Finite Group Databasebeta

← #13067656

Subgroups — #13067656

Order 1408.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#10623154C211yesmaximal, characteristic
2C11×#484C211yesmaximal, characteristic
3#10622595C211yesmaximal, characteristic
4#10622583C211yesmaximal, characteristic
5#10622176C211yesmaximal, characteristic
6#10622107C211yesmaximal, characteristic
7#10622105C211yesmaximal, characteristic
8C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10#66997—21no—
11#66977C2211yescharacteristic
12C2×Dic11⋊C4C2211yescharacteristic
13#66942—21no—
14#66942—21no—
15#66941—21no—
16#66931—21no—
17#66930—21no—
18C11×#107—21no—
19C11×#103—21no—
20C11×C22⋊C8C2211yescharacteristic
21C11⋊#95—21no—
22C11⋊#95—21no—
23C11⋊#95C2211yescharacteristic
24C22⋊(C11⋊C8)C2211yescharacteristic
25#66874—21no—
26#66871—21no—
27C2×Q8×C11D411yescharacteristic
28C22×C4×C11—21no—
29C22×C4×C11C2311yescharacteristic
30C22×Dic11—21no—
31C22×Dic11D411yescharacteristic
32C22×Dic11D411yescharacteristic
33C2×Dic22—21no—
34C2×Dic22D411yescharacteristic
35C2×C8×C11—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4D411yescharacteristic
40C11×C22⋊C4—21no—
41C22⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11D411yescharacteristic
44Dic11⋊C4—21no—
45Dic11⋊C4—21no—
46Dic11⋊C4—21no—
47Dic11⋊C4—21no—
48Dic11⋊C4—21no—
49Dic11⋊C4—21no—
50Dic11⋊C4—21no—
51C4×Dic11—21no—
52C4×Dic11—21no—
53C2×C11⋊C8—21no—
54#1617—111nomaximal, Sylow
55C23×C11C2×D411yescharacteristic
56Q8×C11—41no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—42no—
61C2×C4×C11—41no—
62C2×C4×C11C2×D411yescharacteristic
63C2×C4×C11C2×D411yescharacteristic
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—21no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73C2×Dic11Q1612yes—
74Dic22—41no—
75Dic22—81no—
76C8×C11—41no—
77C11⋊C8—41no—
78#544—111no—
79#484—111no—
80#484D1111yescharacteristic
81#400—111no—
82#328—111no—
83#328—111no—
84#324—111no—
85C22×C11—21no—
86C22×C11—21no—
87C22×C11#12011yescharacteristic
88C22×C11C2×Q1611yescharacteristic
89C22×C11#13711yescharacteristic
90C4×C11—21no—
91C4×C11—21no—
92C4×C11—41no—
93C4×C11—41no—
94C4×C11—81no—
95Dic11—22no—
96Dic11—41no—
97Dic11—41no—
98Dic11—41no—
99Dic11—81no—
100C4⋊Q8—221no—
101C4⋊Q8—221no—
102#125—221no—
103#125—221no—
104C22⋊Q8—111no—
105C22⋊Q8—221no—
106C22⋊Q8C2×D1111yescharacteristic
107#117—221no—
108C2×C4⋊C4—111no—
109C2×C4⋊C4C2×D1111yescharacteristic
110#107—21no—
111#107—221no—
112#103—21no—
113#103—221no—
114C22⋊C8—111no—
115C22⋊C8C2×D1111yescharacteristic
116#95—111no—
117#95—221no—
118#95—221no—
119C2×C11—21no—
120C2×C11—21no—
121C2×C11#45111yescharacteristic
122C2×C11#45411yescharacteristic
123C2×C11#45811yescharacteristic
124C2×Q8—111no—
125C2×Q8—221no—
126C2×Q8C22⋊D1111yescharacteristic
127C22×C4—21no—
128C22×C4—111no—
129C22×C4—111no—
130C22×C4—221no—
131C22×C4C22×D1111yescharacteristic
132C2×C8—21no—
133C2×C8—221no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—111no—
138C4⋊C4—221no—
139C4⋊C4—221no—
140C4⋊C4—221no—
141C4⋊C4—221no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C4⋊C4—221no—
145C4⋊C4—221no—
146C4⋊C4C22⋊D1111yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—221no—
149C42—221no—
150C42—221no—
151C11#161711yescharacteristic, complemented, Sylow
152C23D4×D1111yescharacteristic
153Q8—41no—
154Q8—441no—
155Q8—881no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—112no—
162C2×C4—221no—
163C2×C4—221no—
164C2×C4—221no—
165C2×C4—221no—
166C2×C4—221no—
167C2×C4—441no—
168C2×C4—441no—
169C2×C4—441no—
170C2×C4—441no—
171C2×C4D4×D1111yescharacteristic
172C2×C4C2×C22⋊D1111yescharacteristic
173C8—41no—
174C8—441no—
175C22—21no—
176C22—21no—
177C22Q16×D1111yescharacteristic
178C22#6697111yescharacteristic
179C22#6699011yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—222no—
186C4—441no—
187C4—441no—
188C4—441no—
189C4—881no—
190C2—21no—
191C2—21no—
192C2#1062266611yescharacteristic
193C2#1062279911yescharacteristic
194C2#1062281411yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#484C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#484D11
hypocenterC11#1617
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
151. C11#1617semidirect

Maximal subgroups

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

subgroupindex
#106231542
C11×#4842
#106225952
#106225832
#106221762
#106221072
#106221052
#161711