Finite Group Databasebeta

← C2×#20299639 #28407327

Subgroups — C2×#20299639 #28407327

Order 14464.

608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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
2#20299639C218yesmaximal, direct product factor
3C2×#16813690C211yesmaximal, characteristic, complemented
4C2×#16813684C212yesmaximal, complemented
5C2×#16813676C211yesmaximal, 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#16813690C2214yescomplemented
15#16813684C2218yescomplemented
16#16813676C2214yescomplemented
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×#90673D412yes—
28#14268655—21no—
29#14268655C2312yes—
30C2×#11744753—21no—
31C4⋊#90673—22no—
32C4⋊#90673C2314yes—
33C22⋊#90673—28no—
34C4×#90673D412yes—
35C4×#90673C2312yes—
36C23×D113—22no—
37C2×D452C2×C412yescomplemented
38C2×C22⋊D113—22no—
39D4×D113—22no—
40D4×D113—22no—
41D4×D113C2×C414yescomplemented
42D4×D113C2314yes—
43C2×C4×D113C2311yescharacteristic
44D904C2×C414yescomplemented
45#14268632C2×C418yescomplemented
46C2×#11744751C2×C411yescharacteristic, complemented
47C8×D113C2×C412yescomplemented
48C8×D113C2312yes—
49C2×D4×C113C2×C412yescomplemented
50D8×C113C2×C414yescomplemented
51C2×C8×C113C2×C411yescharacteristic, complemented
52C23×C113—22no—
53C22×D113—22no—
54C22×D113—24no—
55C22×D113—24no—
56C22×D113—44no—
57C22×D113—44no—
58C22×D113C2×D411yescharacteristic
59C2×#90673—24no—
60C2×#90673—24no—
61C2×#90673—416no—
62C2×#90673—44no—
63C2×#90673C2×D414yes—
64D4×C113—22no—
65D4×C113C22×C414yescomplemented
66C2×C4×C113C22×C411yescharacteristic
67C22⋊D113—24no—
68C22⋊D113—24no—
69C2×Dic113#4111yescharacteristic
70D452—22no—
71D452C22×C414yescomplemented
72C4×D113C22×C411yescharacteristic
73C4×D113C2×D411yescharacteristic
74C4×D113#4111yescharacteristic
75C4×D113C2411yescharacteristic
76#11744753—22no—
77C8×C113C22×C412yescomplemented
78#11744751C22×C412yescomplemented
79C22×C113—24no—
80C22×C113—44no—
81C22×C113C4×D411yescharacteristic
82C2×D113—24no—
83C2×D113—44no—
84C2×D113—44no—
85C2×D113—44no—
86C2×D113—48no—
87C2×D113C4×D411yescharacteristic
88C2×D113AGL(1,ℤ/8)14yes—
89C2×D113C22×D411yescharacteristic
90#90673—24no—
91#90673—44no—
92C4×C113C4×D411yescharacteristic
93C4×C113C23×C411yescharacteristic
94Dic113C4×D411yescharacteristic
95Dic113C2×#4111yescharacteristic
96C2×C113—44no—
97C2×C113#44212yescomplemented
98C2×C113C2×C4×D411yescharacteristic
99D113—44no—
100D113#44212yescomplemented
101D113C2×AGL(1,ℤ/8)12yes—
102C2×#442—1131nomaximal, Sylow
103C113C2×#44211yescharacteristic, complemented, Sylow
104C22×D8—1131no—
105C2×C4×D4—1132no—
106#442—1138no—
107C2×#106—1131no—
108C2×#102—1132no—
109C2×#97—1131no—
110C22×D4—1132no—
111C23×C4—2262no—
112C2×D8—1132no—
113C2×D8—1134no—
114C2×D8—1134no—
115C2×D8—1131no—
116C2×D8#9067311yescharacteristic, complemented
117C22×C8—1131no—
118C22×C8—1131no—
119C4×D4—1138no—
120C4×D4—2264no—
121C2×C4⋊C4—1132no—
122C2×C22⋊C4—2262no—
123C2×C42—1131no—
124#106—1134no—
125#102—1138no—
126#97—1134no—
127C24—2262no—
128C2×D4—1134no—
129C2×D4—1134no—
130C2×D4—1132no—
131C2×D4—2262no—
132C2×D4—2262no—
133C2×D4—2262no—
134C2×D4C2×#9067312yescomplemented
135C22×C4—1131no—
136C22×C4—1132no—
137C22×C4—4528no—
138C22×C4—2268no—
139C22×C4—2262no—
140D8—1138no—
141D8—1134no—
142D8C2×#9067314yescomplemented
143C2×C8—1131no—
144C2×C8—1132no—
145C2×C8—1132no—
146C2×C8—1132no—
147C2×C8—2261no—
148C2×C8—2261no—
149C2×C8C2×#9067311yescharacteristic, complemented
150C4⋊C4—1134no—
151C4⋊C4—2262no—
152C22⋊C4—2268no—
153C42—1132no—
154C42—1132no—
155C23—22no—
156C23—1131no—
157C23—4524no—
158C23—4524no—
159C23—2264no—
160C23—2264no—
161C23—2262no—
162D4—22no—
163D4—1134no—
164D4—2264no—
165D4—2264no—
166D4—2262no—
167D4C22×#9067314yescomplemented
168C2×C4—1131no—
169C2×C4—1131no—
170C2×C4—1131no—
171C2×C4—1131no—
172C2×C4—1131no—
173C2×C4—1134no—
174C2×C4—4524no—
175C2×C4—45216no—
176C2×C4—2264no—
177C2×C4—2264no—
178C2×C4C22×#9067311yescharacteristic
179C8—1132no—
180C8—2262no—
181C8C22×#9067312yescomplemented
182C22—24no—
183C22—44no—
184C22—1134no—
185C22—1131no—
186C22—1131no—
187C22—4524no—
188C22—4524no—
189C22—4528no—
190C22—4524no—
191C22—2264no—
192C22D4×#9067311yescharacteristic
193C4—1131no—
194C4—1131no—
195C4—4524no—
196C4—2264no—
197C4D4×#9067311yescharacteristic
198C4C23×#9067311yescharacteristic
199C2—44no—
200C2—1132no—
201C2—1132no—
202C2—4524no—
203C2#2029963912yesdirect product factor
204C2C2×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×#442
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. #20299639C2direct (N × H)
3. C2×#16813690C2semidirect
4. C2×#16813684C2semidirect
5. C2×#16813676C2semidirect
10. D4×#90673C22semidirect
14. #16813690C22semidirect
15. #16813684C22semidirect
16. #16813676C22semidirect
18. C2×D904C4semidirect
19. C2×#14268632C4semidirect
20. D8×D113C4semidirect
23. C2×D8×C113C4semidirect
37. C2×D452C2×C4semidirect
41. D4×D113C2×C4semidirect
44. D904C2×C4semidirect
45. #14268632C2×C4semidirect
46. C2×#11744751C2×C4semidirect
47. C8×D113C2×C4semidirect
49. C2×D4×C113C2×C4semidirect
50. D8×C113C2×C4semidirect
51. C2×C8×C113C2×C4semidirect
65. D4×C113C22×C4semidirect
71. D452C22×C4semidirect
77. C8×C113C22×C4semidirect
78. #11744751C22×C4semidirect
97. C2×C113#442semidirect
100. D113#442semidirect
103. C113C2×#442semidirect
116. C2×D8#90673semidirect
134. C2×D4C2×#90673semidirect
142. D8C2×#90673semidirect
149. C2×C8C2×#90673semidirect
167. D4C22×#90673semidirect
181. C8C22×#90673semidirect
203. C2#20299639direct (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
#202996392
C2×#168136902
C2×#168136842
C2×#168136762
C2×D8×D1132
C2×#442113