Finite Group Databasebeta

← #13067749

Subgroups — #13067749

Order 1408.

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

normal subgroups only

This group has 214 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#10623110C211yesmaximal, characteristic
2C11×#477C211yesmaximal, characteristic, complemented
3#10622705C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic
5Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#10622121C211yesmaximal, characteristic
7#10622119C211yesmaximal, characteristic, complemented
8C11×C4⋊Q8C2211yescharacteristic
9C4×Q8×C11C2211yescharacteristic
10#66999—21no—
11C2×#4326—22no—
12#66949—22no—
13C4⋊C4×D11—21no—
14C4×D44—21no—
15C4×D44C2211yescharacteristic
16#66923—21no—
17#66922C2211yescharacteristic
18C11×#107—21no—
19C11×C4⋊C8C2211yescharacteristic
20C11×#103—21no—
21#66873—21no—
22#66872—21no—
23C4⋊(C11⋊C8)C2211yescharacteristic
24C4×C11⋊C8C2211yescharacteristic
25C2×Q8×C11—21no—
26C2×Q8×C11D411yescharacteristic
27C2×D44D411yescharacteristic
28C2×C4×D11—22no—
29C2×C4×D11—21no—
30C2×Dic22D412yes—
31C2×C8×C11—21no—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4D411yescharacteristic
36C42×C11—21no—
37C42×C11C2311yescharacteristic
38#4326—44no—
39(C2×D11)⋊C4—22no—
40(C2×D11)⋊C4—21no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11D411yescharacteristic
44Dic11⋊C4—22no—
45Dic11⋊C4—22no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48#1632—111nomaximal, Sylow
49C22×D11—21no—
50Q8×C11—21no—
51Q8×C11—21no—
52Q8×C11—42no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—41no—
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11C2×D411yescharacteristic
58C2×C4×C11C2×D411yescharacteristic
59C2×Dic11—21no—
60C2×Dic11—22no—
61D44—21no—
62D44Q1612yescomplemented
63C4×D11—41no—
64C4×D11—41no—
65C4×D11—82no—
66Dic22—42no—
67C8×C11—41no—
68C11⋊C8—22no—
69C11⋊C8—41no—
70#554—111no—
71#494—111no—
72#477D1111yescharacteristic, complemented
73#476—111no—
74#333—111no—
75Q8⋊C8—111no—
76D4⋊C8—111no—
77C22×C11#12011yescharacteristic
78C2×D11—22no—
79C2×D11—41no—
80C2×D11—41no—
81C4×C11—21no—
82C4×C11—41no—
83C4×C11—41no—
84C4×C11—81no—
85C4×C11C2×Q1611yescharacteristic
86C4×C11#13511yescharacteristic
87C4×C11#13711yescharacteristic
88C4×C11#13711yescharacteristic
89Dic11—41no—
90Dic11—42no—
91C2×Q16—222no—
92C4⋊Q8—111no—
93C4⋊Q8C2×D1111yescharacteristic
94#125—221no—
95C22⋊Q8—222no—
96C22⋊Q8—221no—
97C4×Q8C2×D1111yescharacteristic
98C4×D4—111no—
99C4×D4—221no—
100C2×C4⋊C4—221no—
101#107—21no—
102#106—221no—
103C4⋊C8—111no—
104C4⋊C8C2×D1111yescharacteristic
105#103—21no—
106#102—221no—
107C4×C8—111no—
108C2×C11#45111yescharacteristic
109C2×C11#45211yescharacteristic
110C2×C11#45311yescharacteristic
111D11—42no—
112C2×Q8—21no—
113C2×Q8—112no—
114C2×Q8C22⋊D1111yescharacteristic
115C2×D4—111no—
116C22×C4—222no—
117C22×C4—221no—
118Q16—444no—
119C2×C8—21no—
120C2×C8—221no—
121C2×C8—221no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—111no—
126C4⋊C4—222no—
127C4⋊C4—222no—
128C4⋊C4—221no—
129C4⋊C4—221no—
130C4⋊C4C22⋊D1111yescharacteristic
131C22⋊C4—222no—
132C22⋊C4—221no—
133C42—21no—
134C42C22×D1111yescharacteristic
135C11#163211yescharacteristic, complemented, Sylow
136C23—221no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—442no—
141D4—112no—
142D4—221no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—221no—
147C2×C4—222no—
148C2×C4—441no—
149C2×C4—441no—
150C2×C4—882no—
151C2×C4D4×D1111yescharacteristic
152C2×C4D4×D1111yescharacteristic
153C2×C4C2×C22⋊D1111yescharacteristic
154C8—41no—
155C8—222no—
156C8—441no—
157C22—222no—
158C22—441no—
159C22—441no—
160C22#6699011yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—442no—
166C4—441no—
167C4Q16×D1111yescharacteristic
168C4#6697111yescharacteristic
169C4#6699511yescharacteristic
170C4#6700311yescharacteristic
171C2—442no—
172C2#1062266011yescharacteristic
173C2#1062279911yescharacteristic
174C2#1062281111yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#477C2
socleC22×C11#120
prime radicalC2×D44D4
hypercenter#477D11
hypocenterC11#1632
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. C11×#477C2semidirect
3. #10622705C2semidirect
5. Q8⋊(C11⋊C8)C2semidirect
7. #10622119C2semidirect
62. D44Q16semidirect
72. #477D11semidirect
135. C11#1632semidirect

Maximal subgroups

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

subgroupindex
#106231102
C11×#4772
#106227052
#106226972
Q8⋊(C11⋊C8)2
#106221212
#106221192
#163211