Finite Group Databasebeta

← #13080902

Subgroups — #13080902

Order 1408.

374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623258C211yesmaximal, characteristic
2#10623115C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic, complemented
4#10622802C212yesmaximal, complemented
5#10622799C212yesmaximal, complemented
6#10622694C211yesmaximal, characteristic, complemented
7C4×#4326C211yesmaximal, characteristic, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622451C211yesmaximal, characteristic
10#10622428C212yesmaximal, complemented
11#10622415C212yesmaximal, complemented
12C2×Q8×D11C2212yes—
13C2×C11×Q16C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15C4×Q8×C11C2211yescharacteristic
16#66999C2212yes—
17#66999C2212yes—
18C2×#4326C2211yescharacteristic
19C2×#4313C2212yes—
20#66951—22no—
21#66949—22no—
22#66946—21no—
23#66945C2212yes—
24#66941—21no—
25#66928—21no—
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22—21no—
29C4×Dic22C2211yescharacteristic
30C11×C4⋊C8C2211yescharacteristic
31C11×#103C2212yes—
32#66899C2212yes—
33#66899C2211yescharacteristic
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66881C2212yes—
37#66880C2212yes—
38#66874C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2312yes—
42C2×Q8×C11C2311yescharacteristic
43Q8×D11—24no—
44Q8×D11—42no—
45C2×D44D411yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11C2312yes—
48C2×Dic22—22no—
49C2×Dic22—21no—
50C2×Dic22C2311yescharacteristic
51C11×Q16—42no—
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2311yescharacteristic
57C42×C11—21no—
58C42×C11C2311yescharacteristic
59#4326—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4D412yes—
64C4⋊Dic11—21no—
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2312yes—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—21no—
71C4×Dic11—22no—
72C4×Dic11—21no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#4313—42no—
76#3328—111nomaximal, Sylow
77C22×D11C2×D412yes—
78Q8×C11—21no—
79Q8×C11—22no—
80Q8×C11—21no—
81Q8×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11C2×D412yes—
92D44—22no—
93C4×D11—22no—
94C4×D11—22no—
95C4×D11—44no—
96Dic22—21no—
97Dic22—44no—
98Dic22—42no—
99Dic22#4112yes—
100C8×C11—22no—
101C11⋊C8—21no—
102C11⋊C8—21no—
103#556—111no—
104D4×Q8—111no—
105#487—111no—
106#485—112no—
107#475—111no—
108#470—112no—
109#462D1111yescharacteristic, complemented
110#451—112no—
111C4×Q16—111no—
112#436—111no—
113#419—112no—
114C22×C11C22×D411yescharacteristic
115C2×D11—22no—
116C2×D11—22no—
117C2×D11—22no—
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—42no—
121C4×C11—41no—
122C4×C11#13712yes—
123C4×C11C2×#4111yescharacteristic
124C4×C11H(5,𝔽2)11yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—42no—
128Dic11—41no—
129C22×Q8—112no—
130C2×Q16—111no—
131C2×Q16C2×D1112yes—
132C2×M16—112no—
133C4⋊Q8—111no—
134C4⋊Q8—221no—
135C4⋊Q8C2×D1111yescharacteristic
136#126—222no—
137#124—221no—
138C22⋊Q8—112no—
139C22⋊Q8—112no—
140C22⋊Q8—222no—
141C4×Q8—111no—
142C4×Q8—221no—
143C4×Q8C2×D1111yescharacteristic
144C4×D4—111no—
145C4×D4—221no—
146#117—112no—
147#107—111no—
148#106—112no—
149C4⋊C8C2×D1111yescharacteristic
150#103—112no—
151#103—111no—
152#103—112no—
153#103—112no—
154#103—111no—
155#103C2×D1112yes—
156C22⋊C8—112no—
157C4×C8—111no—
158C2×C11#54611yescharacteristic
159C2×C11C2×#13711yescharacteristic
160C2×C11#57811yescharacteristic
161D11—42no—
162C2×Q8—111no—
163C2×Q8—222no—
164C2×Q8—221no—
165C2×Q8—224no—
166C2×Q8—442no—
167C2×Q8C22×D1112yes—
168C2×Q8C22×D1111yescharacteristic
169C2×D4—111no—
170C22×C4—112no—
171C22×C4—222no—
172Q16—42no—
173Q16—222no—
174M16—442no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8C22×D1112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—112no—
183C4⋊C4—111no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4C22×D1111yescharacteristic
189C22⋊C4—112no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4—222no—
193C42—21no—
194C42—222no—
195C42—221no—
196C42C22×D1111yescharacteristic
197C11#332811yescharacteristic, complemented, Sylow
198C23—112no—
199Q8—21no—
200Q8—22no—
201Q8—21no—
202Q8—22no—
203Q8—112no—
204Q8—221no—
205Q8—444no—
206Q8—442no—
207D4—222no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—112no—
212C2×C4—221no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4—444no—
218C2×C4D4×D1111yescharacteristic
219C2×C4D4×D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—22no—
222C8—221no—
223C8—221no—
224C22—222no—
225C22—222no—
226C22—222no—
227C22C2×D4×D1111yescharacteristic
228C4—21no—
229C4—41no—
230C4—42no—
231C4—41no—
232C4—222no—
233C4—222no—
234C4—442no—
235C4—441no—
236C4#6697112yes—
237C4#6703711yescharacteristic
238C4#41×D1111yescharacteristic
239C2—442no—
240C2#1062314311yescharacteristic
241C2C2×#6697111yescharacteristic
242C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#462D11
hypocenterC11#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C11×#462C2semidirect
4. #10622802C2semidirect
5. #10622799C2semidirect
6. #10622694C2semidirect
7. C4×#4326C2semidirect
8. #10622464C2semidirect
10. #10622428C2semidirect
11. #10622415C2semidirect
109. #462D11semidirect
197. C11#3328semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106231152
C11×#4622
#106228022
#106227992
#106226942
C4×#43262
#106224642
#106224512
#106224282
#106224152
#332811