Finite Group Databasebeta

← #16845003

Subgroups — #16845003

Order 3968.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#14521797C211yesmaximal, characteristic, complemented
2#14521436C212yesmaximal, complemented
3#14520791C211yesmaximal, characteristic, complemented
4#14520788C212yesmaximal, complemented
5C31×#490C211yesmaximal, characteristic, complemented
6C31×#127C2211yescharacteristic
7C31×#125C2211yescharacteristic
8C2×#92480—22no—
9C2×#92479—22no—
10#11758473—22no—
11#11758472—22no—
12#11758471—22no—
13#11758452C2212yes—
14C31×#102—22no—
15C31×#97C2211yescharacteristic
16#11758391C2212yes—
17C2×D4×C31—21no—
18C2×D4×C31—22no—
19C2×D124—22no—
20C2×D124D412yes—
21C2×C4×D31—22no—
22C2×Dic62D412yes—
23C2×C8×C31—21no—
24C4⋊C4×C31—22no—
25C4⋊C4×C31D412yes—
26C42×C31C2311yescharacteristic
27#92480—44no—
28#92479—44no—
29(C2×D31)⋊C4—22no—
30(C2×D31)⋊C4—22no—
31(C2×D31)⋊C4—22no—
32Dic31⋊C4—22no—
33C2×C31⋊C8—22no—
34C23×C31—41no—
35C22×D31—22no—
36D4×C31—42no—
37D4×C31—42no—
38D4×C31—42no—
39C2×C4×C31—22no—
40C2×C4×C31C2×D412yes—
41C2×C4×C31C2×D411yescharacteristic
42C2×Dic31—22no—
43D124—42no—
44D124—82no—
45C4×D31—82no—
46Dic62—42no—
47C8×C31—41no—
48C31⋊C8—24no—
49#1656—311nomaximal, Sylow
50C22×C31—82no—
51C22×C31—81no—
52C22×C31#12011yescharacteristic
53C2×D31—42no—
54C2×D31—42no—
55C2×D31—42no—
56C4×C31—22no—
57C4×C31—21no—
58C4×C31—42no—
59Dic31—42no—
60#562—311no—
61#496—312no—
62#490D3111yescharacteristic, complemented
63#330—311no—
64#329—312no—
65C2×C31—161no—
66C2×C31#45312yes—
67C2×C31#45411yescharacteristic
68D31—82no—
69C2×SD16—622no—
70C2×D8—622no—
71#127C2×D3111yescharacteristic
72#125C2×D3111yescharacteristic
73#124—312no—
74#123—622no—
75C22⋊Q8—622no—
76#121—622no—
77#102—22no—
78#97—312no—
79#97C2×D3111yescharacteristic
80C31#165611yescharacteristic, complemented, Sylow
81C2×Q8—312no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—312no—
85C2×D4—622no—
86C22×C4—622no—
87SD16—1244no—
88D8—1244no—
89C2×C8—21no—
90C2×C8—622no—
91C4⋊C4—22no—
92C4⋊C4—622no—
93C4⋊C4C22⋊D3112yes—
94C22⋊C4—622no—
95C22⋊C4—622no—
96C22⋊C4—622no—
97C42C22×D3111yescharacteristic
98C23—41no—
99C23—622no—
100Q8—1242no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—1242no—
105D4—2482no—
106C2×C4—22no—
107C2×C4—622no—
108C2×C4—2482no—
109C2×C4D4×D3112yes—
110C2×C4C2×C22⋊D3111yescharacteristic
111C8—41no—
112C8—624no—
113C22—82no—
114C22—81no—
115C22—1242no—
116C22—1242no—
117C22—1242no—
118C22#1175851411yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1242no—
123C2—161no—
124C2—2482no—
125C2#1452121512yes—
126C2#1452122111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#490C2
socleC22×C31#120
hypercenter#490D31
hypocenterC31#1656
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14521797C2semidirect
2. #14521436C2semidirect
3. #14520791C2semidirect
4. #14520788C2semidirect
5. C31×#490C2semidirect
62. #490D31semidirect
80. C31#1656semidirect

Maximal subgroups

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

subgroupindex
#145217972
#145214362
#145207912
#145207882
C31×#4902
#165631