Finite Group Databasebeta

← #13079013

Subgroups — #13079013

Order 1408.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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×#125C211yesmaximal, characteristic, complemented
2#10623199C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622681C211yesmaximal, characteristic, complemented
5#10622669C211yesmaximal, characteristic, complemented
6#10622416C212yesmaximal, complemented
7#10622410C212yesmaximal, complemented
8#10622384C212yesmaximal, complemented
9#10622377C212yesmaximal, complemented
10#10622310C211yesmaximal, characteristic, complemented
11C4×#4313C211yesmaximal, characteristic, complemented
12C2×#4343C2211yescharacteristic
13C2×#4341C2211yescharacteristic
14C11×#125C2211yescharacteristic
15C11×#124C2211yescharacteristic
16#66997C2211yescharacteristic
17#66993C2211yescharacteristic
18C2×#4313C2212yes—
19C4⋊C4×D11—22no—
20C4⋊C4×D11C2212yes—
21#66943C2212yes—
22#66942—22no—
23#66937—22no—
24(C22⋊D11)⋊C4—22no—
25#66928C2211yescharacteristic
26C42×D11C2211yescharacteristic
27#66923C2211yescharacteristic
28C11×#103C2212yes—
29C11×#102C2212yes—
30C4×C8×C11C2211yescharacteristic
31#66899C2212yes—
32#66896C2212yes—
33#66885C2212yes—
34#66880C2212yes—
35#66879C2212yes—
36#66874C2212yes—
37#66873C2212yes—
38C4×C11⋊C8C2211yescharacteristic
39C2×Q8×C11C2311yescharacteristic
40C2×D4×C11C2311yescharacteristic
41C2×C22⋊D11—22no—
42C2×C22⋊D11—21no—
43C22×Dic11—21no—
44#4343—24no—
45#4341—24no—
46C2×D44—21no—
47C2×D44C2311yescharacteristic
48C2×C4×D11—21no—
49C2×C4×D11—22no—
50C2×C4×D11D412yes—
51C2×C4×D11C2311yescharacteristic
52C2×Dic22C2311yescharacteristic
53C2×C8×C11C2312yes—
54C11×C4⋊C4—22no—
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—22no—
57C42×C11C2311yescharacteristic
58(C2×D11)⋊C4—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65C4×Dic11D412yes—
66C4×Dic11C2311yescharacteristic
67C2×C11⋊C8C2312yes—
68#4313—24no—
69#3142—111nomaximal, Sylow
70C23×C11—21no—
71C22×D11—21no—
72C22×D11C2×D411yescharacteristic
73Q8×C11—22no—
74D4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—44no—
80C22⋊D11—42no—
81C2×Dic11—22no—
82C2×Dic11—21no—
83C2×Dic11—42no—
84C2×Dic11C2×D412yes—
85C2×Dic11C2×D411yescharacteristic
86D44—22no—
87D44—42no—
88C4×D11—42no—
89C4×D11—44no—
90C4×D11—42no—
91C4×D11#4114yes—
92Dic22—22no—
93C8×C11—22no—
94C11⋊C8—22no—
95#532—111no—
96C2×#125—111no—
97#491—112no—
98#490—112no—
99#488—111no—
100#488—111no—
101#488—111no—
102#488D1111yescharacteristic, complemented
103#417—112no—
104#417—112no—
105C4×M16—111no—
106C22×C11—41no—
107C22×C11—42no—
108C22×C11C22×D411yescharacteristic
109C2×D11—22no—
110C2×D11—41no—
111C2×D11—42no—
112C2×D11#12412yes—
113C4×C11—22no—
114C4×C11—41no—
115C4×C11—42no—
116C4×C11C2×#4112yes—
117Dic11—22no—
118Dic11—41no—
119Dic11—42no—
120Dic11#12412yes—
121C2×#41—111no—
122C2×#41—111no—
123C2×M16—112no—
124C4⋊Q8—111no—
125#127—111no—
126#125—112no—
127#125—111no—
128#125—222no—
129#125C2×D1111yescharacteristic
130#124—111no—
131#124C2×D1111yescharacteristic
132#121—222no—
133C4×D4—222no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—222no—
136C2×C42—111no—
137#103—112no—
138#103—112no—
139#103—112no—
140#103C2×D1112yes—
141#102—112no—
142#102—112no—
143#102—112no—
144#102C2×D1112yes—
145#97—112no—
146C4×C8—111no—
147C4×C8C2×D1111yescharacteristic
148C2×C11—81no—
149C2×C11C2×#12411yescharacteristic
150C2×C11#57512yes—
151D11—22no—
152D11—81no—
153#41—224no—
154#41—224no—
155C2×Q8—111no—
156C2×Q8C22×D1111yescharacteristic
157C2×D4—111no—
158C2×D4—221no—
159C2×D4—222no—
160C2×D4—221no—
161C2×D4C22×D1111yescharacteristic
162C22×C4—111no—
163C22×C4—112no—
164C22×C4—221no—
165C22×C4—222no—
166C22×C4—221no—
167M16—224no—
168C2×C8—112no—
169C2×C8C22×D1112yes—
170C4⋊C4—22no—
171C4⋊C4—112no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4C22×D1112yes—
178C22⋊C4—22no—
179C22⋊C4—222no—
180C42—112no—
181C42—111no—
182C42C22×D1111yescharacteristic
183C11#314211yescharacteristic, complemented, Sylow
184C23—21no—
185C23—111no—
186C23—221no—
187Q8—22no—
188Q8—222no—
189D4—22no—
190D4—222no—
191D4—442no—
192D4—444no—
193D4—442no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—111no—
197C2×C4—114no—
198C2×C4—112no—
199C2×C4—221no—
200C2×C4—222no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—444no—
204C2×C4—442no—
205C2×C4D4×D1112yes—
206C2×C4C23×D1111yescharacteristic
207C8—22no—
208C8—222no—
209C22—42no—
210C22—41no—
211C22—112no—
212C22—222no—
213C22—442no—
214C22—441no—
215C22C2×D4×D1111yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—112no—
220C4—222no—
221C4—442no—
222C4—441no—
223C4#41×D1112yes—
224C2—81no—
225C2—222no—
226C2—881no—
227C2D11×#12411yescharacteristic
228C2#1062329912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radical#10623199C2
hypercenter#488D11
hypocenterC11#3142
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. D11×#125C2semidirect
3. C11×#488C2semidirect
4. #10622681C2semidirect
5. #10622669C2semidirect
6. #10622416C2semidirect
7. #10622410C2semidirect
8. #10622384C2semidirect
9. #10622377C2semidirect
10. #10622310C2semidirect
11. C4×#4313C2semidirect
102. #488D11semidirect
183. C11#3142semidirect

Maximal subgroups

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

subgroupindex
D11×#1252
#106231992
C11×#4882
#106226812
#106226692
#106224162
#106224102
#106223842
#106223772
#106223102
C4×#43132
#314211