Finite Group Databasebeta

← C2×#20268140 #27205453

Subgroups — C2×#20268140 #27205453

Order 13184.

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

normal subgroups only

This group has 424 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
1C2×#15693020C211yesmaximal, characteristic
2C2×#15693019C211yesmaximal, characteristic
3#20268140C218yesmaximal, direct product factor
4C2×#15692946C211yesmaximal, characteristic
5C2×#15692945C211yesmaximal, characteristic
6C2×#15692944C211yesmaximal, characteristic
7C2×C8×Dic103C211yesmaximal, characteristic
8C2×#103×C103C211yesmaximal, characteristic
9C22×Dic206—21no—
10C22×Dic206C2211yescharacteristic
11C22×C103⋊C8C2211yescharacteristic
12#15693020—22no—
13#15693020C2214yes—
14#15693019—22no—
15#15693019C2214yes—
16C2×C4⋊Dic103C2211yescharacteristic
17C2×Dic103⋊C4—21no—
18C2×Dic103⋊C4—21no—
19C2×Dic103⋊C4—21no—
20C2×C4×Dic103C2211yescharacteristic
21#15692946C2214yes—
22#15692945C2214yes—
23#15692944C2214yes—
24C8×Dic103C2214yes—
25C22×Q8×C103C2211yescharacteristic
26C22×C8×C103C2211yescharacteristic
27C2×C4⋊C4×C103C2211yescharacteristic
28#103×C103C2214yes—
29C2×Dic206—22no—
30C2×Dic206—22no—
31C2×Dic206—21no—
32C2×Dic206—24no—
33C2×Dic206—44no—
34C2×Dic206C2312yes—
35C22×Dic103—21no—
36C22×Dic103—21no—
37C22×Dic103D411yescharacteristic
38C22×Dic103D411yescharacteristic
39C2×C103⋊C8—22no—
40C2×C103⋊C8C2312yes—
41C4⋊Dic103—21no—
42C4⋊Dic103C2312yes—
43Dic103⋊C4—24no—
44Dic103⋊C4—24no—
45Dic103⋊C4—24no—
46C4×Dic103D412yes—
47C4×Dic103C2312yes—
48C2×Q8×C103—21no—
49C2×Q8×C103—22no—
50C2×Q8×C103—22no—
51C2×Q8×C103C2312yes—
52C22×C4×C103—21no—
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55C2×C8×C103—22no—
56C2×C8×C103C2312yes—
57C4⋊C4×C103—21no—
58C4⋊C4×C103C2312yes—
59C23×C103C2×D411yescharacteristic
60Q8×C103—22no—
61Q8×C103—22no—
62Q8×C103—42no—
63C2×C4×C103—22no—
64C2×C4×C103—22no—
65C2×C4×C103—42no—
66C2×C4×C103—42no—
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103#4112yes—
69C2×C4×C103#4112yes—
70C2×C4×C103C2411yescharacteristic
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—42no—
74C2×Dic103—42no—
75C2×Dic103SD1614yes—
76C2×Dic103Q1614yes—
77C2×Dic103C2×D412yes—
78C2×Dic103C2×D412yes—
79Dic206—22no—
80Dic206—22no—
81Dic206—42no—
82Dic206—48no—
83C8×C103—22no—
84C103⋊C8—22no—
85C22×C103#12412yes—
86C22×C103C2×SD1612yes—
87C22×C103C2×Q1612yes—
88C22×C103C22×D411yescharacteristic
89C4×C103—42no—
90C4×C103—42no—
91C4×C103#12412yes—
92C4×C103C2×#4111yescharacteristic
93C4×C103C2×#4111yescharacteristic
94Dic103—42no—
95Dic103—42no—
96Dic103C2×SD1614yes—
97Dic103C2×Q1614yes—
98C2×C103#48714yescomplemented
99C2×C103C2×#12411yescharacteristic
100C2×C103C22×SD1611yescharacteristic
101C2×C103C22×Q1611yescharacteristic
102C2×#487—1031nomaximal, Sylow
103C103C2×#48711yescharacteristic, complemented, Sylow
104C2×C4⋊Q8—1031no—
105C2×C4⋊Q8—1031no—
106#487—1038no—
107C2×#103—1031no—
108C2×#103—1031no—
109C2×#103—1031no—
110C2×#103D10311yescharacteristic
111C2×C4×C8—1031no—
112C22×Q8—1031no—
113C22×Q8—2061no—
114C22×Q8C2×D10311yescharacteristic
115C22×C8—1031no—
116C22×C8C2×D10311yescharacteristic
117C4⋊Q8—1034no—
118C4⋊Q8—1034no—
119C4⋊Q8—2062no—
120C4⋊Q8—2062no—
121C2×C4⋊C4—1031no—
122C2×C4⋊C4—2061no—
123C2×C4⋊C4—2061no—
124C2×C4⋊C4—2061no—
125C2×C4⋊C4C2×D10311yescharacteristic
126C2×C42—1031no—
127#103—1034no—
128#103—1034no—
129#103—1034no—
130#103C2×D10314yes—
131C4×C8—1034no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—1032no—
136C2×Q8—4124no—
137C2×Q8—2064no—
138C2×Q8—2062no—
139C2×Q8—2062no—
140C2×Q8—2061no—
141C2×Q8C22×D10312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—1031no—
145C22×C4—1031no—
146C22×C4—2061no—
147C22×C4—2061no—
148C22×C4C22×D10311yescharacteristic
149C2×C8—22no—
150C2×C8—1032no—
151C2×C8—2062no—
152C2×C8C22×D10312yes—
153C4⋊C4—21no—
154C4⋊C4—1032no—
155C4⋊C4—2064no—
156C4⋊C4—2064no—
157C4⋊C4—2064no—
158C4⋊C4—2061no—
159C4⋊C4C22×D10312yes—
160C42—1032no—
161C42—1032no—
162C23D4×D10311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—42no—
166Q8—4128no—
167Q8—4122no—
168Q8—2062no—
169Q8—2062no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—1032no—
175C2×C4—1032no—
176C2×C4—1034no—
177C2×C4—1034no—
178C2×C4—4122no—
179C2×C4—4122no—
180C2×C4—2062no—
181C2×C4—2062no—
182C2×C4D4×D10311yescharacteristic
183C2×C4#1311010412yes—
184C2×C4#1311010512yes—
185C2×C4C23×D10311yescharacteristic
186C8—22no—
187C8—2062no—
188C22#1569300712yes—
189C22SD16×D10312yes—
190C22Q16×D10312yes—
191C22C2×D4×D10311yescharacteristic
192C4—42no—
193C4—42no—
194C4—1034no—
195C4—1034no—
196C4—4122no—
197C4—4122no—
198C4#1569300712yes—
199C4C2×#1311010411yescharacteristic
200C4C2×#1311010511yescharacteristic
201C2#2026814014yesdirect product factor
202C2C2×#1569300711yescharacteristic
203C2C2×SD16×D10311yescharacteristic
204C2C2×Q16×D10311yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#103×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#103D103
hypocenterC103C2×#487
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #20268140C2direct (N × H)
98. C2×C103#487semidirect
103. C103C2×#487semidirect
201. C2#20268140direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156930202
C2×#156930192
#202681402
C2×#156929462
C2×#156929452
C2×#156929442
C2×C8×Dic1032
C2×#103×C1032
C2×#487103