Finite Group Databasebeta

← #13070592

Subgroups — #13070592

Order 1408.

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

normal subgroups only

This group has 206 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#10623284C211yesmaximal, characteristic
2C11×#473C211yesmaximal, characteristic, complemented
3C2×#66893C211yesmaximal, characteristic, complemented
4#10622792C211yesmaximal, characteristic, complemented
5#10622199C211yesmaximal, characteristic, complemented
6#10622135C211yesmaximal, characteristic, complemented
7#10622134C211yesmaximal, characteristic, complemented
8#67043—21no—
9C11×#137—21no—
10C2×C11×Q16C2211yescharacteristic
11C11×#131C2211yescharacteristic
12#66962—21no—
13#66962—22no—
14C2×Dic44—21no—
15C2×Dic44C2211yescharacteristic
16#66957—21no—
17#66957C2211yescharacteristic
18C11×#108C2211yescharacteristic
19C11×#101—21no—
20#66893—21no—
21#66893—22no—
22#66892—21no—
23#66876C2211yescharacteristic
24C2×C11⋊C16C2211yescharacteristic
25C11×#41D411yescharacteristic
26C2×Q8×C11—21no—
27Q8×D11—41no—
28#4341—42no—
29#4341—41no—
30#4339—22no—
31#4339—21no—
32C2×Dic22—22no—
33C2×Dic22—21no—
34C11×Q16—21no—
35C11×Q16—21no—
36C11×Q16—41no—
37C11×SD16—41no—
38C11×M16—21no—
39C11×M16—21no—
40C11×M16D411yescharacteristic
41C2×C8×C11—21no—
42C2×C8×C11C2311yescharacteristic
43Dic44—22no—
44Dic44—21no—
45Dic44D411yescharacteristic
46Dic44D412yes—
47D88D411yescharacteristic
48#4314—22no—
49#4314—21no—
50C11⋊C16—21no—
51C11⋊C16—21no—
52#2195—111nomaximal, Sylow
53Q8×C11—41no—
54Q8×C11—41no—
55Q8×C11D811yescharacteristic
56D4×C11—21no—
57D4×C11D811yescharacteristic
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11C2×D411yescharacteristic
61C22⋊D11—42no—
62C22⋊D11—41no—
63C2×Dic11—42no—
64C2×Dic11—41no—
65D44—21no—
66C4×D11—42no—
67C4×D11—41no—
68Dic22—22no—
69Dic22—21no—
70Dic22—42no—
71Dic22—41no—
72C8×C11—21no—
73C8×C11—41no—
74C8×C11C2×D411yescharacteristic
75C8×C11C2×D411yescharacteristic
76#578—111no—
77#510—111no—
78C2×Q32—111no—
79#473D1111yescharacteristic, complemented
80#362—111no—
81#359—111no—
82#350—111no—
83C22×C11—21no—
84C22×C11AGL(1,ℤ/8)11yescharacteristic
85C2×D11—41no—
86C4×C11—21no—
87C4×C11—81no—
88C4×C11#12011yescharacteristic
89C4×C11C2×D811yescharacteristic
90Dic11—41no—
91Dic11—42no—
922−1+4—221no—
93#137—21no—
94#137—222no—
95#137—221no—
96#135—111no—
97#135—221no—
98C2×Q16—111no—
99C2×Q16—221no—
100C2×Q16C2×D1111yescharacteristic
101#131C2×D1111yescharacteristic
102Q32—222no—
103Q32—221no—
104SD32—221no—
105M32—111no—
106C2×C16—111no—
107#108C2×D1111yescharacteristic
108#101—21no—
109C2×C11—21no—
110C2×C11—41no—
111C2×C11#44711yescharacteristic
112D11—81no—
113#41—222no—
114#41—221no—
115#41—442no—
116#41—441no—
117#41C22⋊D1111yescharacteristic
118C2×Q8—21no—
119C2×Q8—222no—
120C2×Q8—221no—
121C2×Q8—441no—
122Q16—21no—
123Q16—21no—
124Q16—41no—
125Q16—112no—
126Q16—111no—
127Q16—222no—
128Q16—221no—
129SD16—41no—
130SD16—222no—
131SD16—221no—
132D8—111no—
133M16—21no—
134M16—21no—
135M16C22⋊D1111yescharacteristic
136C2×C8—21no—
137C2×C8C22×D1111yescharacteristic
138C16—221no—
139C16—221no—
140C11#219511yescharacteristic, complemented, Sylow
141Q8—41no—
142Q8—41no—
143Q8—222no—
144Q8—221no—
145Q8—442no—
146Q8—441no—
147Q8#432311yescharacteristic
148D4—21no—
149D4—221no—
150D4—442no—
151D4—441no—
152D4#432311yescharacteristic
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—442no—
156C2×C4—442no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4C2×C22⋊D1111yescharacteristic
160C8—21no—
161C8—41no—
162C8D4×D1111yescharacteristic
163C8D4×D1111yescharacteristic
164C22—21no—
165C22—441no—
166C22#6700211yescharacteristic
167C4—21no—
168C4—81no—
169C4—442no—
170C4—441no—
171C4C2×#432311yescharacteristic
172C4#6699011yescharacteristic
173C2—21no—
174C2—41no—
175C2—881no—
176C2#1062264911yescharacteristic
subgroupG/H
centerC2#10622649
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#473C2
socleC2×C11#447
prime radical#10623284C2
hypercenter#473D11
hypocenterC11#2195
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C11×#473C2semidirect
3. C2×#66893C2semidirect
4. #10622792C2semidirect
5. #10622199C2semidirect
6. #10622135C2semidirect
7. #10622134C2semidirect
79. #473D11semidirect
140. C11#2195semidirect

Maximal subgroups

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

subgroupindex
#106232842
C11×#4732
C2×#668932
#106227922
#106221992
#106221352
#106221342
#219511