Finite Group Databasebeta

← C2×#20268075 #27204908

Subgroups — C2×#20268075 #27204908

Order 13184.

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

normal subgroups only

This group has 416 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×#15692986C211yesmaximal, characteristic
3#20268075C218yesmaximal, direct product factor
4C2×#15692952C211yesmaximal, characteristic
5C2×Dic103⋊C8C211yesmaximal, characteristic
6C2×#15692946C211yesmaximal, characteristic
7C2×#15692944C211yesmaximal, characteristic
8C2×#106×C103C211yesmaximal, characteristic
9C22×Dic206—21no—
10C22×Dic206C2211yescharacteristic
11C22×C103⋊C8C2211yescharacteristic
12#15693020—22no—
13#15693020C2214yes—
14#15692986—22no—
15#15692986C2214yes—
16C2×C4⋊Dic103C2211yescharacteristic
17C2×Dic103⋊C4—21no—
18C2×Dic103⋊C4—21no—
19C2×C4×Dic103—21no—
20C2×C4×Dic103C2211yescharacteristic
21#15692952C2214yes—
22Dic103⋊C8C2214yes—
23#15692946C2214yes—
24#15692944C2214yes—
25C22×C8×C103C2211yescharacteristic
26C2×C4⋊C4×C103C2211yescharacteristic
27C2×C4⋊C4×C103C2211yescharacteristic
28#106×C103C2214yes—
29C2×Dic206—21no—
30C2×Dic206—22no—
31C2×Dic206—24no—
32C2×Dic206—44no—
33C2×Dic206Q814yescomplemented
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—
45C4×Dic103—24no—
46C4×Dic103D412yes—
47C4×Dic103C2312yes—
48C22×C4×C103—21no—
49C22×C4×C103—21no—
50C22×C4×C103C2311yescharacteristic
51C2×C8×C103—22no—
52C2×C8×C103C2312yes—
53C4⋊C4×C103—21no—
54C4⋊C4×C103—21no—
55C4⋊C4×C103C2312yes—
56C4⋊C4×C103C2312yes—
57C23×C103C2×D411yescharacteristic
58C2×C4×C103—22no—
59C2×C4×C103—22no—
60C2×C4×C103—42no—
61C2×C4×C103—42no—
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×Q812yes—
64C2×C4×C103#4112yes—
65C2×C4×C103C2411yescharacteristic
66C2×Dic103—24no—
67C2×Dic103—22no—
68C2×Dic103—22no—
69C2×Dic103—22no—
70C2×Dic103—42no—
71C2×Dic103SD1614yes—
72C2×Dic103C2×D412yes—
73C2×Dic103C2×D412yes—
74Dic206—24no—
75Dic206—22no—
76Dic206—48no—
77Dic206C2×Q814yescomplemented
78C8×C103—22no—
79C103⋊C8—22no—
80C22×C103C22⋊Q812yes—
81C22×C103C2×SD1612yes—
82C22×C103#13712yes—
83C22×C103C22×D411yescharacteristic
84C4×C103—42no—
85C4×C103—42no—
86C4×C103C22⋊Q812yes—
87C4×C103C22×Q811yescharacteristic
88C4×C103C2×#4111yescharacteristic
89Dic103—24no—
90Dic103—22no—
91Dic103—42no—
92Dic103C2×SD1614yes—
93C2×C103#47514yescomplemented
94C2×C103C2×C22⋊Q811yescharacteristic
95C2×C103C22×SD1611yescharacteristic
96C2×C103C2×#13711yescharacteristic
97C2×#475—1031nomaximal, Sylow
98C103C2×#47511yescharacteristic, complemented, Sylow
99C2×C4⋊Q8—1031no—
100C2×C4×Q8—1031no—
101#475—1038no—
102C2×#106—1031no—
103C2×#106D10311yescharacteristic
104C2×C4⋊C8—1031no—
105C2×#103—1031no—
106C2×#103—1031no—
107C22×Q8—1031no—
108C22×Q8—2061no—
109C22×C8—1031no—
110C22×C8C2×D10311yescharacteristic
111C4⋊Q8—1034no—
112C4⋊Q8—2062no—
113C4×Q8—1034no—
114C4×Q8—2062no—
115C2×C4⋊C4—1031no—
116C2×C4⋊C4—2061no—
117C2×C4⋊C4—2061no—
118C2×C4⋊C4C2×D10311yescharacteristic
119C2×C4⋊C4C2×D10311yescharacteristic
120C2×C42—1031no—
121C2×C42—2061no—
122#106—1034no—
123#106C2×D10314yes—
124C4⋊C8—1034no—
125#103—1034no—
126#103—1034no—
127C2×Q8—1034no—
128C2×Q8—1032no—
129C2×Q8—4124no—
130C2×Q8—2064no—
131C2×Q8—2061no—
132C2×Q8—2062no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—1031no—
136C22×C4—1031no—
137C22×C4—2061no—
138C22×C4—2061no—
139C22×C4C22×D10311yescharacteristic
140C2×C8—22no—
141C2×C8—1032no—
142C2×C8—2062no—
143C2×C8C22×D10312yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1032no—
147C4⋊C4—2064no—
148C4⋊C4—2064no—
149C4⋊C4—2061no—
150C4⋊C4C22×D10312yes—
151C4⋊C4C22×D10312yes—
152C42—1032no—
153C42—1032no—
154C42—2064no—
155C23D4×D10311yescharacteristic
156Q8—1034no—
157Q8—4128no—
158Q8—2062no—
159Q8—2064no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1032no—
165C2×C4—1034no—
166C2×C4—1032no—
167C2×C4—4122no—
168C2×C4—2062no—
169C2×C4—2062no—
170C2×C4—2064no—
171C2×C4—2062no—
172C2×C4D4×D10311yescharacteristic
173C2×C4Q8×D10312yes—
174C2×C4#1311010512yes—
175C2×C4C23×D10311yescharacteristic
176C8—22no—
177C8—2062no—
178C22#1569299912yes—
179C22SD16×D10312yes—
180C22#1569305012yes—
181C22C2×D4×D10311yescharacteristic
182C4—42no—
183C4—42no—
184C4—1034no—
185C4—4122no—
186C4—2064no—
187C4—2062no—
188C4#1569299912yes—
189C4C2×Q8×D10311yescharacteristic
190C4C2×#1311010511yescharacteristic
191C2#2026807514yesdirect product factor
192C2C2×#1569299911yescharacteristic
193C2C2×SD16×D10311yescharacteristic
194C2C2×#1569305011yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#106×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#106D103
hypocenterC103C2×#475
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #20268075C2direct (N × H)
33. C2×Dic206Q8semidirect
77. Dic206C2×Q8semidirect
93. C2×C103#475semidirect
98. C103C2×#475semidirect
191. C2#20268075direct (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×#156929862
#202680752
C2×#156929522
C2×Dic103⋊C82
C2×#156929462
C2×#156929442
C2×#106×C1032
C2×#475103