Finite Group Databasebeta

← C2×#20292940 #28346332

Subgroups — C2×#20292940 #28346332

Order 13696.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16812083C211yesmaximal, characteristic
2#20292940C218yesmaximal, direct product factor
3C2×#16812042C212yesmaximal, complemented
4C2×#16812029C212yesmaximal, complemented
5C2×C22⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C107C211yesmaximal, characteristic, complemented
7C22×D428C2211yescharacteristic
8C22×C22⋊D107—21no—
9C22×C107⋊C8C2212yes—
10#16812083—22no—
11#16812083C2214yes—
12C2×C4⋊Dic107C2211yescharacteristic
13C2×(C2×D107)⋊C4—21no—
14#16812042C2218yescomplemented
15#16812029C2218yescomplemented
16C22⋊(C107⋊C8)C2214yescomplemented
17C23×C4×C107—21no—
18C23×C4×C107C2211yescharacteristic
19C2×C4⋊C4×C107—22no—
20C2×C4⋊C4×C107—21no—
21C2×C4⋊C4×C107C2212yes—
22C2×C4⋊C4×C107C2214yescomplemented
23C23×D107—21no—
24C2×D428—24no—
25C2×D428—21no—
26C2×D428C2312yes—
27C2×C22⋊D107—24no—
28C2×C22⋊D107—44no—
29C22×Dic107—21no—
30C2×C107⋊C8—24no—
31C2×C107⋊C8C2314yes—
32C4⋊Dic107—21no—
33C4⋊Dic107C2312yes—
34(C2×D107)⋊C4—24no—
35C24×C107D411yescharacteristic
36C22×C4×C107—24no—
37C22×C4×C107—22no—
38C22×C4×C107—24no—
39C22×C4×C107—44no—
40C22×C4×C107D411yescharacteristic
41C22×C4×C107D412yes—
42C22×C4×C107C2312yes—
43C22×C4×C107C2311yescharacteristic
44C4⋊C4×C107—22no—
45C4⋊C4×C107—24no—
46C4⋊C4×C107C2314yes—
47C23×C107—22no—
48C23×C107—22no—
49C23×C107D814yes—
50C23×C107C2×D412yes—
51C23×C107C2×D411yescharacteristic
52C22×D107—22no—
53C22×D107—42no—
54C22×D107—42no—
55C22×D107—42no—
56C2×C4×C107—22no—
57C2×C4×C107—24no—
58C2×C4×C107—24no—
59C2×C4×C107—24no—
60C2×C4×C107—48no—
61C2×C4×C107—44no—
62C2×C4×C107C2×D412yes—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107#4114yes—
65C2×C4×C107C2411yescharacteristic
66C22⋊D107—48no—
67C2×Dic107—22no—
68C2×Dic107—42no—
69D428—24no—
70D428—42no—
71C107⋊C8—24no—
72C22×C107—22no—
73C22×C107—22no—
74C22×C107—28no—
75C22×C107#12312yes—
76C22×C107C2×D814yes—
77C22×C107C2×D812yes—
78C22×C107#13712yes—
79C22×C107C22×D411yescharacteristic
80C2×D107—42no—
81C2×D107—42no—
82C2×D107—42no—
83C2×D107—84no—
84C4×C107—22no—
85C4×C107—44no—
86C4×C107#12312yes—
87C4×C107C2×#4112yes—
88Dic107—42no—
89C2×C107—24no—
90C2×C107#48014yescomplemented
91C2×C107C2×#12311yescharacteristic
92C2×C107C22×D811yescharacteristic
93C2×C107C2×#13711yescharacteristic
94D107—82no—
95C2×#480—1071nomaximal, Sylow
96C107C2×#48011yescharacteristic, complemented, Sylow
97C2×#121—1071no—
98C22×C4⋊C4D10711yescharacteristic, complemented
99#480—1078no—
100C2×#107—1072no—
101C2×#102—1072no—
102C2×C22⋊C8—1071no—
103C22×D4—1071no—
104C22×D4—2141no—
105C23×C4—21no—
106C23×C4C2×D10711yescharacteristic
107C22×C8—1072no—
108#121—1074no—
109#121—2142no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—1071no—
113C2×C4⋊C4C2×D10712yes—
114C2×C4⋊C4C2×D10714yescomplemented
115C2×C22⋊C4—2141no—
116#107—1078no—
117#102—1078no—
118C22⋊C8—1074no—
119C24—2141no—
120C24C22⋊D10711yescharacteristic
121C2×D4—1072no—
122C2×D4—4284no—
123C2×D4—2144no—
124C2×D4—2141no—
125C2×D4—2144no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—2141no—
131C22×C4C22⋊D10712yes—
132C22×C4C22⋊D10711yescharacteristic
133C22×C4C22×D10712yes—
134C22×C4C22×D10711yescharacteristic
135C2×C8—1074no—
136C2×C8—2144no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—1072no—
140C4⋊C4—2141no—
141C4⋊C4C22×D10714yes—
142C22⋊C4—2144no—
143C23—22no—
144C23—22no—
145C23—4282no—
146C23—4282no—
147C23—4282no—
148C23—2142no—
149C23#1313380314yes—
150C23C2×C22⋊D10712yes—
151C23C2×C22⋊D10711yescharacteristic
152D4—4288no—
153D4—4282no—
154D4—2144no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—4282no—
162C2×C4—2142no—
163C2×C4C2×C22⋊D10712yes—
164C2×C4C2×C22⋊D10711yescharacteristic
165C2×C4#1313381814yes—
166C2×C4C23×D10711yescharacteristic
167C8—2144no—
168C22—22no—
169C22—22no—
170C22—28no—
171C22—8564no—
172C22—4282no—
173C22—4282no—
174C22—4282no—
175C22#1681209212yes—
176C22C2×#1313380314yes—
177C22C2×#1313380312yes—
178C22#1681214012yes—
179C22C22×C22⋊D10711yescharacteristic
180C4—22no—
181C4—44no—
182C4—4282no—
183C4#1681209212yes—
184C4C2×#1313381812yes—
185C2—24no—
186C2—8562no—
187C2#2029294014yesdirect product factor
188C2C2×#1681209211yescharacteristic
189C2C22×#1313380311yescharacteristic
190C2C2×#1681214011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC22×C4⋊C4×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812083C2
hypercenterC22×C4⋊C4D107
hypocenterC107C2×#480
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20292940C2direct (N × H)
3. C2×#16812042C2semidirect
4. C2×#16812029C2semidirect
5. C2×C22⋊(C107⋊C8)C2semidirect
6. C22×C4⋊C4×C107C2semidirect
14. #16812042C22semidirect
15. #16812029C22semidirect
16. C22⋊(C107⋊C8)C22semidirect
22. C2×C4⋊C4×C107C22semidirect
90. C2×C107#480semidirect
96. C107C2×#480semidirect
98. C22×C4⋊C4D107semidirect
114. C2×C4⋊C4C2×D107semidirect
187. C2#20292940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120832
#202929402
C2×#168120422
C2×#168120292
C2×C22⋊(C107⋊C8)2
C22×C4⋊C4×C1072
C2×#480107