Finite Group Databasebeta

← #28334792

Subgroups — #28334792

Order 13696.

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

normal subgroups only

This group has 252 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
1C2×#16812065C211yesmaximal, characteristic
2#20292681C212yesmaximal, complemented
3#20292352C212yesmaximal, complemented
4#20292351C211yesmaximal, characteristic
5#323×C107C211yesmaximal, characteristic
6C23×Dic107C411yescharacteristic
7#16812065—22no—
8#16812065—22no—
9C2×Dic107⋊C4C411yescharacteristic
10C2×Dic107⋊C4C2211yescharacteristic
11C2×C22⋊Dic107C411yescharacteristic
12C2×C4×Dic107C411yescharacteristic
13C2×C4×Dic107C2211yescharacteristic
14Dic107⋊C8—22no—
15C22⋊(C107⋊C8)C2212yes—
16#16812019—22no—
17C2×C22⋊C4×C107C2211yescharacteristic
18C22⋊C8×C107C2212yes—
19C22×Dic107—22no—
20C22×Dic107—21no—
21C22×Dic107—21no—
22C22×Dic107—22no—
23C22×Dic107C2×C411yescharacteristic
24C22×Dic107C2×C411yescharacteristic
25C22×Dic107C2×C411yescharacteristic
26C22×Dic107C2×C411yescharacteristic
27C2×C107⋊C8—22no—
28Dic107⋊C4—22no—
29Dic107⋊C4—22no—
30C22⋊Dic107—22no—
31C4×Dic107—21no—
32C4×Dic107—21no—
33C4×Dic107D412yes—
34C4×Dic107D412yes—
35C24×C107C2×C411yescharacteristic
36C22×C4×C107C2×C411yescharacteristic
37C22×C4×C107C2311yescharacteristic
38C2×C8×C107—22no—
39C22⋊C4×C107—22no—
40C23×C107—21no—
41C23×C107—21no—
42C23×C107—41no—
43C23×C107—41no—
44C23×C107M1612yes—
45C23×C107C22×C411yescharacteristic
46C2×C4×C107—21no—
47C2×C4×C107—41no—
48C2×C4×C107—41no—
49C2×C4×C107C2×D412yes—
50C2×Dic107—24no—
51C2×Dic107—24no—
52C2×Dic107—21no—
53C2×Dic107—21no—
54C2×Dic107—21no—
55C2×Dic107—21no—
56C2×Dic107—21no—
57C2×Dic107—41no—
58C2×Dic107—41no—
59C2×Dic107C22⋊C411yescharacteristic
60C2×Dic107C22⋊C411yescharacteristic
61C2×Dic107C22⋊C412yes—
62C2×Dic107M1612yes—
63C8×C107—42no—
64C107⋊C8—42no—
65C22×C107—21no—
66C22×C107—21no—
67C22×C107—22no—
68C22×C107—42no—
69C22×C107—42no—
70C22×C107—41no—
71C22×C107—41no—
72C22×C107C2×C22⋊C411yescharacteristic
73C22×C107C2×M1611yescharacteristic
74C22×C107C2×M1611yescharacteristic
75C4×C107—22no—
76C4×C107—41no—
77Dic107—21no—
78Dic107—21no—
79Dic107—22no—
80Dic107—22no—
81Dic107—41no—
82C2×C107—21no—
83C2×C107—21no—
84C2×C107—42no—
85C2×C107#40711yescharacteristic
86C2×C107#41011yescharacteristic
87C2×C107#41311yescharacteristic
88#1464—1071nomaximal, Sylow
89C107#146411yescharacteristic, complemented, Sylow
90C2×#117—1071no—
91#432—1072no—
92#324—1072no—
93#323—1071no—
94#323D10711yescharacteristic
95C23×C4—1071no—
96#117—2142no—
97#117—2142no—
98C2×C4⋊C4—1071no—
99C2×C4⋊C4—1071no—
100C2×C22⋊C4—1071no—
101C2×C22⋊C4C2×D10711yescharacteristic
102C2×C42—1071no—
103C2×C42—1071no—
104C4⋊C8—2142no—
105C22⋊C8—1072no—
106C22⋊C8C2×D10712yes—
107#97—2142no—
108C24C4×D10711yescharacteristic
109C22×C4—1071no—
110C22×C4—1071no—
111C22×C4—1071no—
112C22×C4—1071no—
113C22×C4—2141no—
114C22×C4—2141no—
115C22×C4—2142no—
116C22×C4—2142no—
117C22×C4C4×D10711yescharacteristic
118C22×C4C22×D10711yescharacteristic
119C2×C8—22no—
120C2×C8—2142no—
121C4⋊C4—2142no—
122C4⋊C4—2142no—
123C22⋊C4—22no—
124C22⋊C4—2142no—
125C42—1072no—
126C42—1072no—
127C42—2141no—
128C42—2141no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23#1313380112yes—
134C23C2×C4×D10711yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—1071no—
139C2×C4—1071no—
140C2×C4—1072no—
141C2×C4—1072no—
142C2×C4—4281no—
143C2×C4—4281no—
144C2×C4—2141no—
145C2×C4—2144no—
146C2×C4—2144no—
147C2×C4—2141no—
148C2×C4—2141no—
149C2×C4—2141no—
150C2×C4—2141no—
151C2×C4D4×D10712yes—
152C8—42no—
153C8—4282no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D10711yescharacteristic
162C22M16×D10711yescharacteristic
163C22C2×#1313380111yescharacteristic
164C4—22no—
165C4—41no—
166C4—4281no—
167C4—2142no—
168C4—2141no—
169C4—2141no—
170C4—2142no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2#2029258911yescharacteristic
175C2#2029259911yescharacteristic
176C2#2029260811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#323×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC24×C107C2×C4
cosocleC22×C4×C107C23
hypercenter#323D107
hypocenterC107#1464
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20292681C2semidirect
3. #20292352C2semidirect
89. C107#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#168120652
#202926812
#202923522
#202923512
#323×C1072
#1464107