Finite Group Databasebeta

← C2×#10622690 #13077939

Subgroups — C2×#10622690 #13077939

Order 1408.

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

normal subgroups only

This group has 844 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×#67037C211yesmaximal, characteristic, complemented
2C2×C11×#127C211yesmaximal, characteristic, complemented
3C2×#66985C212yesmaximal, complemented
4C2×#66897C211yesmaximal, characteristic, complemented
5#10622690C218yesmaximal, direct product factor
6C2×#66869C212yesmaximal, complemented
7C22×D4×C11—22no—
8C22×D4×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic, complemented
10C22×C22⋊D11—22no—
11#67037—22no—
12#67037—24no—
13#67037C2214yescomplemented
14C2×#4341—22no—
15C2×D4×D11—22no—
16C2×#4339C2212yes—
17C11×#127—22no—
18C11×#127C2214yescomplemented
19C2×C42×C11C2211yescharacteristic, complemented
20C2×#4324—22no—
21#66985—24no—
22#66985C2218yescomplemented
23C2×#4323—22no—
24C2×#4318C2212yescomplemented
25#66897C2214yescomplemented
26#66869C2218yescomplemented
27C24×C11—21no—
28C24×C11D412yes—
29C23×D11—22no—
30C2×D4×C11—28no—
31C2×D4×C11—22no—
32C2×D4×C11—22no—
33C2×D4×C11—22no—
34C2×D4×C11—22no—
35C2×D4×C11—21no—
36C2×D4×C11—48no—
37C2×D4×C11D412yes—
38C2×D4×C11C2312yes—
39C2×D4×C11C2312yescomplemented
40C22×C4×C11—21no—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—24no—
43C2×C22⋊D11—28no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—28no—
46C22×Dic11—22no—
47#4341—28no—
48#4341—28no—
49D4×D11—28no—
50D4×D11—28no—
51#4339—22no—
52#4339—22no—
53#4339D414yescomplemented
54#4339C2314yes—
55C2×D44D412yescomplemented
56C2×C4×D11—22no—
57C2×Dic22D412yescomplemented
58C42×C11—21no—
59C42×C11C2312yescomplemented
60#4324—28no—
61#4323—28no—
62#4318—22no—
63#4318C2314yescomplemented
64C2×C11⋊C8—22no—
65C2×#453—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—44no—
70C23×C11—44no—
71C23×C11—41no—
72C23×C11—41no—
73C23×C11C2×D411yescharacteristic
74C23×C11C2×D414yes—
75C22×D11—22no—
76C22×D11—28no—
77C22×D11—84no—
78D4×C11—24no—
79D4×C11—24no—
80D4×C11—24no—
81D4×C11—416no—
82D4×C11—42no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D412yes—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C22⋊D11—216no—
90C22⋊D11—24no—
91C22⋊D11—24no—
92C2×Dic11—28no—
93C2×Dic11—22no—
94D44—22no—
95D44C2×D414yescomplemented
96C4×D11—24no—
97C4×D11—24no—
98Dic22—22no—
99Dic22C2×D414yescomplemented
100C11⋊C8—24no—
101C2×H(5,𝔽2)—111no—
102C2×AGL(1,ℤ/8)—112no—
103C2×#127D1111yescharacteristic, complemented
104#453—118no—
105C2×#104—112no—
106C2×#100—111no—
107C22×C11—22no—
108C22×C11—24no—
109C22×C11—44no—
110C22×C11—44no—
111C22×C11—44no—
112C22×C11—42no—
113C22×C11—82no—
114C22×C11—82no—
115C22×C11—82no—
116C22×C11#12011yescharacteristic
117C22×C11#12011yescharacteristic
118C22×C11C22×D411yescharacteristic
119C2×D11—24no—
120C2×D11—44no—
121C2×D11—88no—
122C4×C11—24no—
123C4×C11#12012yes—
124C4×C11C22×D412yes—
125Dic11—24no—
126H(5,𝔽2)—114no—
127H(5,𝔽2)—224no—
128H(5,𝔽2)—222no—
129C2×#41—112no—
130C2×#41—222no—
131C22×D4—22no—
132C22×D4—222no—
133C22×D4—222no—
134C22×D4C2×D1111yescharacteristic
135C22×D4C2×D1111yescharacteristic, complemented
136AGL(1,ℤ/8)—118no—
137AGL(1,ℤ/8)—224no—
138C2×SD16—222no—
139C2×D8—222no—
140C2×M16—112no—
141#127—22no—
142#127C2×D1114yescomplemented
143C2×C42C2×D1111yescharacteristic, complemented
144#104—118no—
145#100—114no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11—44no—
149C2×C11—82no—
150C2×C11#45312yescomplemented
151C2×C11C2×#12011yescharacteristic
152D11—44no—
153C24—21no—
154C24—222no—
155C24C22⋊D1112yes—
156#41—114no—
157#41—114no—
158#41—228no—
159#41—228no—
160#41—222no—
161#41—222no—
162C2×Q8—112no—
163C2×D4—28no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—21no—
169C2×D4—48no—
170C2×D4—112no—
171C2×D4—228no—
172C2×D4—228no—
173C2×D4—224no—
174C2×D4—228no—
175C2×D4—222no—
176C2×D4—228no—
177C2×D4C22⋊D1112yes—
178C2×D4C22×D1112yes—
179C2×D4C22×D1112yescomplemented
180C22×C4—21no—
181C22×C4—222no—
182C22×C4—222no—
183C22×C4C22×D1111yescharacteristic
184SD16—228no—
185D8—228no—
186M16—114no—
187M16—222no—
188C2×C8—222no—
189C42—21no—
190C42C22×D1112yescomplemented
191C11C2×#45311yescharacteristic, complemented, Sylow
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—228no—
200C23—222no—
201C23—884no—
202C23C2×C22⋊D1111yescharacteristic
203C23C2×C22⋊D1114yes—
204Q8—114no—
205Q8—222no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—114no—
212D4—2216no—
213D4—224no—
214D4—224no—
215D4—222no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—228no—
219C2×C4—222no—
220C2×C4—224no—
221C2×C4—224no—
222C2×C4D4×D1112yes—
223C2×C4D4×D1112yes—
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—224no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—224no—
237C22—444no—
238C22—888no—
239C22#6699011yescharacteristic
240C22#6699011yescharacteristic
241C22C22×C22⋊D1111yescharacteristic
242C4—24no—
243C4—224no—
244C4#6699012yes—
245C4C2×D4×D1112yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—444no—
251C2#1062269012yesdirect product factor
252C2C2×#6699011yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#127C2
socleC22×C11#120
hypercenterC2×#127D11
hypocenterC11C2×#453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#67037C2semidirect
2. C2×C11×#127C2semidirect
3. C2×#66985C2semidirect
4. C2×#66897C2semidirect
5. #10622690C2direct (N × H)
6. C2×#66869C2semidirect
9. C22×D4×C11C22semidirect
13. #67037C22semidirect
18. C11×#127C22semidirect
19. C2×C42×C11C22semidirect
22. #66985C22semidirect
24. C2×#4318C22semidirect
25. #66897C22semidirect
26. #66869C22semidirect
39. C2×D4×C11C23semidirect
53. #4339D4semidirect
55. C2×D44D4semidirect
57. C2×Dic22D4semidirect
59. C42×C11C23semidirect
63. #4318C23semidirect
95. D44C2×D4semidirect
99. Dic22C2×D4semidirect
103. C2×#127D11semidirect
135. C22×D4C2×D11semidirect
142. #127C2×D11semidirect
143. C2×C42C2×D11semidirect
150. C2×C11#453semidirect
179. C2×D4C22×D11semidirect
190. C42C22×D11semidirect
191. C11C2×#453semidirect
251. C2#10622690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#670372
C2×C11×#1272
C2×#669852
C2×#668972
#106226902
C2×#668692
C2×#45311