Finite Group Databasebeta

← #13067639

Subgroups — #13067639

Order 1408.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#10623165C211yesmaximal, characteristic
2C11×#484C211yesmaximal, characteristic, complemented
3#10622605C211yesmaximal, characteristic
4#10622583C211yesmaximal, characteristic, complemented
5#10622176C211yesmaximal, characteristic, complemented
6#10622106C211yesmaximal, characteristic
7#10622105C211yesmaximal, characteristic, complemented
8C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10#66999—21no—
11C2×(C2×D11)⋊C4—21no—
12C2×(C2×D11)⋊C4C2211yescharacteristic
13#66977C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15#66950—21no—
16#66949—21no—
17#66949—21no—
18C22⋊C4×D11—21no—
19#66931—21no—
20C11×#107—21no—
21C11×#103—21no—
22C11×C22⋊C8C2211yescharacteristic
23C11⋊#95C2211yescharacteristic
24C22⋊(C11⋊C8)C2211yescharacteristic
25#66874—21no—
26#66871—21no—
27C23×D11D411yescharacteristic
28C2×Q8×C11D411yescharacteristic
29C22×C4×C11—21no—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C22×Dic11D411yescharacteristic
33C2×C4×D11—21no—
34C2×C4×D11—21no—
35C2×Dic22—21no—
36C2×Dic22D411yescharacteristic
37C2×C8×C11—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C11×C4⋊C4D411yescharacteristic
42C11×C22⋊C4—21no—
43C22⋊Dic11—21no—
44(C2×D11)⋊C4—21no—
45(C2×D11)⋊C4—21no—
46(C2×D11)⋊C4—21no—
47(C2×D11)⋊C4—21no—
48(C2×D11)⋊C4—42no—
49C4⋊Dic11—21no—
50C4⋊Dic11D411yescharacteristic
51Dic11⋊C4—21no—
52Dic11⋊C4—21no—
53Dic11⋊C4—21no—
54Dic11⋊C4—42no—
55C2×C11⋊C8—21no—
56#1614—111nomaximal, Sylow
57C23×C11C2×D411yescharacteristic
58C22×D11—21no—
59C22×D11—21no—
60C22×D11—41no—
61C22×D11—41no—
62C22×D11Q1612yes—
63Q8×C11—41no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×Dic11—22no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C4×D11—81no—
80C4×D11—81no—
81Dic22—41no—
82Dic22—81no—
83C8×C11—41no—
84C11⋊C8—41no—
85#543—111no—
86#484—111no—
87#484D1111yescharacteristic, complemented
88#399—111no—
89#328—111no—
90#328—111no—
91#323—111no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11#12011yescharacteristic
95C22×C11C2×Q1611yescharacteristic
96C22×C11#13711yescharacteristic
97C2×D11—22no—
98C2×D11—41no—
99C2×D11—41no—
100C2×D11—42no—
101C2×D11—81no—
102C4×C11—21no—
103C4×C11—21no—
104C4×C11—41no—
105C4×C11—41no—
106C4×C11—81no—
107Dic11—42no—
108Dic11—41no—
109Dic11—41no—
110Dic11—41no—
111C22⋊Q8—111no—
112C22⋊Q8—221no—
113C22⋊Q8—221no—
114C22⋊Q8—221no—
115C22⋊Q8—221no—
116C22⋊Q8—221no—
117C22⋊Q8C2×D1111yescharacteristic
118C2×C4⋊C4—221no—
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C22⋊C4—111no—
121C2×C22⋊C4—221no—
122C2×C22⋊C4—221no—
123#107—21no—
124#107—221no—
125#103—21no—
126#103—221no—
127C22⋊C8—111no—
128C22⋊C8C2×D1111yescharacteristic
129#95—111no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11#45111yescharacteristic
133C2×C11#45311yescharacteristic
134C2×C11#45811yescharacteristic
135D11—42no—
136C24—111no—
137C2×Q8—111no—
138C2×Q8—221no—
139C2×Q8C22⋊D1111yescharacteristic
140C22×C4—21no—
141C22×C4—111no—
142C22×C4—221no—
143C22×C4—221no—
144C22×C4—221no—
145C22×C4C22×D1111yescharacteristic
146C2×C8—21no—
147C2×C8—221no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—111no—
152C4⋊C4—221no—
153C4⋊C4—221no—
154C4⋊C4—221no—
155C4⋊C4—221no—
156C4⋊C4—442no—
157C4⋊C4C22⋊D1111yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—221no—
160C22⋊C4—221no—
161C22⋊C4—221no—
162C22⋊C4—221no—
163C22⋊C4—221no—
164C22⋊C4—442no—
165C11#161411yescharacteristic, complemented, Sylow
166C23—112no—
167C23—221no—
168C23—221no—
169C23—441no—
170C23—441no—
171C23D4×D1111yescharacteristic
172Q8—41no—
173Q8—441no—
174Q8—881no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—222no—
182C2×C4—221no—
183C2×C4—221no—
184C2×C4—221no—
185C2×C4—441no—
186C2×C4—441no—
187C2×C4—441no—
188C2×C4—881no—
189C2×C4—881no—
190C2×C4D4×D1111yescharacteristic
191C2×C4C2×C22⋊D1111yescharacteristic
192C8—41no—
193C8—441no—
194C22—21no—
195C22—21no—
196C22—222no—
197C22—442no—
198C22—441no—
199C22—441no—
200C22—881no—
201C22Q16×D1111yescharacteristic
202C22#6697111yescharacteristic
203C22#6699011yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C4—81no—
209C4—442no—
210C4—441no—
211C4—441no—
212C4—441no—
213C2—21no—
214C2—21no—
215C2—442no—
216C2#1062266611yescharacteristic
217C2#1062279911yescharacteristic
218C2#1062281111yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#484C2
socleC22×C11#120
prime radicalC23×D11D4
hypercenter#484D11
hypocenterC11#1614
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C11×#484C2semidirect
4. #10622583C2semidirect
5. #10622176C2semidirect
7. #10622105C2semidirect
87. #484D11semidirect
165. C11#1614semidirect

Maximal subgroups

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

subgroupindex
#106231652
C11×#4842
#106226052
#106225832
#106221762
#106221062
#106221052
#161411