Finite Group Databasebeta

← #27194875

Subgroups — #27194875

Order 13184.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692977C212yesmaximal
2C2×#15692977C211yesmaximal, characteristic
3#20267558C211yesmaximal, characteristic
4#20267557C212yesmaximal
5#342×C103C211yesmaximal, characteristic
6C23×Dic103C2211yescharacteristic
7#15692977—24no—
8#15692977—22no—
9#15692977—22no—
10#15692977C418yescomplemented
11C2×Dic103⋊C4—22no—
12C2×Dic103⋊C4C412yescomplemented
13C2×C22⋊Dic103C2211yescharacteristic
14C2×C22⋊Dic103C2212yes—
15C2×C4×Dic103—22no—
16C2×C4×Dic103C412yescomplemented
17C2×C22⋊C4×C103C2211yescharacteristic
18C2×C22⋊C4×C103C2212yes—
19C22×Dic103—22no—
20C22×Dic103C2×C412yes—
21C22×Dic103C2×C411yescharacteristic
22C22×Dic103C2×C411yescharacteristic
23C22×Dic103C2×C414yes—
24C22×Dic103D412yes—
25C22×Dic103D412yes—
26C22×Dic103D412yes—
27C22×Dic103Q812yes—
28Dic103⋊C4—28no—
29Dic103⋊C4—24no—
30C22⋊Dic103—22no—
31C22⋊Dic103—22no—
32C22⋊Dic103C2×C414yes—
33C4×Dic103—28no—
34C4×Dic103—22no—
35C4×Dic103—22no—
36C24×C103C2311yescharacteristic
37C22×C4×C103—22no—
38C22×C4×C103C2×C412yes—
39C22⋊C4×C103—22no—
40C22⋊C4×C103—22no—
41C22⋊C4×C103C2×C414yes—
42C23×C103—42no—
43C23×C103C22×C411yescharacteristic
44C23×C103C22×C412yes—
45C23×C103C2×D412yes—
46C23×C103C2×D411yescharacteristic
47C23×C103C2×Q811yescharacteristic
48C2×C4×C103—22no—
49C2×C4×C103—24no—
50C2×C4×C103—44no—
51C2×C4×C103—42no—
52C2×Dic103—22no—
53C2×Dic103—24no—
54C2×Dic103—44no—
55C2×Dic103—42no—
56C2×Dic103C4212yes—
57C2×Dic103C4212yes—
58C2×Dic103C22⋊C414yes—
59C2×Dic103C22⋊C411yescharacteristic
60C2×Dic103C22⋊C411yescharacteristic
61C2×Dic103C22⋊C414yes—
62C2×Dic103C22⋊C412yes—
63C2×Dic103C4⋊C412yes—
64C2×Dic103C4⋊C412yes—
65C2×Dic103C4⋊C414yes—
66C2×Dic103C4⋊C414yes—
67C22×C103—22no—
68C22×C103—24no—
69C22×C103—42no—
70C22×C103—41no—
71C22×C103—41no—
72C22×C103C2×C4211yescharacteristic
73C22×C103C2×C22⋊C412yes—
74C22×C103C2×C22⋊C411yescharacteristic
75C22×C103C2×C4⋊C411yescharacteristic
76C22×C103C2×C4⋊C412yes—
77C4×C103—44no—
78C4×C103—42no—
79Dic103—44no—
80Dic103—42no—
81Dic103#9512yes—
82Dic103#9514yes—
83Dic103#9512yes—
84C2×C103—22no—
85C2×C103—21no—
86C2×C103—21no—
87C2×C103—22no—
88C2×C103C2×#9511yescharacteristic
89C2×C103#41012yes—
90#1740—1031nomaximal, Sylow
91C103#174011yescharacteristic, complemented, Sylow
92C2×#117—1031no—
93C2×#117—1032no—
94#342—1032no—
95#342—1031no—
96#342D10311yescharacteristic
97C23×C4—1031no—
98#117—1038no—
99#117—2062no—
100#117—2062no—
101#117—2064no—
102C2×C4⋊C4—1032no—
103C2×C4⋊C4—2062no—
104C2×C22⋊C4—1032no—
105C2×C22⋊C4—1031no—
106C2×C22⋊C4C2×D10311yescharacteristic
107C2×C22⋊C4C2×D10312yes—
108C2×C42—1032no—
109C2×C42—2062no—
110C24C22×D10311yescharacteristic
111C22×C4—22no—
112C22×C4—1031no—
113C22×C4—1031no—
114C22×C4—1034no—
115C22×C4—1032no—
116C22×C4—1032no—
117C22×C4—1032no—
118C22×C4—1032no—
119C22×C4—1032no—
120C22×C4—2062no—
121C22×C4C4×D10312yes—
122C4⋊C4—2064no—
123C4⋊C4—2068no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—1034no—
127C22⋊C4—2062no—
128C22⋊C4—2062no—
129C22⋊C4C4×D10314yes—
130C42—2062no—
131C42—2062no—
132C42—2068no—
133C23—42no—
134C23C2×C4×D10311yescharacteristic
135C23C2×C4×D10312yes—
136C23D4×D10312yes—
137C23D4×D10311yescharacteristic
138C23Q8×D10311yescharacteristic
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—44no—
142C2×C4—42no—
143C2×C4—1032no—
144C2×C4—1032no—
145C2×C4—1034no—
146C2×C4—1034no—
147C2×C4—1031no—
148C2×C4—1031no—
149C2×C4—1032no—
150C2×C4—1032no—
151C2×C4—1032no—
152C2×C4—1034no—
153C2×C4—1034no—
154C2×C4—4124no—
155C2×C4—4122no—
156C2×C4—2064no—
157C2×C4—2062no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22C42×D10311yescharacteristic
164C22C22⋊C4×D10312yes—
165C22C22⋊C4×D10311yescharacteristic
166C22C4⋊C4×D10311yescharacteristic
167C22C4⋊C4×D10312yes—
168C4—44no—
169C4—42no—
170C4—1032no—
171C4—1034no—
172C4—1032no—
173C4—4124no—
174C4—4122no—
175C2—22no—
176C2—21no—
177C2—21no—
178C2—22no—
179C2#95×D10311yescharacteristic
180C2#2026776312yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC22×C103C2×C42
FrattiniC24C22×D103
Fitting#342×C103C2
socleC22×C103C2×C22⋊C4
prime radical, cosocleC24×C103C23
hypercenter#342D103
hypocenterC103#1740
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
10. #15692977C4semidirect
12. C2×Dic103⋊C4C4semidirect
16. C2×C4×Dic103C4semidirect
91. C103#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#156929772
#202675582
#202675572
#342×C1032
#1740103