Finite Group Databasebeta

← #28344728

Subgroups — #28344728

Order 13696.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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#20292569C213yesmaximal
2#20292561C213yesmaximal
3#20292559C213yesmaximal
4#20292548C213yesmaximal
5#20292497C211yesmaximal, characteristic
6#20292495C211yesmaximal, characteristic
7#383×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C2×C4⋊Dic107C2213yes—
10C2×C4⋊Dic107C2213yes—
11C2×C4⋊Dic107C2213yes—
12C2×Dic107⋊C4C2213yes—
13C2×Dic107⋊C4C2213yes—
14C107⋊#95C2213yes—
15C107⋊#95C2213yes—
16C107⋊#95C2213yes—
17C107⋊#95C2213yes—
18C2×C42×C107C2211yescharacteristic
19#95×C107C2213yes—
20#95×C107C2213yes—
21C2×Dic214—43no—
22C22×Dic107C2313yes—
23C22×Dic107C2313yes—
24C22×Dic107C2311yescharacteristic
25C22×Dic107C2311yescharacteristic
26C4⋊Dic107—43no—
27C4⋊Dic107—43no—
28C4⋊Dic107—43no—
29Dic107⋊C4—43no—
30Dic107⋊C4—43no—
31C22×C4×C107C2311yescharacteristic
32C22×C4×C107C2313yes—
33C22×C4×C107C2313yes—
34C42×C107Q814yescomplemented
35C23×C107C2411yescharacteristic
36C2×C4×C107—23no—
37C2×C4×C107—23no—
38C2×C4×C107—23no—
39C2×C4×C107—23no—
40C2×C4×C107—26no—
41C2×C4×C107C2×Q816yes—
42C2×Dic107—23no—
43C2×Dic107—23no—
44C2×Dic107—23no—
45C2×Dic107—23no—
46C2×Dic107—23no—
47C2×Dic107—23no—
48C2×Dic107—26no—
49Dic214—44no—
50C22×C107C22×Q811yescharacteristic
51C22×C107H(5,𝔽2)13yes—
52C22×C1072−1+413yes—
53C4×C107—26no—
54C4×C107—41no—
55C4×C107—43no—
56Dic107—41no—
57Dic107—41no—
58Dic107—43no—
59Dic107—43no—
60C2×C107#54413yes—
61C2×C107#56011yescharacteristic
62C2×C107#56313yes—
63#2843—1071nomaximal, Sylow
64C107#284311yescharacteristic, complemented, Sylow
65#400—1073no—
66#398—1073no—
67#398—1073no—
68#395—1073no—
69#384—1071no—
70#383—1071no—
71#383D10711yescharacteristic
72C22×Q8—1071no—
73C2×C4⋊C4—1073no—
74C2×C4⋊C4—1073no—
75C2×C4⋊C4—1073no—
76C2×C4⋊C4—1073no—
77C2×C4⋊C4—1073no—
78C2×C42C2×D10711yescharacteristic
79#95—1073no—
80#95—1073no—
81#95—1073no—
82#95—1073no—
83#95C2×D10713yes—
84#95C2×D10713yes—
85C2×Q8—4283no—
86C22×C4—1073no—
87C22×C4—1071no—
88C22×C4—1071no—
89C22×C4—1073no—
90C22×C4C22×D10713yes—
91C22×C4C22×D10711yescharacteristic
92C22×C4C22×D10713yes—
93C4⋊C4—4283no—
94C4⋊C4—4283no—
95C4⋊C4—4283no—
96C4⋊C4—4283no—
97C4⋊C4—4283no—
98C42Dic21414yescomplemented
99C23C23×D10711yescharacteristic
100Q8—4284no—
101C2×C4—23no—
102C2×C4—23no—
103C2×C4—23no—
104C2×C4—23no—
105C2×C4—26no—
106C2×C4—2143no—
107C2×C4—2143no—
108C2×C4—2143no—
109C2×C4—2143no—
110C2×C4—2143no—
111C2×C4—2143no—
112C2×C4—2146no—
113C2×C4C2×Dic21416yes—
114C22C22×Dic21411yescharacteristic
115C22#1681215513yes—
116C22#1681215613yes—
117C4—26no—
118C4—43no—
119C4—41no—
120C4—4283no—
121C4—4281no—
122C4—4281no—
123C4—4283no—
124C2#2029325513yes—
125C2#2029336811yescharacteristic
126C2#2029337913yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#383×C107C2
hypercenter#383D107
hypocenterC107#2843
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
34. C42×C107Q8semidirect
64. C107#2843semidirect
98. C42Dic214semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925612
#202925592
#202925482
#202924972
#202924952
#383×C1072
#2843107