Finite Group Databasebeta

← #13080970

Subgroups — #13080970

Order 1408.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#10623261C211yesmaximal, characteristic, complemented
2#10623082C211yesmaximal, characteristic
3C11×#476C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5C4×#4324C211yesmaximal, characteristic, complemented
6#10622475C212yesmaximal, complemented
7D11×#106C212yesmaximal, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622447C211yesmaximal, characteristic, complemented
10#10622391C212yesmaximal, complemented
11#10622390C212yesmaximal, complemented
12C2×#4339—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C4×D4×C11C2211yescharacteristic
15#66999—22no—
16#66991C2212yes—
17C2×#4324C2211yescharacteristic
18#66977—21no—
19C2×C8×D11C2212yes—
20#66950C2212yes—
21#66946—21no—
22C4⋊C4×D11C2212yes—
23C4⋊C4×D11C2212yes—
24#66943—21no—
25#66936—22no—
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#106C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#102C2212yes—
32#66896C2211yescharacteristic
33(C2×D11)⋊C8C2212yes—
34#66881C2212yes—
35#66880C2212yes—
36#66874C2211yescharacteristic
37#66872C2211yescharacteristic
38#66872C2212yes—
39#66872C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C2×C22⋊D11—22no—
45#4339—44no—
46C2×D44D411yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C2×C4×D11C2312yes—
50C2×Dic22—21no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C4⋊C4C2311yescharacteristic
56C11×C22⋊C4—21no—
57C42×C11C2311yescharacteristic
58C22⋊Dic11—22no—
59#4324—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4D412yes—
62C4⋊Dic11—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2312yes—
66C4⋊Dic11C2311yescharacteristic
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—21no—
70C4×Dic11—21no—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73C8×D11—24no—
74#3335—111nomaximal, Sylow
75C23×C11—21no—
76C22×D11C2×D412yes—
77Q8×C11—81no—
78D4×C11—21no—
79D4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—42no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C22⋊D11—44no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11C2×D412yes—
91D44SD1614yescomplemented
92C4×D11—22no—
93C4×D11—22no—
94C4×D11—44no—
95C4×D11—82no—
96Dic22—21no—
97Dic22—21no—
98Dic22—42no—
99C8×C11—22no—
100C11⋊C8—21no—
101C11⋊C8#4112yescomplemented
102#554—111no—
103#547—111no—
104#498—111no—
105#483—112no—
106#481—112no—
107#476D1111yescharacteristic, complemented
108#475—111no—
109#465—112no—
110C4×SD16—111no—
111C8×D4—111no—
112C2×#106—112no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11C22×D411yescharacteristic
117C2×D11—22no—
118C2×D11—22no—
119C2×D11C2×SD1614yes—
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—42no—
123C4×C11C2×SD1612yes—
124C4×C11C2×#4111yescharacteristic
125C4×C112−1+411yescharacteristic
126Dic11—22no—
127Dic11—41no—
128Dic11—42no—
129Dic11—41no—
130C2×#41—221no—
131C2×SD16—111no—
132C22×C8—112no—
133C4⋊Q8—111no—
134C4⋊Q8C2×D1111yescharacteristic
135#125—221no—
136#123—222no—
137C22⋊Q8—112no—
138C22⋊Q8—222no—
139C22⋊Q8—221no—
140#121—112no—
141C4×Q8—111no—
142C4×D4—111no—
143C4×D4—221no—
144C4×D4C2×D1111yescharacteristic
145C2×C4⋊C4—112no—
146C2×C4⋊C4—112no—
147#106—112no—
148#106—111no—
149#106—112no—
150#106—112no—
151#106C2×D1112yes—
152C4⋊C8C2×D1111yescharacteristic
153#103—112no—
154#103—111no—
155#102—111no—
156#102C2×D1112yes—
157C22⋊C8—112no—
158C4×C8—111no—
159C2×C11—81no—
160C2×C11#54711yescharacteristic
161C2×C11C22×SD1611yescharacteristic
162C2×C11#57711yescharacteristic
163D11—24no—
164#41—444no—
165C2×Q8—21no—
166C2×Q8—111no—
167C2×Q8—221no—
168C2×D4—111no—
169C2×D4—222no—
170C2×D4C22×D1111yescharacteristic
171C22×C4—21no—
172C22×C4—112no—
173C22×C4—222no—
174C22×C4—222no—
175SD16—222no—
176C2×C8—111no—
177C2×C8—111no—
178C2×C8—224no—
179C2×C8C22×D1112yes—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—111no—
183C4⋊C4—112no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4C22×D1112yes—
190C4⋊C4C22×D1111yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—112no—
193C22⋊C4—222no—
194C22⋊C4—222no—
195C42—221no—
196C42C22×D1111yescharacteristic
197C11#333511yescharacteristic, complemented, Sylow
198C23—21no—
199C23—112no—
200Q8—81no—
201Q8—221no—
202Q8—221no—
203Q8—442no—
204D4—21no—
205D4—21no—
206D4—114no—
207D4—444no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—112no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4—444no—
218C2×C4—882no—
219C2×C4D4×D1111yescharacteristic
220C2×C4D4×D1111yescharacteristic
221C2×C4C23×D1111yescharacteristic
222C8—22no—
223C8—112no—
224C8—221no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—114no—
229C22—222no—
230C22—222no—
231C22C2×D4×D1111yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—222no—
236C4—442no—
237C4—441no—
238C4—441no—
239C4SD16×D1112yes—
240C4#6704011yescharacteristic
241C4#41×D1111yescharacteristic
242C2—81no—
243C2—224no—
244C2#1062316211yescharacteristic
245C2C2×SD16×D1111yescharacteristic
246C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#476C2
socleC22×C11C22×D4
prime radical#10623082C2
hypercenter#476D11
hypocenterC11#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10623261C2semidirect
3. C11×#476C2semidirect
4. #10622692C2semidirect
5. C4×#4324C2semidirect
6. #10622475C2semidirect
7. D11×#106C2semidirect
8. #10622464C2semidirect
9. #10622447C2semidirect
10. #10622391C2semidirect
11. #10622390C2semidirect
91. D44SD16semidirect
101. C11⋊C8#41semidirect
107. #476D11semidirect
197. C11#3335semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106230822
C11×#4762
#106226922
C4×#43242
#106224752
D11×#1062
#106224642
#106224472
#106223912
#106223902
#333511