Finite Group Databasebeta

← C2×#20298878 #28400319

Subgroups — C2×#20298878 #28400319

Order 14464.

480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16813622C211yesmaximal, characteristic, complemented
2#20298878C218yesmaximal, direct product factor
3C2×#16813555C212yesmaximal, complemented
4C2×C4⋊#11744751C211yesmaximal, characteristic, complemented
5C2×#16813543C212yesmaximal
6C2×C4×D4×C113C211yesmaximal, characteristic
7C22×Dic226—21no—
8C22×#11744751C2212yes—
9#16813622—22no—
10#16813622C2214yescomplemented
11C2×C4⋊Dic113—21no—
12C2×C4⋊Dic113C2212yes—
13#16813555C2218yescomplemented
14C4⋊#11744751C2214yescomplemented
15#16813543C2218yes—
16C22×D4×C113C2211yescharacteristic
17C23×C4×C113—21no—
18C4×D4×C113—22no—
19C4×D4×C113C2214yes—
20C2×C4⋊C4×C113C2211yescharacteristic
21C2×C22⋊C4×C113—21no—
22C2×C42×C113C2211yescharacteristic
23C2×Dic226—24no—
24C2×Dic226—44no—
25C22×Dic113—22no—
26C2×#11744751—24no—
27C2×#11744751C2314yes—
28C4⋊Dic113—24no—
29C4⋊Dic113—22no—
30C4⋊Dic113C2314yes—
31C24×C113—21no—
32C2×D4×C113—21no—
33C2×D4×C113—22no—
34C2×D4×C113Q814yescomplemented
35C2×D4×C113C2312yes—
36C22×C4×C113—21no—
37C22×C4×C113—24no—
38C22×C4×C113—44no—
39C22×C4×C113D411yescharacteristic
40C22×C4×C113D411yescharacteristic
41C22×C4×C113C2311yescharacteristic
42C4⋊C4×C113—21no—
43C4⋊C4×C113C2312yes—
44C22⋊C4×C113—24no—
45C42×C113D412yes—
46C42×C113C2312yes—
47C23×C113—24no—
48C23×C113—22no—
49C23×C113—42no—
50C23×C113—42no—
51C23×C113C2×D411yescharacteristic
52D4×C113—24no—
53D4×C113—22no—
54D4×C113C2×Q814yescomplemented
55C2×C4×C113—22no—
56C2×C4×C113—22no—
57C2×C4×C113—42no—
58C2×C4×C113—48no—
59C2×C4×C113D814yes—
60C2×C4×C113C2×D412yes—
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×Q812yes—
64C2×C4×C113#4112yes—
65C2×C4×C113C2411yescharacteristic
66C2×Dic113—24no—
67C2×Dic113—44no—
68Dic226—48no—
69#11744751—24no—
70C22×C113—24no—
71C22×C113—42no—
72C22×C113—42no—
73C22×C113—48no—
74C22×C113C22⋊Q812yes—
75C22×C113C2×D812yes—
76C22×C113#13712yes—
77C22×C113C22×D411yescharacteristic
78C4×C113—22no—
79C4×C113—42no—
80C4×C113C22⋊Q812yes—
81C4×C113C2×D814yes—
82C4×C113C22×Q811yescharacteristic
83C4×C113C2×#4111yescharacteristic
84Dic113—44no—
85C2×C113—44no—
86C2×C113#47414yescomplemented
87C2×C113C2×C22⋊Q811yescharacteristic
88C2×C113C22×D811yescharacteristic
89C2×C113C2×#13711yescharacteristic
90C2×#474—1131nomaximal, Sylow
91C113C2×#47411yescharacteristic, complemented, Sylow
92C2×C4⋊Q8—1131no—
93C2×C4×D4D11311yescharacteristic
94#474—1138no—
95C2×#107—1132no—
96C2×C4⋊C8—1131no—
97C2×#102—1132no—
98C22×Q8—2261no—
99C22×D4C2×D11311yescharacteristic
100C23×C4—21no—
101C22×C8—1132no—
102C4⋊Q8—1134no—
103C4⋊Q8—2262no—
104C4×D4—22no—
105C4×D4C2×D11314yes—
106C2×C4⋊C4—1132no—
107C2×C4⋊C4—2261no—
108C2×C4⋊C4C2×D11311yescharacteristic
109C2×C22⋊C4—21no—
110C2×C42C2×D11311yescharacteristic
111#107—1138no—
112C4⋊C8—1134no—
113#102—1138no—
114C24—21no—
115C2×Q8—4524no—
116C2×Q8—2264no—
117C2×D4—21no—
118C2×D4—22no—
119C2×D4Dic22614yescomplemented
120C2×D4C22×D11312yes—
121C22×C4—21no—
122C22×C4—24no—
123C22×C4—44no—
124C22×C4—2262no—
125C22×C4C22⋊D11311yescharacteristic
126C22×C4C22⋊D11311yescharacteristic
127C22×C4C22×D11311yescharacteristic
128C2×C8—1134no—
129C2×C8—2264no—
130C4⋊C4—21no—
131C4⋊C4—1134no—
132C4⋊C4—2262no—
133C4⋊C4—2264no—
134C4⋊C4C22×D11312yes—
135C22⋊C4—24no—
136C42C22⋊D11312yes—
137C42C22×D11312yes—
138C23—24no—
139C23—22no—
140C23—42no—
141C23—42no—
142C23C2×C22⋊D11311yescharacteristic
143Q8—4528no—
144D4—24no—
145D4—22no—
146D4C2×Dic22614yescomplemented
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—48no—
151C2×C4—4524no—
152C2×C4—2264no—
153C2×C4#1426863214yes—
154C2×C4C2×C22⋊D11312yes—
155C2×C4C2×C22⋊D11311yescharacteristic
156C2×C4C2×C22⋊D11312yes—
157C2×C4C2×Dic22612yes—
158C2×C4#1426864712yes—
159C2×C4C23×D11311yescharacteristic
160C8—2264no—
161C22—24no—
162C22—42no—
163C22—48no—
164C22—42no—
165C22#1681360112yes—
166C22C2×#1426863212yes—
167C22#1681365212yes—
168C22C22×C22⋊D11311yescharacteristic
169C4—22no—
170C4—42no—
171C4—4524no—
172C4#1681360112yes—
173C4C2×#1426863214yes—
174C4C22×Dic22611yescharacteristic
175C4C2×#1426864711yescharacteristic
176C2—44no—
177C2#2029887814yesdirect product factor
178C2C2×#1681360111yescharacteristic
179C2C22×#1426863211yescharacteristic
180C2C2×#1681365211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC23×C113C2×D4
prime radicalC22×D4×C113C22
hypercenterC2×C4×D4D113
hypocenterC113C2×#474
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16813622C2semidirect
2. #20298878C2direct (N × H)
3. C2×#16813555C2semidirect
4. C2×C4⋊#11744751C2semidirect
10. #16813622C22semidirect
13. #16813555C22semidirect
14. C4⋊#11744751C22semidirect
34. C2×D4×C113Q8semidirect
54. D4×C113C2×Q8semidirect
86. C2×C113#474semidirect
91. C113C2×#474semidirect
119. C2×D4Dic226semidirect
146. D4C2×Dic226semidirect
177. C2#20298878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168136222
#202988782
C2×#168135552
C2×C4⋊#117447512
C2×#168135432
C2×C4×D4×C1132
C2×#474113