Finite Group Databasebeta

← C2×#20267831 #27203727

Subgroups — C2×#20267831 #27203727

Order 13184.

536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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
1C22×#13110089C211yesmaximal, characteristic
2C2×#15692980C211yesmaximal, characteristic
3#20267831C218yesmaximal, direct product factor
4C2×#15692954C212yesmaximal, complemented
5C2×#15692952C212yesmaximal, complemented
6C22×C4⋊C4×C103C211yesmaximal, characteristic
7C2×#13110089C418yescomplemented
8C2×#13110089C2214yes—
9C22×C103⋊C8C2212yes—
10#15692980—22no—
11#15692980C2214yes—
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×C22⋊Dic103—21no—
15C2×C4×Dic103—21no—
16#15692954C2218yescomplemented
17#15692952C2218yescomplemented
18C23×C4×C103—21no—
19C23×C4×C103C2211yescharacteristic
20C2×C4⋊C4×C103—21no—
21C2×C4⋊C4×C103—22no—
22C2×C4⋊C4×C103C2212yes—
23C2×C4⋊C4×C103C2214yes—
24C22×Dic103—21no—
25C22×Dic103—21no—
26#13110089C2×C4116yescomplemented
27C2×C103⋊C8C2×C418yescomplemented
28C2×C103⋊C8C2314yes—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103C2312yes—
32C4⋊Dic103C2312yes—
33C22⋊Dic103—24no—
34C4×Dic103—24no—
35C24×C103D411yescharacteristic
36C22×C4×C103—24no—
37C22×C4×C103—22no—
38C22×C4×C103—44no—
39C22×C4×C103C2×C414yes—
40C22×C4×C103D411yescharacteristic
41C22×C4×C103D412yes—
42C22×C4×C103Q814yes—
43C22×C4×C103C2311yescharacteristic
44C22×C4×C103C2312yes—
45C4⋊C4×C103—24no—
46C4⋊C4×C103—22no—
47C4⋊C4×C103C2314yes—
48C23×C103—22no—
49C23×C103—22no—
50C23×C103C4⋊C414yes—
51C23×C103C2×D412yes—
52C23×C103C2×D411yescharacteristic
53C2×C4×C103—24no—
54C2×C4×C103—48no—
55C2×C4×C103—44no—
56C2×C4×C103C4⋊C418yes—
57C2×C4×C103C4⋊C414yes—
58C2×C4×C103C22×C412yes—
59C2×C4×C103C22×C414yes—
60C2×C4×C103C2×D412yes—
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×Q814yes—
63C2×C4×C103C2×Q812yes—
64C2×C4×C103C2411yescharacteristic
65C2×Dic103—22no—
66C2×Dic103—22no—
67C2×Dic103—42no—
68C2×Dic103—42no—
69C103⋊C8C22×C418yescomplemented
70C22×C103—22no—
71C22×C103—22no—
72C22×C103—28no—
73C22×C103C2×C4⋊C414yes—
74C22×C103C2×C4⋊C412yes—
75C22×C103AGL(1,ℤ/8)12yes—
76C22×C103#13712yes—
77C22×C103C22×D411yescharacteristic
78C4×C103—44no—
79C4×C103C2×C4⋊C412yes—
80C4×C103C2×C4⋊C414yes—
81C4×C103C23×C411yescharacteristic
82C4×C103C22×Q811yescharacteristic
83Dic103—42no—
84Dic103—42no—
85C2×C103—24no—
86C2×C103#42814yescomplemented
87C2×C103C22×C4⋊C411yescharacteristic
88C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
89C2×C103C2×#13711yescharacteristic
90C2×#428—1031nomaximal, Sylow
91C103C2×#42811yescharacteristic, complemented, Sylow
92C22×M16—1031no—
93C2×#117—1031no—
94C22×C4⋊C4D10311yescharacteristic
95#428—1038no—
96C2×#107—1032no—
97C2×#106—1032no—
98C23×C4—21no—
99C23×C4C2×D10311yescharacteristic
100C2×M16—1038no—
101C2×M16—1034no—
102C22×C8—1032no—
103#117—1034no—
104#117—2062no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—1031no—
108C2×C4⋊C4—1031no—
109C2×C4⋊C4C2×D10312yes—
110C2×C4⋊C4C2×D10314yes—
111C2×C22⋊C4—2061no—
112C2×C42—2061no—
113#107—1038no—
114#106—1038no—
115C24C22⋊D10311yescharacteristic
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—2061no—
120C22×C4—2061no—
121C22×C4Dic20614yes—
122C22×C4C4×D10314yes—
123C22×C4C22⋊D10312yes—
124C22×C4C22⋊D10311yescharacteristic
125C22×C4C22×D10312yes—
126C22×C4C22×D10311yescharacteristic
127M16—10316no—
128C2×C8—1038no—
129C2×C8—1034no—
130C4⋊C4—24no—
131C4⋊C4—22no—
132C4⋊C4—1032no—
133C4⋊C4—1032no—
134C4⋊C4—2061no—
135C4⋊C4—2061no—
136C4⋊C4C22×D10314yes—
137C22⋊C4—2064no—
138C42—2064no—
139C23—22no—
140C23—22no—
141C23Dic103⋊C414yes—
142C23C2×C22⋊D10312yes—
143C23C2×C22⋊D10311yescharacteristic
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—4122no—
148C2×C4—4122no—
149C2×C4—2062no—
150C2×C4—2062no—
151C2×C4Dic103⋊C418yes—
152C2×C4Dic103⋊C414yes—
153C2×C4C2×C4×D10312yes—
154C2×C4C2×C4×D10314yes—
155C2×C4C2×C22⋊D10312yes—
156C2×C4C2×C22⋊D10311yescharacteristic
157C2×C4C2×Dic20614yes—
158C2×C4C2×Dic20612yes—
159C2×C4C23×D10311yescharacteristic
160C8—1038no—
161C22—22no—
162C22—22no—
163C22—28no—
164C22C2×Dic103⋊C414yes—
165C22C2×Dic103⋊C412yes—
166C22#1569304712yes—
167C22#1569305212yes—
168C22C22×C22⋊D10311yescharacteristic
169C4—44no—
170C4—4122no—
171C4—4122no—
172C4C2×Dic103⋊C412yes—
173C4C2×Dic103⋊C414yes—
174C4C22×C4×D10311yescharacteristic
175C4C22×Dic20611yescharacteristic
176C2—24no—
177C2#2026783114yesdirect product factor
178C2C22×Dic103⋊C411yescharacteristic
179C2C2×#1569304711yescharacteristic
180C2C2×#1569305211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
FittingC22×C4⋊C4×C103C2
socleC23×C103C2×D4
prime radicalC24×C103D4
cosocleC2×C4×C103C24
hypercenterC22×C4⋊C4D103
hypocenterC103C2×#428
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20267831C2direct (N × H)
4. C2×#15692954C2semidirect
5. C2×#15692952C2semidirect
7. C2×#13110089C4semidirect
16. #15692954C22semidirect
17. #15692952C22semidirect
26. #13110089C2×C4semidirect
27. C2×C103⋊C8C2×C4semidirect
69. C103⋊C8C22×C4semidirect
86. C2×C103#428semidirect
91. C103C2×#428semidirect
177. C2#20267831direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100892
C2×#156929802
#202678312
C2×#156929542
C2×#156929522
C22×C4⋊C4×C1032
C2×#428103