Finite Group Databasebeta

← #13070162

Subgroups — #13070162

Order 1408.

238 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 85 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#10622590C211yesmaximal, characteristic
6C2×#66872C211yesmaximal, characteristic
7#10622188C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4×Dic11C2211yescharacteristic
14C22×C11⋊C8C2211yescharacteristic
15C11×#103—22no—
16#66899—22no—
17C11⋊#95—22no—
18C11⋊#95—22no—
19#66882—22no—
20#66872—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—
42C4×Dic11—21no—
43C4×Dic11—21no—
44C2×C11⋊C8—21no—
45C2×C11⋊C8—21no—
46C2×C11⋊C8D412yes—
47#2097—111nomaximal, Sylow
48C23×C11C2×D411yescharacteristic
49Q8×C11—22no—
50Q8×C11—22no—
51Q8×C11—41no—
52Q8×C11—41no—
53C2×C4×C11—22no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—42no—
58C2×C4×C11C2×D411yescharacteristic
59C2×C4×C11C2×D411yescharacteristic
60C2×C4×C11C2×Q811yescharacteristic
61C2×C4×C11#4111yescharacteristic
62C2×C4×C11#4111yescharacteristic
63C2×C4×C11#4111yescharacteristic
64C2×Dic11—22no—
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C2×Dic11—42no—
70C2×Dic11—42no—
71C8×C11—22no—
72C11⋊C8—22no—
73C2×#107—111no—
74C2×#106—111no—
75C2×#103—111no—
76C2×#103D1111yescharacteristic
77#391—111no—
78#382—111no—
79#336—111no—
80C22×C11C22⋊Q811yescharacteristic
81C22×C11#12311yescharacteristic
82C22×C11#12711yescharacteristic
83C22×C11#13512yes—
84C22×C11#13712yes—
85C4×C11—42no—
86C4×C11—81no—
87C4×C11C22⋊Q811yescharacteristic
88C4×C11C22⋊Q811yescharacteristic
89C4×C11#12311yescharacteristic
90C4×C11#12311yescharacteristic
91Dic11—42no—
92Dic11—81no—
93Dic11—81no—
94C22×Q8C2×D1111yescharacteristic
95C22×C8—111no—
96C22×C8C2×D1111yescharacteristic
97C2×C4⋊C4—111no—
98C2×C4⋊C4—111no—
99C2×C4⋊C4C2×D1111yescharacteristic
100C2×C42—111no—
101#107—222no—
102#106—222no—
103#103—22no—
104#103—222no—
105#95—222no—
106#95—222no—
107C2×C11#39911yescharacteristic
108C2×C11#47912yes—
109C2×C11#48512yes—
110C2×C11#49511yescharacteristic
111C2×C11#49711yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8Dic2212yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—112no—
121C22×C4—221no—
122C22×C4—221no—
123C22×C4C22×D1111yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—112no—
127C2×C8—221no—
128C2×C8—221no—
129C2×C8C22⋊D1112yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—221no—
133C4⋊C4—221no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C42—221no—
137C42—221no—
138C11#209711yescharacteristic, complemented, Sylow
139C23D4×D1111yescharacteristic
140Q8—22no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—222no—
150C2×C4—222no—
151C2×C4—222no—
152C2×C4—442no—
153C2×C4—442no—
154C2×C4—441no—
155C2×C4—441no—
156C2×C4C2×Dic2211yescharacteristic
157C2×C4#433911yescharacteristic
158C2×C4D4×D1111yescharacteristic
159C2×C4#434111yescharacteristic
160C2×C4#434111yescharacteristic
161C2×C4C2×C22⋊D1111yescharacteristic
162C8—22no—
163C8—222no—
164C22#6693111yescharacteristic
165C22#6693611yescharacteristic
166C22#6696812yes—
167C22#6697212yes—
168C22#6699311yescharacteristic
169C4—42no—
170C4—81no—
171C4—442no—
172C4—881no—
173C4—881no—
174C4#6693111yescharacteristic
175C4#6693611yescharacteristic
176C4#6697711yescharacteristic
177C4#6698811yescharacteristic
178C2#1062240912yes—
179C2#1062242712yes—
180C2#1062256211yescharacteristic
181C2#1062278011yescharacteristic
182C2#1062280411yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#103D11
hypocenterC11#2097
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
138. C11#2097semidirect

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
#106225902
C2×#668722
#106221882
#209711