Finite Group Databasebeta

← #27203775

Subgroups — #27203775

Order 13184.

484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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×C42×D103C211yesmaximal, characteristic
2#20267846C214yesmaximal, complemented
3#20267842C214yesmaximal, complemented
4#20267814C212yesmaximal, complemented
5#20267754C212yesmaximal
6C4×#13110089C211yesmaximal, characteristic, complemented
7C4×M16×C103C211yesmaximal, characteristic, complemented
8C22×C4×D103C412yes—
9C22×C4×D103C2211yescharacteristic
10C2×#13110089C2212yes—
11C2×C4×Dic103C412yes—
12C2×C4×Dic103C2211yescharacteristic
13C42×D103C412yes—
14C42×D103C412yes—
15C42×D103C2212yes—
16C42×D103C2212yes—
17Dic103⋊C8C2218yescomplemented
18(C2×D103)⋊C8C2218yes—
19#15692932C2212yescomplemented
20C4×C103⋊C8C2212yescomplemented
21C2×M16×C103C2212yes—
22C2×C42×C103C2211yescharacteristic
23#97×C103C2212yescomplemented
24C4×C8×C103C2212yescomplemented
25C23×D103C2×C411yescharacteristic
26C22×Dic103C2×C411yescharacteristic
27C22×Dic103C2×C412yes—
28C2×C4×D103—24no—
29C2×C4×D103—28no—
30C2×C4×D103C2×C412yes—
31C2×C4×D103C2×C412yes—
32C2×C4×D103C2×C412yes—
33C2×C4×D103C2×C412yes—
34C2×C4×D103C2×C412yes—
35C2×C4×D103C2312yes—
36#13110089—24no—
37C2×C103⋊C8C2314yes—
38C4×Dic103C2×C411yescharacteristic
39C4×Dic103C2×C411yescharacteristic
40C4×Dic103C2×C412yes—
41C4×Dic103C2×C412yes—
42C4×Dic103C2×C412yes—
43C4×Dic103C2×C412yes—
44C4×Dic103C2312yes—
45C22×C4×C103C2×C412yes—
46C22×C4×C103C2311yescharacteristic
47M16×C103—24no—
48C2×C8×C103C2314yes—
49C42×C103C2×C412yes—
50C42×C103C2311yescharacteristic
51C42×C103C2311yescharacteristic
52C23×C103C22×C411yescharacteristic
53C22×D103—22no—
54C22×D103—24no—
55C22×D103C22×C412yes—
56C2×C4×C103—24no—
57C2×C4×C103C22×C412yes—
58C2×C4×C103C22×C411yescharacteristic
59C2×C4×C103C22×C412yes—
60C2×C4×C103#4114yes—
61C2×C4×C103C2411yescharacteristic
62C2×Dic103—22no—
63C2×Dic103—24no—
64C2×Dic103C22×C412yes—
65C2×Dic103C22×C412yes—
66C2×Dic103C22×C412yes—
67C4×D103—24no—
68C4×D103—24no—
69C4×D103—24no—
70C4×D103—24no—
71C4×D103—24no—
72C4×D103M1618yescomplemented
73C8×C103—24no—
74C103⋊C8—24no—
75C22×C103—22no—
76C22×C103#11712yes—
77C22×C103C23×C411yescharacteristic
78C2×D103—28no—
79C2×D103—22no—
80C2×D103—22no—
81C2×D103C2×M1614yes—
82C4×C103—22no—
83C4×C103#11712yes—
84C4×C103C2×M1614yes—
85C4×C103C2×#4112yes—
86Dic103—22no—
87Dic103—22no—
88Dic103C2×M1614yes—
89C2×C103—22no—
90C2×C103C2×#11711yescharacteristic
91C2×C103C22×M1612yes—
92D103—24no—
93#2920—1031nomaximal, Sylow
94C103#292011yescharacteristic, complemented, Sylow
95C22×C42—1031no—
96#432—1034no—
97#431—1034no—
98#423—1032no—
99#407—1032no—
100C4×M16—1031no—
101C4×M16D10311yescharacteristic, complemented
102C23×C4—1032no—
103C23×C4—1031no—
104C2×M16—1032no—
105C2×M16C2×D10312yes—
106C2×C42—1032no—
107C2×C42—1031no—
108C2×C42—1032no—
109C2×C42—1032no—
110C2×C42—1032no—
111C2×C42—1032no—
112C2×C42C2×D10311yescharacteristic
113C4⋊C8—1038no—
114C22⋊C8—1038no—
115#97—1032no—
116#97C2×D10312yescomplemented
117C4×C8—1032no—
118C4×C8C2×D10312yescomplemented
119C24—1031no—
120C22×C4—1032no—
121C22×C4—1032no—
122C22×C4—1031no—
123C22×C4—1032no—
124C22×C4—1032no—
125C22×C4—1032no—
126C22×C4—1032no—
127C22×C4—1032no—
128C22×C4—2068no—
129C22×C4—2064no—
130C22×C4C4×D10312yes—
131C22×C4C22×D10311yescharacteristic
132M16—24no—
133M16—2064no—
134C2×C8—1034no—
135C2×C8C22×D10314yes—
136C42—1031no—
137C42—1032no—
138C42—1032no—
139C42—1032no—
140C42—1031no—
141C42—1032no—
142C42—1032no—
143C42C4×D10312yes—
144C42C22×D10311yescharacteristic
145C42C22×D10311yescharacteristic
146C23—1032no—
147C23—2064no—
148C23—2062no—
149C23C2×C4×D10311yescharacteristic
150C2×C4—24no—
151C2×C4—1032no—
152C2×C4—1038no—
153C2×C4—1032no—
154C2×C4—1032no—
155C2×C4—2064no—
156C2×C4—2064no—
157C2×C4—2064no—
158C2×C4—2062no—
159C2×C4—2064no—
160C2×C4—2064no—
161C2×C4—2064no—
162C2×C4C2×C4×D10312yes—
163C2×C4C2×C4×D10311yescharacteristic
164C2×C4C2×C4×D10312yes—
165C2×C4#1311010514yes—
166C2×C4C23×D10311yescharacteristic
167C8—24no—
168C8—2064no—
169C22—22no—
170C22—1034no—
171C22—2068no—
172C22—2062no—
173C22—2062no—
174C22#1569297812yes—
175C22C22×C4×D10311yescharacteristic
176C4—22no—
177C4—1034no—
178C4—2062no—
179C4—2062no—
180C4#1569297812yes—
181C4M16×D10314yes—
182C4C2×#1311010512yes—
183C2—22no—
184C2—2064no—
185C2C2×#1569297811yescharacteristic
186C2C2×M16×D10312yes—
subgroupG/H
centerC42C22×D103
commutator, socleC22×C103C23×C4
FrattiniC2×C4C23×D103
FittingC4×M16×C103C2
prime radicalC23×D103C2×C4
cosocleC2×C4×C103C24
hypercenterC4×M16D103
hypocenterC103#2920
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #20267846C2semidirect
3. #20267842C2semidirect
4. #20267814C2semidirect
6. C4×#13110089C2semidirect
7. C4×M16×C103C2semidirect
17. Dic103⋊C8C22semidirect
19. #15692932C22semidirect
20. C4×C103⋊C8C22semidirect
23. #97×C103C22semidirect
24. C4×C8×C103C22semidirect
72. C4×D103M16semidirect
94. C103#2920semidirect
101. C4×M16D103semidirect
116. #97C2×D103semidirect
118. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1032
#202678462
#202678422
#202678142
#202677542
C4×#131100892
C4×M16×C1032
#2920103