterC107#2835
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #20292568C2semidirect
2. #20292565C2semidirect
4. #20292546C2semidirect
7. #395×C107C2semidirect
71. C107#2835semidirect
76. #395D107semidirect

Maximal subgroups

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

subgroupindex
#202925682
#202925652
#202925562
#202925462
#202925382
#202924982
#395×C1072
#2835107