Finite Group Databasebeta

← #38768153

Subgroups — #38768153

Order 25472.

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

normal subgroups only

This group has 182 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
1C199⋊#564C211yesmaximal, characteristic, complemented
2#27164384C211yesmaximal, characteristic
3#27164383C212yesmaximal
4#27163759C212yesmaximal, complemented
5#330×C199C211yesmaximal, characteristic, complemented
6#20263952C2211yescharacteristic
7#20263947C2212yes—
8#20263946—22no—
9#20263945—22no—
10#20263945—22no—
11#20263877—22no—
12#20263877—22no—
13#20263875—22no—
14#20263866C2211yescharacteristic
15#125×C199C2211yescharacteristic
16#97×C199C2212yes—
17C2×D796—21no—
18C2×D796—22no—
19C2×C199⋊C8—21no—
20C4⋊Dic199—22no—
21C4⋊Dic199D412yes—
22C4⋊Dic199D412yes—
23Dic199⋊C4—22no—
24Dic199⋊C4—22no—
25Dic199⋊C4—22no—
26Dic199⋊C4—22no—
27C4×Dic199—22no—
28C2×C8×C199—22no—
29C4⋊C4×C199—22no—
30C4⋊C4×C199D412yes—
31C42×C199C2311yescharacteristic
32C22×D199—41no—
33D796—44no—
34D796—42no—
35C2×Dic199—22no—
36C2×Dic199—22no—
37C199⋊C8—41no—
38C2×C4×C199—22no—
39C2×C4×C199C2×D412yes—
40C2×C4×C199C2×D411yescharacteristic
41C8×C199—42no—
42C22×C199#12011yescharacteristic
43C2×D199—82no—
44C2×D199—81no—
45C4×C199—22no—
46C4×C199—21no—
47C4×C199—42no—
48Dic199—42no—
49Dic199—42no—
50C2×C199#45412yes—
51C2×C199#45411yescharacteristic
52D199—161no—
53C199#165811yescharacteristic, complemented, Sylow
54#1658—1991nomaximal, Sylow
55#564—1991no—
56#490—1991no—
57#490—1992no—
58#330—1992no—
59#330D19911yescharacteristic, complemented
60#127—1991no—
61#125—3982no—
62#125—3982no—
63#125—3982no—
64#125—1992no—
65#125C2×D19911yescharacteristic
66#102—3982no—
67#102—3982no—
68#102—3982no—
69#97—1991no—
70#97C2×D19912yes—
71C2×D4—3982no—
72C2×D4—3981no—
73C2×C8—22no—
74C2×C8—3981no—
75C4⋊C4—22no—
76C4⋊C4—3982no—
77C4⋊C4—3982no—
78C4⋊C4—3982no—
79C4⋊C4—3982no—
80C4⋊C4—3982no—
81C4⋊C4—1992no—
82C4⋊C4—1992no—
83C4⋊C4D79612yes—
84C42—3982no—
85C42C22×D19911yescharacteristic
86C23—7961no—
87D4—7964no—
88D4—7962no—
89C2×C4—22no—
90C2×C4—3982no—
91C2×C4—3982no—
92C2×C4D4×D19912yes—
93C2×C4C2×D79611yescharacteristic
94C8—42no—
95C8—7961no—
96C22—15922no—
97C22—15921no—
98C22#2026392511yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—7962no—
103C4—7962no—
104C2—31841no—
105C2#2716419212yes—
106C2#2716419311yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199#120
prime radical#20263952C22
hypercenter#330D199
hypocenterC199#1658
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C199⋊#564C2semidirect
4. #27163759C2semidirect
5. #330×C199C2semidirect
53. C199#1658semidirect
59. #330D199semidirect

Maximal subgroups

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

subgroupindex
C199⋊#5642
#271643842
#271643832
#271637592
#330×C1992
#1658199