Finite Group Databasebeta

← #13079689

Subgroups — #13079689

Order 1408.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#10623246C211yesmaximal, characteristic
2#10623228C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic, complemented
4#10622689C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622396C212yesmaximal, complemented
7#10622389C212yesmaximal, complemented
8#10622380C212yesmaximal, complemented
9#10622375C212yesmaximal, complemented
10#10622328C211yesmaximal, characteristic, complemented
11#10622322C211yesmaximal, characteristic, complemented
12C2×#4341C2211yescharacteristic
13C2×D4×D11C2211yescharacteristic
14C11×#127C2211yescharacteristic
15C11×#125C2211yescharacteristic, complemented
16#66993C2211yescharacteristic
17#66992—22no—
18#66990—22no—
19#66989C2211yescharacteristic
20C2×#4324C2212yes—
21C2×#4324C2212yescomplemented
22C2×Dic44C2212yescomplemented
23C2×#4314C2212yes—
24#66951—22no—
25#66950C2212yes—
26#66943—22no—
27#66940C2212yescomplemented
28#66928C2211yescharacteristic
29#66925C2211yescharacteristic
30#66922C2211yescharacteristic, complemented
31C11×#102C2212yes—
32C11×#102C2212yescomplemented
33C11×#97C2211yescharacteristic, complemented
34(C2×D11)⋊C8C2212yes—
35Dic11⋊C8C2212yescomplemented
36#66874C2212yescomplemented
37#66873C2212yes—
38C4×C11⋊C8C2211yescharacteristic, complemented
39C23×D11—21no—
40C2×D4×C11—22no—
41C2×D4×C11C2311yescharacteristic
42C2×D4×C11C2311yescharacteristic
43C2×C22⋊D11—21no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—21no—
46C22×Dic11—21no—
47#4341—42no—
48D4×D11—42no—
49C2×D44C2311yescharacteristic
50C2×C4×D11C2311yescharacteristic
51C2×Dic22C2311yescharacteristic
52C2×Dic22C2312yes—
53C2×C8×C11C2312yes—
54C11×C4⋊C4—22no—
55C11×C4⋊C4C2312yes—
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58#4324—42no—
59#4324—42no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4D412yes—
63C4⋊Dic11—22no—
64C4⋊Dic11—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4D412yes—
67C4×Dic11—22no—
68C4×Dic11C2311yescharacteristic
69C2×C11⋊C8C2312yes—
70Dic44—42no—
71#4314—42no—
72#3222—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C22×D11—21no—
76C22×D11—42no—
77C22×D11—82no—
78C22×D11C2×D411yescharacteristic
79D4×C11—22no—
80D4×C11—22no—
81D4×C11—82no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D412yes—
84C2×C4×C11C2411yescharacteristic
85C22⋊D11—42no—
86C22⋊D11—42no—
87C22⋊D11—82no—
88C2×Dic11—22no—
89C2×Dic11—21no—
90C2×Dic11—42no—
91C2×Dic11C2×D412yes—
92C2×Dic11C2×D411yescharacteristic
93D44—22no—
94C4×D11—22no—
95Dic22—22no—
96Dic22—22no—
97Dic22—22no—
98C8×C11—22no—
99C11⋊C8—22no—
100#541—111no—
101#535—111no—
102#497—111no—
103#492—111no—
104#490D1111yescharacteristic, complemented
105#488—111no—
106#464—112no—
107#460—112no—
108#452—112no—
109#450—112no—
110#433—111no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11C22×D411yescharacteristic
116C2×D11—21no—
117C2×D11—22no—
118C2×D11—41no—
119C2×D11—42no—
120C2×D11—84no—
121C4×C11—22no—
122C4×C11—42no—
123C4×C11H(5,𝔽2)12yes—
124Dic11—21no—
125Dic11—22no—
126Dic11—42no—
127Dic11—41no—
128C2×#41—111no—
129C22×D4—111no—
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16—112no—
134C4⋊Q8—111no—
135#127—111no—
136#127C2×D1111yescharacteristic
137#126—222no—
138#125—222no—
139#125C2×D1111yescharacteristic, complemented
140#124—111no—
141#124—111no—
142C22⋊Q8—112no—
143#121—222no—
144#120—222no—
145C4×Q8—112no—
146#117—111no—
147C4⋊C8—112no—
148#103—112no—
149#102—112no—
150#102C2×D1112yes—
151#102C2×D1112yescomplemented
152C22⋊C8—112no—
153#97C2×D1111yescharacteristic, complemented
154C4×C8—111no—
155C2×C11—81no—
156C2×C11—81no—
157C2×C11#53511yescharacteristic
158C2×C11#57712yes—
159D11—41no—
160D11—81no—
161C24—221no—
162#41—442no—
163C2×Q8—111no—
164C2×Q8—112no—
165C2×D4—22no—
166C2×D4—111no—
167C2×D4—221no—
168C2×D4—222no—
169C2×D4—221no—
170C2×D4—442no—
171C2×D4C22×D1111yescharacteristic
172C2×D4C22×D1111yescharacteristic
173C22×C4—111no—
174C22×C4—221no—
175Q16—442no—
176SD16—442no—
177SD16—442no—
178SD16—442no—
179C2×C8—112no—
180C2×C8C22×D1112yes—
181C4⋊C4—22no—
182C4⋊C4—112no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4C22×D1112yes—
187C22⋊C4—112no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C42—111no—
192C42—222no—
193C42C22×D1111yescharacteristic
194C11#322211yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197C23—111no—
198C23—221no—
199C23—442no—
200C23—882no—
201Q8—222no—
202Q8—222no—
203Q8—222no—
204D4—22no—
205D4—22no—
206D4—82no—
207D4—222no—
208D4—442no—
209D4—442no—
210D4—882no—
211C2×C4—22no—
212C2×C4—112no—
213C2×C4—111no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—221no—
217C2×C4—442no—
218C2×C4D4×D1112yes—
219C2×C4C23×D1111yescharacteristic
220C8—22no—
221C8—222no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22—222no—
227C22—221no—
228C22—442no—
229C22—441no—
230C22—884no—
231C22C2×D4×D1111yescharacteristic
232C4—22no—
233C4—42no—
234C4—222no—
235C4—221no—
236C4—441no—
237C4—442no—
238C4#6704212yes—
239C2—81no—
240C2—81no—
241C2—441no—
242C2—881no—
243C2#1062320511yescharacteristic
244C2#1062330612yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radical#10623246C2
hypercenter#490D11
hypocenterC11#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #10623228C2semidirect
3. C11×#490C2semidirect
4. #10622689C2semidirect
5. #10622681C2semidirect
6. #10622396C2semidirect
7. #10622389C2semidirect
8. #10622380C2semidirect
9. #10622375C2semidirect
10. #10622328C2semidirect
11. #10622322C2semidirect
15. C11×#125C22semidirect
21. C2×#4324C22semidirect
22. C2×Dic44C22semidirect
27. #66940C22semidirect
30. #66922C22semidirect
32. C11×#102C22semidirect
33. C11×#97C22semidirect
35. Dic11⋊C8C22semidirect
36. #66874C22semidirect
38. C4×C11⋊C8C22semidirect
104. #490D11semidirect
139. #125C2×D11semidirect
151. #102C2×D11semidirect
153. #97C2×D11semidirect
194. C11#3222semidirect

Maximal subgroups

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

subgroupindex
#106232462
#106232282
C11×#4902
#106226892
#106226812
#106223962
#106223892
#106223802
#106223752
#106223282
#106223222
#322211