Finite Group Databasebeta

← #28335195

Subgroups — #28335195

Order 13696.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#20293178C211yesmaximal, characteristic
2#20292649C212yesmaximal, complemented
3#20292376C211yesmaximal, characteristic, complemented
4#20292370C212yesmaximal, complemented
5#333×C107C211yesmaximal, characteristic, complemented
6C2×#13133819C412yes—
7C2×#13133801—22no—
8#16812106C2211yescharacteristic
9#16812098C412yes—
10#16812084—22no—
11#16812071—22no—
12C42×D107C2211yescharacteristic
13C4⋊(C107⋊C8)C2212yes—
14Dic107⋊C8—22no—
15C4⋊Q8×C107C2211yescharacteristic
16C4⋊C8×C107C2212yes—
17#13133819—44no—
18C2×D428—22no—
19C2×D428—22no—
20C2×D428C2×C412yes—
21C2×C4×D107—22no—
22C2×C4×D107C2×C411yescharacteristic
23C2×C4×D107D412yes—
24#13133801—44no—
25C2×C107⋊C8—22no—
26(C2×D107)⋊C4—24no—
27C4×Dic107C2×C411yescharacteristic
28C4×Dic107D412yes—
29C2×Q8×C107C2×C412yes—
30C2×C8×C107—22no—
31C4⋊C4×C107—22no—
32C42×C107C2311yescharacteristic
33C22×D107—22no—
34C22×D107C22⋊C411yescharacteristic
35Q8×C107—42no—
36C2×C4×C107—22no—
37C2×C4×C107C22×C411yescharacteristic
38C2×C4×C107C2×D412yes—
39C2×Dic107C22⋊C412yes—
40C2×Dic107C22⋊C411yescharacteristic
41D428—42no—
42D428—44no—
43D428—42no—
44D428—42no—
45C4×D107—22no—
46C4×D107—22no—
47C4×D107—22no—
48C4×D107—44no—
49C8×C107—42no—
50C107⋊C8—42no—
51C22×C107C2×C22⋊C411yescharacteristic
52C2×D107—21no—
53C2×D107—22no—
54C2×D107—42no—
55C2×D107—44no—
56C4×C107—21no—
57C4×C107—42no—
58C4×C107AGL(1,ℤ/8)12yes—
59C4×C107#13712yes—
60Dic107—22no—
61Dic107#10012yes—
62C2×C107C2×#10011yescharacteristic
63C2×C107#41712yes—
64D107—41no—
65D107—82no—
66#1560—1071nomaximal, Sylow
67C107#156011yescharacteristic, complemented, Sylow
68#532—1071no—
69#423—1072no—
70#333—1071no—
71#333D10711yescharacteristic, complemented
72#331—1072no—
73C2×#41—1072no—
74C2×M16—2142no—
75C4⋊Q8C2×D10711yescharacteristic
76#127—1071no—
77#124—1072no—
78#121—2142no—
79C4×D4—2142no—
80C2×C42—1071no—
81C4⋊C8—1072no—
82C4⋊C8—2142no—
83C4⋊C8C2×D10712yes—
84#41—4284no—
85C2×Q8C4×D10712yes—
86C2×D4—1072no—
87C2×D4—2142no—
88C2×D4—2142no—
89C22×C4—1071no—
90C22×C4—1072no—
91C22×C4—2142no—
92M16—4284no—
93C2×C8—22no—
94C2×C8—2142no—
95C4⋊C4—22no—
96C22⋊C4—2144no—
97C42—1071no—
98C42—1072no—
99C42C22×D10711yescharacteristic
100C23—1071no—
101C23—2142no—
102Q8—42no—
103D4—4282no—
104D4—4284no—
105D4—4282no—
106D4—4282no—
107C2×C4—22no—
108C2×C4—1071no—
109C2×C4—1072no—
110C2×C4—4284no—
111C2×C4—2142no—
112C2×C4—2142no—
113C2×C4—2142no—
114C2×C4C2×C4×D10711yescharacteristic
115C2×C4D4×D10712yes—
116C8—42no—
117C8—4282no—
118C22—4284no—
119C22—4282no—
120C22—2142no—
121C22—2141no—
122C22C22⋊C4×D10711yescharacteristic
123C4—21no—
124C4—42no—
125C4—1072no—
126C4—2142no—
127C4#1681213612yes—
128C4#1681214112yes—
129C2—8562no—
130C2—4281no—
131C2#100×D10711yescharacteristic
132C2#2029262712yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#333×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293178C2
cosocleC42×C107C23
hypercenter#333D107
hypocenterC107#1560
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20292649C2semidirect
3. #20292376C2semidirect
4. #20292370C2semidirect
5. #333×C107C2semidirect
67. C107#1560semidirect
71. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202931782
#202926492
#202923762
#202923702
#333×C1072
#1560107