Finite Group Databasebeta

← #38768178

Subgroups — #38768178

Order 25472.

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

normal subgroups only

This group has 172 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#27164428C212yesmaximal
2#27164388C211yesmaximal, characteristic
3#27163760C212yesmaximal
4#27163760C211yesmaximal, characteristic
5#564×C199C211yesmaximal, characteristic
6#20263955C2211yescharacteristic
7#20263888—22no—
8#20263886—22no—
9#20263878—22no—
10#20263866C2212yes—
11#20263866C2211yescharacteristic
12#125×C199—22no—
13#125×C199—22no—
14#125×C199—22no—
15#125×C199C2212yes—
16#125×C199C2211yescharacteristic
17C2×Dic398—21no—
18C2×C199⋊C8—22no—
19C2×C199⋊C8—21no—
20C4⋊Dic199—22no—
21C4⋊C4×C199—22no—
22C4⋊C4×C199—22no—
23C4⋊C4×C199—22no—
24C4⋊C4×C199—22no—
25C4⋊C4×C199—22no—
26C4⋊C4×C199—22no—
27C4⋊C4×C199D412yes—
28C4⋊C4×C199D412yes—
29C4⋊C4×C199D412yes—
30C42×C199—22no—
31C42×C199C2311yescharacteristic
32Dic398—42no—
33C2×Dic199—41no—
34C199⋊C8—24no—
35C199⋊C8—41no—
36C2×C4×C199—22no—
37C2×C4×C199—22no—
38C2×C4×C199—22no—
39C2×C4×C199C2×D412yes—
40C2×C4×C199C2×D411yescharacteristic
41C22×C199#12011yescharacteristic
42C4×C199—21no—
43C4×C199—22no—
44C4×C199—42no—
45C4×C199—42no—
46C4×C199—42no—
47Dic199—81no—
48C2×C199#45411yescharacteristic
49C2×C199#45612yes—
50C199#166311yescharacteristic, complemented, Sylow
51#1663—1991nomaximal, Sylow
52#564D19911yescharacteristic
53#501—1992no—
54#491—1991no—
55#330—1992no—
56#330—1991no—
57C4⋊Q8—1991no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D19911yescharacteristic
62#125C2×D19912yes—
63#107—3982no—
64#106—3982no—
65#103—3982no—
66#97—1991no—
67#97—1992no—
68C2×Q8—3981no—
69C2×C8—3981no—
70C2×C8—3982no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—3982no—
78C4⋊C4C22⋊D19912yes—
79C4⋊C4C22⋊D19912yes—
80C4⋊C4C22⋊D19912yes—
81C42—22no—
82C42C22×D19911yescharacteristic
83Q8—7962no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—7961no—
88C2×C4C2×C22⋊D19912yes—
89C2×C4C2×C22⋊D19911yescharacteristic
90C8—7961no—
91C8—3984no—
92C22#2026392411yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—15921no—
99C2#2716419111yescharacteristic
100C2#2716420112yes—
subgroupG/H
centerC22#20263924
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#564×C199C2
socle, prime radicalC22×C199#120
hypercenter#564D199
hypocenterC199#1663
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C199#1663semidirect

Maximal subgroups

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

subgroupindex
#271644282
#271643882
#271637602
#564×C1992
#1663199