Finite Group Databasebeta

← D4×D1108 #31800638

Subgroups — D4×D1108 #31800638

Order 17728.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×D1108C212yesmaximal, complemented
2C2×D4×D277C212yesmaximal, complemented
3#22579877C211yesmaximal, characteristic, complemented
4#22579855C212yesmaximal, complemented
5#22579854C212yesmaximal, complemented
6#22579850C214yesmaximal, complemented
7C4×D1108C211yesmaximal, characteristic, complemented
8C4×D4×C277C211yesmaximal, characteristic, complemented
9C23×D277C2214yescomplemented
10C2×D1108—28no—
11C2×D1108C2211yescharacteristic
12C2×D1108C2214yescomplemented
13C2×D1108C2212yescomplemented
14C2×D1108C2212yescomplemented
15C2×D1108C2212yescomplemented
16C2×C22⋊D277C2214yescomplemented
17D4×D277—28no—
18C2×C4×D277C2212yescomplemented
19C4⋊Dic277C2211yescharacteristic, complemented
20#17984540C2212yescomplemented
21#17984540C2214yescomplemented
22C2×D4×C277C2211yescharacteristic
23C22×C4×C277C2212yescomplemented
24C4⋊C4×C277C2211yescharacteristic, complemented
25C22⋊C4×C277C2212yescomplemented
26C42×C277C2211yescharacteristic, complemented
27C22×D277—28no—
28C22×D277—28no—
29C22×D277—44no—
30C22×D277C2314yes—
31C22×D277C2312yes—
32D1108—28no—
33D1108—24no—
34D1108—24no—
35D1108—42no—
36D1108D414yesdirect product factor
37C22⋊D277—28no—
38C2×Dic277C2312yes—
39C4×D277—24no—
40C23×C277C2312yes—
41D4×C277D414yescomplemented
42C2×C4×C277—24no—
43C2×C4×C277C2311yescharacteristic
44C2×C4×C277C2312yes—
45C2×C4×C277C2311yescharacteristic
46C2×C4×C277C2311yescharacteristic
47C22×C277—22no—
48C22×C277—22no—
49C22×C277C2×D414yescomplemented
50C22×C277C2411yescharacteristic
51C2×D277—22no—
52C2×D277—22no—
53C2×D277—24no—
54C2×D277—24no—
55C2×D277—24no—
56C2×D277—416no—
57C2×D277C2×D414yescomplemented
58C4×C277—22no—
59C4×C277—21no—
60C4×C277C2×D412yescomplemented
61C4×C277C2×D412yescomplemented
62Dic277—22no—
63C2×C277—24no—
64C2×C277C22×D411yescharacteristic
65C2×C277C22×D411yescharacteristic
66C2×C277H(5,𝔽2)11yescharacteristic
67D277—24no—
68D277—44no—
69C277D4211yescharacteristic, complemented, Sylow
70D42—2771nomaximal, Sylow
71C22×D4—2772no—
72C22×D4—2772no—
73#127—2771no—
74#121—2772no—
75#121—2772no—
76#120—2774no—
77C4×D4—2771no—
78C4×D4D27711yescharacteristic, complemented
79C24—2774no—
80C2×D4—2774no—
81C2×D4—2771no—
82C2×D4—2774no—
83C2×D4—2772no—
84C2×D4—2772no—
85C2×D4—2772no—
86C2×D4—5548no—
87C2×D4—5548no—
88C2×D4C2×D27711yescharacteristic
89C22×C4—2772no—
90C22×C4C2×D27712yescomplemented
91C4⋊C4—2771no—
92C4⋊C4C2×D27711yescharacteristic, complemented
93C22⋊C4—2772no—
94C22⋊C4—2774no—
95C22⋊C4C2×D27712yescomplemented
96C42C2×D27711yescharacteristic, complemented
97C23—2772no—
98C23—2774no—
99C23—5548no—
100C23—5548no—
101C23—11084no—
102C23C22×D27712yes—
103D4—2774no—
104D4—5548no—
105D4—5548no—
106D4—5544no—
107D4—5544no—
108D4—11082no—
109D4D110814yesdirect product factor
110C2×C4—24no—
111C2×C4—2772no—
112C2×C4—5544no—
113C2×C4C22×D27711yescharacteristic
114C2×C4C22×D27712yes—
115C2×C4C22×D27711yescharacteristic
116C2×C4C22×D27711yescharacteristic
117C22—22no—
118C22—22no—
119C22—2774no—
120C22—5542no—
121C22—5542no—
122C22—5544no—
123C22—5544no—
124C22—5544no—
125C22—110816no—
126C22C2×D110814yescomplemented
127C22C23×D27711yescharacteristic
128C4—22no—
129C4—21no—
130C4—5542no—
131C4D4×D27712yescomplemented
132C4C2×D110812yescomplemented
133C2—24no—
134C2—5544no—
135C2—11084no—
136C2C2×D4×D27711yescharacteristic
137C2C22×D110811yescharacteristic
138C2#2257992611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D277
commutator, socle, cosocleC22×C277C24
FittingC4×D4×C277C2
hypercenterC4×D4D277
hypocenterC277D42
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1108C2semidirect
2. C2×D4×D277C2semidirect
3. #22579877C2semidirect
4. #22579855C2semidirect
5. #22579854C2semidirect
6. #22579850C2semidirect
7. C4×D1108C2semidirect
8. C4×D4×C277C2semidirect
9. C23×D277C22semidirect
12. C2×D1108C22semidirect
13. C2×D1108C22semidirect
14. C2×D1108C22semidirect
15. C2×D1108C22semidirect
16. C2×C22⋊D277C22semidirect
18. C2×C4×D277C22semidirect
19. C4⋊Dic277C22semidirect
20. #17984540C22semidirect
21. #17984540C22semidirect
23. C22×C4×C277C22semidirect
24. C4⋊C4×C277C22semidirect
25. C22⋊C4×C277C22semidirect
26. C42×C277C22semidirect
36. D1108D4direct (N × H)
41. D4×C277D4semidirect
49. C22×C277C2×D4semidirect
57. C2×D277C2×D4semidirect
60. C4×C277C2×D4semidirect
61. C4×C277C2×D4semidirect
69. C277D42semidirect
78. C4×D4D277semidirect
90. C22×C4C2×D277semidirect
92. C4⋊C4C2×D277semidirect
95. C22⋊C4C2×D277semidirect
96. C42C2×D277semidirect
109. D4D1108direct (N × H)
126. C22C2×D1108semidirect
131. C4D4×D277semidirect
132. C4C2×D1108semidirect

Maximal subgroups

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

subgroupindex
C22×D11082
C2×D4×D2772
#225798772
#225798552
#225798542
#225798502
C4×D11082
C4×D4×C2772
D42277