Finite Group Databasebeta

← D4×D1172 #34036765

Subgroups — D4×D1172 #34036765

Order 18752.

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×D1172C212yesmaximal, complemented
2C2×D4×D293C212yesmaximal, complemented
3#22627621C211yesmaximal, characteristic, complemented
4#22627599C212yesmaximal, complemented
5#22627598C212yesmaximal, complemented
6#22627594C214yesmaximal, complemented
7C4×D1172C211yesmaximal, characteristic, complemented
8C4×D4×C293C211yesmaximal, characteristic, complemented
9C23×D293C2214yescomplemented
10C2×D1172—28no—
11C2×D1172C2211yescharacteristic
12C2×D1172C2214yescomplemented
13C2×D1172C2212yescomplemented
14C2×D1172C2212yescomplemented
15C2×D1172C2212yescomplemented
16C2×C22⋊D293C2214yescomplemented
17D4×D293—28no—
18C2×C4×D293C2212yescomplemented
19C4⋊Dic293C2211yescharacteristic, complemented
20#17989779C2212yescomplemented
21#17989779C2214yescomplemented
22C2×D4×C293C2211yescharacteristic
23C22×C4×C293C2212yescomplemented
24C4⋊C4×C293C2211yescharacteristic, complemented
25C22⋊C4×C293C2212yescomplemented
26C42×C293C2211yescharacteristic, complemented
27C22×D293—28no—
28C22×D293—28no—
29C22×D293—44no—
30C22×D293C2314yes—
31C22×D293C2312yes—
32D1172—28no—
33D1172—24no—
34D1172—24no—
35D1172—42no—
36D1172D414yesdirect product factor
37C22⋊D293—28no—
38C2×Dic293C2312yes—
39C4×D293—24no—
40C23×C293C2312yes—
41D4×C293D414yescomplemented
42C2×C4×C293—24no—
43C2×C4×C293C2311yescharacteristic
44C2×C4×C293C2312yes—
45C2×C4×C293C2311yescharacteristic
46C2×C4×C293C2311yescharacteristic
47C22×C293—22no—
48C22×C293—22no—
49C22×C293C2×D414yescomplemented
50C22×C293C2411yescharacteristic
51C2×D293—22no—
52C2×D293—22no—
53C2×D293—24no—
54C2×D293—24no—
55C2×D293—24no—
56C2×D293—416no—
57C2×D293C2×D414yescomplemented
58C4×C293—22no—
59C4×C293—21no—
60C4×C293C2×D412yescomplemented
61C4×C293C2×D412yescomplemented
62Dic293—22no—
63C2×C293—24no—
64C2×C293C22×D411yescharacteristic
65C2×C293C22×D411yescharacteristic
66C2×C293H(5,𝔽2)11yescharacteristic
67D293—24no—
68D293—44no—
69C293D4211yescharacteristic, complemented, Sylow
70D42—2931nomaximal, Sylow
71C22×D4—2932no—
72C22×D4—2932no—
73#127—2931no—
74#121—2932no—
75#121—2932no—
76#120—2934no—
77C4×D4—2931no—
78C4×D4D29311yescharacteristic, complemented
79C24—2934no—
80C2×D4—2934no—
81C2×D4—2931no—
82C2×D4—2934no—
83C2×D4—2932no—
84C2×D4—2932no—
85C2×D4—2932no—
86C2×D4—5868no—
87C2×D4—5868no—
88C2×D4C2×D29311yescharacteristic
89C22×C4—2932no—
90C22×C4C2×D29312yescomplemented
91C4⋊C4—2931no—
92C4⋊C4C2×D29311yescharacteristic, complemented
93C22⋊C4—2932no—
94C22⋊C4—2934no—
95C22⋊C4C2×D29312yescomplemented
96C42C2×D29311yescharacteristic, complemented
97C23—2932no—
98C23—2934no—
99C23—5868no—
100C23—5868no—
101C23—11724no—
102C23C22×D29312yes—
103D4—2934no—
104D4—5868no—
105D4—5868no—
106D4—5864no—
107D4—5864no—
108D4—11722no—
109D4D117214yesdirect product factor
110C2×C4—24no—
111C2×C4—2932no—
112C2×C4—5864no—
113C2×C4C22×D29311yescharacteristic
114C2×C4C22×D29312yes—
115C2×C4C22×D29311yescharacteristic
116C2×C4C22×D29311yescharacteristic
117C22—22no—
118C22—22no—
119C22—2934no—
120C22—5862no—
121C22—5862no—
122C22—5864no—
123C22—5864no—
124C22—5864no—
125C22—117216no—
126C22C2×D117214yescomplemented
127C22C23×D29311yescharacteristic
128C4—22no—
129C4—21no—
130C4—5862no—
131C4D4×D29312yescomplemented
132C4C2×D117212yescomplemented
133C2—24no—
134C2—5864no—
135C2—11724no—
136C2C2×D4×D29311yescharacteristic
137C2C22×D117211yescharacteristic
138C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
FittingC4×D4×C293C2
hypercenterC4×D4D293
hypocenterC293D42
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1172C2semidirect
2. C2×D4×D293C2semidirect
3. #22627621C2semidirect
4. #22627599C2semidirect
5. #22627598C2semidirect
6. #22627594C2semidirect
7. C4×D1172C2semidirect
8. C4×D4×C293C2semidirect
9. C23×D293C22semidirect
12. C2×D1172C22semidirect
13. C2×D1172C22semidirect
14. C2×D1172C22semidirect
15. C2×D1172C22semidirect
16. C2×C22⋊D293C22semidirect
18. C2×C4×D293C22semidirect
19. C4⋊Dic293C22semidirect
20. #17989779C22semidirect
21. #17989779C22semidirect
23. C22×C4×C293C22semidirect
24. C4⋊C4×C293C22semidirect
25. C22⋊C4×C293C22semidirect
26. C42×C293C22semidirect
36. D1172D4direct (N × H)
41. D4×C293D4semidirect
49. C22×C293C2×D4semidirect
57. C2×D293C2×D4semidirect
60. C4×C293C2×D4semidirect
61. C4×C293C2×D4semidirect
69. C293D42semidirect
78. C4×D4D293semidirect
90. C22×C4C2×D293semidirect
92. C4⋊C4C2×D293semidirect
95. C22⋊C4C2×D293semidirect
96. C42C2×D293semidirect
109. D4D1172direct (N × H)
126. C22C2×D1172semidirect
131. C4D4×D293semidirect
132. C4C2×D1172semidirect

Maximal subgroups

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

subgroupindex
C22×D11722
C2×D4×D2932
#226276212
#226275992
#226275982
#226275942
C4×D11722
C4×D4×C2932
D42293