Finite Group Databasebeta

← #27193144

Subgroups — #27193144

Order 13184.

146 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 37 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#20267558C211yesmaximal, characteristic
2#20267515C211yesmaximal, characteristic
3#397×C103C211yesmaximal, characteristic
4C2×C22⋊Dic103—21no—
5C22⋊(C103⋊C8)—21no—
6C2×C4⋊C4×C103C411yescharacteristic, complemented
7C2×C22⋊C4×C103—21no—
8C2×C22⋊C4×C103C2211yescharacteristic
9#95×C103—21no—
10#95×C103C411yescharacteristic, complemented
11C22×Dic103—41no—
12C2×C103⋊C8—41no—
13C22⋊Dic103—22no—
14C22⋊Dic103—41no—
15C24×C103D411yescharacteristic
16C22×C4×C103—21no—
17C22×C4×C103—21no—
18C22×C4×C103C2×C411yescharacteristic
19C22×C4×C103D411yescharacteristic
20C4⋊C4×C103—41no—
21C22⋊C4×C103—41no—
22C22⋊C4×C103—41no—
23C22⋊C4×C103—41no—
24C23×C103—21no—
25C23×C103—21no—
26C23×C103—41no—
27C23×C103—41no—
28C23×C103C22⋊C411yescharacteristic
29C23×C103D811yescharacteristic
30C23×C103SD1611yescharacteristic
31C2×C4×C103—21no—
32C2×C4×C103—21no—
33C2×C4×C103—41no—
34C2×C4×C103—41no—
35C2×C4×C103—41no—
36C2×C4×C103—41no—
37C2×C4×C103—41no—
38C2×C4×C103—41no—
39C2×C4×C103—41no—
40C2×C4×C103—41no—
41C2×Dic103—42no—
42C2×Dic103—81no—
43C2×Dic103—81no—
44C103⋊C8—81no—
45C22×C103—21no—
46C22×C103—21no—
47C22×C103—21no—
48C22×C103—21no—
49C22×C103—41no—
50C22×C103—41no—
51C22×C103—41no—
52C22×C103—41no—
53C22×C103—81no—
54C22×C103#9911yescharacteristic
55C22×C103#10211yescharacteristic
56C22×C103#10411yescharacteristic
57C4×C103—41no—
58C4×C103—41no—
59C4×C103—81no—
60C4×C103—81no—
61Dic103—82no—
62C2×C103—21no—
63C2×C103—21no—
64C2×C103—41no—
65C2×C103—41no—
66C2×C103#32711yescharacteristic
67C2×C103#35211yescharacteristic
68C2×C103#35411yescharacteristic
69#1344—1031nomaximal, Sylow
70C103#134411yescharacteristic, complemented, Sylow
71#397D10311yescharacteristic
72#342—1031no—
73#323—1031no—
74C2×C4⋊C4Dic10311yescharacteristic, complemented
75C2×C22⋊C4—21no—
76C2×C22⋊C4—2061no—
77C2×C22⋊C4C2×D10311yescharacteristic
78C22⋊C8—2061no—
79#95—21no—
80#95Dic10311yescharacteristic, complemented
81C24C22⋊D10311yescharacteristic
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—4121no—
85C22×C4C2×Dic10311yescharacteristic
86C22×C4C22⋊D10311yescharacteristic
87C2×C8—4121no—
88C4⋊C4—41no—
89C22⋊C4—41no—
90C22⋊C4—41no—
91C22⋊C4—41no—
92C22⋊C4—4121no—
93C22⋊C4—2062no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23C22⋊Dic10311yescharacteristic
99C23#1311009011yescharacteristic
100C23#1311009311yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—8241no—
112C2×C4—8241no—
113C2×C4—4122no—
114C8—8241no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1569293611yescharacteristic
125C22#1569294211yescharacteristic
126C22#1569294811yescharacteristic
127C4—41no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—8242no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#2026752511yescharacteristic
137C2#2026758111yescharacteristic
138C2#2026758611yescharacteristic
subgroupG/H
centerC22#15692936
commutatorC22×C4×C103C2×C4
FrattiniC2×C22⋊C4C2×D103
Fitting#397×C103C2
socleC22×C103#99
prime radicalC24×C103D4
cosocleC2×C22⋊C4×C103C22
hypercenter#397D103
hypocenterC103#1344
LCSG ▷ C22×C4×C103 ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊C4×C103C4semidirect
10. #95×C103C4semidirect
70. C103#1344semidirect
74. C2×C4⋊C4Dic103semidirect
80. #95Dic103semidirect

Maximal subgroups

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

subgroupindex
#202675582
#202675152
#397×C1032
#1344103