Finite Group Databasebeta

← #27193677

Subgroups — #27193677

Order 13184.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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#20267755C211yesmaximal, characteristic
2#20267654C211yesmaximal, characteristic
3#20267528C214yesmaximal, complemented
4C2×C22⋊Q8×C103C211yesmaximal, characteristic
5C2×#13110089—21no—
6C2×C22⋊Dic103—21no—
7C22⋊(C103⋊C8)—21no—
8C22⋊(C103⋊C8)C2212yes—
9C103⋊#95—21no—
10C103⋊#95C2212yes—
11C22×Q8×C103C411yescharacteristic, complemented
12C23×C4×C103C2211yescharacteristic
13C22⋊Q8×C103—21no—
14C22⋊Q8×C103—21no—
15C22⋊Q8×C103C412yescomplemented
16C22⋊Q8×C103C2212yes—
17C2×C4⋊C4×C103—21no—
18C2×C4⋊C4×C103C411yescharacteristic, complemented
19C2×C22⋊C4×C103—21no—
20C22×Dic103—22no—
21#13110089—42no—
22C2×C103⋊C8—22no—
23C22⋊Dic103—42no—
24C24×C103D411yescharacteristic
25C2×Q8×C103—21no—
26C2×Q8×C103—42no—
27C2×Q8×C103C2×C412yes—
28C22×C4×C103—21no—
29C22×C4×C103—21no—
30C22×C4×C103—42no—
31C22×C4×C103C2×C411yescharacteristic
32C22×C4×C103C2×C411yescharacteristic
33C22×C4×C103D411yescharacteristic
34C22×C4×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C4⋊C4×C103—22no—
38C4⋊C4×C103—21no—
39C4⋊C4×C103—22no—
40C4⋊C4×C103C2×C412yes—
41C22⋊C4×C103—22no—
42C22⋊C4×C103—22no—
43C23×C103—22no—
44C23×C103—22no—
45C23×C103—41no—
46C23×C103C22⋊C411yescharacteristic
47C23×C103C22⋊C411yescharacteristic
48C23×C103C2×D411yescharacteristic
49Q8×C103—42no—
50Q8×C103—42no—
51C2×C4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—22no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103—42no—
60C2×C4×C103—42no—
61C2×C4×C103C22⋊C411yescharacteristic
62C2×C4×C103C22⋊C411yescharacteristic
63C2×C4×C103C22×C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×Dic103—42no—
66C2×Dic103—42no—
67C2×Dic103—42no—
68C103⋊C8—42no—
69C22×C103—21no—
70C22×C103—21no—
71C22×C103—21no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103—44no—
77C22×C103#9912yes—
78C22×C103C2×C22⋊C411yescharacteristic
79C22×C103#13712yes—
80C4×C103—21no—
81C4×C103—21no—
82C4×C103—21no—
83C4×C103—21no—
84C4×C103—42no—
85C4×C103—42no—
86Dic103—82no—
87C2×C103—22no—
88C2×C103—22no—
89C2×C103—41no—
90C2×C103C2×#9911yescharacteristic
91C2×C103#41911yescharacteristic
92C2×C103#42111yescharacteristic
93#1511—1031nomaximal, Sylow
94C103#151111yescharacteristic, complemented, Sylow
95C2×C22⋊Q8D10311yescharacteristic
96#407—1031no—
97#381—1031no—
98#328—1034no—
99C22×Q8Dic10311yescharacteristic, complemented
100C23×C4C2×D10311yescharacteristic
101C2×M16—2061no—
102C22⋊Q8—21no—
103C22⋊Q8—21no—
104C22⋊Q8Dic10312yescomplemented
105C22⋊Q8C2×D10312yes—
106C2×C4⋊C4—21no—
107C2×C4⋊C4Dic10311yescharacteristic, complemented
108C2×C22⋊C4—21no—
109C2×C22⋊C4—2061no—
110C22⋊C8—1032no—
111C22⋊C8—2061no—
112#95—1032no—
113#95—2061no—
114C24C22⋊D10311yescharacteristic
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×Dic10312yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—42no—
121C22×C4—2062no—
122C22×C4C2×Dic10311yescharacteristic
123C22×C4C2×Dic10311yescharacteristic
124C22×C4C22⋊D10311yescharacteristic
125C22×C4C22⋊D10311yescharacteristic
126C22×C4C22⋊D10311yescharacteristic
127C22×C4C22×D10311yescharacteristic
128M16—4122no—
129C2×C8—2062no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4C2×Dic10312yes—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—4122no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊Dic10311yescharacteristic
141C23C22⋊Dic10311yescharacteristic
142C23C2×C22⋊D10311yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—4122no—
156C2×C4—4122no—
157C2×C4—4122no—
158C2×C4C22⋊Dic10311yescharacteristic
159C2×C4C22⋊Dic10311yescharacteristic
160C2×C4C22×Dic10311yescharacteristic
161C2×C4C2×C22⋊D10311yescharacteristic
162C8—4122no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1569293612yes—
172C22C2×C22⋊Dic10311yescharacteristic
173C22#1569305212yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—8242no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1569293611yescharacteristic
185C2#2026780011yescharacteristic
186C2#2026780811yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C22⋊Q8×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC24×C103D4
cosocleC22×C4×C103C23
hypercenterC2×C22⋊Q8D103
hypocenterC103#1511
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20267528C2semidirect
11. C22×Q8×C103C4semidirect
15. C22⋊Q8×C103C4semidirect
18. C2×C4⋊C4×C103C4semidirect
94. C103#1511semidirect
99. C22×Q8Dic103semidirect
104. C22⋊Q8Dic103semidirect
107. C2×C4⋊C4Dic103semidirect

Maximal subgroups

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

subgroupindex
#202677552
#202676542
#202675282
C2×C22⋊Q8×C1032
#1511103