Finite Group Databasebeta

← #44537284

Subgroups — #44537284

Order 31424.

346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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×C22⋊D491C211yesmaximal, characteristic, complemented
2#30628320C212yesmaximal, complemented
3#30628318C212yesmaximal, complemented
4#30628309C214yesmaximal, complemented
5#30628306C212yesmaximal, complemented
6#30628305C212yesmaximal, complemented
7C2×C22⋊Dic491C211yesmaximal, characteristic, complemented
8C22×D4×C491C211yesmaximal, characteristic, complemented
9C23×D491C2211yescharacteristic, complemented
10C2×C22⋊D491—24no—
11C2×C22⋊D491C2212yes—
12C2×C22⋊D491C2212yescomplemented
13C2×C22⋊D491C2214yescomplemented
14C22×Dic491C2211yescharacteristic, complemented
15C22×Dic491C2212yescomplemented
16Dic491⋊C4C2214yescomplemented
17C22⋊Dic491C2212yescomplemented
18C22⋊Dic491C2212yescomplemented
19C22⋊Dic491C2214yescomplemented
20(C2×D491)⋊C4C2214yescomplemented
21C24×C491C2211yescharacteristic
22C24×C491C2211yescharacteristic, complemented
23C2×D4×C491—24no—
24C2×D4×C491C2212yes—
25C2×D4×C491C2212yescomplemented
26C22×C4×C491C2211yescharacteristic, complemented
27C22×D491—22no—
28C22×D491—42no—
29C22×D491C2312yes—
30C22⋊D491—24no—
31C22⋊D491—24no—
32C22⋊D491—44no—
33C2×Dic491—22no—
34C2×Dic491—42no—
35C2×Dic491C2314yes—
36C2×Dic491C2312yes—
37C23×C491—22no—
38C23×C491—42no—
39C23×C491—42no—
40C23×C491D414yescomplemented
41C23×C491C2312yes—
42C23×C491C2311yescharacteristic
43C23×C491C2311yescharacteristic
44C23×C491C2311yescharacteristic
45D4×C491—24no—
46D4×C491—24no—
47C2×C4×C491—22no—
48C2×C4×C491C2312yes—
49C22×C491—22no—
50C22×C491—22no—
51C22×C491—22no—
52C22×C491—22no—
53C22×C491—24no—
54C22×C491—44no—
55C22×C491—44no—
56C22×C491C2×D412yes—
57C22×C491C2×D412yes—
58C22×C491C2×D412yes—
59C22×C491C2411yescharacteristic
60C2×D491—22no—
61C2×D491—24no—
62C2×D491—44no—
63C4×C491—22no—
64Dic491—22no—
65Dic491—24no—
66C2×C491—22no—
67C2×C491—22no—
68C2×C491—22no—
69C2×C491—42no—
70C2×C491C22×D411yescharacteristic
71C2×C491H(5,𝔽2)12yes—
72D491—42no—
73C491#53411yescharacteristic, complemented, Sylow
74#534—4911nomaximal, Sylow
75C22×D4—4911no—
76C22×D4D49111yescharacteristic, complemented
77#123—4912no—
78#123—4912no—
79#121—4914no—
80#120—4912no—
81#120—4912no—
82C2×C22⋊C4—4911no—
83C24—4911no—
84C24C2×D49111yescharacteristic
85C24C2×D49111yescharacteristic, complemented
86C2×D4—24no—
87C2×D4—9824no—
88C2×D4—4914no—
89C2×D4—4912no—
90C2×D4—4912no—
91C2×D4C2×D49112yes—
92C2×D4C2×D49112yescomplemented
93C22×C4—4912no—
94C22×C4—4911no—
95C22×C4C2×D49111yescharacteristic, complemented
96C4⋊C4—4914no—
97C22⋊C4—4912no—
98C22⋊C4—4912no—
99C22⋊C4—4914no—
100C22⋊C4—4914no—
101C23—22no—
102C23—42no—
103C23—42no—
104C23—19642no—
105C23—9822no—
106C23—4912no—
107C23C22⋊D49114yescomplemented
108C23C22×D49112yes—
109C23C22×D49111yescharacteristic
110C23C22×D49111yescharacteristic
111C23C22×D49111yescharacteristic
112D4—24no—
113D4—24no—
114D4—19644no—
115D4—9824no—
116D4—9824no—
117C2×C4—22no—
118C2×C4—19642no—
119C2×C4—9822no—
120C2×C4—4914no—
121C2×C4—4912no—
122C2×C4C22×D49112yes—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—22no—
127C22—24no—
128C22—44no—
129C22—44no—
130C22—19644no—
131C22—9822no—
132C22—9824no—
133C22C2×C22⋊D49112yes—
134C22C2×C22⋊D49112yes—
135C22C2×C22⋊D49112yes—
136C22C23×D49111yescharacteristic
137C4—22no—
138C4—9822no—
139C4—9824no—
140C2—22no—
141C2—22no—
142C2—22no—
143C2—42no—
144C2—19642no—
145C2C22×C22⋊D49111yescharacteristic
146C2#3062838212yes—
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC22×D4×C491C2
hypercenterC22×D4D491
hypocenterC491#534
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D491C2semidirect
2. #30628320C2semidirect
3. #30628318C2semidirect
4. #30628309C2semidirect
5. #30628306C2semidirect
6. #30628305C2semidirect
7. C2×C22⋊Dic491C2semidirect
8. C22×D4×C491C2semidirect
9. C23×D491C22semidirect
12. C2×C22⋊D491C22semidirect
13. C2×C22⋊D491C22semidirect
14. C22×Dic491C22semidirect
15. C22×Dic491C22semidirect
16. Dic491⋊C4C22semidirect
17. C22⋊Dic491C22semidirect
18. C22⋊Dic491C22semidirect
19. C22⋊Dic491C22semidirect
20. (C2×D491)⋊C4C22semidirect
22. C24×C491C22semidirect
25. C2×D4×C491C22semidirect
26. C22×C4×C491C22semidirect
40. C23×C491D4semidirect
73. C491#534semidirect
76. C22×D4D491semidirect
85. C24C2×D491semidirect
92. C2×D4C2×D491semidirect
95. C22×C4C2×D491semidirect
107. C23C22⋊D491semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4912
#306283202
#306283182
#306283092
#306283062
#306283052
C2×C22⋊Dic4912
C22×D4×C4912
#534491