Finite Group Databasebeta

← #13070599

Subgroups — #13070599

Order 1408.

354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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#10623248C211yesmaximal, characteristic, complemented
2C11×#453C211yesmaximal, characteristic, complemented
3#10622857C212yesmaximal, complemented
4#10622183C211yesmaximal, characteristic, complemented
5#10622113C212yesmaximal, complemented
6C11×H(5,𝔽2)C2211yescharacteristic, complemented
7C2×D4×D11—22no—
8C11×AGL(1,ℤ/8)—21no—
9C11×#127C2211yescharacteristic
10#66991—22no—
11#66990—21no—
12#66990—22no—
13#66990C2212yes—
14C4×D44—21no—
15C11×#104—21no—
16C11×#100C2211yescharacteristic, complemented
17#66898—22no—
18#66898C2212yescomplemented
19C23×D11—21no—
20C23×D11D412yescomplemented
21C11×#41—21no—
22C11×#41—41no—
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11—41no—
26C2×D4×C11D411yescharacteristic, complemented
27C2×D4×C11C2311yescharacteristic
28C2×C22⋊D11—22no—
29C2×C22⋊D11—22no—
30C2×C22⋊D11—42no—
31D4×D11—48no—
32C2×D44—21no—
33C2×C4×D11—22no—
34C11×SD16—41no—
35C11×D8—41no—
36C11×M16—21no—
37C42×C11D411yescharacteristic, complemented
38C22⋊Dic11—21no—
39C22⋊Dic11—22no—
40C22⋊Dic11D412yescomplemented
41(C2×D11)⋊C4—22no—
42(C2×D11)⋊C4—42no—
43C4⋊Dic11—21no—
44#2196—111nomaximal, Sylow
45C23×C11—22no—
46C23×C11—21no—
47C23×C11C2×D412yes—
48C22×D11—22no—
49C22×D11—44no—
50C22×D11—44no—
51C22×D11—42no—
52C22×D11—81no—
53Q8×C11—21no—
54D4×C11—21no—
55D4×C11—41no—
56D4×C11—41no—
57D4×C11—44no—
58D4×C11—42no—
59D4×C11—41no—
60C2×C4×C11—21no—
61C2×C4×C11—22no—
62C2×C4×C11—41no—
63C2×C4×C11C2×D411yescharacteristic
64C22⋊D11—44no—
65C22⋊D11—44no—
66C22⋊D11—84no—
67C2×Dic11—22no—
68C2×Dic11—42no—
69D44—24no—
70C4×D11—44no—
71C8×C11—41no—
72D42—111no—
73B(4,𝔽2)—112no—
74#453D1111yescharacteristic, complemented
75#353—111no—
76AΣL(1,𝔽16)—112no—
77C22×C11—22no—
78C22×C11—42no—
79C22×C11—42no—
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—82no—
83C22×C11#12011yescharacteristic
84C2×D11—24no—
85C2×D11—42no—
86C2×D11—42no—
87C2×D11—44no—
88C2×D11—82no—
89C2×D11—84no—
90C4×C11—22no—
91C4×C11—21no—
92C4×C11—41no—
93Dic11—42no—
94Dic11—82no—
95H(5,𝔽2)C2×D1111yescharacteristic, complemented
96C22×D4—222no—
97AGL(1,ℤ/8)—21no—
98#127C2×D1111yescharacteristic
99#121—222no—
100#120—112no—
101#120—221no—
102#120—222no—
103C4×D4—221no—
104#104—21no—
105#100C2×D1111yescharacteristic, complemented
106#99—112no—
107#99—222no—
108C2×C11—21no—
109C2×C11—42no—
110C2×C11—81no—
111C2×C11—81no—
112C2×C11B(4,𝔽2)11yescharacteristic
113D11—44no—
114C24—112no—
115C24—221no—
116#41—21no—
117#41—41no—
118C2×D4—22no—
119C2×D4—22no—
120C2×D4—41no—
121C2×D4—221no—
122C2×D4—222no—
123C2×D4—222no—
124C2×D4—448no—
125C2×D4—442no—
126C2×D4C22⋊D1111yescharacteristic, complemented
127C2×D4C22×D1111yescharacteristic
128C22×C4—222no—
129SD16—41no—
130D8—41no—
131M16—21no—
132C4⋊C4—221no—
133C22⋊C4—112no—
134C22⋊C4—221no—
135C22⋊C4—222no—
136C22⋊C4—222no—
137C22⋊C4—442no—
138C42C22⋊D1111yescharacteristic, complemented
139C11#219611yescharacteristic, complemented, Sylow
140C23—22no—
141C23—21no—
142C23—222no—
143C23—442no—
144C23—444no—
145C23—444no—
146C23—881no—
147C23D4×D1112yes—
148Q8—21no—
149D4—21no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—42no—
154D4—41no—
155D4—224no—
156D4—444no—
157D4—444no—
158D4—884no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—222no—
163C2×C4—444no—
164C2×C4—442no—
165C2×C4C2×C22⋊D1111yescharacteristic
166C8—41no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—82no—
173C22—224no—
174C22—442no—
175C22—444no—
176C22—442no—
177C22—882no—
178C22—884no—
179C22#6699011yescharacteristic
180C4—22no—
181C4—21no—
182C4—41no—
183C4—442no—
184C4—882no—
185C2—21no—
186C2—42no—
187C2—81no—
188C2—81no—
189C2—444no—
190C2#1062264511yescharacteristic
subgroupG/H
centerC2#10622645
commutator, cosocleC2×D4×C11C23
FrattiniC2×D4C22×D11
FittingC11×#453C2
socleC2×C11B(4,𝔽2)
hypercenter#453D11
hypocenterC11#2196
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #10623248C2semidirect
2. C11×#453C2semidirect
3. #10622857C2semidirect
4. #10622183C2semidirect
5. #10622113C2semidirect
6. C11×H(5,𝔽2)C22semidirect
16. C11×#100C22semidirect
18. #66898C22semidirect
20. C23×D11D4semidirect
26. C2×D4×C11D4semidirect
37. C42×C11D4semidirect
40. C22⋊Dic11D4semidirect
74. #453D11semidirect
95. H(5,𝔽2)C2×D11semidirect
105. #100C2×D11semidirect
126. C2×D4C22⋊D11semidirect
138. C42C22⋊D11semidirect
139. C11#2196semidirect

Maximal subgroups

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

subgroupindex
#106232482
C11×#4532
#106228572
#106221832
#106221132
#219611