Finite Group Databasebeta

← #13079740

Subgroups — #13079740

Order 1408.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10623247C211yesmaximal, characteristic
3C11×#486C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5#10622683C211yesmaximal, characteristic, complemented
6#10622390C214yesmaximal, complemented
7#10622374C214yesmaximal, complemented
8#10622298C211yesmaximal, characteristic, complemented
9#10622293C211yesmaximal, characteristic, complemented
10C2×Q8×D11—21no—
11C2×#4341—21no—
12C11×C4⋊Q8C2211yescharacteristic
13C11×#127C2211yescharacteristic
14#66997—21no—
15#66991—21no—
16#66991C2212yes—
17#66989—21no—
18D4×Dic11—21no—
19D4×Dic11C2212yes—
20C4⋊C4×D11—21no—
21C4⋊C4×D11C2212yes—
22#66941—21no—
23#66941C2212yes—
24C42×D11C2211yescharacteristic
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C11×#102C2214yes—
28C4×C8×C11C2211yescharacteristic
29#66896C2214yes—
30(C2×D11)⋊C8C2212yes—
31#66881C2214yes—
32Dic11⋊C8C2212yes—
33#66872C2214yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C2×C22⋊D11—22no—
40C22×Dic11—22no—
41Q8×D11—44no—
42#4341—44no—
43C2×C4×D11—22no—
44C2×C4×D11D411yescharacteristic
45C2×C4×D11D411yescharacteristic
46C2×C4×D11C2311yescharacteristic
47C2×Dic22—22no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×C8×C11C2312yes—
51C11×C4⋊C4—21no—
52C11×C4⋊C4C2312yes—
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55C22⋊Dic11—22no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11D411yescharacteristic
63C4×Dic11D411yescharacteristic
64C4×Dic11C2311yescharacteristic
65C2×C11⋊C8C2312yes—
66#3227—111nomaximal, Sylow
67C23×C11—22no—
68C22×D11C2×D411yescharacteristic
69Q8×C11—42no—
70D4×C11—24no—
71D4×C11—42no—
72D4×C11—42no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2411yescharacteristic
77C22⋊D11—44no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—44no—
81C2×Dic11C2×D411yescharacteristic
82C2×Dic11C2×D411yescharacteristic
83C2×Dic11C2×D411yescharacteristic
84C4×D11—22no—
85C4×D11—22no—
86C4×D11—44no—
87C4×D11SD1614yes—
88Dic22—44no—
89Dic22—42no—
90Dic22—42no—
91C8×C11—22no—
92C11⋊C8—22no—
93#532—111no—
94C2×C4⋊Q8—111no—
95#498—111no—
96#498—111no—
97#486—111no—
98#486D1111yescharacteristic, complemented
99#481—114no—
100#476—114no—
101#431—111no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11C22×D411yescharacteristic
106C2×D11—21no—
107C2×D11—21no—
108C2×D11C2×SD1612yes—
109C4×C11—42no—
110C4×C11C2×SD1612yes—
111C4×C11AGL(1,ℤ/8)12yes—
112C4×C112−1+412yes—
113Dic11—21no—
114Dic11—21no—
115Dic11—42no—
116Dic11—42no—
117Dic11C2×SD1612yes—
118C2×#41—221no—
119C22×Q8—221no—
120C4⋊Q8—112no—
121C4⋊Q8—111no—
122C4⋊Q8—111no—
123C4⋊Q8—221no—
124C4⋊Q8—221no—
125C4⋊Q8C2×D1111yescharacteristic
126#127C2×D1111yescharacteristic
127#124—221no—
128#121—112no—
129#121—221no—
130C4×D4—112no—
131C4×D4—221no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—221no—
134C2×C42—111no—
135#106—114no—
136#106—114no—
137C4⋊C8—112no—
138#102—114no—
139#102C2×D1114yes—
140C22⋊C8—112no—
141C4×C8—111no—
142C4×C8C2×D1111yescharacteristic
143C2×C11—82no—
144C2×C11#53611yescharacteristic
145C2×C11C22×SD1611yescharacteristic
146C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
147D11—22no—
148#41—444no—
149C2×Q8—21no—
150C2×Q8—222no—
151C2×Q8—221no—
152C2×Q8—221no—
153C2×Q8—444no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—222no—
157C2×D4C22×D1112yes—
158C22×C4—111no—
159C22×C4—111no—
160C22×C4—111no—
161C22×C4—222no—
162C22×C4—222no—
163C2×C8—112no—
164C2×C8C22×D1112yes—
165C4⋊C4—21no—
166C4⋊C4—112no—
167C4⋊C4—112no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—221no—
171C4⋊C4—221no—
172C4⋊C4C22×D1112yes—
173C22⋊C4—222no—
174C22⋊C4—222no—
175C42—111no—
176C42—111no—
177C42—111no—
178C42C22×D1111yescharacteristic
179C11#322711yescharacteristic, complemented, Sylow
180C23—22no—
181C23—111no—
182Q8—42no—
183Q8—444no—
184Q8—442no—
185Q8—442no—
186D4—24no—
187D4—42no—
188D4—42no—
189D4—444no—
190C2×C4—22no—
191C2×C4—111no—
192C2×C4—114no—
193C2×C4—111no—
194C2×C4—111no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—444no—
200C2×C4—444no—
201C2×C4D4×D1111yescharacteristic
202C2×C4D4×D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—22no—
205C8—222no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—112no—
210C22—221no—
211C22—221no—
212C22C2×D4×D1111yescharacteristic
213C4—42no—
214C4—112no—
215C4—221no—
216C4—221no—
217C4—442no—
218C4—442no—
219C4#6696412yes—
220C4SD16×D1112yes—
221C4#6704312yes—
222C2—82no—
223C2—222no—
224C2#1062320611yescharacteristic
225C2C2×#6696411yescharacteristic
226C2C2×SD16×D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#486C2
socleC22×C11C22×D4
prime radical#10623247C2
hypercenter#486D11
hypocenterC11#3227
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. D11×C4⋊Q8C2semidirect
3. C11×#486C2semidirect
4. #10622692C2semidirect
5. #10622683C2semidirect
6. #10622390C2semidirect
7. #10622374C2semidirect
8. #10622298C2semidirect
9. #10622293C2semidirect
98. #486D11semidirect
179. C11#3227semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106232472
C11×#4862
#106226922
#106226832
#106223902
#106223742
#106222982
#106222932
#322711