Finite Group Databasebeta

← #13067775

Subgroups — #13067775

Order 1408.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#10623252C211yesmaximal, characteristic
2#10622706C211yesmaximal, characteristic
3#10622463C211yesmaximal, characteristic
4#10622463C211yesmaximal, characteristic
5C11×#332C211yesmaximal, characteristic
6#10622122C211yesmaximal, characteristic
7#10622122C211yesmaximal, characteristic
8C11×C4⋊Q8C2211yescharacteristic
9Q8×Dic11—21no—
10#66997—21no—
11#66943—21no—
12#66942—22no—
13#66940—21no—
14#66922C2211yescharacteristic
15C4×Dic22C2211yescharacteristic
16C4×Dic22C2211yescharacteristic
17C11×C4⋊C8C2211yescharacteristic
18C11×C4⋊C8C2211yescharacteristic
19#66882—21no—
20#66882—21no—
21#66880—21no—
22#66880—21no—
23#66874—22no—
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×Dic22—21no—
27C2×Dic22D411yescharacteristic
28C2×Dic22D411yescharacteristic
29C2×C8×C11—21no—
30C2×C8×C11—21no—
31C11×C4⋊C4—21no—
32C11×C4⋊C4D412yes—
33C42×C11C2311yescharacteristic
34C4⋊Dic11—22no—
35C4⋊Dic11—21no—
36C4⋊Dic11—21no—
37C4⋊Dic11D411yescharacteristic
38C4⋊Dic11D411yescharacteristic
39Dic11⋊C4—22no—
40Dic11⋊C4—22no—
41Dic11⋊C4—21no—
42Dic11⋊C4—21no—
43C4×Dic11—22no—
44C4×Dic11—21no—
45C4×Dic11—21no—
46C2×C11⋊C8—21no—
47#1636—111nomaximal, Sylow
48Q8×C11—41no—
49Q8×C11—41no—
50C2×C4×C11—22no—
51C2×C4×C11C2×D411yescharacteristic
52C2×C4×C11C2×D411yescharacteristic
53C2×C4×C11C2×D411yescharacteristic
54C2×Dic11—21no—
55C2×Dic11—21no—
56C2×Dic11—21no—
57C2×Dic11—21no—
58C2×Dic11—41no—
59Dic22—21no—
60Dic22—21no—
61Dic22—21no—
62Dic22—42no—
63Dic22Q1612yes—
64C8×C11—41no—
65C8×C11—41no—
66C11⋊C8—41no—
67#557—111no—
68#487—111no—
69#477—111no—
70#477—111no—
71#332D1111yescharacteristic
72Q8⋊C8—111no—
73Q8⋊C8—111no—
74C22×C11#12011yescharacteristic
75C4×C11—21no—
76C4×C11—42no—
77C4×C11C2×Q1611yescharacteristic
78C4×C11#13511yescharacteristic
79C4×C11#13711yescharacteristic
80C4×C11#13711yescharacteristic
81Dic11—22no—
82Dic11—41no—
83Dic11—41no—
84Dic11—41no—
85Dic11—81no—
86C4⋊Q8—111no—
87C4⋊Q8—221no—
88C4⋊Q8C2×D1111yescharacteristic
89#125—221no—
90#125—222no—
91C4×Q8—111no—
92C4×Q8—111no—
93C4×Q8—221no—
94C4×Q8—221no—
95#107—221no—
96#107—221no—
97C4⋊C8C2×D1111yescharacteristic
98C4⋊C8C2×D1111yescharacteristic
99#103—221no—
100#103—221no—
101#103—222no—
102C4×C8—111no—
103C2×C11#45111yescharacteristic
104C2×C11#45211yescharacteristic
105C2×C11#45411yescharacteristic
106C2×Q8—21no—
107C2×Q8—111no—
108C2×Q8—111no—
109C2×Q8—221no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—221no—
113C4⋊C4—21no—
114C4⋊C4—111no—
115C4⋊C4—111no—
116C4⋊C4—222no—
117C4⋊C4—222no—
118C4⋊C4—222no—
119C4⋊C4—221no—
120C4⋊C4—221no—
121C4⋊C4—221no—
122C4⋊C4—221no—
123C4⋊C4D4412yes—
124C42—222no—
125C42—221no—
126C42—221no—
127C42C22×D1111yescharacteristic
128C11#163611yescharacteristic, complemented, Sylow
129Q8—41no—
130Q8—41no—
131Q8—112no—
132Q8—221no—
133Q8—221no—
134Q8—221no—
135Q8—442no—
136C2×C4—22no—
137C2×C4—221no—
138C2×C4—221no—
139C2×C4—221no—
140C2×C4—221no—
141C2×C4—441no—
142C2×C4C2×D4411yescharacteristic
143C2×C4D4×D1111yescharacteristic
144C2×C4D4×D1111yescharacteristic
145C8—41no—
146C8—41no—
147C8—441no—
148C22#6693511yescharacteristic
149C4—21no—
150C4—42no—
151C4—222no—
152C4—441no—
153C4—441no—
154C4—441no—
155C4—881no—
156C4#6696511yescharacteristic
157C4#6696811yescharacteristic
158C4#6696811yescharacteristic
159C4Q16×D1111yescharacteristic
160C2#1062236611yescharacteristic
161C2#1062239611yescharacteristic
162C2#1062242111yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#332C2
socle, prime radicalC22×C11#120
hypercenter#332D11
hypocenterC11#1636
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
128. C11#1636semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106227062
#106224632
C11×#3322
#106221222
#163611