Finite Group Databasebeta

← C2×#10622497 #13078523

Subgroups — C2×#10622497 #13078523

Order 1408.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66950C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C2×C11×#107C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C8C211yesmaximal, characteristic
5C2×#66880C211yesmaximal, characteristic, complemented
6C2×#66874C211yesmaximal, characteristic, complemented
7C2×#66871C211yesmaximal, characteristic, complemented
8#10622497C218yesmaximal, direct product factor
9C22×C4×D11—21no—
10C22×C4×D11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C22×C8×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4—21no—
16C2×C4⋊Dic11—21no—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4—21no—
19C22×C11⋊C8C2211yescharacteristic
20#66950—22no—
21#66950C2214yes—
22C4⋊C4×D11—22no—
23C4⋊C4×D11C2214yes—
24C11×#107C2214yescomplemented
25(C2×D11)⋊C8C2214yes—
26#66880C2214yescomplemented
27#66874C2214yescomplemented
28#66871C2214yescomplemented
29C23×D11D411yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11C2311yescharacteristic
33C22×Dic11—21no—
34C22×Dic11—21no—
35C22×Dic11D411yescharacteristic
36C2×C4×D11—24no—
37C2×C4×D11—22no—
38C2×C4×D11—22no—
39C2×C4×D11—44no—
40C2×C4×D11D412yes—
41C2×C4×D11C2312yes—
42C2×Dic22—21no—
43C2×Dic22—22no—
44C2×Dic22—22no—
45C2×Dic22C2312yes—
46C2×C8×C11—22no—
47C2×C8×C11C2312yes—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4C2312yes—
51C11×C4⋊C4C2312yes—
52(C2×D11)⋊C4—24no—
53C4⋊Dic11—24no—
54C4⋊Dic11—21no—
55C4⋊Dic11C2312yes—
56Dic11⋊C4—24no—
57C2×C11⋊C8—22no—
58C2×C11⋊C8C2312yes—
59C2×#484—111nomaximal, Sylow
60C23×C11C2×D411yescharacteristic
61C22×D11—22no—
62C22×D11—22no—
63C22×D11Q1614yes—
64C22×D11C2×D412yes—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—42no—
68C2×C4×C11—42no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11#4112yes—
71C2×C4×C11#4112yes—
72C2×C4×C11C2411yescharacteristic
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—42no—
77C2×Dic11—42no—
78C2×Dic11C2×D412yes—
79C4×D11—24no—
80C4×D11—22no—
81C4×D11—22no—
82C4×D11—48no—
83Dic22—22no—
84Dic22—22no—
85Dic22—42no—
86C8×C11—22no—
87C11⋊C8—22no—
88C2×C22⋊Q8—111no—
89C22×C4⋊C4—111no—
90#484—118no—
91C2×#107—111no—
92C2×#107D1111yescharacteristic, complemented
93C2×#103—111no—
94C2×#103—111no—
95C2×C22⋊C8—111no—
96C22×C11#12312yes—
97C22×C11C2×Q1612yes—
98C22×C11AGL(1,ℤ/8)12yes—
99C22×C11C22×D411yescharacteristic
100C2×D11—22no—
101C2×D11—22no—
102C2×D11—28no—
103C2×D11C2×Q1614yes—
104C4×C11—42no—
105C4×C11—42no—
106C4×C11#12312yes—
107C4×C11C2×#4111yescharacteristic
108C4×C11C2×#4111yescharacteristic
109Dic11—22no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8—111no—
113C23×C4—111no—
114C23×C4—221no—
115C22×C8—111no—
116C22×C8C2×D1111yescharacteristic
117C22⋊Q8—114no—
118C22⋊Q8—222no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4—114no—
121C2×C4⋊C4—222no—
122C2×C4⋊C4—221no—
123C2×C4⋊C4—221no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—221no—
127#107—114no—
128#107C2×D1114yescomplemented
129#103—114no—
130#103—114no—
131C22⋊C8—114no—
132C2×C11#48414yescomplemented
133C2×C11C2×#12311yescharacteristic
134C2×C11C22×Q1611yescharacteristic
135C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
136D11—24no—
137C24—111no—
138C2×Q8—112no—
139C2×Q8—221no—
140C2×Q8—222no—
141C2×Q8—222no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—111no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4—224no—
148C22×C4—222no—
149C22×C4—222no—
150C22×C4—221no—
151C22×C4—221no—
152C22×C4—444no—
153C22×C4C22×D1111yescharacteristic
154C2×C8—22no—
155C2×C8—112no—
156C2×C8—222no—
157C2×C8C22×D1112yes—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—112no—
161C4⋊C4—224no—
162C4⋊C4—224no—
163C4⋊C4—221no—
164C4⋊C4C22×D1112yes—
165C4⋊C4C22×D1112yes—
166C22⋊C4—224no—
167C11C2×#48411yescharacteristic, complemented, Sylow
168C23—114no—
169C23—112no—
170C23—222no—
171C23—222no—
172C23D4×D1111yescharacteristic
173Q8—222no—
174Q8—222no—
175Q8—442no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—112no—
181C2×C4—222no—
182C2×C4—224no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—448no—
188C2×C4—442no—
189C2×C4—442no—
190C2×C4#433912yes—
191C2×C4D4×D1111yescharacteristic
192C2×C4#434312yes—
193C2×C4C23×D1111yescharacteristic
194C8—22no—
195C8—222no—
196C22—114no—
197C22—228no—
198C22—222no—
199C22—222no—
200C22#6694712yes—
201C22#6696412yes—
202C22Q16×D1112yes—
203C22C2×D4×D1111yescharacteristic
204C4—42no—
205C4—42no—
206C4—222no—
207C4—442no—
208C4—442no—
209C4#6694712yes—
210C4C2×#433911yescharacteristic
211C4C2×#434311yescharacteristic
212C2—224no—
213C2#1062249714yesdirect product factor
214C2C2×#6694711yescharacteristic
215C2C2×#6696411yescharacteristic
216C2C2×Q16×D1111yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#107C2
socleC23×C11C2×D4
prime radicalC23×D11D4
hypercenterC2×#107D11
hypocenterC11C2×#484
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. C2×C11×#107C2semidirect
5. C2×#66880C2semidirect
6. C2×#66874C2semidirect
7. C2×#66871C2semidirect
8. #10622497C2direct (N × H)
24. C11×#107C22semidirect
26. #66880C22semidirect
27. #66874C22semidirect
28. #66871C22semidirect
92. C2×#107D11semidirect
128. #107C2×D11semidirect
132. C2×C11#484semidirect
167. C11C2×#484semidirect
213. C2#10622497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#669502
C2×C4⋊C4×D112
C2×C11×#1072
C2×(C2×D11)⋊C82
C2×#668802
C2×#668742
C2×#668712
#106224972
C2×#48411