Finite Group Databasebeta

← D4×D1208 #34080787

Subgroups — D4×D1208 #34080787

Order 19328.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×D1208C212yesmaximal, complemented
2D4×D604C212yesmaximal, complemented
3#23752589C211yesmaximal, characteristic, complemented
4#23752448C212yesmaximal, complemented
5#23752408C212yesmaximal, complemented
6#23752348C214yesmaximal, complemented
7C4×D1208C211yesmaximal, characteristic, complemented
8C8×D4×C151C211yesmaximal, characteristic, complemented
9C22×D604C2214yescomplemented
10C2×D4×D151—22no—
11C2×D1208—28no—
12C2×D1208C2211yescharacteristic
13C2×D1208C2212yescomplemented
14C2×D1208C2214yescomplemented
15C2×D1208C2212yescomplemented
16#18012736C2212yescomplemented
17#18012714—22no—
18#18012713C2214yescomplemented
19#18012709—24no—
20C4×D604C2212yescomplemented
21#18012673C2211yescharacteristic, complemented
22#18012661C2214yescomplemented
23#18012661C2212yescomplemented
24C22×C8×C151C2212yescomplemented
25C4×D4×C151C2211yescharacteristic
26C4⋊C8×C151C2211yescharacteristic, complemented
27C22⋊C8×C151C2212yescomplemented
28C4×C8×C151C2211yescharacteristic, complemented
29C23×D151—24no—
30C2×D604—28no—
31C2×D604—24no—
32C2×D604—22no—
33C2×D604—22no—
34C2×D604—44no—
35C2×D604C2314yes—
36C2×D604C2312yes—
37C2×C22⋊D151—24no—
38D4×D151—48no—
39C2×C4×D151—22no—
40D1208—28no—
41D1208—24no—
42D1208—42no—
43D1208D414yesdirect product factor
44C4⋊Dic151C2312yes—
45(C2×D151)⋊C4—22no—
46(C2×D151)⋊C4—24no—
47C2×D4×C151D411yescharacteristic
48C22×C4×C151C2312yes—
49C2×C8×C151—24no—
50C2×C8×C151C2311yescharacteristic
51C2×C8×C151C2312yes—
52C2×C8×C151C2311yescharacteristic
53C4⋊C4×C151D411yescharacteristic
54C22⋊C4×C151D412yes—
55C42×C151C2311yescharacteristic
56C22×D151—22no—
57C22×D151—24no—
58C22×D151—48no—
59C22×D151—48no—
60C22×D151—84no—
61D604—24no—
62D604—22no—
63D604—24no—
64D604—48no—
65D604—44no—
66D604—82no—
67D604C2×D414yescomplemented
68C22⋊D151—48no—
69C2×Dic151—22no—
70C4×D151—44no—
71C23×C151C2×D412yes—
72D4×C151D814yescomplemented
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D412yes—
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2411yescharacteristic
79C8×C151—22no—
80C8×C151—21no—
81C8×C151C2×D412yescomplemented
82C22×C151—22no—
83C22×C151—22no—
84C22×C151C2×D814yescomplemented
85C22×C151C22×D411yescharacteristic
86C2×D151—24no—
87C2×D151—42no—
88C2×D151—42no—
89C2×D151—44no—
90C2×D151—44no—
91C2×D151—44no—
92C2×D151—816no—
93C4×C151—22no—
94C4×C151—21no—
95C4×C151C2×D812yescomplemented
96C4×C151C22×D411yescharacteristic
97C4×C151H(5,𝔽2)11yescharacteristic
98Dic151—42no—
99C2×C151—24no—
100C2×C151D4211yescharacteristic
101C2×C151C22×D811yescharacteristic
102C2×C151#57611yescharacteristic
103D151—44no—
104D151—84no—
105C151D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1511nomaximal, Sylow
107C22×D8—1512no—
108D42—1512no—
109#493—1511no—
110#466—1512no—
111#459—1512no—
112#447—1514no—
113C4×D8—1511no—
114C8×D4D15111yescharacteristic, complemented
115C22×D4—3022no—
116C22×D4—1514no—
117C2×D8—3028no—
118C2×D8—1514no—
119C2×D8—1512no—
120C2×D8—1512no—
121C2×D8—1511no—
122C22×C8C2×D15112yescomplemented
123#127—1512no—
124#121—3022no—
125#121—1514no—
126#120—3024no—
127C4×D4—1512no—
128C4×D4C2×D15111yescharacteristic
129#107—1511no—
130C4⋊C8C2×D15111yescharacteristic, complemented
131#102—1512no—
132#102—1514no—
133C22⋊C8C2×D15112yescomplemented
134C4×C8C2×D15111yescharacteristic, complemented
135C24—3024no—
136C2×D4—3028no—
137C2×D4—3024no—
138C2×D4—3024no—
139C2×D4—3022no—
140C2×D4—3022no—
141C2×D4—6044no—
142C2×D4—6048no—
143C2×D4—1514no—
144C2×D4—1512no—
145C2×D4D60411yescharacteristic
146C22×C4—3022no—
147C22×C4C22×D15112yes—
148D8—3028no—
149D8—3024no—
150D8—6042no—
151D8—1514no—
152C2×C8—24no—
153C2×C8C22×D15111yescharacteristic
154C2×C8C22×D15112yes—
155C2×C8C22×D15111yescharacteristic
156C4⋊C4—1512no—
157C4⋊C4D60411yescharacteristic
158C22⋊C4—3022no—
159C22⋊C4—3024no—
160C22⋊C4D60412yes—
161C42C22×D15111yescharacteristic
162C23—3022no—
163C23—3024no—
164C23—6048no—
165C23—6048no—
166C23—12084no—
167C23C2×D60412yes—
168D4—3024no—
169D4—3022no—
170D4—3024no—
171D4—6048no—
172D4—6048no—
173D4—6044no—
174D4—1514no—
175D4—12082no—
176D4D120814yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3022no—
180C2×C4—6044no—
181C2×C4C2×D60411yescharacteristic
182C2×C4C2×D60412yes—
183C2×C4C2×D60411yescharacteristic
184C2×C4C23×D15111yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D15112yescomplemented
188C22—22no—
189C22—22no—
190C22—3024no—
191C22—6042no—
192C22—6042no—
193C22—6044no—
194C22—6044no—
195C22—6044no—
196C22—120816no—
197C22C2×D120814yescomplemented
198C22C22×D60411yescharacteristic
199C4—21no—
200C4—22no—
201C4—6042no—
202C4C2×D120812yescomplemented
203C4C2×D4×D15111yescharacteristic
204C4#1801278511yescharacteristic
205C2—24no—
206C2—6044no—
207C2—12084no—
208C2D4×D60411yescharacteristic
209C2C22×D120811yescharacteristic
210C2#2375301711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
hypercenterC8×D4D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1208C2semidirect
2. D4×D604C2semidirect
3. #23752589C2semidirect
4. #23752448C2semidirect
5. #23752408C2semidirect
6. #23752348C2semidirect
7. C4×D1208C2semidirect
8. C8×D4×C151C2semidirect
9. C22×D604C22semidirect
13. C2×D1208C22semidirect
14. C2×D1208C22semidirect
15. C2×D1208C22semidirect
16. #18012736C22semidirect
18. #18012713C22semidirect
20. C4×D604C22semidirect
21. #18012673C22semidirect
22. #18012661C22semidirect
23. #18012661C22semidirect
24. C22×C8×C151C22semidirect
26. C4⋊C8×C151C22semidirect
27. C22⋊C8×C151C22semidirect
28. C4×C8×C151C22semidirect
43. D1208D4direct (N × H)
67. D604C2×D4semidirect
72. D4×C151D8semidirect
81. C8×C151C2×D4semidirect
84. C22×C151C2×D8semidirect
95. C4×C151C2×D8semidirect
105. C151D4×D8semidirect
114. C8×D4D151semidirect
122. C22×C8C2×D151semidirect
130. C4⋊C8C2×D151semidirect
133. C22⋊C8C2×D151semidirect
134. C4×C8C2×D151semidirect
176. D4D1208direct (N × H)
187. C8D4×D151semidirect
197. C22C2×D1208semidirect
202. C4C2×D1208semidirect

Maximal subgroups

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

subgroupindex
C22×D12082
D4×D6042
#237525892
#237524482
#237524082
#237523482
C4×D12082
C8×D4×C1512
D4×D8151