Finite Group Databasebeta

← #13070152

Subgroups — #13070152

Order 1408.

254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×C11×#103C211yesmaximal, characteristic
2#10622843C211yesmaximal, characteristic
3C2×#66899C211yesmaximal, characteristic
4C2×#66882C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic
6C2×#66871C211yesmaximal, characteristic
7#10622188C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×Dic11⋊C4—22no—
14C2×C4×Dic11C2211yescharacteristic
15C22×C11⋊C8C2211yescharacteristic
16C11×#103—22no—
17#66899—22no—
18C11⋊#95—22no—
19#66882—22no—
20#66871—22no—
21C2×Q8×C11—21no—
22C2×Q8×C11—21no—
23C2×Q8×C11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11Q812yes—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11C2311yescharacteristic
30C22×Dic11—21no—
31C22×Dic11—21no—
32C22×Dic11D412yes—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11D412yes—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C4⋊Dic11—21no—
39C4⋊Dic11—21no—
40C4⋊Dic11—21no—
41C4⋊Dic11—21no—
42Dic11⋊C4—44no—
43C4×Dic11—21no—
44C4×Dic11—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8D412yes—
48#2095—111nomaximal, Sylow
49C23×C11C2×D411yescharacteristic
50Q8×C11—22no—
51Q8×C11—22no—
52Q8×C11—41no—
53Q8×C11—41no—
54C2×C4×C11—22no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11—42no—
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11C2×Q811yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×C4×C11#4111yescharacteristic
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C2×Dic11—42no—
70C2×Dic11—42no—
71C2×Dic11Q1614yes—
72C8×C11—22no—
73C11⋊C8—22no—
74C2×#107—111no—
75C2×#107—111no—
76C2×#103—111no—
77C2×#103D1111yescharacteristic
78#391—111no—
79#384—111no—
80#336—111no—
81C22×C11C22⋊Q811yescharacteristic
82C22×C11#12311yescharacteristic
83C22×C11#12711yescharacteristic
84C22×C11C2×Q1612yes—
85C22×C11AGL(1,ℤ/8)12yes—
86C4×C11—42no—
87C4×C11—81no—
88C4×C11C22⋊Q811yescharacteristic
89C4×C11C22⋊Q811yescharacteristic
90C4×C11#12311yescharacteristic
91C4×C11#12311yescharacteristic
92Dic11—24no—
93Dic11—81no—
94Dic11—81no—
95C22×Q8C2×D1111yescharacteristic
96C22×C8—111no—
97C22×C8C2×D1111yescharacteristic
98C2×C4⋊C4—111no—
99C2×C4⋊C4—111no—
100C2×C4⋊C4—222no—
101C2×C4⋊C4C2×D1111yescharacteristic
102C2×C42—111no—
103#107—222no—
104#107—222no—
105#103—22no—
106#103—222no—
107#95—222no—
108C2×C11#39911yescharacteristic
109C2×C11#47712yes—
110C2×C11#48412yes—
111C2×C11#49411yescharacteristic
112C2×C11#49611yescharacteristic
113C2×Q8—21no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8Dic2212yes—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—112no—
122C22×C4—221no—
123C22×C4—221no—
124C22×C4C22×D1111yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—112no—
128C2×C8—221no—
129C2×C8—221no—
130C2×C8C22⋊D1112yes—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—221no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C4⋊C4—221no—
137C4⋊C4—444no—
138C42—221no—
139C42—221no—
140C11#209511yescharacteristic, complemented, Sylow
141C23D4×D1111yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—114no—
152C2×C4—222no—
153C2×C4—222no—
154C2×C4—442no—
155C2×C4—442no—
156C2×C4—441no—
157C2×C4—441no—
158C2×C4C2×Dic2211yescharacteristic
159C2×C4#433911yescharacteristic
160C2×C4D4×D1111yescharacteristic
161C2×C4#434111yescharacteristic
162C2×C4#434111yescharacteristic
163C2×C4C2×C22⋊D1111yescharacteristic
164C8—22no—
165C8—222no—
166C22#6693111yescharacteristic
167C22#6693611yescharacteristic
168C22#6696712yes—
169C22Q16×D1112yes—
170C22#6699311yescharacteristic
171C4—42no—
172C4—81no—
173C4—224no—
174C4—881no—
175C4—881no—
176C4#6693111yescharacteristic
177C4#6693611yescharacteristic
178C4#6697711yescharacteristic
179C4#6698811yescharacteristic
180C2#1062240712yes—
181C2#1062242212yes—
182C2#1062256211yescharacteristic
183C2#1062278911yescharacteristic
184C2#1062279411yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#103D11
hypocenterC11#2095
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
140. C11#2095semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1032
#106228432
C2×#668992
C2×#668822
#106225892
C2×#668712
#106221882
#209511