Finite Group Databasebeta

← C22⋊C16×D107 #28338067

Subgroups — C22⋊C16×D107 #28338067

Order 13696.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×C8×D107C211yesmaximal, characteristic
2C2×C16×D107C212yesmaximal, complemented
3C22⋊(C107⋊C16)C211yesmaximal, characteristic, complemented
4(C2×D107)⋊C16C212yesmaximal, complemented
5C22⋊C16×C107C211yesmaximal, characteristic, complemented
6C22×C4×D107C411yescharacteristic
7C22×C107⋊C8C411yescharacteristic
8C2×C8×D107—24no—
9C2×C8×D107C411yescharacteristic
10C2×C8×D107C411yescharacteristic
11C2×C8×D107C2211yescharacteristic
12C2×C8×D107C2211yescharacteristic
13C2×C107⋊C16C2212yescomplemented
14C16×D107—24no—
15C22×C8×C107C2211yescharacteristic
16C2×C16×C107C2212yescomplemented
17C23×D107C811yescharacteristic
18C22×Dic107C811yescharacteristic
19C2×C4×D107—22no—
20C2×C4×D107—22no—
21C2×C4×D107C811yescharacteristic
22C2×C4×D107C811yescharacteristic
23C2×C4×D107C2×C411yescharacteristic
24C2×C4×D107C2×C411yescharacteristic
25C2×C107⋊C8—22no—
26C2×C107⋊C8C2×C411yescharacteristic
27C2×C107⋊C8C2×C411yescharacteristic
28C8×D107—22no—
29C8×D107—22no—
30C8×D107—22no—
31C8×D107D414yes—
32C107⋊C16—22no—
33C22×C4×C107C2×C411yescharacteristic
34C2×C8×C107—22no—
35C2×C8×C107C2×C411yescharacteristic
36C2×C8×C107C2311yescharacteristic
37C16×C107—22no—
38C23×C107C2×C811yescharacteristic
39C22×D107—22no—
40C22×D107—22no—
41C22×D107C1614yescomplemented
42C22×D107C2×C811yescharacteristic
43C22×D107C2×C811yescharacteristic
44C2×C4×C107—21no—
45C2×C4×C107—21no—
46C2×C4×C107C2×C811yescharacteristic
47C2×C4×C107C22×C411yescharacteristic
48C2×Dic107—22no—
49C2×Dic107C2×C811yescharacteristic
50C2×Dic107C2×C811yescharacteristic
51C4×D107—22no—
52C4×D107—21no—
53C4×D107—21no—
54C4×D107—22no—
55C4×D107C22⋊C412yes—
56C4×D107M1612yes—
57C8×C107—21no—
58C8×C107C2×D412yes—
59C107⋊C8—21no—
60C107⋊C8C22⋊C412yes—
61C22×C107—21no—
62C22×C107—21no—
63C22×C107C2×C1612yescomplemented
64C22×C107C22×C811yescharacteristic
65C2×D107—21no—
66C2×D107—21no—
67C2×D107—28no—
68C2×D107C22⋊C812yes—
69C2×D107C2×C1612yes—
70C2×D107C2×C1612yescomplemented
71C2×D107M3212yes—
72C4×C107—21no—
73C4×C107C2×C22⋊C411yescharacteristic
74C4×C107C2×M1611yescharacteristic
75Dic107—21no—
76Dic107C22⋊C812yes—
77C2×C107—22no—
78C2×C107C2×C22⋊C811yescharacteristic
79C2×C107C22×C1611yescharacteristic
80C2×C107C2×M3211yescharacteristic
81D107—22no—
82D107C22⋊C1614yesdirect product factor
83C2×C22⋊C16—1071nomaximal, Sylow
84C107C2×C22⋊C1611yescharacteristic, complemented, Sylow
85C23×C8—1071no—
86C22×C16—1072no—
87C22⋊C16—1071no—
88C22⋊C16—1072no—
89C22⋊C16D10711yescharacteristic, direct product factor
90C23×C4—1071no—
91C22×C8—1071no—
92C22×C8—1071no—
93C22×C8—1071no—
94C22×C8—1071no—
95C22×C8—1071no—
96C22×C8—2144no—
97C22×C8C2×D10711yescharacteristic
98C2×C16—1072no—
99C2×C16—2144no—
100C2×C16C2×D10712yescomplemented
101C24—1071no—
102C22×C4—1071no—
103C22×C4—1071no—
104C22×C4—1071no—
105C22×C4—1071no—
106C22×C4—1071no—
107C22×C4—2142no—
108C22×C4—2142no—
109C22×C4C4×D10711yescharacteristic
110C2×C8—22no—
111C2×C8—1071no—
112C2×C8—1074no—
113C2×C8—1071no—
114C2×C8—2142no—
115C2×C8—2142no—
116C2×C8—2142no—
117C2×C8—2142no—
118C2×C8C4×D10711yescharacteristic
119C2×C8C22×D10711yescharacteristic
120C16—22no—
121C16—2142no—
122C23—1071no—
123C23—1074no—
124C23—1071no—
125C23—2142no—
126C23—2142no—
127C23C8×D10711yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—1071no—
131C2×C4—1072no—
132C2×C4—1072no—
133C2×C4—1071no—
134C2×C4—2142no—
135C2×C4—2142no—
136C2×C4—2142no—
137C2×C4—2141no—
138C2×C4—2141no—
139C2×C4C8×D10711yescharacteristic
140C2×C4C2×C4×D10711yescharacteristic
141C8—21no—
142C8—1072no—
143C8—2141no—
144C8D4×D10712yes—
145C22—21no—
146C22—21no—
147C22—1072no—
148C22—1072no—
149C22—1072no—
150C22—1072no—
151C22—2148no—
152C22—2141no—
153C22—2141no—
154C22C16×D10712yescomplemented
155C22C2×C8×D10711yescharacteristic
156C4—21no—
157C4—1072no—
158C4—2141no—
159C4C22⋊C4×D10711yescharacteristic
160C4M16×D10711yescharacteristic
161C2—22no—
162C2—1074no—
163C2—2142no—
164C2C22⋊C8×D10711yescharacteristic
165C2C2×C16×D10711yescharacteristic
166C2M32×D10711yescharacteristic
subgroupG/H
center, FrattiniC2×C8C22×D107
commutatorC2×C107C22×C16
FittingC22⋊C16×C107C2
socleC22×C107C22×C8
prime radicalC23×D107C8
cosocleC2×C8×C107C23
hypercenterC22⋊C16D107
hypocenterC107C2×C22⋊C16
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×C16×D107C2semidirect
3. C22⋊(C107⋊C16)C2semidirect
4. (C2×D107)⋊C16C2semidirect
5. C22⋊C16×C107C2semidirect
13. C2×C107⋊C16C22semidirect
16. C2×C16×C107C22semidirect
41. C22×D107C16semidirect
63. C22×C107C2×C16semidirect
70. C2×D107C2×C16semidirect
82. D107C22⋊C16direct (N × H)
84. C107C2×C22⋊C16semidirect
89. C22⋊C16D107direct (N × H)
100. C2×C16C2×D107semidirect
154. C22C16×D107semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D1072
C2×C16×D1072
C22⋊(C107⋊C16)2
(C2×D107)⋊C162
C22⋊C16×C1072
C2×C22⋊C16107