Finite Group Databasebeta

← #13081203

Subgroups — #13081203

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#10623257C211yesmaximal, characteristic
2#10623115C211yesmaximal, characteristic, complemented
3C11×#475C211yesmaximal, characteristic, complemented
4#10622691C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic, complemented
6#10622479C212yesmaximal, complemented
7#10622474C212yesmaximal, complemented
8#10622459C211yesmaximal, characteristic, complemented
9#10622451C211yesmaximal, characteristic, complemented
10#10622425C212yesmaximal, complemented
11#10622422C212yesmaximal, complemented
12C2×#4343—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#66999—21no—
16#66999C2212yes—
17C2×#4325C2211yescharacteristic
18C2×#4313C2212yes—
19#66951—22no—
20#66948C2212yes—
21#66947—22no—
22#66945C2212yes—
23C4⋊C4×D11C2212yes—
24#66928—21no—
25C4×D44C2211yescharacteristic
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22—21no—
29C11×#106C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#103C2212yes—
32#66899C2211yescharacteristic
33#66885C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66882C2212yes—
36#66873C2211yescharacteristic
37#66872C2211yescharacteristic
38#66871C2212yes—
39#66871C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11C2311yescharacteristic
43#4343—44no—
44C2×D44—22no—
45C2×D44D411yescharacteristic
46C2×D44C2311yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11—21no—
49C2×C4×D11C2312yes—
50C2×Dic22—21no—
51C2×C8×C11C2312yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C4⋊C4C2311yescharacteristic
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58#4325—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—21no—
63(C2×D11)⋊C4D412yes—
64C4⋊Dic11—21no—
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#4313—24no—
74#3353—111nomaximal, Sylow
75C22×D11—21no—
76C22×D11C2×D412yes—
77Q8×C11—21no—
78Q8×C11—21no—
79Q8×C11—42no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11C2×D412yes—
89D44—22no—
90D44—21no—
91D44—21no—
92D44—44no—
93C4×D11—22no—
94C4×D11—22no—
95C4×D11—44no—
96C4×D11—42no—
97Dic22—42no—
98C8×C11—22no—
99C11⋊C8—21no—
100C11⋊C8#4112yescomplemented
101#556—111no—
102#547—111no—
103#500—111no—
104#484—112no—
105#482—112no—
106#475D1111yescharacteristic, complemented
107#474—111no—
108#468—112no—
109C4×SD16—111no—
110#436—111no—
111#428—112no—
112C22×C11C22×D411yescharacteristic
113C2×D11—22no—
114C2×D11—22no—
115C2×D11—22no—
116C2×D11—41no—
117C2×D11—41no—
118C2×D11—41no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11AGL(1,ℤ/8)12yes—
124C4×C11C2×#4111yescharacteristic
125C4×C112−1+411yescharacteristic
126Dic11—22no—
127Dic11—42no—
128Dic11—41no—
129C2×#41—221no—
130C2×SD16—111no—
131C2×M16—112no—
132C4⋊Q8—111no—
133C4⋊Q8C2×D1111yescharacteristic
134#126—222no—
135#124—221no—
136#123—222no—
137C22⋊Q8—112no—
138C22⋊Q8—221no—
139#121—112no—
140C4×Q8—221no—
141C4×Q8C2×D1111yescharacteristic
142C4×D4—111no—
143C4×D4—111no—
144#117—112no—
145C2×C4⋊C4—112no—
146#107—112no—
147#107—112no—
148#107—112no—
149#106—111no—
150#106C2×D1112yes—
151C4⋊C8C2×D1111yescharacteristic
152#103—111no—
153#103C2×D1112yes—
154#102—112no—
155#102—111no—
156C22⋊C8—112no—
157C4×C8—111no—
158C2×C11#54711yescharacteristic
159C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
160C2×C11#57811yescharacteristic
161D11—42no—
162D11—81no—
163#41—444no—
164C2×Q8—21no—
165C2×Q8—221no—
166C2×Q8C22×D1111yescharacteristic
167C2×D4—111no—
168C2×D4—111no—
169C2×D4—222no—
170C22×C4—112no—
171C22×C4—222no—
172C22×C4—221no—
173SD16—222no—
174M16—224no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8C22×D1112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—111no—
181C4⋊C4—112no—
182C4⋊C4—111no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—221no—
186C4⋊C4C22×D1111yescharacteristic
187C4⋊C4C22×D1112yes—
188C22⋊C4—112no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4—221no—
193C42—21no—
194C42—222no—
195C42C22×D1111yescharacteristic
196C11#335311yescharacteristic, complemented, Sylow
197C23—112no—
198C23—221no—
199Q8—21no—
200Q8—21no—
201Q8—42no—
202Q8—442no—
203D4—222no—
204D4—221no—
205D4—221no—
206D4—444no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—112no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—444no—
216C2×C4—442no—
217C2×C4D4×D1111yescharacteristic
218C2×C4D4×D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—22no—
221C8—112no—
222C8—221no—
223C22—222no—
224C22—222no—
225C22—222no—
226C22—441no—
227C22—441no—
228C22—441no—
229C22C2×D4×D1111yescharacteristic
230C4—21no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—222no—
235C4—441no—
236C4—442no—
237C4#6696712yes—
238C4#6704011yescharacteristic
239C4#41×D1111yescharacteristic
240C2—442no—
241C2—881no—
242C2#1062316211yescharacteristic
243C2C2×#6696711yescharacteristic
244C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#475C2
socleC22×C11C22×D4
prime radical#10623257C2
hypercenter#475D11
hypocenterC11#3353
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #10623115C2semidirect
3. C11×#475C2semidirect
4. #10622691C2semidirect
5. C4×#4325C2semidirect
6. #10622479C2semidirect
7. #10622474C2semidirect
8. #10622459C2semidirect
9. #10622451C2semidirect
10. #10622425C2semidirect
11. #10622422C2semidirect
100. C11⋊C8#41semidirect
106. #475D11semidirect
196. C11#3353semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106231152
C11×#4752
#106226912
C4×#43252
#106224792
#106224742
#106224592
#106224512
#106224252
#106224222
#335311