Finite Group Databasebeta

← C2×#10622483 #13078366

Subgroups — C2×#10622483 #13078366

Order 1408.

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

normal subgroups only

This group has 480 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×#66946C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C2×C11×#106C211yesmaximal, characteristic, complemented
4C2×#66885C211yesmaximal, characteristic
5C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
6C2×#66873C211yesmaximal, characteristic
7C2×#66872C211yesmaximal, characteristic, complemented
8#10622483C218yesmaximal, direct product factor
9C22×D44C2211yescharacteristic
10C22×C4×D11—21no—
11C22×Dic22—21no—
12C22×C8×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4—21no—
18C2×C4×Dic11C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66946—22no—
21#66946C2214yes—
22#66941—22no—
23#66941C2214yescomplemented
24C11×#106C2214yescomplemented
25#66885C2214yes—
26Dic11⋊C8C2214yescomplemented
27#66873C2214yes—
28#66872C2214yescomplemented
29C23×D11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11C2311yescharacteristic
33C22×Dic11—21no—
34C22×Dic11D411yescharacteristic
35C22×Dic11D411yescharacteristic
36C2×D44—21no—
37C2×D44—22no—
38C2×D44Q814yescomplemented
39C2×D44C2312yes—
40C2×C4×D11—24no—
41C2×C4×D11—44no—
42C2×Dic22—24no—
43C2×Dic22—44no—
44C2×C8×C11—22no—
45C2×C8×C11C2312yes—
46C11×C4⋊C4—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4C2312yes—
49C11×C4⋊C4C2312yes—
50(C2×D11)⋊C4—24no—
51C4⋊Dic11—21no—
52C4⋊Dic11C2312yes—
53Dic11⋊C4—24no—
54C4×Dic11D412yes—
55C4×Dic11C2312yes—
56C2×C11⋊C8—22no—
57C2×C11⋊C8C2312yes—
58C2×#476—111nomaximal, Sylow
59C23×C11C2×D411yescharacteristic
60C22×D11—24no—
61C22×D11—22no—
62C22×D11—42no—
63C22×D11—42no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—42no—
67C2×C4×C11—42no—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×Q812yes—
70C2×C4×C11#4112yes—
71C2×C4×C11C2411yescharacteristic
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—42no—
75C2×Dic11SD1614yes—
76C2×Dic11C2×D412yes—
77C2×Dic11C2×D412yes—
78D44—24no—
79D44—22no—
80D44C2×Q814yescomplemented
81C4×D11—48no—
82Dic22—48no—
83C8×C11—22no—
84C11⋊C8—22no—
85C2×C4⋊Q8—111no—
86C2×C4×D4—111no—
87#476—118no—
88C2×#106—111no—
89C2×#106D1111yescharacteristic, complemented
90C2×C4⋊C8—111no—
91C2×#102—111no—
92C2×#102—111no—
93C22×C11C22⋊Q812yes—
94C22×C11C2×SD1612yes—
95C22×C11AGL(1,ℤ/8)12yes—
96C22×C11C22×D411yescharacteristic
97C2×D11—24no—
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—48no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11C22⋊Q812yes—
104C4×C11C22×Q811yescharacteristic
105C4×C11C2×#4111yescharacteristic
106Dic11—22no—
107Dic11—42no—
108Dic11C2×SD1614yes—
109C22×Q8—221no—
110C22×D4—111no—
111C23×C4—221no—
112C22×C8—111no—
113C22×C8C2×D1111yescharacteristic
114C4⋊Q8—114no—
115C4⋊Q8—222no—
116C4×D4—114no—
117C4×D4—222no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—221no—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4—221no—
123C2×C42—111no—
124#106—114no—
125#106C2×D1114yescomplemented
126C4⋊C8—114no—
127#102—114no—
128#102—114no—
129C2×C11#47614yescomplemented
130C2×C11C2×C22⋊Q811yescharacteristic
131C2×C11C22×SD1611yescharacteristic
132C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
133D11—44no—
134C24—221no—
135C2×Q8—224no—
136C2×Q8—444no—
137C2×D4—114no—
138C2×D4—112no—
139C2×D4—222no—
140C2×D4—221no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—111no—
144C22×C4—111no—
145C22×C4—224no—
146C22×C4—221no—
147C22×C4—444no—
148C22×C4C22×D1111yescharacteristic
149C2×C8—22no—
150C2×C8—112no—
151C2×C8—222no—
152C2×C8C22×D1112yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—112no—
156C4⋊C4—224no—
157C4⋊C4—221no—
158C4⋊C4C22×D1112yes—
159C4⋊C4C22×D1112yes—
160C22⋊C4—224no—
161C42—112no—
162C42—112no—
163C11C2×#47611yescharacteristic, complemented, Sylow
164C23—224no—
165C23—222no—
166C23—442no—
167C23—442no—
168C23D4×D1111yescharacteristic
169Q8—448no—
170D4—114no—
171D4—224no—
172D4—222no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—114no—
178C2×C4—112no—
179C2×C4—112no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—448no—
183C2×C4—442no—
184C2×C4#433912yes—
185C2×C4D4×D1111yescharacteristic
186C2×C4Q8×D1112yes—
187C2×C4C23×D1111yescharacteristic
188C8—22no—
189C8—222no—
190C22—224no—
191C22—448no—
192C22—442no—
193C22—442no—
194C22#6694912yes—
195C22SD16×D1112yes—
196C22#6696712yes—
197C22C2×D4×D1111yescharacteristic
198C4—42no—
199C4—42no—
200C4—114no—
201C4—222no—
202C4—442no—
203C4#6694912yes—
204C4C2×#433911yescharacteristic
205C4C2×Q8×D1111yescharacteristic
206C2—444no—
207C2#1062248314yesdirect product factor
208C2C2×#6694911yescharacteristic
209C2C2×SD16×D1111yescharacteristic
210C2C2×#6696711yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#106C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenterC2×#106D11
hypocenterC11C2×#476
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C2×C11×#106C2semidirect
5. C2×Dic11⋊C8C2semidirect
7. C2×#66872C2semidirect
8. #10622483C2direct (N × H)
23. #66941C22semidirect
24. C11×#106C22semidirect
26. Dic11⋊C8C22semidirect
28. #66872C22semidirect
38. C2×D44Q8semidirect
80. D44C2×Q8semidirect
89. C2×#106D11semidirect
125. #106C2×D11semidirect
129. C2×C11#476semidirect
163. C11C2×#476semidirect
207. C2#10622483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#669462
C2×#669412
C2×C11×#1062
C2×#668852
C2×Dic11⋊C82
C2×#668732
C2×#668722
#106224832
C2×#47611