Finite Group Databasebeta

← D8×D604 #34080786

Subgroups — D8×D604 #34080786

Order 19328.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D8×D151C212yesmaximal, complemented
2D4×D604C212yesmaximal, complemented
3#23752589C211yesmaximal, characteristic, complemented
4#23752449C212yesmaximal, complemented
5#23752407C212yesmaximal, complemented
6#23752347C214yesmaximal, complemented
7C8×D604C211yesmaximal, characteristic, complemented
8C4×D8×C151C211yesmaximal, characteristic, complemented
9C22×D604—22no—
10C2×D4×D151C2214yescomplemented
11C2×D1208C2212yescomplemented
12C2×D1208C2212yescomplemented
13C2×#14558989C2214yescomplemented
14D8×D151—28no—
15C2×C8×D151C2212yescomplemented
16#18012736C2212yescomplemented
17#18012714C2214yescomplemented
18#18012713—22no—
19#18012709—24no—
20C4×D604C2211yescharacteristic
21C4⋊(C151⋊C8)C2211yescharacteristic, complemented
22#18012659C2214yescomplemented
23(C2×D151)⋊C8C2212yescomplemented
24C2×D8×C151C2211yescharacteristic
25C4×D4×C151C2212yescomplemented
26#107×C151C2211yescharacteristic, complemented
27#102×C151C2212yescomplemented
28C4×C8×C151C2211yescharacteristic, complemented
29C23×D151—24no—
30C2×D604—24no—
31C2×D604—22no—
32C2×D604—22no—
33C2×D604—48no—
34C2×D604D411yescharacteristic
35C2×D604C2314yes—
36C2×C22⋊D151—24no—
37D4×D151—28no—
38D4×D151—44no—
39C2×C4×D151C2312yes—
40D1208—24no—
41D1208—42no—
42#14558989—28no—
43C2×C151⋊C8C2312yes—
44C8×D151—24no—
45C4⋊Dic151D411yescharacteristic
46(C2×D151)⋊C4—24no—
47(C2×D151)⋊C4D412yes—
48C2×D4×C151C2312yes—
49C22×C4×C151—22no—
50D8×C151D414yescomplemented
51C2×C8×C151C2311yescharacteristic
52C2×C8×C151C2311yescharacteristic
53C4⋊C4×C151C2312yes—
54C22⋊C4×C151—22no—
55C42×C151C2311yescharacteristic
56C22×D151—24no—
57C22×D151—48no—
58C22×D151—48no—
59C22×D151—84no—
60C22×D151C2×D412yes—
61D604—24no—
62D604—24no—
63D604—48no—
64D604—44no—
65D604—82no—
66D604D814yesdirect product factor
67C22⋊D151—48no—
68C2×Dic151C2×D412yes—
69C4×D151—22no—
70C4×D151—22no—
71C151⋊C8—22no—
72C23×C151—22no—
73D4×C151—22no—
74D4×C151C2×D414yescomplemented
75C2×C4×C151—22no—
76C2×C4×C151—44no—
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2411yescharacteristic
80C8×C151—21no—
81C8×C151C2×D412yescomplemented
82C22×C151—24no—
83C22×C151—42no—
84C22×C151—42no—
85C22×C151C22×D411yescharacteristic
86C2×D151—22no—
87C2×D151—22no—
88C2×D151—44no—
89C2×D151—44no—
90C2×D151—44no—
91C2×D151—816no—
92C2×D151C2×D814yescomplemented
93C4×C151—21no—
94C4×C151—42no—
95C4×C151C2×D812yescomplemented
96C4×C151C22×D411yescharacteristic
97C4×C151H(5,𝔽2)11yescharacteristic
98Dic151—22no—
99C2×C151—44no—
100C2×C151D4211yescharacteristic
101C2×C151C22×D811yescharacteristic
102C2×C151#57611yescharacteristic
103D151—24no—
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×D8D15111yescharacteristic, complemented
114C8×D4—1511no—
115C22×D4—3022no—
116C22×D4—1514no—
117C2×D8—3028no—
118C2×D8—1514no—
119C2×D8—1512no—
120C2×D8—1512no—
121C2×D8C2×D15111yescharacteristic
122C22×C8—1512no—
123#127—1512no—
124#121—3022no—
125#121—1514no—
126#120—3024no—
127C4×D4—1511no—
128C4×D4C2×D15112yescomplemented
129#107C2×D15111yescharacteristic, complemented
130C4⋊C8—1511no—
131#102—1514no—
132#102C2×D15112yescomplemented
133C22⋊C8—1512no—
134C4×C8C2×D15111yescharacteristic, complemented
135C24—3024no—
136C2×D4—3024no—
137C2×D4—3028no—
138C2×D4—3024no—
139C2×D4—3022no—
140C2×D4—3022no—
141C2×D4—6048no—
142C2×D4—6044no—
143C2×D4—1511no—
144C2×D4—1514no—
145C2×D4C22×D15112yes—
146C22×C4—22no—
147C22×C4—1512no—
148D8—3028no—
149D8—3024no—
150D8—6042no—
151D8D60414yesdirect product factor
152C2×C8—3024no—
153C2×C8—1512no—
154C2×C8C22×D15111yescharacteristic
155C2×C8C22×D15111yescharacteristic
156C4⋊C4—1511no—
157C4⋊C4C22×D15112yes—
158C22⋊C4—22no—
159C22⋊C4—3024no—
160C22⋊C4—1512no—
161C42C22×D15111yescharacteristic
162C23—22no—
163C23—3024no—
164C23—6048no—
165C23—6048no—
166C23—1512no—
167C23—12084no—
168D4—22no—
169D4—3024no—
170D4—3024no—
171D4—6048no—
172D4—6048no—
173D4—6044no—
174D4—1514no—
175D4—12082no—
176D4C2×D60414yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—1512no—
182C2×C4D4×D15111yescharacteristic
183C2×C4D4×D15111yescharacteristic
184C2×C4C23×D15111yescharacteristic
185C8—21no—
186C8—3022no—
187C8C2×D60412yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—3022no—
192C22—3022no—
193C22—6044no—
194C22—6044no—
195C22—6044no—
196C22—1514no—
197C22—120816no—
198C22C2×D4×D15111yescharacteristic
199C4—21no—
200C4—42no—
201C4—3022no—
202C4D8×D15112yescomplemented
203C4C22×D60411yescharacteristic
204C4#1801278511yescharacteristic
205C2—44no—
206C2—3024no—
207C2—12084no—
208C2D4×D60411yescharacteristic
209C2C2×D8×D15111yescharacteristic
210C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D151C2semidirect
2. D4×D604C2semidirect
3. #23752589C2semidirect
4. #23752449C2semidirect
5. #23752407C2semidirect
6. #23752347C2semidirect
7. C8×D604C2semidirect
8. C4×D8×C151C2semidirect
10. C2×D4×D151C22semidirect
11. C2×D1208C22semidirect
12. C2×D1208C22semidirect
13. C2×#14558989C22semidirect
15. C2×C8×D151C22semidirect
16. #18012736C22semidirect
17. #18012714C22semidirect
21. C4⋊(C151⋊C8)C22semidirect
22. #18012659C22semidirect
23. (C2×D151)⋊C8C22semidirect
25. C4×D4×C151C22semidirect
26. #107×C151C22semidirect
27. #102×C151C22semidirect
28. C4×C8×C151C22semidirect
50. D8×C151D4semidirect
66. D604D8direct (N × H)
74. D4×C151C2×D4semidirect
81. C8×C151C2×D4semidirect
92. C2×D151C2×D8semidirect
95. C4×C151C2×D8semidirect
105. C151D4×D8semidirect
113. C4×D8D151semidirect
128. C4×D4C2×D151semidirect
129. #107C2×D151semidirect
132. #102C2×D151semidirect
134. C4×C8C2×D151semidirect
151. D8D604direct (N × H)
176. D4C2×D604semidirect
187. C8C2×D604semidirect
202. C4D8×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
D4×D6042
#237525892
#237524492
#237524072
#237523472
C8×D6042
C4×D8×C1512
D4×D8151