Finite Group Databasebeta

← #27205686

Subgroups — #27205686

Order 13184.

380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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#20268348C211yesmaximal, characteristic
2#20268197C214yesmaximal, complemented
3#20268194C212yesmaximal, complemented
4#20268187C212yesmaximal, complemented
5#20267831C214yesmaximal
6C4×#13110089C211yesmaximal, characteristic
7C2×C4⋊Q8×C103C211yesmaximal, characteristic
8C2×#13110089C2212yes—
9#15693021C2211yescharacteristic
10#15693021C2211yescharacteristic
11#15693013C2212yes—
12#15693000—21no—
13#15693000—21no—
14C4×Dic206—21no—
15C4×Dic206—21no—
16#15692980C2212yes—
17#15692954C2218yes—
18#15692952C2218yes—
19#15692932C2212yes—
20C4×C103⋊C8C2212yes—
21C22×Q8×C103—21no—
22C4⋊Q8×C103—21no—
23C4⋊Q8×C103—21no—
24C4⋊Q8×C103C2212yes—
25C4⋊Q8×C103C2212yes—
26C2×C4⋊C4×C103—21no—
27C2×C4⋊C4×C103C2212yes—
28C2×C42×C103C2211yescharacteristic
29C2×Dic206—21no—
30C2×Dic206—21no—
31#13110089Q818yescomplemented
32C2×C103⋊C8C2314yes—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103C2312yes—
36C4⋊Dic103C2312yes—
37Dic103⋊C4—22no—
38Dic103⋊C4—22no—
39C22⋊Dic103—22no—
40C4×Dic103—22no—
41C2×Q8×C103—22no—
42C2×Q8×C103—22no—
43C2×Q8×C103—44no—
44C22×C4×C103—22no—
45C22×C4×C103D411yescharacteristic
46C22×C4×C103D411yescharacteristic
47C22×C4×C103C2311yescharacteristic
48C4⋊C4×C103—22no—
49C4⋊C4×C103—22no—
50C4⋊C4×C103—22no—
51C4⋊C4×C103C2314yes—
52C42×C103D411yescharacteristic
53C42×C103D411yescharacteristic
54C42×C103C2311yescharacteristic
55C42×C103C2311yescharacteristic
56C23×C103C2×D411yescharacteristic
57Q8×C103—44no—
58Q8×C103—44no—
59C2×C4×C103—22no—
60C2×C4×C103—22no—
61C2×C4×C103—24no—
62C2×C4×C103—44no—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×C4×C103C2×D411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×Q814yes—
69C2×C4×C103C2411yescharacteristic
70C2×Dic103—22no—
71C2×Dic103—22no—
72Dic206—42no—
73Dic206—42no—
74C103⋊C8C2×Q818yescomplemented
75C22×C103—21no—
76C22×C103—21no—
77C22×C103C4⋊Q812yes—
78C22×C103C22×D411yescharacteristic
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—44no—
82C4×C103C4⋊Q812yes—
83C4×C103AGL(1,ℤ/8)12yes—
84C4×C103#13712yes—
85C4×C103C22×Q812yes—
86Dic103—42no—
87Dic103—42no—
88C2×C103—22no—
89C2×C103C2×C4⋊Q811yescharacteristic
90C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
91C2×C103C2×#13711yescharacteristic
92#3165—1031nomaximal, Sylow
93C103#316511yescharacteristic, complemented, Sylow
94#533—1031no—
95C2×C4⋊Q8D10311yescharacteristic
96#501—1034no—
97#500—1032no—
98#498—1032no—
99#428—1034no—
100C4×M16—1031no—
101C22×Q8—21no—
102C2×M16—1032no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—1031no—
106C4⋊Q8—1031no—
107C4⋊Q8C2×D10312yes—
108C4⋊Q8C2×D10312yes—
109#125—1032no—
110C22⋊Q8—2061no—
111C22⋊Q8—2061no—
112C4×Q8—2061no—
113C4×Q8—2061no—
114#117—1032no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4C2×D10312yes—
117C2×C42C2×D10311yescharacteristic
118#107—1038no—
119#106—1038no—
120#97—1032no—
121C4×C8—1032no—
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—44no—
125C2×Q8—2061no—
126C2×Q8—2061no—
127C22×C4—22no—
128C22×C4C22⋊D10311yescharacteristic
129C22×C4C22⋊D10311yescharacteristic
130C22×C4C22×D10311yescharacteristic
131M16—1038no—
132C2×C8—1034no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—1032no—
137C4⋊C4—1032no—
138C4⋊C4—2062no—
139C4⋊C4—2062no—
140C4⋊C4—2061no—
141C4⋊C4—2061no—
142C4⋊C4C22×D10314yes—
143C22⋊C4—2062no—
144C42—2062no—
145C42C22⋊D10311yescharacteristic
146C42C22⋊D10311yescharacteristic
147C42C22×D10311yescharacteristic
148C42C22×D10311yescharacteristic
149C23C2×C22⋊D10311yescharacteristic
150Q8—44no—
151Q8—44no—
152Q8—4122no—
153Q8—4122no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—2062no—
159C2×C4—2062no—
160C2×C4C2×C22⋊D10311yescharacteristic
161C2×C4C2×C22⋊D10311yescharacteristic
162C2×C4C2×C22⋊D10311yescharacteristic
163C2×C4C2×C22⋊D10311yescharacteristic
164C2×C4C2×C22⋊D10311yescharacteristic
165C2×C4Q8×D10314yes—
166C2×C4C23×D10311yescharacteristic
167C8—1038no—
168C22—21no—
169C22—21no—
170C22#1569301912yes—
171C22C22×C22⋊D10311yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—4122no—
176C4—4122no—
177C4#1569301912yes—
178C4#1569304712yes—
179C4#1569305212yes—
180C4C2×Q8×D10312yes—
181C2—22no—
182C2C2×#1569301911yescharacteristic
183C2C2×#1569304711yescharacteristic
184C2C2×#1569305211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C4⋊Q8×C103C2
socleC22×C103C22×D4
prime radicalC23×C103C2×D4
hypercenterC2×C4⋊Q8D103
hypocenterC103#3165
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20268197C2semidirect
3. #20268194C2semidirect
4. #20268187C2semidirect
31. #13110089Q8semidirect
74. C103⋊C8C2×Q8semidirect
93. C103#3165semidirect

Maximal subgroups

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

subgroupindex
#202683482
#202681972
#202681942
#202681872
#202678312
C4×#131100892
C2×C4⋊Q8×C1032
#3165103