Finite Group Databasebeta

← #13070586

Subgroups — #13070586

Order 1408.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#10623288C211yesmaximal, characteristic
2C2×C11×SD32C211yesmaximal, characteristic, complemented
3#10622805C211yesmaximal, characteristic, complemented
4#10622792C211yesmaximal, characteristic, complemented
5#10622201C211yesmaximal, characteristic, complemented
6#10622148C211yesmaximal, characteristic, complemented
7#10622146C211yesmaximal, characteristic, complemented
8#67037—21no—
9C2×C11×Q16C2211yescharacteristic, complemented
10C2×C11×D8C2211yescharacteristic
11#66995—21no—
12#66985—21no—
13#66965—21no—
14#66964—22no—
15D8×D11—21no—
16#66957C2211yescharacteristic
17#66954C2211yescharacteristic
18C11×SD32—22no—
19C2×C11×C16C2211yescharacteristic, complemented
20#66900—21no—
21#66893—21no—
22#66892—21no—
23#66883C2211yescharacteristic, complemented
24#66876C2211yescharacteristic, complemented
25C2×Q8×C11—21no—
26C2×D4×C11—21no—
27C2×C22⋊D11—42no—
28#4341—22no—
29#4341—41no—
30D4×D11—22no—
31D4×D11—41no—
32#4339—21no—
33#4339D411yescharacteristic
34C11×Q16—21no—
35C11×Q16—21no—
36C11×D8—21no—
37C11×D8D412yes—
38C2×C8×C11C2311yescharacteristic
39#4326—41no—
40#4325—41no—
41#4324—22no—
42#4323—22no—
43#4318—21no—
44#4318D411yescharacteristic
45Dic44D411yescharacteristic
46D88D411yescharacteristic
47#4314—21no—
48#4313—21no—
49C8×D11—21no—
50C11×C16—21no—
51C11⋊C16—21no—
52#2194—111nomaximal, Sylow
53C23×C11—41no—
54C22×D11—42no—
55Q8×C11—41no—
56Q8×C11—41no—
57D4×C11—22no—
58D4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11C2×D411yescharacteristic
61C22⋊D11—21no—
62C22⋊D11—42no—
63C22⋊D11—42no—
64C22⋊D11—41no—
65C2×Dic11—42no—
66D44—21no—
67D44D811yescharacteristic
68C4×D11—21no—
69C4×D11—41no—
70Dic22—21no—
71Dic22D811yescharacteristic
72C8×C11C2×D411yescharacteristic
73C8×C11C2×D411yescharacteristic
74C11⋊C8—21no—
75C11⋊C8—41no—
76#576—111no—
77#510—111no—
78C2×SD32D1111yescharacteristic, complemented
79#473—111no—
80#361—111no—
81#359—111no—
82#350—111no—
83C22×C11—42no—
84C22×C11—161no—
85C22×C11AGL(1,ℤ/8)11yescharacteristic
86C2×D11—21no—
87C2×D11—41no—
88C2×D11—162no—
89C4×C11—81no—
90C4×C11#12011yescharacteristic
91C4×C11C2×D811yescharacteristic
92Dic11—21no—
93Dic11—41no—
94H(5,𝔽2)—221no—
95#137—221no—
96AGL(1,ℤ/8)—221no—
97AGL(1,ℤ/8)—222no—
98#135—111no—
99#135—221no—
100C2×Q16C2×D1111yescharacteristic, complemented
101C2×D8—221no—
102C2×D8C2×D1111yescharacteristic
103#131—111no—
104Q32—221no—
105SD32—22no—
106SD32—221no—
107M32—111no—
108C2×C16C2×D1111yescharacteristic, complemented
109#108—111no—
110#101—221no—
111C2×C11—21no—
112C2×C11—82no—
113C2×C11#44711yescharacteristic
114D11—41no—
115D11—81no—
116#41—111no—
117#41—222no—
118#41—221no—
119#41—441no—
120C2×Q8—21no—
121C2×D4—21no—
122C2×D4—222no—
123C2×D4—441no—
124C2×D4—442no—
125Q16—21no—
126Q16—21no—
127Q16—111no—
128Q16—441no—
129SD16—222no—
130SD16—221no—
131SD16—441no—
132D8—21no—
133D8—111no—
134D8—222no—
135D8C22⋊D1112yes—
136M16—111no—
137M16—221no—
138M16—221no—
139C2×C8—221no—
140C2×C8C22×D1111yescharacteristic
141C16—21no—
142C16—221no—
143C11#219411yescharacteristic, complemented, Sylow
144C23—41no—
145C23—442no—
146Q8—41no—
147Q8—41no—
148Q8—111no—
149Q8—221no—
150D4—22no—
151D4—41no—
152D4—111no—
153D4—221no—
154D4—221no—
155D4—442no—
156D4—442no—
157D4—441no—
158C2×C4—41no—
159C2×C4—221no—
160C2×C4—442no—
161C2×C4—441no—
162C2×C4D4×D1111yescharacteristic
163C8—221no—
164C8—441no—
165C8D4×D1111yescharacteristic
166C8C2×C22⋊D1111yescharacteristic
167C22—42no—
168C22—161no—
169C22—221no—
170C22—441no—
171C22—1762no—
172C22#6696411yescharacteristic
173C4—81no—
174C4—221no—
175C4—441no—
176C4D8×D1111yescharacteristic
177C4#6699011yescharacteristic
178C2—21no—
179C2—82no—
180C2—441no—
181C2—881no—
182C2#1062276911yescharacteristic
subgroupG/H
centerC2#10622769
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC2×C11×SD32C2
socleC2×C11#447
prime radical#10623288C2
hypercenterC2×SD32D11
hypocenterC11#2194
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. C2×C11×SD32C2semidirect
3. #10622805C2semidirect
4. #10622792C2semidirect
5. #10622201C2semidirect
6. #10622148C2semidirect
7. #10622146C2semidirect
9. C2×C11×Q16C22semidirect
19. C2×C11×C16C22semidirect
23. #66883C22semidirect
24. #66876C22semidirect
78. C2×SD32D11semidirect
100. C2×Q16C2×D11semidirect
108. C2×C16C2×D11semidirect
143. C11#2194semidirect

Maximal subgroups

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

subgroupindex
#106232882
C2×C11×SD322
#106228052
#106227922
#106222012
#106221482
#106221462
#219411