Finite Group Databasebeta

← #28416624

Subgroups — #28416624

Order 14912.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#21418580C211yesmaximal, characteristic
2#21418518C212yesmaximal, complemented
3#21418450C211yesmaximal, characteristic, complemented
4#21418449C212yesmaximal, complemented
5#123×C233C211yesmaximal, characteristic, complemented
6#16836594—21no—
7#16836593—22no—
8C2×C22⋊D233—21no—
9C2×C22⋊D233C2212yes—
10D4×D233—22no—
11#16836573—22no—
12C22⋊Dic233C2212yescomplemented
13#16836571—22no—
14C2×D4×C233C2211yescharacteristic
15C22×C4×C233C2211yescharacteristic, complemented
16C4⋊C4×C233—21no—
17C22⋊C4×C233—21no—
18C22⋊C4×C233C2211yescharacteristic, complemented
19C22×D233—21no—
20C22×D233D412yes—
21Dic466—21no—
22D932—21no—
23C22⋊D233—22no—
24C22⋊D233—22no—
25C22⋊D233—22no—
26C2×Dic233—21no—
27C2×Dic233—22no—
28C2×Dic233D412yes—
29C4×D233—22no—
30C23×C233D411yescharacteristic
31C23×C233C2311yescharacteristic
32D4×C233—22no—
33C2×C4×C233—21no—
34C2×C4×C233—21no—
35C2×C4×C233—22no—
36C2×C4×C233D411yescharacteristic
37C22×C233—21no—
38C22×C233—41no—
39C22×C233—41no—
40C22×C233C2×D412yes—
41C22×C233C2×D411yescharacteristic
42C2×D233—22no—
43C2×D233—42no—
44C2×D233—81no—
45C4×C233—21no—
46C4×C233—41no—
47C4×C233—41no—
48Dic233—22no—
49Dic233—42no—
50C2×C233—22no—
51C2×C233—21no—
52C2×C233—41no—
53C2×C233#12011yescharacteristic
54D233—42no—
55C233#45811yescharacteristic, complemented, Sylow
56#458—2331nomaximal, Sylow
57H(5,𝔽2)—2331no—
58#123—2332no—
59#123D23311yescharacteristic, complemented
60#99—2331no—
61#99—2332no—
62#41—4662no—
63#41—4661no—
64C2×D4—4662no—
65C2×D4—4661no—
66C2×D4—2332no—
67C2×D4C2×D23311yescharacteristic
68C22×C4C2×D23311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—4662no—
71C22⋊C4—21no—
72C22⋊C4—4662no—
73C22⋊C4—2332no—
74C22⋊C4C2×D23311yescharacteristic, complemented
75C23—4661no—
76C23—2332no—
77C23C22⋊D23311yescharacteristic
78C23C22×D23311yescharacteristic
79Q8—4661no—
80D4—22no—
81D4—4661no—
82D4—4662no—
83D4—4662no—
84D4—4662no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—4662no—
89C2×C4—4662no—
90C2×C4—4661no—
91C2×C4—2332no—
92C2×C4C22⋊D23311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—18641no—
97C22—9322no—
98C22—4662no—
99C22D4×D23312yes—
100C22C2×C22⋊D23311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—9322no—
105C4—4662no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—9322no—
110C2#2141850311yescharacteristic
subgroupG/H
centerC2#21418503
commutator, cosocleC23×C233C23
FrattiniC23C22×D233
Fitting#123×C233C2
socleC2×C233#120
prime radical#21418580C2
hypercenter#123D233
hypocenterC233#458
LCSG ▷ C23×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #21418518C2semidirect
3. #21418450C2semidirect
4. #21418449C2semidirect
5. #123×C233C2semidirect
12. C22⋊Dic233C22semidirect
15. C22×C4×C233C22semidirect
18. C22⋊C4×C233C22semidirect
55. C233#458semidirect
59. #123D233semidirect
68. C22×C4C2×D233semidirect
74. C22⋊C4C2×D233semidirect

Maximal subgroups

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

subgroupindex
#214185802
#214185182
#214184502
#214184492
#123×C2332
#458233