Finite Group Databasebeta

← C2×#20268109 #27205043

Subgroups — C2×#20268109 #27205043

Order 13184.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15692995C211yesmaximal, characteristic
2#20268109C218yesmaximal, direct product factor
3C2×#15692952C212yesmaximal, complemented
4C2×#15692941C212yesmaximal, complemented
5C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C103C211yesmaximal, characteristic, complemented
7C22×D412C2211yescharacteristic
8C22×C22⋊D103—21no—
9C22×C103⋊C8C2212yes—
10#15692995—22no—
11#15692995C2214yes—
12C2×C4⋊Dic103C2211yescharacteristic
13C2×(C2×D103)⋊C4—21no—
14#15692952C2218yescomplemented
15#15692941C2218yescomplemented
16C22⋊(C103⋊C8)C2214yescomplemented
17C23×C4×C103—21no—
18C23×C4×C103C2211yescharacteristic
19C2×C4⋊C4×C103—22no—
20C2×C4⋊C4×C103—21no—
21C2×C4⋊C4×C103C2212yes—
22C2×C4⋊C4×C103C2214yescomplemented
23C23×D103—21no—
24C2×D412—24no—
25C2×D412—21no—
26C2×D412C2312yes—
27C2×C22⋊D103—24no—
28C2×C22⋊D103—44no—
29C22×Dic103—21no—
30C2×C103⋊C8—24no—
31C2×C103⋊C8C2314yes—
32C4⋊Dic103—21no—
33C4⋊Dic103C2312yes—
34(C2×D103)⋊C4—24no—
35C24×C103D411yescharacteristic
36C22×C4×C103—24no—
37C22×C4×C103—22no—
38C22×C4×C103—24no—
39C22×C4×C103—44no—
40C22×C4×C103D411yescharacteristic
41C22×C4×C103D412yes—
42C22×C4×C103C2312yes—
43C22×C4×C103C2311yescharacteristic
44C4⋊C4×C103—22no—
45C4⋊C4×C103—24no—
46C4⋊C4×C103C2314yes—
47C23×C103—22no—
48C23×C103—22no—
49C23×C103SD1614yes—
50C23×C103C2×D412yes—
51C23×C103C2×D411yescharacteristic
52C22×D103—22no—
53C22×D103—42no—
54C22×D103—42no—
55C22×D103—42no—
56C2×C4×C103—22no—
57C2×C4×C103—24no—
58C2×C4×C103—24no—
59C2×C4×C103—24no—
60C2×C4×C103—48no—
61C2×C4×C103—44no—
62C2×C4×C103C2×D412yes—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103#4114yes—
65C2×C4×C103C2411yescharacteristic
66C22⋊D103—48no—
67C2×Dic103—22no—
68C2×Dic103—42no—
69D412—24no—
70D412—42no—
71C103⋊C8—24no—
72C22×C103—22no—
73C22×C103—22no—
74C22×C103—28no—
75C22×C103#12312yes—
76C22×C103C2×SD1614yes—
77C22×C103C2×SD1612yes—
78C22×C103AGL(1,ℤ/8)12yes—
79C22×C103C22×D411yescharacteristic
80C2×D103—42no—
81C2×D103—42no—
82C2×D103—42no—
83C2×D103—84no—
84C4×C103—22no—
85C4×C103—44no—
86C4×C103#12312yes—
87C4×C103C2×#4112yes—
88Dic103—42no—
89C2×C103—24no—
90C2×C103#48114yescomplemented
91C2×C103C2×#12311yescharacteristic
92C2×C103C22×SD1611yescharacteristic
93C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
94D103—82no—
95C2×#481—1031nomaximal, Sylow
96C103C2×#48111yescharacteristic, complemented, Sylow
97C2×#121—1031no—
98C22×C4⋊C4D10311yescharacteristic, complemented
99#481—1038no—
100C2×#106—1032no—
101C2×#102—1032no—
102C2×C22⋊C8—1031no—
103C22×D4—1031no—
104C22×D4—2061no—
105C23×C4—21no—
106C23×C4C2×D10311yescharacteristic
107C22×C8—1032no—
108#121—1034no—
109#121—2062no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—1031no—
113C2×C4⋊C4C2×D10312yes—
114C2×C4⋊C4C2×D10314yescomplemented
115C2×C22⋊C4—2061no—
116#106—1038no—
117#102—1038no—
118C22⋊C8—1034no—
119C24—2061no—
120C24C22⋊D10311yescharacteristic
121C2×D4—1032no—
122C2×D4—4124no—
123C2×D4—2064no—
124C2×D4—2061no—
125C2×D4—2064no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—2061no—
131C22×C4C22⋊D10312yes—
132C22×C4C22⋊D10311yescharacteristic
133C22×C4C22×D10312yes—
134C22×C4C22×D10311yescharacteristic
135C2×C8—1034no—
136C2×C8—2064no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—1032no—
140C4⋊C4—2061no—
141C4⋊C4C22×D10314yes—
142C22⋊C4—2064no—
143C23—22no—
144C23—22no—
145C23—4122no—
146C23—4122no—
147C23—4122no—
148C23—2062no—
149C23#1311009214yes—
150C23C2×C22⋊D10312yes—
151C23C2×C22⋊D10311yescharacteristic
152D4—4128no—
153D4—4122no—
154D4—2064no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—4122no—
162C2×C4—2062no—
163C2×C4C2×C22⋊D10312yes—
164C2×C4C2×C22⋊D10311yescharacteristic
165C2×C4#1311010514yes—
166C2×C4C23×D10311yescharacteristic
167C8—2064no—
168C22—22no—
169C22—22no—
170C22—28no—
171C22—8244no—
172C22—4122no—
173C22—4122no—
174C22—4122no—
175C22#1569300412yes—
176C22C2×#1311009214yes—
177C22C2×#1311009212yes—
178C22#1569304712yes—
179C22C22×C22⋊D10311yescharacteristic
180C4—22no—
181C4—44no—
182C4—4122no—
183C4#1569300412yes—
184C4C2×#1311010512yes—
185C2—24no—
186C2—8242no—
187C2#2026810914yesdirect product factor
188C2C2×#1569300411yescharacteristic
189C2C22×#1311009211yescharacteristic
190C2C2×#1569304711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×C4⋊C4×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692995C2
hypercenterC22×C4⋊C4D103
hypocenterC103C2×#481
LCSG ▷ C2×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
2. #20268109C2direct (N × H)
3. C2×#15692952C2semidirect
4. C2×#15692941C2semidirect
5. C2×C22⋊(C103⋊C8)C2semidirect
6. C22×C4⋊C4×C103C2semidirect
14. #15692952C22semidirect
15. #15692941C22semidirect
16. C22⋊(C103⋊C8)C22semidirect
22. C2×C4⋊C4×C103C22semidirect
90. C2×C103#481semidirect
96. C103C2×#481semidirect
98. C22×C4⋊C4D103semidirect
114. C2×C4⋊C4C2×D103semidirect
187. C2#20268109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156929952
#202681092
C2×#156929522
C2×#156929412
C2×C22⋊(C103⋊C8)2
C22×C4⋊C4×C1032
C2×#481103