Finite Group Databasebeta

← C2×#20268041 #27204737

Subgroups — C2×#20268041 #27204737

Order 13184.

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

normal subgroups only

This group has 596 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
1C22×#13110088C211yesmaximal, characteristic, complemented
2C2×#15692992C212yesmaximal, complemented
3#20268041C218yesmaximal, direct product factor
4C2×#15692953C211yesmaximal, characteristic, complemented
5C2×#15692942C212yesmaximal, complemented
6C22×D8×C103C211yesmaximal, characteristic, complemented
7C22×C22⋊D103—22no—
8C22×C4×D103C2211yescharacteristic
9C2×#13110088—24no—
10C2×#13110088C2214yescomplemented
11C22×C103⋊C8C2211yescharacteristic
12#15692992—24no—
13#15692992C2218yescomplemented
14C2×C4⋊Dic103C2212yes—
15C2×C22⋊Dic103—22no—
16#15692953C2214yescomplemented
17#15692942C2218yescomplemented
18C22×D4×C103C2212yes—
19C2×D8×C103—24no—
20C2×D8×C103C2214yescomplemented
21C22×C8×C103C2211yescharacteristic
22C23×D103D411yescharacteristic
23C2×C22⋊D103—28no—
24C2×C22⋊D103—48no—
25C22×Dic103—22no—
26C22×Dic103D411yescharacteristic
27C2×C4×D103—22no—
28C2×C4×D103—22no—
29C2×C4×D103D412yes—
30C2×C4×D103C2312yes—
31#13110088—28no—
32C2×C103⋊C8—22no—
33C2×C103⋊C8C2312yes—
34C4⋊Dic103—22no—
35C4⋊Dic103C2314yes—
36C22⋊Dic103—28no—
37C24×C103—22no—
38C2×D4×C103—24no—
39C2×D4×C103—22no—
40C2×D4×C103—24no—
41C2×D4×C103C2314yes—
42C22×C4×C103C2311yescharacteristic
43D8×C103—28no—
44C2×C8×C103D414yescomplemented
45C2×C8×C103C2312yes—
46C23×C103—24no—
47C23×C103—44no—
48C23×C103—44no—
49C23×C103—44no—
50C23×C103C2×D411yescharacteristic
51C22×D103—22no—
52C22×D103—24no—
53C22×D103C2×D412yes—
54D4×C103—24no—
55D4×C103—24no—
56D4×C103—44no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D412yes—
59C2×C4×C103#4112yes—
60C2×C4×C103C2411yescharacteristic
61C22⋊D103—416no—
62C2×Dic103—22no—
63C2×Dic103—24no—
64C2×Dic103—44no—
65C2×Dic103C2×D412yes—
66C4×D103—24no—
67C4×D103—22no—
68C4×D103—22no—
69C8×C103C2×D414yescomplemented
70C103⋊C8—22no—
71C22×C103—44no—
72C22×C103—44no—
73C22×C103—44no—
74C22×C103—88no—
75C22×C103#12112yes—
76C22×C103AGL(1,ℤ/8)14yes—
77C22×C103C22×D411yescharacteristic
78C2×D103—22no—
79C2×D103—24no—
80C2×D103—44no—
81C4×C103#12112yes—
82C4×C103C22×D411yescharacteristic
83C4×C103C2×#4111yescharacteristic
84Dic103—22no—
85Dic103—44no—
86C2×C103—84no—
87C2×C103#46914yescomplemented
88C2×C103C2×#12111yescharacteristic
89C2×C103C2×AGL(1,ℤ/8)12yes—
90D103—42no—
91C2×#469—1031nomaximal, Sylow
92C103C2×#46911yescharacteristic, complemented, Sylow
93C22×D8D10311yescharacteristic, complemented
94C22×M16—1031no—
95C2×#121—1032no—
96#469—1038no—
97C2×#106—1031no—
98C2×#102—1032no—
99C22×D4—2062no—
100C22×D4C2×D10312yes—
101C23×C4—1031no—
102C2×D8—24no—
103C2×D8C2×D10314yescomplemented
104C2×M16—1034no—
105C2×M16—2064no—
106C22×C8—1031no—
107C22×C8C2×D10311yescharacteristic
108#121—1038no—
109#121—2064no—
110C2×C4⋊C4—1032no—
111C2×C22⋊C4—2062no—
112#106—1034no—
113#102—1038no—
114C24—22no—
115C24—1031no—
116C2×D4—22no—
117C2×D4—24no—
118C2×D4—24no—
119C2×D4—4128no—
120C2×D4—2068no—
121C2×D4C22×D10314yes—
122C22×C4—1031no—
123C22×C4—1032no—
124C22×C4—1032no—
125C22×C4—2062no—
126C22×C4—2062no—
127C22×C4—2062no—
128C22×C4C22×D10311yescharacteristic
129D8—28no—
130M16—2068no—
131C2×C8—1032no—
132C2×C8—2062no—
133C2×C8C22⋊D10314yescomplemented
134C2×C8C22×D10312yes—
135C4⋊C4—1034no—
136C4⋊C4—2062no—
137C22⋊C4—2068no—
138C23—24no—
139C23—44no—
140C23—44no—
141C23—44no—
142C23—1032no—
143C23—2062no—
144C23—2064no—
145C23D4×D10311yescharacteristic
146D4—24no—
147D4—24no—
148D4—44no—
149D4—41216no—
150C2×C4—1032no—
151C2×C4—4124no—
152C2×C4—2064no—
153C2×C4—2062no—
154C2×C4—2062no—
155C2×C4—2062no—
156C2×C4—2064no—
157C2×C4D4×D10311yescharacteristic
158C2×C4C2×C22⋊D10312yes—
159C2×C4#1311010412yes—
160C2×C4C23×D10311yescharacteristic
161C8—2062no—
162C8C2×C22⋊D10314yescomplemented
163C22—44no—
164C22—44no—
165C22—44no—
166C22—88no—
167C22—4124no—
168C22—2064no—
169C22—2062no—
170C22#1569299212yes—
171C22#1569304514yes—
172C22C2×D4×D10311yescharacteristic
173C4—4124no—
174C4—2062no—
175C4#1569299212yes—
176C4C22×C22⋊D10311yescharacteristic
177C4C2×#1311010411yescharacteristic
178C2—84no—
179C2—4122no—
180C2#2026804114yesdirect product factor
181C2C2×#1569299211yescharacteristic
182C2C2×#1569304512yes—
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×D8×C103C2
socleC23×C103C2×D4
hypercenterC22×D8D103
hypocenterC103C2×#469
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#13110088C2semidirect
2. C2×#15692992C2semidirect
3. #20268041C2direct (N × H)
4. C2×#15692953C2semidirect
5. C2×#15692942C2semidirect
6. C22×D8×C103C2semidirect
10. C2×#13110088C22semidirect
13. #15692992C22semidirect
16. #15692953C22semidirect
17. #15692942C22semidirect
20. C2×D8×C103C22semidirect
44. C2×C8×C103D4semidirect
69. C8×C103C2×D4semidirect
87. C2×C103#469semidirect
92. C103C2×#469semidirect
93. C22×D8D103semidirect
103. C2×D8C2×D103semidirect
133. C2×C8C22⋊D103semidirect
162. C8C2×C22⋊D103semidirect
180. C2#20268041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100882
C2×#156929922
#202680412
C2×#156929532
C2×#156929422
C22×D8×C1032
C2×#469103