Finite Group Databasebeta

← D8×D428 #28348137

Subgroups — D8×D428 #28348137

Order 13696.

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×D107C212yesmaximal, complemented
2D4×D428C212yesmaximal, complemented
3#20293004C211yesmaximal, characteristic, complemented
4#20292864C212yesmaximal, complemented
5#20292822C212yesmaximal, complemented
6#20292762C214yesmaximal, complemented
7C8×D428C211yesmaximal, characteristic, complemented
8C4×D8×C107C211yesmaximal, characteristic, complemented
9C22×D428—22no—
10C2×D4×D107C2214yescomplemented
11C2×D856C2212yescomplemented
12C2×D856C2212yescomplemented
13C2×#13133803C2214yescomplemented
14D8×D107—28no—
15C2×C8×D107C2212yescomplemented
16#16812106C2212yescomplemented
17#16812084C2214yescomplemented
18#16812083—22no—
19#16812079—24no—
20C4×D428C2211yescharacteristic
21C4⋊(C107⋊C8)C2211yescharacteristic, complemented
22#16812029C2214yescomplemented
23(C2×D107)⋊C8C2212yescomplemented
24C2×D8×C107C2211yescharacteristic
25C4×D4×C107C2212yescomplemented
26#107×C107C2211yescharacteristic, complemented
27#102×C107C2212yescomplemented
28C4×C8×C107C2211yescharacteristic, complemented
29C23×D107—24no—
30C2×D428—24no—
31C2×D428—22no—
32C2×D428—22no—
33C2×D428—48no—
34C2×D428D411yescharacteristic
35C2×D428C2314yes—
36C2×C22⋊D107—24no—
37D4×D107—28no—
38D4×D107—44no—
39C2×C4×D107C2312yes—
40D856—24no—
41D856—42no—
42#13133803—28no—
43C2×C107⋊C8C2312yes—
44C8×D107—24no—
45C4⋊Dic107D411yescharacteristic
46(C2×D107)⋊C4—24no—
47(C2×D107)⋊C4D412yes—
48C2×D4×C107C2312yes—
49C22×C4×C107—22no—
50D8×C107D414yescomplemented
51C2×C8×C107C2311yescharacteristic
52C2×C8×C107C2311yescharacteristic
53C4⋊C4×C107C2312yes—
54C22⋊C4×C107—22no—
55C42×C107C2311yescharacteristic
56C23×C107—22no—
57C22×D107—24no—
58C22×D107—48no—
59C22×D107—48no—
60C22×D107—84no—
61C22×D107C2×D412yes—
62D4×C107—22no—
63D4×C107C2×D414yescomplemented
64C2×C4×C107—22no—
65C2×C4×C107—44no—
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107C2×D411yescharacteristic
68C2×C4×C107C2411yescharacteristic
69C22⋊D107—48no—
70C2×Dic107C2×D412yes—
71D428—24no—
72D428—24no—
73D428—48no—
74D428—44no—
75D428—82no—
76D428D814yesdirect product factor
77C4×D107—22no—
78C4×D107—22no—
79C8×C107—21no—
80C8×C107C2×D412yescomplemented
81C107⋊C8—22no—
82C22×C107—24no—
83C22×C107—42no—
84C22×C107—42no—
85C22×C107C22×D411yescharacteristic
86C2×D107—22no—
87C2×D107—22no—
88C2×D107—44no—
89C2×D107—44no—
90C2×D107—44no—
91C2×D107—816no—
92C2×D107C2×D814yescomplemented
93C4×C107—21no—
94C4×C107—42no—
95C4×C107C2×D812yescomplemented
96C4×C107C22×D411yescharacteristic
97C4×C107H(5,𝔽2)11yescharacteristic
98Dic107—22no—
99C2×C107—44no—
100C2×C107D4211yescharacteristic
101C2×C107C22×D811yescharacteristic
102C2×C107#57611yescharacteristic
103D107—24no—
104D107—84no—
105D4×D8—1071nomaximal, Sylow
106C107D4×D811yescharacteristic, complemented, Sylow
107C22×D8—1072no—
108D42—1072no—
109#493—1071no—
110#466—1072no—
111#459—1072no—
112#447—1074no—
113C4×D8D10711yescharacteristic, complemented
114C8×D4—1071no—
115C22×D4—1074no—
116C22×D4—2142no—
117C2×D8—1074no—
118C2×D8—1072no—
119C2×D8—1072no—
120C2×D8—2148no—
121C2×D8C2×D10711yescharacteristic
122C22×C8—1072no—
123#127—1072no—
124#121—1074no—
125#121—2142no—
126#120—2144no—
127C4×D4—1071no—
128C4×D4C2×D10712yescomplemented
129#107C2×D10711yescharacteristic, complemented
130C4⋊C8—1071no—
131#102—1074no—
132#102C2×D10712yescomplemented
133C22⋊C8—1072no—
134C4×C8C2×D10711yescharacteristic, complemented
135C24—2144no—
136C2×D4—1071no—
137C2×D4—1074no—
138C2×D4—4288no—
139C2×D4—4284no—
140C2×D4—2144no—
141C2×D4—2144no—
142C2×D4—2148no—
143C2×D4—2142no—
144C2×D4—2142no—
145C2×D4C22×D10712yes—
146C22×C4—22no—
147C22×C4—1072no—
148D8—4282no—
149D8—2148no—
150D8—2144no—
151D8D42814yesdirect product factor
152C2×C8—1072no—
153C2×C8—2144no—
154C2×C8C22×D10711yescharacteristic
155C2×C8C22×D10711yescharacteristic
156C4⋊C4—1071no—
157C4⋊C4C22×D10712yes—
158C22⋊C4—22no—
159C22⋊C4—1072no—
160C22⋊C4—2144no—
161C42C22×D10711yescharacteristic
162C23—22no—
163C23—8564no—
164C23—1072no—
165C23—4288no—
166C23—4288no—
167C23—2144no—
168D4—22no—
169D4—8562no—
170D4—1074no—
171D4—4288no—
172D4—4288no—
173D4—4284no—
174D4—2144no—
175D4—2144no—
176D4C2×D42814yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—1072no—
180C2×C4—2142no—
181C2×C4—2142no—
182C2×C4D4×D10711yescharacteristic
183C2×C4D4×D10711yescharacteristic
184C2×C4C23×D10711yescharacteristic
185C8—21no—
186C8—2142no—
187C8C2×D42812yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—85616no—
192C22—1074no—
193C22—4284no—
194C22—4284no—
195C22—4284no—
196C22—2142no—
197C22—2142no—
198C22C2×D4×D10711yescharacteristic
199C4—21no—
200C4—42no—
201C4—2142no—
202C4D8×D10712yescomplemented
203C4C22×D42811yescharacteristic
204C4#1681215511yescharacteristic
205C2—44no—
206C2—8564no—
207C2—2144no—
208C2D4×D42811yescharacteristic
209C2C2×D8×D10711yescharacteristic
210C2#2029342911yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×D8×C107C2
socleC22×C107C22×D4
hypercenterC4×D8D107
hypocenterC107D4×D8
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D107C2semidirect
2. D4×D428C2semidirect
3. #20293004C2semidirect
4. #20292864C2semidirect
5. #20292822C2semidirect
6. #20292762C2semidirect
7. C8×D428C2semidirect
8. C4×D8×C107C2semidirect
10. C2×D4×D107C22semidirect
11. C2×D856C22semidirect
12. C2×D856C22semidirect
13. C2×#13133803C22semidirect
15. C2×C8×D107C22semidirect
16. #16812106C22semidirect
17. #16812084C22semidirect
21. C4⋊(C107⋊C8)C22semidirect
22. #16812029C22semidirect
23. (C2×D107)⋊C8C22semidirect
25. C4×D4×C107C22semidirect
26. #107×C107C22semidirect
27. #102×C107C22semidirect
28. C4×C8×C107C22semidirect
50. D8×C107D4semidirect
63. D4×C107C2×D4semidirect
76. D428D8direct (N × H)
80. C8×C107C2×D4semidirect
92. C2×D107C2×D8semidirect
95. C4×C107C2×D8semidirect
106. C107D4×D8semidirect
113. C4×D8D107semidirect
128. C4×D4C2×D107semidirect
129. #107C2×D107semidirect
132. #102C2×D107semidirect
134. C4×C8C2×D107semidirect
151. D8D428direct (N × H)
176. D4C2×D428semidirect
187. C8C2×D428semidirect
202. C4D8×D107semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1072
D4×D4282
#202930042
#202928642
#202928222
#202927622
C8×D4282
C4×D8×C1072
D4×D8107