Finite Group Databasebeta

← #13067641

Subgroups — #13067641

Order 1408.

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

normal subgroups only

This group has 236 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
2#10622657C212yesmaximal, complemented
3#10622562C211yesmaximal, characteristic
4#10622176C212yesmaximal, complemented
5#10622163C211yesmaximal, characteristic
6C11×C22⋊Q8—22no—
7C11×C22⋊Q8—21no—
8C11×C22⋊Q8—22no—
9C11×C22⋊Q8C2212yes—
10C2×C11×C22⋊C4—21no—
11C2×C11×C22⋊C4C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15#66899—22no—
16C11⋊#95C2211yescharacteristic
17C22⋊(C11⋊C8)C2212yes—
18#66871—22no—
19C24×C11D411yescharacteristic
20C2×Q8×C11—21no—
21C2×Q8×C11D412yes—
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11D411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C22×Dic11—21no—
27C22×Dic11—21no—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—22no—
30C11×C4⋊C4—22no—
31C11×C4⋊C4D412yes—
32C11×C22⋊C4—22no—
33C11×C22⋊C4—22no—
34C11×C22⋊C4—22no—
35C22⋊Dic11—42no—
36C4⋊Dic11—22no—
37Dic11⋊C4—42no—
38C2×C11⋊C8—22no—
39#1614—111nomaximal, Sylow
40C23×C11—21no—
41C23×C11—21no—
42C23×C11—41no—
43C23×C11—41no—
44C23×C11Q1612yes—
45C23×C11C2×D411yescharacteristic
46Q8×C11—42no—
47Q8×C11—81no—
48C2×C4×C11—22no—
49C2×C4×C11—21no—
50C2×C4×C11—22no—
51C2×C4×C11—41no—
52C2×C4×C11—41no—
53C2×C4×C11—81no—
54C2×C4×C11—81no—
55C2×C4×C11C2×D412yes—
56C2×Dic11—22no—
57C2×Dic11—41no—
58C2×Dic11—41no—
59C2×Dic11—41no—
60C2×Dic11—41no—
61C2×Dic11—41no—
62C11⋊C8—42no—
63#543D1111yescharacteristic
64#484—112no—
65#399—111no—
66#328—112no—
67#323—111no—
68C22×C11—21no—
69C22×C11—21no—
70C22×C11—22no—
71C22×C11—42no—
72C22×C11—41no—
73C22×C11—41no—
74C22×C11—81no—
75C22×C11#12011yescharacteristic
76C22×C11C2×Q1611yescharacteristic
77C22×C11#13711yescharacteristic
78C4×C11—22no—
79C4×C11—41no—
80C4×C11—42no—
81C4×C11—42no—
82Dic11—42no—
83Dic11—81no—
84C22⋊Q8—22no—
85C22⋊Q8—21no—
86C22⋊Q8—22no—
87C22⋊Q8C2×D1112yes—
88C2×C4⋊C4—111no—
89C2×C4⋊C4—221no—
90C2×C22⋊C4—21no—
91C2×C22⋊C4—221no—
92C2×C22⋊C4C2×D1111yescharacteristic
93#107—222no—
94#103—222no—
95C22⋊C8—112no—
96#95—111no—
97C2×C11—21no—
98C2×C11—21no—
99C2×C11—42no—
100C2×C11#45111yescharacteristic
101C2×C11#45311yescharacteristic
102C2×C11#45811yescharacteristic
103C24C22⋊D1111yescharacteristic
104C2×Q8—21no—
105C2×Q8C22⋊D1112yes—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—221no—
109C22×C4—221no—
110C22×C4C22⋊D1111yescharacteristic
111C22×C4C22×D1111yescharacteristic
112C2×C8—222no—
113C4⋊C4—21no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—222no—
117C4⋊C4—442no—
118C4⋊C4C22⋊D1112yes—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—442no—
123C11#161411yescharacteristic, complemented, Sylow
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#432612yes—
129C23C2×C22⋊D1111yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—222no—
140C2×C4—441no—
141C2×C4—441no—
142C2×C4—441no—
143C2×C4—441no—
144C2×C4—441no—
145C2×C4C2×C22⋊D1112yes—
146C8—442no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#6699511yescharacteristic
155C22C2×#432611yescharacteristic
156C22#6700611yescharacteristic
157C4—22no—
158C4—41no—
159C4—42no—
160C4—42no—
161C4—442no—
162C4—881no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1062284111yescharacteristic
167C2#1062285411yescharacteristic
168C2#1062285611yescharacteristic
subgroupG/H
centerC22#67006
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#543C2
socleC22×C11#120
prime radicalC24×C11D4
hypercenter#543D11
hypocenterC11#1614
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
2. #10622657C2semidirect
4. #10622176C2semidirect
123. C11#1614semidirect

Maximal subgroups

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

subgroupindex
C11×#5432
#106226572
#106225622
#106221762
#106221632
#161411