Finite Group Databasebeta

← #38767475

Subgroups — #38767475

Order 25472.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D199C211yesmaximal, characteristic
2#27164073C212yesmaximal
3#27163760C211yesmaximal, characteristic, complemented
4#27163759C212yesmaximal, complemented
5#330×C199C211yesmaximal, characteristic, complemented
6#20263947C2211yescharacteristic
7#20263946C412yes—
8#20263945—22no—
9C4⋊C4×D199—22no—
10C4⋊C4×D199C412yes—
11C42×D199C2211yescharacteristic
12Dic199⋊C8—22no—
13(C2×D199)⋊C8—22no—
14#20263866C2212yes—
15#125×C199C2211yescharacteristic
16#97×C199C2212yes—
17C2×C4×D199—22no—
18C2×C4×D199C2×C411yescharacteristic
19C2×C4×D199D412yes—
20C2×C199⋊C8—22no—
21C4⋊Dic199—22no—
22C4⋊Dic199C2×C412yes—
23Dic199⋊C4—22no—
24Dic199⋊C4—22no—
25Dic199⋊C4—22no—
26C4×Dic199C2×C411yescharacteristic
27C4×Dic199D412yes—
28C2×C8×C199—22no—
29C4⋊C4×C199—22no—
30C4⋊C4×C199C2×C412yes—
31C42×C199C2311yescharacteristic
32C22×D199C22⋊C411yescharacteristic
33C2×Dic199—22no—
34C2×Dic199C22⋊C412yes—
35C2×Dic199C22⋊C411yescharacteristic
36C4×D199—22no—
37C4×D199—42no—
38C4×D199—44no—
39C199⋊C8—42no—
40C2×C4×C199—22no—
41C2×C4×C199C22×C411yescharacteristic
42C2×C4×C199C2×D412yes—
43C8×C199—42no—
44C22×C199C2×C22⋊C411yescharacteristic
45C2×D199—22no—
46C2×D199#10112yes—
47C4×C199—21no—
48C4×C199—22no—
49C4×C199—42no—
50Dic199—21no—
51Dic199—22no—
52Dic199—42no—
53C2×C199C2×#10111yescharacteristic
54C2×C199#42112yes—
55D199—22no—
56C199#153411yescharacteristic, complemented, Sylow
57#1534—1991nomaximal, Sylow
58C2×#125—1991no—
59#432—1992no—
60#330—1991no—
61#330—1992no—
62#330D19911yescharacteristic, complemented
63#125—3982no—
64#125—1992no—
65#125—1991no—
66#125C2×D19911yescharacteristic
67C2×C4⋊C4—3982no—
68C2×C4⋊C4—1992no—
69C2×C42—1991no—
70C4⋊C8—3982no—
71C22⋊C8—3982no—
72#97—1992no—
73#97C2×D19912yes—
74C22×C4—3982no—
75C22×C4—1992no—
76C22×C4—1991no—
77C2×C8—22no—
78C2×C8—3982no—
79C4⋊C4—22no—
80C4⋊C4—3982no—
81C4⋊C4—3982no—
82C4⋊C4—3982no—
83C4⋊C4—3982no—
84C4⋊C4—1992no—
85C4⋊C4C4×D19912yes—
86C42—1991no—
87C42—1992no—
88C42C22×D19911yescharacteristic
89C23—1991no—
90C2×C4—22no—
91C2×C4—7962no—
92C2×C4—7964no—
93C2×C4—3982no—
94C2×C4—3982no—
95C2×C4—1991no—
96C2×C4—1992no—
97C2×C4C2×C4×D19911yescharacteristic
98C2×C4D4×D19912yes—
99C8—42no—
100C8—7962no—
101C22—3982no—
102C22—1992no—
103C22C22⋊C4×D19911yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—7962no—
108C4—3981no—
109C4—3982no—
110C2—3982no—
111C2#101×D19911yescharacteristic
112C2#2716403312yes—
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D199C22⋊C4
cosocleC42×C199C23
hypercenter#330D199
hypocenterC199#1534
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #27163760C2semidirect
4. #27163759C2semidirect
5. #330×C199C2semidirect
56. C199#1534semidirect
62. #330D199semidirect

Maximal subgroups

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

subgroupindex
#125×D1992
#271640732
#271637602
#271637592
#330×C1992
#1534199