Finite Group Databasebeta

← #13067660

Subgroups — #13067660

Order 1408.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#10623031C211yesmaximal, characteristic
2#10622599C211yesmaximal, characteristic
3#10622335C212yesmaximal
4C11×#324C211yesmaximal, characteristic
5#10622105C212yesmaximal
6C2×C11×C4⋊C4C2211yescharacteristic
7#66979—21no—
8C2×C4⋊Dic11C2211yescharacteristic
9#66977—21no—
10#66977C2212yes—
11#66943—22no—
12#66941—22no—
13C11×C22⋊C8C2212yes—
14C11⋊#95—21no—
15C11⋊#95—21no—
16C11⋊#95C2211yescharacteristic
17#66882—22no—
18#66880—22no—
19C22×C4×C11D411yescharacteristic
20C22×C4×C11D411yescharacteristic
21C22×C4×C11C2311yescharacteristic
22C22×Dic11—21no—
23C22×Dic11—21no—
24C2×Dic22—21no—
25C2×Dic22D412yes—
26C2×C8×C11—22no—
27C11×C4⋊C4—22no—
28C22⋊Dic11—22no—
29C4⋊Dic11—21no—
30C4⋊Dic11—21no—
31C4⋊Dic11—21no—
32C4⋊Dic11—22no—
33C4⋊Dic11D412yes—
34Dic11⋊C4—22no—
35Dic11⋊C4—22no—
36C4×Dic11—22no—
37#1617—111nomaximal, Sylow
38C23×C11C2×D411yescharacteristic
39C2×C4×C11—21no—
40C2×C4×C11—21no—
41C2×C4×C11—21no—
42C2×C4×C11—41no—
43C2×C4×C11—41no—
44C2×C4×C11Q1612yes—
45C2×C4×C11C2×D412yes—
46C2×Dic11—22no—
47C2×Dic11—22no—
48C2×Dic11—41no—
49C2×Dic11—41no—
50C2×Dic11—42no—
51C2×Dic11—41no—
52C2×Dic11—41no—
53Dic22—42no—
54Dic22—81no—
55C8×C11—42no—
56#544—111no—
57#484—112no—
58#400—111no—
59#328—112no—
60#324D1111yescharacteristic
61C22×C11—21no—
62C22×C11—21no—
63C22×C11#12011yescharacteristic
64C22×C11C2×Q1611yescharacteristic
65C22×C11#13711yescharacteristic
66C4×C11—22no—
67C4×C11—22no—
68C4×C11—41no—
69Dic11—42no—
70Dic11—42no—
71Dic11—81no—
72Dic11—81no—
73C4⋊Q8—222no—
74#125—222no—
75C22⋊Q8—112no—
76C22⋊Q8—221no—
77#117—221no—
78C2×C4⋊C4—111no—
79C2×C4⋊C4C2×D1111yescharacteristic
80#107—222no—
81#103—222no—
82C22⋊C8C2×D1112yes—
83#95—111no—
84#95—221no—
85#95—221no—
86C2×C11—21no—
87C2×C11—21no—
88C2×C11#45111yescharacteristic
89C2×C11#45411yescharacteristic
90C2×C11#45811yescharacteristic
91C2×Q8—112no—
92C2×Q8—221no—
93C22×C4—221no—
94C22×C4—221no—
95C22×C4D4411yescharacteristic
96C22×C4D4411yescharacteristic
97C22×C4C22×D1111yescharacteristic
98C2×C8—22no—
99C4⋊C4—22no—
100C4⋊C4—112no—
101C4⋊C4—221no—
102C4⋊C4—221no—
103C4⋊C4—221no—
104C4⋊C4—222no—
105C4⋊C4—222no—
106C4⋊C4—222no—
107C22⋊C4—222no—
108C42—222no—
109C11#161711yescharacteristic, complemented, Sylow
110C23C2×D4411yescharacteristic
111Q8—442no—
112Q8—881no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—222no—
119C2×C4—222no—
120C2×C4—441no—
121C2×C4—441no—
122C2×C4—442no—
123C2×C4—441no—
124C2×C4—441no—
125C2×C4Dic4412yes—
126C2×C4D4×D1112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#6693511yescharacteristic
131C22C2×Dic4411yescharacteristic
132C22#6696211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—442no—
137C4—442no—
138C4—881no—
139C4—881no—
140C2—21no—
141C2—21no—
142C2#1062235211yescharacteristic
143C2#1062235511yescharacteristic
144C2#1062236611yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#324C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#324D11
hypocenterC11#1617
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
109. C11#1617semidirect

Maximal subgroups

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

subgroupindex
#106230312
#106225992
#106223352
C11×#3242
#106221052
#161711