Finite Group Databasebeta

← #13080082

Subgroups — #13080082

Order 1408.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#10623174C212yesmaximal, complemented
2C11×#470C211yesmaximal, characteristic, complemented
3#10622798C212yesmaximal, complemented
4#10622748C211yesmaximal, characteristic
5#10622732C211yesmaximal, characteristic, complemented
6#10622661C212yesmaximal, complemented
7#10622483C212yesmaximal, complemented
8#10622432C212yesmaximal, complemented
9#10622404C212yesmaximal, complemented
10C2×C11×Q16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C11×C22⋊Q8C2212yes—
13#67000C2212yes—
14Q8×Dic11C2212yes—
15C2×#4325C2212yes—
16#66983C2212yes—
17#66979C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C2×D88C2211yescharacteristic
20#66951—22no—
21#66950—22no—
22#66946C2212yes—
23#66941C2212yes—
24#66938—22no—
25#66936—22no—
26C11×#106C2211yescharacteristic
27C11×#103C2212yes—
28#66899C2212yes—
29#66885C2212yes—
30#66881C2211yescharacteristic
31Dic11⋊C8C2212yes—
32Dic11⋊C8C2212yes—
33#66873C2212yes—
34#66872C2212yes—
35C2×Q8×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×D44C2312yes—
39C2×C4×D11—22no—
40C2×Dic22—22no—
41C11×Q16—41no—
42C11×M16—41no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2311yescharacteristic
45C11×C4⋊C4—22no—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C22⋊Dic11D411yescharacteristic
49C22⋊Dic11D411yescharacteristic
50#4325—42no—
51(C2×D11)⋊C4—22no—
52(C2×D11)⋊C4—22no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11D412yes—
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59C4×Dic11—22no—
60C4×Dic11C2312yes—
61C2×C11⋊C8—41no—
62C2×C11⋊C8C2312yes—
63D88—41no—
64#3263—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67Q8×C11—22no—
68Q8×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2411yescharacteristic
75C22⋊D11—82no—
76C2×Dic11—22no—
77C2×Dic11C2×D412yes—
78C2×Dic11C2×D412yes—
79D44—22no—
80D44—22no—
81C4×D11—82no—
82Dic22—82no—
83C8×C11—21no—
84C8×C11—21no—
85C11⋊C8—22no—
86#542—112no—
87#476—112no—
88#475—112no—
89#470D1111yescharacteristic, complemented
90#469—111no—
91#465—112no—
92#464—112no—
93#463—112no—
94#424—111no—
95C22×C11—21no—
96C22×C11—22no—
97C22×C11C22×D411yescharacteristic
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—42no—
101C4×C11—21no—
102C4×C11—42no—
103C4×C11—42no—
104C4×C11H(5,𝔽2)11yescharacteristic
105C4×C112−1+411yescharacteristic
106Dic11—22no—
107Dic11—22no—
108Dic11—42no—
109C2×Q16C2×D1111yescharacteristic
110C2×SD16—112no—
111C2×D8—111no—
112C2×M16C2×D1111yescharacteristic
113C22×C8—111no—
114C4⋊Q8—112no—
115#126—222no—
116#124—112no—
117#124—222no—
118#123—222no—
119C22⋊Q8—222no—
120C22⋊Q8C2×D1112yes—
121#121—112no—
122C4×Q8—112no—
123C4×D4—112no—
124#117—111no—
125#106—111no—
126#106—112no—
127#106C2×D1111yescharacteristic
128C4⋊C8—112no—
129C4⋊C8—112no—
130#103—112no—
131#103C2×D1112yes—
132#102—112no—
133#102—112no—
134C2×C11—41no—
135C2×C11#53711yescharacteristic
136C2×C11#57712yes—
137D11—82no—
138C2×Q8—222no—
139C2×Q8C22×D1112yes—
140C2×D4—112no—
141C2×D4—222no—
142C22×C4—222no—
143C22×C4C22×D1111yescharacteristic
144Q16—41no—
145SD16—442no—
146D8—441no—
147M16—41no—
148C2×C8—112no—
149C2×C8—441no—
150C2×C8C22×D1111yescharacteristic
151C2×C8C22×D1111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—112no—
154C4⋊C4—112no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4C22×D1112yes—
158C22⋊C4—22no—
159C22⋊C4—111no—
160C22⋊C4—111no—
161C22⋊C4—222no—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C22⋊C4—222no—
165C42—112no—
166C42—222no—
167C11#326311yescharacteristic, complemented, Sylow
168C23—222no—
169C23D4×D1111yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—882no—
173D4—222no—
174D4—222no—
175D4—882no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—112no—
181C2×C4—112no—
182C2×C4—222no—
183C2×C4—882no—
184C2×C4D4×D1111yescharacteristic
185C2×C4C23×D1111yescharacteristic
186C8—21no—
187C8—21no—
188C8—222no—
189C22—22no—
190C22—21no—
191C22—442no—
192C22—442no—
193C22—442no—
194C22C2×D4×D1111yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—222no—
199C4—222no—
200C4—442no—
201C4#6703711yescharacteristic
202C4#6704311yescharacteristic
203C2—41no—
204C2—882no—
205C2#1062312811yescharacteristic
206C2#1062330912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
prime radical#10622748C2
hypercenter#470D11
hypocenterC11#3263
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #10623174C2semidirect
2. C11×#470C2semidirect
3. #10622798C2semidirect
5. #10622732C2semidirect
6. #10622661C2semidirect
7. #10622483C2semidirect
8. #10622432C2semidirect
9. #10622404C2semidirect
89. #470D11semidirect
167. C11#3263semidirect

Maximal subgroups

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

subgroupindex
#106231742
C11×#4702
#106227982
#106227482
#106227322
#106226612
#106224832
#106224322
#106224042
#326311