Finite Group Databasebeta

← #38768145

Subgroups — #38768145

Order 25472.

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#27164766C211yesmaximal, characteristic, complemented
2#27164407C212yesmaximal, complemented
3#27164384C211yesmaximal, characteristic, complemented
4#27163757C212yesmaximal, complemented
5#330×C199C211yesmaximal, characteristic, complemented
6C2×#15691875—22no—
7C2×D1592—22no—
8#20263952C2211yescharacteristic
9#20263943C2212yes—
10#20263940—22no—
11#20263933—22no—
12#20263930—22no—
13#20263875—22no—
14#20263866C2211yescharacteristic
15#125×C199C2211yescharacteristic
16#97×C199C2212yes—
17C2×Dic398D412yes—
18C2×D796—22no—
19C2×D796—22no—
20C2×D796—21no—
21C2×D796D412yes—
22C2×C4×D199—22no—
23#15691875—44no—
24D1592—44no—
25C2×C199⋊C8—21no—
26Dic199⋊C4—22no—
27(C2×D199)⋊C4—22no—
28(C2×D199)⋊C4—22no—
29(C2×D199)⋊C4—22no—
30C2×C8×C199—22no—
31C4⋊C4×C199—22no—
32C4⋊C4×C199D412yes—
33C42×C199C2311yescharacteristic
34C22×D199—22no—
35C22×D199—41no—
36Dic398—42no—
37D796—42no—
38D796—42no—
39D796—42no—
40D796—42no—
41D796—82no—
42C2×Dic199—22no—
43C4×D199—82no—
44C199⋊C8—41no—
45C2×C4×C199—22no—
46C2×C4×C199C2×D412yes—
47C2×C4×C199C2×D411yescharacteristic
48C8×C199—24no—
49C22×C199#12011yescharacteristic
50C2×D199—42no—
51C2×D199—42no—
52C2×D199—42no—
53C2×D199—82no—
54C2×D199—81no—
55C4×C199—22no—
56C4×C199—21no—
57C4×C199—42no—
58Dic199—42no—
59C2×C199#45312yes—
60C2×C199#45411yescharacteristic
61D199—82no—
62D199—161no—
63C199#165611yescharacteristic, complemented, Sylow
64#1656—1991nomaximal, Sylow
65#562—1991no—
66#496—1992no—
67#490—1991no—
68#330D19911yescharacteristic, complemented
69#329—1992no—
70C2×SD16—3982no—
71C2×D8—3982no—
72#127—1991no—
73#125C2×D19911yescharacteristic
74#124—1992no—
75#123—3982no—
76C22⋊Q8—3982no—
77#121—3982no—
78#102—3982no—
79#97—1991no—
80#97C2×D19912yes—
81C2×Q8—1992no—
82C2×D4—3982no—
83C2×D4—3982no—
84C2×D4—3981no—
85C2×D4—1992no—
86C22×C4—3982no—
87SD16—7964no—
88D8—7964no—
89C2×C8—22no—
90C2×C8—3981no—
91C4⋊C4—22no—
92C4⋊C4—3982no—
93C4⋊C4D79612yes—
94C22⋊C4—3982no—
95C22⋊C4—3982no—
96C22⋊C4—3982no—
97C42C22×D19911yescharacteristic
98C23—7961no—
99C23—3982no—
100Q8—7962no—
101D4—7962no—
102D4—7962no—
103D4—7962no—
104D4—7962no—
105D4—15922no—
106C2×C4—22no—
107C2×C4—15922no—
108C2×C4—3982no—
109C2×C4D4×D19912yes—
110C2×C4C2×D79611yescharacteristic
111C8—24no—
112C8—7961no—
113C22—7962no—
114C22—7962no—
115C22—7962no—
116C22—15922no—
117C22—15921no—
118C22#2026392511yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—7962no—
123C2—15922no—
124C2—31841no—
125C2#2716418712yes—
126C2#2716419311yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199#120
hypercenter#330D199
hypocenterC199#1656
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. #27164766C2semidirect
2. #27164407C2semidirect
3. #27164384C2semidirect
4. #27163757C2semidirect
5. #330×C199C2semidirect
63. C199#1656semidirect
68. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271647662
#271644072
#271643842
#271637572
#330×C1992
#1656199