Finite Group Databasebeta

← #27193455

Subgroups — #27193455

Order 13184.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#15692977C211yesmaximal, characteristic
2#20267841C212yesmaximal, complemented
3#20267516C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic
5#323×C103C211yesmaximal, characteristic
6C23×Dic103C411yescharacteristic
7#15692977—22no—
8#15692977—22no—
9C2×Dic103⋊C4C411yescharacteristic
10C2×Dic103⋊C4C2211yescharacteristic
11C2×C22⋊Dic103C411yescharacteristic
12C2×C4×Dic103C411yescharacteristic
13C2×C4×Dic103C2211yescharacteristic
14Dic103⋊C8—22no—
15C22⋊(C103⋊C8)C2212yes—
16C8×Dic103—22no—
17C2×C22⋊C4×C103C2211yescharacteristic
18C22⋊C8×C103C2212yes—
19C22×Dic103—21no—
20C22×Dic103—21no—
21C22×Dic103—22no—
22C22×Dic103C814yescomplemented
23C22×Dic103C2×C411yescharacteristic
24C22×Dic103C2×C411yescharacteristic
25C22×Dic103C2×C411yescharacteristic
26C22×Dic103C2×C411yescharacteristic
27C2×C103⋊C8—22no—
28Dic103⋊C4—22no—
29Dic103⋊C4—22no—
30C22⋊Dic103—22no—
31C4×Dic103—21no—
32C4×Dic103—21no—
33C4×Dic103D412yes—
34C4×Dic103D412yes—
35C24×C103C2×C411yescharacteristic
36C22×C4×C103C2×C411yescharacteristic
37C22×C4×C103C2311yescharacteristic
38C2×C8×C103—22no—
39C22⋊C4×C103—22no—
40C23×C103—21no—
41C23×C103—21no—
42C23×C103—41no—
43C23×C103—41no—
44C23×C103C2×C812yes—
45C23×C103C22×C411yescharacteristic
46C2×C4×C103—21no—
47C2×C4×C103—41no—
48C2×C4×C103—41no—
49C2×C4×C103C2×D412yes—
50C2×Dic103—21no—
51C2×Dic103—21no—
52C2×Dic103—24no—
53C2×Dic103—24no—
54C2×Dic103—21no—
55C2×Dic103—41no—
56C2×Dic103—41no—
57C2×Dic103C22⋊C412yes—
58C2×Dic103C22⋊C411yescharacteristic
59C2×Dic103C22⋊C411yescharacteristic
60C2×Dic103C2×C812yes—
61C2×Dic103C2×C812yes—
62C2×Dic103M1612yes—
63C8×C103—42no—
64C103⋊C8—42no—
65C22×C103—21no—
66C22×C103—21no—
67C22×C103—22no—
68C22×C103—42no—
69C22×C103—42no—
70C22×C103—41no—
71C22×C103—41no—
72C22×C103C2×C22⋊C411yescharacteristic
73C22×C103C22×C811yescharacteristic
74C22×C103C2×M1611yescharacteristic
75C4×C103—22no—
76C4×C103—41no—
77Dic103—22no—
78Dic103—22no—
79Dic103—41no—
80Dic103C22⋊C812yes—
81Dic103C22⋊C812yes—
82C2×C103—21no—
83C2×C103—21no—
84C2×C103—42no—
85C2×C103C2×C22⋊C811yescharacteristic
86C2×C103#41011yescharacteristic
87C2×C103#41311yescharacteristic
88#1458—1031nomaximal, Sylow
89C103#145811yescharacteristic, complemented, Sylow
90C2×#117—1031no—
91#431—1032no—
92#324—1032no—
93#323—1031no—
94#323D10311yescharacteristic
95C23×C4—1031no—
96#117—2062no—
97#117—2062no—
98C2×C4⋊C4—1031no—
99C2×C4⋊C4—1031no—
100C2×C22⋊C4—1031no—
101C2×C22⋊C4C2×D10311yescharacteristic
102C2×C42—1031no—
103C2×C42—1031no—
104C4⋊C8—2062no—
105C22⋊C8—1032no—
106C22⋊C8C2×D10312yes—
107C4×C8—2062no—
108C24C4×D10311yescharacteristic
109C22×C4—1031no—
110C22×C4—1031no—
111C22×C4—1034no—
112C22×C4—1031no—
113C22×C4—1031no—
114C22×C4—2061no—
115C22×C4—2061no—
116C22×C4—2062no—
117C22×C4C4×D10311yescharacteristic
118C22×C4C22×D10311yescharacteristic
119C2×C8—22no—
120C2×C8—2062no—
121C4⋊C4—2062no—
122C4⋊C4—2062no—
123C22⋊C4—22no—
124C22⋊C4—2062no—
125C42—1032no—
126C42—1032no—
127C42—2061no—
128C42—2061no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23C8×D10312yes—
134C23C2×C4×D10311yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—1031no—
139C2×C4—1031no—
140C2×C4—1032no—
141C2×C4—1032no—
142C2×C4—1032no—
143C2×C4—1032no—
144C2×C4—4121no—
145C2×C4—4121no—
146C2×C4—2064no—
147C2×C4—2064no—
148C2×C4—2061no—
149C2×C4—2061no—
150C2×C4—2061no—
151C2×C4D4×D10312yes—
152C8—42no—
153C8—4122no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D10311yescharacteristic
162C22C2×C8×D10311yescharacteristic
163C22M16×D10311yescharacteristic
164C4—22no—
165C4—41no—
166C4—1032no—
167C4—1032no—
168C4—4121no—
169C4—2062no—
170C4—2062no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2C22⋊C8×D10311yescharacteristic
175C2#2026776311yescharacteristic
176C2#2026777211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC22×C103C22×C8
FrattiniC22×C4C22×D103
Fitting#323×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC24×C103C2×C4
cosocleC22×C4×C103C23
hypercenter#323D103
hypocenterC103#1458
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20267841C2semidirect
3. #20267516C2semidirect
22. C22×Dic103C8semidirect
89. C103#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#156929772
#202678412
#202675162
#202675152
#323×C1032
#1458103