Finite Group Databasebeta

← #13070591

Subgroups — #13070591

Order 1408.

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

normal subgroups only

This group has 206 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#10623302C211yesmaximal, characteristic
2C11×#510C211yesmaximal, characteristic, complemented
3#10622805C211yesmaximal, characteristic, complemented
4C2×#66893C211yesmaximal, characteristic, complemented
5#10622205C211yesmaximal, characteristic, complemented
6#10622155C211yesmaximal, characteristic, complemented
7#10622153C211yesmaximal, characteristic, complemented
8#67043—21no—
9C11×#135C2211yescharacteristic
10C2×C11×Q16C2211yescharacteristic
11#67004—21no—
12#66995—21no—
13Q16×D11—21no—
14#66968—22no—
15#66965—21no—
16C2×Dic44C2211yescharacteristic
17#66954C2211yescharacteristic
18C11×Q32—21no—
19C11×SD32—21no—
20C11×M32C2211yescharacteristic
21#66900—21no—
22#66893—22no—
23#66883C2211yescharacteristic
24C2×C11⋊C16C2211yescharacteristic
25C11×#41—21no—
26C2×Q8×C11—21no—
27Q8×D11—22no—
28#4341—22no—
29#4341—42no—
30#4339—41no—
31#4339D411yescharacteristic
32C2×Dic22—21no—
33C2×Dic22—41no—
34C11×Q16—21no—
35C11×Q16—21no—
36C11×Q16D411yescharacteristic
37C11×SD16—21no—
38C11×D8D411yescharacteristic
39C2×C8×C11C2311yescharacteristic
40#4326—22no—
41#4326—41no—
42#4325—41no—
43#4324—22no—
44#4318—21no—
45#4318D411yescharacteristic
46Dic44—21no—
47Dic44D412yes—
48#4313—21no—
49C8×D11—21no—
50C11×C16—21no—
51C11⋊C16—21no—
52#2195—111nomaximal, Sylow
53Q8×C11—21no—
54Q8×C11—41no—
55Q8×C11—41no—
56D4×C11—21no—
57D4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11C2×D411yescharacteristic
61C22⋊D11—21no—
62C22⋊D11—42no—
63C2×Dic11—42no—
64C2×Dic11—41no—
65D44D811yescharacteristic
66C4×D11—21no—
67C4×D11—42no—
68Dic22—22no—
69Dic22—42no—
70Dic22—41no—
71Dic22D811yescharacteristic
72C8×C11C2×D411yescharacteristic
73C8×C11C2×D411yescharacteristic
74C11⋊C8—21no—
75C11⋊C8—41no—
76#578—111no—
77#510D1111yescharacteristic, complemented
78C2×Q32—111no—
79#473—111no—
80#362—111no—
81#359—111no—
82#350—111no—
83C22×C11—41no—
84C22×C11AGL(1,ℤ/8)11yescharacteristic
85C2×D11—21no—
86C4×C11—41no—
87C4×C11—81no—
88C4×C11#12011yescharacteristic
89C4×C11C2×D811yescharacteristic
90Dic11—21no—
91Dic11—42no—
922−1+4—221no—
93#137—221no—
94#137—222no—
95#137—221no—
96#135—221no—
97#135C2×D1111yescharacteristic
98C2×Q16—111no—
99C2×Q16—221no—
100C2×Q16C2×D1111yescharacteristic
101#131—111no—
102Q32—21no—
103Q32—222no—
104SD32—21no—
105M32C2×D1111yescharacteristic
106C2×C16—111no—
107#108—111no—
108#101—221no—
109C2×C11—21no—
110C2×C11—81no—
111C2×C11#44711yescharacteristic
112D11—41no—
113#41—21no—
114#41—111no—
115#41—222no—
116#41—441no—
117#41—442no—
118C2×Q8—21no—
119C2×Q8—222no—
120C2×Q8—221no—
121C2×Q8—441no—
122Q16—21no—
123Q16—21no—
124Q16—112no—
125Q16—222no—
126Q16—221no—
127Q16—441no—
128Q16C22⋊D1111yescharacteristic
129SD16—21no—
130SD16—222no—
131SD16—441no—
132D8C22⋊D1111yescharacteristic
133M16—111no—
134M16—221no—
135M16—221no—
136C2×C8—221no—
137C2×C8C22×D1111yescharacteristic
138C16—21no—
139C16—221no—
140C11#219511yescharacteristic, complemented, Sylow
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—111no—
145Q8—222no—
146Q8—442no—
147Q8—441no—
148D4—21no—
149D4—41no—
150D4—111no—
151D4—221no—
152D4—442no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—221no—
156C2×C4—442no—
157C2×C4—442no—
158C2×C4—441no—
159C2×C4D4×D1111yescharacteristic
160C8—221no—
161C8—441no—
162C8D4×D1111yescharacteristic
163C8C2×C22⋊D1111yescharacteristic
164C22—41no—
165C22—221no—
166C22#6696411yescharacteristic
167C4—41no—
168C4—81no—
169C4—221no—
170C4—442no—
171C4D8×D1111yescharacteristic
172C4#6699011yescharacteristic
173C2—21no—
174C2—81no—
175C2—441no—
176C2#1062276911yescharacteristic
subgroupG/H
centerC2#10622769
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#510C2
socleC2×C11#447
prime radical#10623302C2
hypercenter#510D11
hypocenterC11#2195
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C11×#510C2semidirect
3. #10622805C2semidirect
4. C2×#66893C2semidirect
5. #10622205C2semidirect
6. #10622155C2semidirect
7. #10622153C2semidirect
77. #510D11semidirect
140. C11#2195semidirect

Maximal subgroups

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

subgroupindex
#106233022
C11×#5102
#106228052
C2×#668932
#106222052
#106221552
#106221532
#219511