Finite Group Databasebeta

← #38766798

Subgroups — #38766798

Order 25472.

158 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 41 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#27163742C211yesmaximal, characteristic
2#27163742C211yesmaximal, characteristic
3#385×C199C211yesmaximal, characteristic
4C22⋊(C199⋊C8)—21no—
5C22⋊(C199⋊C8)—21no—
6C23×C4×C199C411yescharacteristic
7C2×C4⋊C4×C199—21no—
8C2×C22⋊C4×C199C411yescharacteristic
9C2×C22⋊C4×C199C2211yescharacteristic
10#95×C199—21no—
11C2×C199⋊C8—41no—
12C2×C199⋊C8—41no—
13C24×C199C2×C411yescharacteristic
14C22×C4×C199—21no—
15C22×C4×C199—21no—
16C22×C4×C199—42no—
17C22×C4×C199—41no—
18C22×C4×C199D411yescharacteristic
19C22×C4×C199D411yescharacteristic
20C4⋊C4×C199—42no—
21C22⋊C4×C199—21no—
22C22⋊C4×C199—41no—
23C22⋊C4×C199C812yescomplemented
24C199⋊C8—81no—
25C199⋊C8—81no—
26C23×C199—21no—
27C23×C199—21no—
28C23×C199—41no—
29C23×C199—41no—
30C23×C199C22⋊C411yescharacteristic
31C23×C199C2×C811yescharacteristic
32C23×C199M1611yescharacteristic
33C2×C4×C199—22no—
34C2×C4×C199—22no—
35C2×C4×C199—21no—
36C2×C4×C199—21no—
37C2×C4×C199—41no—
38C2×C4×C199—41no—
39C2×C4×C199—41no—
40C2×C4×C199—42no—
41C2×C4×C199—41no—
42C2×C4×C199—41no—
43C2×C4×C199—41no—
44C2×C4×C199—42no—
45C22×C199—21no—
46C22×C199—21no—
47C22×C199—21no—
48C22×C199—21no—
49C22×C199—41no—
50C22×C199—41no—
51C22×C199—42no—
52C22×C199—41no—
53C22×C199—41no—
54C22×C199C22⋊C811yescharacteristic
55C22×C199#9911yescharacteristic
56C22×C199#10111yescharacteristic
57C4×C199—42no—
58C4×C199—42no—
59C4×C199—41no—
60C4×C199—41no—
61C2×C199—21no—
62C2×C199—21no—
63C2×C199—41no—
64C2×C199—41no—
65C2×C199#32411yescharacteristic
66C2×C199AΣL(1,𝔽16)11yescharacteristic
67C2×C199#35211yescharacteristic
68C199#132611yescharacteristic, complemented, Sylow
69#1326—1991nomaximal, Sylow
70#385D19911yescharacteristic
71#323—1991no—
72#323—1991no—
73C23×C4Dic19911yescharacteristic
74C2×C4⋊C4—21no—
75C2×C22⋊C4Dic19911yescharacteristic
76C2×C22⋊C4C2×D19911yescharacteristic
77C22⋊C8—3981no—
78C22⋊C8—3981no—
79#95—21no—
80C24C2×Dic19911yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—42no—
84C22×C4—41no—
85C22×C4C22⋊D19911yescharacteristic
86C22×C4C22⋊D19911yescharacteristic
87C2×C8—7961no—
88C2×C8—7961no—
89C4⋊C4—42no—
90C22⋊C4—21no—
91C22⋊C4—41no—
92C22⋊C4C199⋊C812yescomplemented
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C22⋊Dic19911yescharacteristic
98C23C2×C199⋊C811yescharacteristic
99C23#1569187011yescharacteristic
100C2×C4—22no—
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C8—15921no—
113C8—15921no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22C22⋊(C199⋊C8)11yescharacteristic
124C22#2026387011yescharacteristic
125C22#2026387411yescharacteristic
126C4—42no—
127C4—41no—
128C4—42no—
129C4—41no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2716374411yescharacteristic
135C2#2716380511yescharacteristic
136C2#2716380811yescharacteristic
subgroupG/H
centerC22#20263870
commutatorC23×C199C2×C8
FrattiniC2×C22⋊C4C2×D199
Fitting#385×C199C2
socleC22×C199#99
prime radicalC24×C199C2×C4
cosocleC2×C22⋊C4×C199C22
hypercenter#385D199
hypocenterC199#1326
LCSG ▷ C23×C199 ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
23. C22⋊C4×C199C8semidirect
68. C199#1326semidirect
92. C22⋊C4C199⋊C8semidirect

Maximal subgroups

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

subgroupindex
#271637422
#385×C1992
#1326199