Finite Group Databasebeta

← #27193769

Subgroups — #27193769

Order 13184.

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×D103C211yesmaximal, characteristic
2#20267846C212yesmaximal
3#20267533C211yesmaximal, characteristic, complemented
4#20267532C212yesmaximal, complemented
5#330×C103C211yesmaximal, characteristic, complemented
6#15693013C2211yescharacteristic
7#15693012C412yes—
8#15693011—22no—
9C4⋊C4×D103—22no—
10C4⋊C4×D103C412yes—
11C42×D103C2211yescharacteristic
12Dic103⋊C8—22no—
13(C2×D103)⋊C8—22no—
14#15692932C2212yes—
15#125×C103C2211yescharacteristic
16#97×C103C2212yes—
17C2×C4×D103—22no—
18C2×C4×D103C2×C411yescharacteristic
19C2×C4×D103D412yes—
20C2×C103⋊C8—22no—
21C4⋊Dic103—22no—
22C4⋊Dic103C2×C412yes—
23Dic103⋊C4—22no—
24Dic103⋊C4—22no—
25Dic103⋊C4—22no—
26C4×Dic103C2×C411yescharacteristic
27C4×Dic103D412yes—
28C2×C8×C103—22no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103C2×C412yes—
31C42×C103C2311yescharacteristic
32C22×D103C22⋊C411yescharacteristic
33C2×C4×C103—22no—
34C2×C4×C103C22×C411yescharacteristic
35C2×C4×C103C2×D412yes—
36C2×Dic103—22no—
37C2×Dic103C22⋊C412yes—
38C2×Dic103C22⋊C411yescharacteristic
39C4×D103—22no—
40C4×D103—42no—
41C4×D103—44no—
42C8×C103—42no—
43C103⋊C8—42no—
44C22×C103C2×C22⋊C411yescharacteristic
45C2×D103—22no—
46C2×D103#10112yes—
47C4×C103—21no—
48C4×C103—22no—
49C4×C103—42no—
50Dic103—21no—
51Dic103—22no—
52Dic103—42no—
53C2×C103C2×#10111yescharacteristic
54C2×C103#42112yes—
55D103—22no—
56#1534—1031nomaximal, Sylow
57C103#153411yescharacteristic, complemented, Sylow
58C2×#125—1031no—
59#432—1032no—
60#330—1031no—
61#330—1032no—
62#330D10311yescharacteristic, complemented
63#125—1032no—
64#125—1031no—
65#125—2062no—
66#125C2×D10311yescharacteristic
67C2×C4⋊C4—1032no—
68C2×C4⋊C4—2062no—
69C2×C42—1031no—
70C4⋊C8—2062no—
71C22⋊C8—2062no—
72#97—1032no—
73#97C2×D10312yes—
74C22×C4—1032no—
75C22×C4—1031no—
76C22×C4—2062no—
77C2×C8—22no—
78C2×C8—2062no—
79C4⋊C4—22no—
80C4⋊C4—1032no—
81C4⋊C4—2062no—
82C4⋊C4—2062no—
83C4⋊C4—2062no—
84C4⋊C4—2062no—
85C4⋊C4C4×D10312yes—
86C42—1031no—
87C42—1032no—
88C42C22×D10311yescharacteristic
89C23—1031no—
90C2×C4—22no—
91C2×C4—1032no—
92C2×C4—1031no—
93C2×C4—4122no—
94C2×C4—4124no—
95C2×C4—2062no—
96C2×C4—2062no—
97C2×C4C2×C4×D10311yescharacteristic
98C2×C4D4×D10312yes—
99C8—42no—
100C8—4122no—
101C22—1032no—
102C22—2062no—
103C22C22⋊C4×D10311yescharacteristic
104C4—22no—
105C4—21no—
106C4—42no—
107C4—4122no—
108C4—2062no—
109C4—2061no—
110C2—2062no—
111C2#101×D10311yescharacteristic
112C2#2026780612yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#330×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC22×D103C22⋊C4
cosocleC42×C103C23
hypercenter#330D103
hypocenterC103#1534
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20267533C2semidirect
4. #20267532C2semidirect
5. #330×C103C2semidirect
57. C103#1534semidirect
62. #330D103semidirect

Maximal subgroups

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

subgroupindex
#125×D1032
#202678462
#202675332
#202675322
#330×C1032
#1534103