Finite Group Databasebeta

← #38768173

Subgroups — #38768173

Order 25472.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#27164388C211yesmaximal, characteristic, complemented
2#27164377C212yesmaximal, complemented
3#27163760C211yesmaximal, characteristic, complemented
4#27163758C212yesmaximal, complemented
5#562×C199C211yesmaximal, characteristic
6#20263955C2211yescharacteristic
7#20263879—22no—
8#20263878—22no—
9#20263876—22no—
10#20263866C2211yescharacteristic
11#20263866C2212yes—
12#125×C199C2211yescharacteristic
13#124×C199C2212yes—
14#123×C199—22no—
15C22⋊Q8×C199—22no—
16#121×C199—22no—
17C2×Dic398—21no—
18C2×C199⋊C8—22no—
19C2×C199⋊C8—21no—
20C4⋊Dic199—22no—
21C2×Q8×C199D412yes—
22C2×D4×C199—22no—
23C2×D4×C199D412yes—
24C22×C4×C199—22no—
25C4⋊C4×C199—22no—
26C4⋊C4×C199—22no—
27C4⋊C4×C199D412yes—
28C22⋊C4×C199—22no—
29C22⋊C4×C199—22no—
30C22⋊C4×C199—22no—
31C42×C199C2311yescharacteristic
32Dic398—42no—
33C2×Dic199—41no—
34C199⋊C8—41no—
35C199⋊C8—42no—
36C23×C199—22no—
37Q8×C199—42no—
38D4×C199—42no—
39D4×C199—82no—
40C2×C4×C199—22no—
41C2×C4×C199—22no—
42C2×C4×C199—82no—
43C2×C4×C199C2×D411yescharacteristic
44C2×C4×C199C2×D412yes—
45C22×C199—42no—
46C22×C199—42no—
47C22×C199—42no—
48C22×C199#12011yescharacteristic
49C4×C199—21no—
50C4×C199—22no—
51C4×C199—42no—
52C4×C199—42no—
53Dic199—81no—
54C2×C199—82no—
55C2×C199#45411yescharacteristic
56C2×C199#45512yes—
57C199#166211yescharacteristic, complemented, Sylow
58#1662—1991nomaximal, Sylow
59#562D19911yescharacteristic
60#491—1991no—
61#489—1992no—
62#330—1991no—
63#329—1992no—
64C4⋊Q8—1991no—
65#125C2×D19911yescharacteristic
66#124C2×D19912yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—3982no—
71#103—3982no—
72#102—3982no—
73#97—1991no—
74#97—1992no—
75C2×Q8—3981no—
76C2×Q8C22⋊D19912yes—
77C2×D4—22no—
78C2×D4C22⋊D19912yes—
79C22×C4—22no—
80C2×C8—3982no—
81C2×C8—3981no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—3982no—
85C4⋊C4C22⋊D19912yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D19911yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—7962no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—7961no—
99C2×C4C2×C22⋊D19911yescharacteristic
100C2×C4C2×C22⋊D19912yes—
101C8—7961no—
102C8—7962no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#2026392411yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—15921no—
112C2—82no—
113C2#2716419111yescharacteristic
114C2#2716419612yes—
subgroupG/H
centerC22#20263924
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting, prime radical#562×C199C2
socleC22×C199#120
hypercenter#562D199
hypocenterC199#1662
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #27164388C2semidirect
2. #27164377C2semidirect
3. #27163760C2semidirect
4. #27163758C2semidirect
57. C199#1662semidirect

Maximal subgroups

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

subgroupindex
#271643882
#271643772
#271637602
#271637582
#562×C1992
#1662199