Finite Group Databasebeta

← #13067539

Subgroups — #13067539

Order 1408.

316 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C11×#543C211yesmaximal, characteristic, complemented
2#10622659C212yesmaximal, complemented
3#10622573C211yesmaximal, characteristic
4#10622176C212yesmaximal, complemented
5#10622163C211yesmaximal, characteristic, complemented
6C22×C22⋊D11—21no—
7C22×D44C2211yescharacteristic
8C11×C22⋊Q8—22no—
9C11×C22⋊Q8—21no—
10C11×C22⋊Q8—22no—
11C11×C22⋊Q8C2212yes—
12C2×C11×C22⋊C4—21no—
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×#4325—22no—
15C2×(C2×D11)⋊C4—21no—
16C11⋊#95C2211yescharacteristic
17C22⋊(C11⋊C8)C2212yes—
18#66873—22no—
19C24×C11D411yescharacteristic
20C23×D11—21no—
21C2×Q8×C11—21no—
22C2×Q8×C11D412yescomplemented
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11D411yescharacteristic
26C22×C4×C11C2311yescharacteristic
27C2×C22⋊D11—42no—
28C2×C22⋊D11—42no—
29C2×C22⋊D11—42no—
30C22×Dic11—21no—
31C2×D44—22no—
32C2×D44—42no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—22no—
35C11×C4⋊C4—22no—
36C11×C4⋊C4D412yescomplemented
37C11×C22⋊C4—22no—
38C11×C22⋊C4—22no—
39C11×C22⋊C4—22no—
40#4325—44no—
41(C2×D11)⋊C4—42no—
42C2×C11⋊C8—22no—
43#1596—111nomaximal, Sylow
44C23×C11—21no—
45C23×C11—21no—
46C23×C11—41no—
47C23×C11—41no—
48C23×C11SD1612yescomplemented
49C23×C11C2×D411yescharacteristic
50C22×D11—22no—
51C22×D11—41no—
52C22×D11—41no—
53C22×D11—41no—
54C22×D11—41no—
55C22×D11—41no—
56C22×D11—41no—
57Q8×C11—42no—
58Q8×C11—81no—
59C2×C4×C11—22no—
60C2×C4×C11—21no—
61C2×C4×C11—22no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—81no—
65C2×C4×C11—81no—
66C2×C4×C11C2×D412yes—
67C22⋊D11—48no—
68C2×Dic11—22no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71D44—24no—
72D44—42no—
73C11⋊C8—42no—
74#543D1111yescharacteristic, complemented
75#450—112no—
76#392—111no—
77#328—112no—
78#323—111no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11—22no—
82C22×C11—42no—
83C22×C11—41no—
84C22×C11—41no—
85C22×C11—81no—
86C22×C11#12011yescharacteristic
87C22×C11C2×SD1611yescharacteristic
88C22×C11#13711yescharacteristic
89C2×D11—42no—
90C2×D11—42no—
91C2×D11—42no—
92C2×D11—81no—
93C2×D11—81no—
94C2×D11—81no—
95C2×D11—81no—
96C4×C11—22no—
97C4×C11—41no—
98C4×C11—42no—
99C4×C11—42no—
100Dic11—42no—
101C22×D4—111no—
102C22×D4—221no—
103C2×SD16—222no—
104C22⋊Q8—22no—
105C22⋊Q8—21no—
106C22⋊Q8—22no—
107C22⋊Q8C2×D1112yes—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—221no—
110C2×C22⋊C4C2×D1111yescharacteristic
111#102—222no—
112C22⋊C8—112no—
113#95—111no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11—42no—
117C2×C11#44811yescharacteristic
118C2×C11#45311yescharacteristic
119C2×C11B(4,𝔽2)11yescharacteristic
120D11—82no—
121C24—221no—
122C24C22⋊D1111yescharacteristic
123C2×Q8—21no—
124C2×Q8C22⋊D1112yescomplemented
125C2×D4—222no—
126C2×D4—442no—
127C2×D4—442no—
128C2×D4—442no—
129C2×D4—442no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—221no—
133C22×C4C22⋊D1111yescharacteristic
134C22×C4C22×D1111yescharacteristic
135SD16—444no—
136C2×C8—222no—
137C4⋊C4—21no—
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4C22⋊D1112yescomplemented
141C22⋊C4—22no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—442no—
145C11#159611yescharacteristic, complemented, Sylow
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—222no—
151C23—441no—
152C23—441no—
153C23—441no—
154C23—441no—
155C23—441no—
156C23—441no—
157C23#432512yescomplemented
158C23C2×C22⋊D1111yescharacteristic
159Q8—42no—
160Q8—81no—
161D4—224no—
162D4—442no—
163D4—448no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—222no—
172C2×C4—441no—
173C2×C4—441no—
174C2×C4C2×C22⋊D1112yes—
175C8—442no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—442no—
184C22—442no—
185C22—442no—
186C22—881no—
187C22—881no—
188C22—881no—
189C22—881no—
190C22C2×#432511yescharacteristic
191C22#6699511yescharacteristic
192C22#6700611yescharacteristic
193C4—22no—
194C4—41no—
195C4—42no—
196C4—42no—
197C4—442no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—882no—
202C2#1062284011yescharacteristic
203C2#1062285411yescharacteristic
204C2#1062285711yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#543C2
socleC22×C11#120
prime radical#10622573C2
hypercenter#543D11
hypocenterC11#1596
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. C11×#543C2semidirect
2. #10622659C2semidirect
4. #10622176C2semidirect
5. #10622163C2semidirect
22. C2×Q8×C11D4semidirect
36. C11×C4⋊C4D4semidirect
48. C23×C11SD16semidirect
74. #543D11semidirect
124. C2×Q8C22⋊D11semidirect
140. C4⋊C4C22⋊D11semidirect
145. C11#1596semidirect
157. C23#4325semidirect

Maximal subgroups

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

subgroupindex
C11×#5432
#106226592
#106225732
#106221762
#106221632
#159611