Finite Group Databasebeta

← #27194447

Subgroups — #27194447

Order 13184.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C103⋊#564C211yesmaximal, characteristic, complemented
2#20268157C211yesmaximal, characteristic
3#20268156C212yesmaximal
4#20267532C212yesmaximal, complemented
5#330×C103C211yesmaximal, characteristic, complemented
6#15693018C2211yescharacteristic
7#15693013C2212yes—
8#15693012—22no—
9#15693011—22no—
10#15693011—22no—
11#15692943—22no—
12#15692943—22no—
13#15692941—22no—
14#15692932C2211yescharacteristic
15#125×C103C2211yescharacteristic
16#97×C103C2212yes—
17C2×D412—21no—
18C2×D412—22no—
19C2×C103⋊C8—21no—
20C4⋊Dic103—22no—
21C4⋊Dic103D412yes—
22C4⋊Dic103D412yes—
23Dic103⋊C4—22no—
24Dic103⋊C4—22no—
25Dic103⋊C4—22no—
26Dic103⋊C4—22no—
27C4×Dic103—22no—
28C2×C8×C103—22no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103D412yes—
31C42×C103C2311yescharacteristic
32C22×D103—41no—
33C2×C4×C103—22no—
34C2×C4×C103C2×D412yes—
35C2×C4×C103C2×D411yescharacteristic
36C2×Dic103—22no—
37C2×Dic103—22no—
38D412—42no—
39D412—44no—
40C8×C103—42no—
41C103⋊C8—41no—
42C22×C103#12011yescharacteristic
43C2×D103—82no—
44C2×D103—81no—
45C4×C103—21no—
46C4×C103—22no—
47C4×C103—42no—
48Dic103—42no—
49Dic103—42no—
50C2×C103#45412yes—
51C2×C103#45411yescharacteristic
52D103—161no—
53#1658—1031nomaximal, Sylow
54C103#165811yescharacteristic, complemented, Sylow
55#564—1031no—
56#490—1031no—
57#490—1032no—
58#330—1032no—
59#330D10311yescharacteristic, complemented
60#127—1031no—
61#125—1032no—
62#125—2062no—
63#125—2062no—
64#125—2062no—
65#125C2×D10311yescharacteristic
66#102—2062no—
67#102—2062no—
68#102—2062no—
69#97—1031no—
70#97C2×D10312yes—
71C2×D4—2062no—
72C2×D4—2061no—
73C2×C8—22no—
74C2×C8—2061no—
75C4⋊C4—22no—
76C4⋊C4—1032no—
77C4⋊C4—1032no—
78C4⋊C4—2062no—
79C4⋊C4—2062no—
80C4⋊C4—2062no—
81C4⋊C4—2062no—
82C4⋊C4—2062no—
83C4⋊C4D41212yes—
84C42—2062no—
85C42C22×D10311yescharacteristic
86C23—4121no—
87D4—4124no—
88D4—4122no—
89C2×C4—22no—
90C2×C4—2062no—
91C2×C4—2062no—
92C2×C4D4×D10312yes—
93C2×C4C2×D41211yescharacteristic
94C8—42no—
95C8—4121no—
96C22—8242no—
97C22—8241no—
98C22#1569299111yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4122no—
103C4—4122no—
104C2—16481no—
105C2#2026796512yes—
106C2#2026796611yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#330×C103C2
socleC22×C103#120
prime radical#15693018C22
hypercenter#330D103
hypocenterC103#1658
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C103⋊#564C2semidirect
4. #20267532C2semidirect
5. #330×C103C2semidirect
54. C103#1658semidirect
59. #330D103semidirect

Maximal subgroups

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

subgroupindex
C103⋊#5642
#202681572
#202681562
#202675322
#330×C1032
#1658103