Finite Group Databasebeta

← C2×D8×#90673 #28407321

Subgroups — C2×D8×#90673 #28407321

Order 14464.

616 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 178 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×D4×#90673C212yesmaximal, complemented
2D8×#90673C218yesmaximal, direct product factor
3C2×#16813691C211yesmaximal, characteristic, complemented
4C2×#16813684C212yesmaximal, complemented
5C2×C8×#90673C211yesmaximal, characteristic, complemented
6C2×D8×D113C211yesmaximal, characteristic
7C23×#90673—22no—
8C2×#14268655C2211yescharacteristic
9D4×#90673—24no—
10D4×#90673C2218yescomplemented
11C2×C4⋊#90673C2212yes—
12C2×C22⋊#90673—22no—
13C2×C4×#90673C2211yescharacteristic
14#16813691C2214yescomplemented
15#16813684C2218yescomplemented
16C8×#90673C2214yescomplemented
17C2×D4×D113C2212yes—
18C2×D904C411yescharacteristic, complemented
19C2×#14268632C412yescomplemented
20D8×D113C414yescomplemented
21D8×D113C2214yes—
22C2×C8×D113C2211yescharacteristic
23C2×D8×C113C411yescharacteristic, complemented
24C22×#90673—22no—
25C22×#90673—28no—
26C22×#90673—48no—
27C22×#90673D411yescharacteristic
28C22×#90673D411yescharacteristic
29#14268655—21no—
30#14268655C2312yes—
31C2×#11744753—21no—
32C4⋊#90673—22no—
33C4⋊#90673C2314yes—
34C22⋊#90673—28no—
35C4×#90673D412yes—
36C4×#90673C2312yes—
37C23×D113—22no—
38C2×D452C2×C412yescomplemented
39C2×C22⋊D113—22no—
40D4×D113—22no—
41D4×D113—22no—
42D4×D113C2×C414yescomplemented
43D4×D113C2314yes—
44C2×C4×D113C2311yescharacteristic
45D904C2×C414yescomplemented
46#14268632C2×C418yescomplemented
47C2×#11744751C2×C411yescharacteristic, complemented
48C8×D113C2×C412yescomplemented
49C8×D113C2312yes—
50C2×D4×C113C2×C412yescomplemented
51D8×C113C2×C414yescomplemented
52C2×C8×C113C2×C411yescharacteristic, complemented
53C23×C113—22no—
54C22×D113—22no—
55C22×D113—24no—
56C22×D113—24no—
57C22×D113—44no—
58C22×D113—44no—
59C22×D113C2×D411yescharacteristic
60C2×#90673—22no—
61C2×#90673—24no—
62C2×#90673—44no—
63C2×#90673—416no—
64C2×#90673D814yesdirect product factor
65C2×#90673C2×D412yes—
66C2×#90673C2×D412yes—
67D4×C113—22no—
68D4×C113C22×C414yescomplemented
69C2×C4×C113C22×C411yescharacteristic
70C22⋊D113—24no—
71C22⋊D113—24no—
72C2×Dic113#4111yescharacteristic
73D452—22no—
74D452C22×C414yescomplemented
75C4×D113C22×C411yescharacteristic
76C4×D113C2×D411yescharacteristic
77C4×D113#4111yescharacteristic
78C4×D113C2411yescharacteristic
79#11744753—22no—
80C8×C113C22×C412yescomplemented
81#11744751C22×C412yescomplemented
82C22×C113—24no—
83C22×C113—44no—
84C22×C113C4×D411yescharacteristic
85C2×D113—24no—
86C2×D113—44no—
87C2×D113—44no—
88C2×D113—44no—
89C2×D113—48no—
90C2×D113C4×D411yescharacteristic
91C2×D113C2×D812yes—
92C2×D113#13512yes—
93C2×D113C22×D411yescharacteristic
94#90673—22no—
95#90673—44no—
96#90673C2×D814yesdirect product factor
97C4×C113C4×D411yescharacteristic
98C4×C113C23×C411yescharacteristic
99Dic113C4×D411yescharacteristic
100Dic113C2×#4111yescharacteristic
101C2×C113—44no—
102C2×C113C4×D812yescomplemented
103C2×C113C2×C4×D411yescharacteristic
104D113—44no—
105D113C4×D812yescomplemented
106D113C22×D811yescharacteristic
107D113C2×#13511yescharacteristic
108C2×C4×D8—1131nomaximal, Sylow
109C113C2×C4×D811yescharacteristic, complemented, Sylow
110C22×D8—1131no—
111C2×C4×D4—1132no—
112C4×D8—1138no—
113C2×#107—1131no—
114C2×#102—1132no—
115C2×C4×C8—1131no—
116C22×D4—1132no—
117C23×C4—2262no—
118C2×D8—1132no—
119C2×D8—1134no—
120C2×D8—1134no—
121C2×D8—1131no—
122C2×D8#9067311yescharacteristic, direct product factor
123C22×C8—1131no—
124C22×C8—1131no—
125C4×D4—1138no—
126C4×D4—2264no—
127C2×C4⋊C4—1132no—
128C2×C22⋊C4—2262no—
129C2×C42—1131no—
130#107—1134no—
131#102—1138no—
132C4×C8—1134no—
133C24—2262no—
134C2×D4—1134no—
135C2×D4—1134no—
136C2×D4—1132no—
137C2×D4—2262no—
138C2×D4—2262no—
139C2×D4—2262no—
140C2×D4C2×#9067312yescomplemented
141C22×C4—1131no—
142C22×C4—1131no—
143C22×C4—1131no—
144C22×C4—4528no—
145C22×C4—2268no—
146C22×C4—2262no—
147D8—1138no—
148D8—1134no—
149D8C2×#9067314yesdirect product factor
150C2×C8—1131no—
151C2×C8—1132no—
152C2×C8—1132no—
153C2×C8—1132no—
154C2×C8—2261no—
155C2×C8—2261no—
156C2×C8C2×#9067311yescharacteristic, complemented
157C4⋊C4—1134no—
158C4⋊C4—2262no—
159C22⋊C4—2268no—
160C42—1132no—
161C42—1132no—
162C23—22no—
163C23—1131no—
164C23—4524no—
165C23—4524no—
166C23—2264no—
167C23—2264no—
168C23—2262no—
169D4—22no—
170D4—1134no—
171D4—2264no—
172D4—2264no—
173D4—2262no—
174D4C22×#9067314yescomplemented
175C2×C4—1132no—
176C2×C4—1134no—
177C2×C4—1131no—
178C2×C4—1131no—
179C2×C4—1131no—
180C2×C4—1131no—
181C2×C4—1131no—
182C2×C4—1132no—
183C2×C4—45216no—
184C2×C4—4524no—
185C2×C4—2264no—
186C2×C4—2262no—
187C2×C4C22×#9067311yescharacteristic
188C8—1132no—
189C8—2262no—
190C8C22×#9067312yescomplemented
191C22—24no—
192C22—44no—
193C22—1132no—
194C22—1132no—
195C22—1131no—
196C22—1131no—
197C22—4524no—
198C22—4524no—
199C22—4528no—
200C22—4524no—
201C22—2264no—
202C22D4×#9067311yescharacteristic
203C4—1134no—
204C4—1131no—
205C4—1131no—
206C4—4524no—
207C4—2262no—
208C4D4×#9067311yescharacteristic
209C4C23×#9067311yescharacteristic
210C2—44no—
211C2—1131no—
212C2—1131no—
213C2—1132no—
214C2—4524no—
215C2D8×#9067312yesdirect product factor
216C2C2×D4×#9067311yescharacteristic
subgroupG/H
centerC22D4×#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
FittingC2×D8×C113C4
socleC22×C113C4×D4
prime radicalC2×D8×D113C2
cosocleC4×D113C24
hypercenterC2×D8#90673
hypocenterC113C2×C4×D8
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#90673C2semidirect
2. D8×#90673C2direct (N × H)
3. C2×#16813691C2semidirect
4. C2×#16813684C2semidirect
5. C2×C8×#90673C2semidirect
10. D4×#90673C22semidirect
14. #16813691C22semidirect
15. #16813684C22semidirect
16. C8×#90673C22semidirect
18. C2×D904C4semidirect
19. C2×#14268632C4semidirect
20. D8×D113C4semidirect
23. C2×D8×C113C4semidirect
38. C2×D452C2×C4semidirect
42. D4×D113C2×C4semidirect
45. D904C2×C4semidirect
46. #14268632C2×C4semidirect
47. C2×#11744751C2×C4semidirect
48. C8×D113C2×C4semidirect
50. C2×D4×C113C2×C4semidirect
51. D8×C113C2×C4semidirect
52. C2×C8×C113C2×C4semidirect
64. C2×#90673D8direct (N × H)
68. D4×C113C22×C4semidirect
74. D452C22×C4semidirect
80. C8×C113C22×C4semidirect
81. #11744751C22×C4semidirect
96. #90673C2×D8direct (N × H)
102. C2×C113C4×D8semidirect
105. D113C4×D8semidirect
109. C113C2×C4×D8semidirect
122. C2×D8#90673direct (N × H)
140. C2×D4C2×#90673semidirect
149. D8C2×#90673direct (N × H)
156. C2×C8C2×#90673semidirect
174. D4C22×#90673semidirect
190. C8C22×#90673semidirect
215. C2D8×#90673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#906732
D8×#906732
C2×#168136912
C2×#168136842
C2×C8×#906732
C2×D8×D1132
C2×C4×D8113