Finite Group Databasebeta

← #13070566

Subgroups — #13070566

Order 1408.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#10623279C211yesmaximal, characteristic
2C11×#470C211yesmaximal, characteristic, complemented
3#10622792C212yesmaximal, complemented
4#10622191C211yesmaximal, characteristic, complemented
5#10622126C212yesmaximal, complemented
6C2×#4339—21no—
7C2×C11×Q16C2211yescharacteristic, complemented
8C2×C11×M16C2211yescharacteristic
9C11×C22⋊Q8—21no—
10#66962—22no—
11#66961—22no—
12#66957—21no—
13#66957C2212yes—
14C11×#106C2211yescharacteristic, complemented
15C11×#103—21no—
16#66893—22no—
17#66892—22no—
18#66876C2212yescomplemented
19C2×Q8×C11—21no—
20C22×C4×C11D411yescharacteristic
21C2×C22⋊D11—41no—
22#4339—22no—
23#4339—22no—
24#4339—41no—
25#4339—41no—
26C2×D44—21no—
27C2×C4×D11—41no—
28C2×Dic22—21no—
29C11×Q16—22no—
30C11×M16—22no—
31C2×C8×C11D411yescharacteristic
32C2×C8×C11C2311yescharacteristic
33C11×C4⋊C4—21no—
34C11×C4⋊C4—41no—
35C11×C22⋊C4—41no—
36Dic44—21no—
37Dic44D412yes—
38D88—21no—
39D88D412yes—
40#4314—22no—
41#4314—22no—
42C11⋊C16—22no—
43#2191—111nomaximal, Sylow
44C23×C11D811yescharacteristic
45C22×D11—41no—
46Q8×C11—41no—
47Q8×C11—41no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—41no—
51C2×C4×C11—41no—
52C2×C4×C11D811yescharacteristic
53C2×C4×C11C2×D411yescharacteristic
54C22⋊D11—42no—
55C22⋊D11—42no—
56C2×Dic11—41no—
57D44—22no—
58D44—41no—
59C4×D11—42no—
60C4×D11—42no—
61Dic22—22no—
62Dic22—41no—
63C8×C11—21no—
64C8×C11C2×D412yes—
65#575—111no—
66#510—112no—
67#470D1111yescharacteristic, complemented
68#360—112no—
69#349—111no—
70C22×C11—21no—
71C22×C11—41no—
72C22×C11C2×D811yescharacteristic
73C2×D11—42no—
74C2×D11—82no—
75C4×C11—21no—
76C4×C11—81no—
77C4×C11—81no—
78C4×C11#12011yescharacteristic
79C4×C11AGL(1,ℤ/8)11yescharacteristic
80Dic11—42no—
81C2×#41—221no—
82#137—222no—
83AGL(1,ℤ/8)—222no—
84#135—112no—
85#135—221no—
86C2×Q16C2×D1111yescharacteristic, complemented
87C2×M16C2×D1111yescharacteristic
88C22⋊Q8—21no—
89Q32—222no—
90SD32—222no—
91M32—112no—
92#106C2×D1111yescharacteristic, complemented
93#103—21no—
94C2×C11—21no—
95C2×C11—41no—
96C2×C11#44711yescharacteristic
97D11—82no—
98#41—222no—
99#41—222no—
100#41—441no—
101#41—441no—
102C2×Q8—21no—
103C2×Q8—221no—
104C2×D4—221no—
105C2×D4—441no—
106C22×C4—441no—
107C22×C4C22⋊D1111yescharacteristic
108Q16—22no—
109Q16—112no—
110Q16—221no—
111SD16—222no—
112SD16—222no—
113D8—112no—
114D8—221no—
115M16—22no—
116C2×C8C22⋊D1111yescharacteristic
117C2×C8C22×D1111yescharacteristic
118C4⋊C4—21no—
119C4⋊C4—41no—
120C22⋊C4—41no—
121C16—222no—
122C11#219111yescharacteristic, complemented, Sylow
123C23—441no—
124C23#432311yescharacteristic
125Q8—41no—
126Q8—41no—
127Q8—222no—
128Q8—441no—
129D4—222no—
130D4—441no—
131D4—442no—
132D4—442no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—442no—
138C2×C4—441no—
139C2×C4—442no—
140C2×C4#432311yescharacteristic
141C2×C4C2×C22⋊D1111yescharacteristic
142C8—21no—
143C8D4×D1112yes—
144C22—21no—
145C22—41no—
146C22—442no—
147C22—882no—
148C22C2×#432311yescharacteristic
149C4—21no—
150C4—81no—
151C4—81no—
152C4—442no—
153C4#6699011yescharacteristic
154C4#6700211yescharacteristic
155C2—21no—
156C2—41no—
157C2—882no—
158C2#1062264911yescharacteristic
subgroupG/H
centerC2#10622649
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#470C2
socleC2×C11#447
prime radical#10623279C2
hypercenter#470D11
hypocenterC11#2191
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C11×#470C2semidirect
3. #10622792C2semidirect
4. #10622191C2semidirect
5. #10622126C2semidirect
7. C2×C11×Q16C22semidirect
14. C11×#106C22semidirect
18. #66876C22semidirect
67. #470D11semidirect
86. C2×Q16C2×D11semidirect
92. #106C2×D11semidirect
122. C11#2191semidirect

Maximal subgroups

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

subgroupindex
#106232792
C11×#4702
#106227922
#106221912
#106221262
#219111