Finite Group Databasebeta

← #13070596

Subgroups — #13070596

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
2#10622756C211yesmaximal, characteristic, complemented
3#10622522C211yesmaximal, characteristic, complemented
4C2×Dic88C211yesmaximal, characteristic, complemented
5C11×#350C211yesmaximal, characteristic, complemented
6#10622155C211yesmaximal, characteristic, complemented
7#10622148C211yesmaximal, characteristic, complemented
8#67043—21no—
9C11×#131C2211yescharacteristic
10#67004—21no—
11#66962—21no—
12#66962—22no—
13C2×Dic44—21no—
14C2×Dic44C2211yescharacteristic
15C2×Dic44C2211yescharacteristic
16#66957—21no—
17#66957C2211yescharacteristic
18C11×M32C2211yescharacteristic
19C2×C11×C16C2211yescharacteristic
20#66888—21no—
21#66883C2211yescharacteristic
22Dic88—22no—
23Dic88—21no—
24#66864—21no—
25C11×#41D411yescharacteristic
26Q8×D11—41no—
27#4341—42no—
28#4341—41no—
29#4339—22no—
30#4339—21no—
31C2×Dic22—22no—
32C2×Dic22—21no—
33C2×Dic22—21no—
34C11×M16—21no—
35C11×M16D411yescharacteristic
36C2×C8×C11—21no—
37C2×C8×C11C2311yescharacteristic
38#4326—41no—
39#4324—41no—
40#4318—21no—
41Dic44—22no—
42Dic44—21no—
43Dic44—21no—
44Dic44—21no—
45Dic44D411yescharacteristic
46Dic44D412yes—
47D88D411yescharacteristic
48#4314—22no—
49#4314—21no—
50C11×C16—21no—
51C11×C16—21no—
52#2195—111nomaximal, Sylow
53Q8×C11D811yescharacteristic
54D4×C11—21no—
55D4×C11D811yescharacteristic
56C2×C4×C11—21no—
57C2×C4×C11C2×D411yescharacteristic
58C22⋊D11—42no—
59C22⋊D11—41no—
60C2×Dic11—42no—
61C2×Dic11—41no—
62C2×Dic11—41no—
63D44—21no—
64C4×D11—42no—
65C4×D11—41no—
66Dic22—22no—
67Dic22—21no—
68Dic22—42no—
69Dic22—41no—
70Dic22—41no—
71Dic22—41no—
72C8×C11—21no—
73C8×C11C2×D411yescharacteristic
74C8×C11C2×D411yescharacteristic
75C11⋊C8—41no—
76#578—111no—
77#510—111no—
78C2×Q32—111no—
79#473—111no—
80#362—111no—
81#359—111no—
82#350D1111yescharacteristic, complemented
83C22×C11—21no—
84C22×C11AGL(1,ℤ/8)11yescharacteristic
85C2×D11—41no—
86C4×C11—21no—
87C4×C11#12011yescharacteristic
88C4×C11C2×D811yescharacteristic
89Dic11—41no—
90Dic11—42no—
91Dic11—81no—
922−1+4—221no—
93#137—222no—
94#137—221no—
95#137—221no—
96#135—111no—
97#135—221no—
98C2×Q16—111no—
99C2×Q16—111no—
100C2×Q16—221no—
101#131C2×D1111yescharacteristic
102Q32—222no—
103Q32—221no—
104SD32—221no—
105M32C2×D1111yescharacteristic
106C2×C16C2×D1111yescharacteristic
107#108—111no—
108#101—221no—
109C2×C11—21no—
110C2×C11—41no—
111C2×C11#44711yescharacteristic
112D11—81no—
113#41—222no—
114#41—221no—
115#41—442no—
116#41—441no—
117#41D4411yescharacteristic
118C2×Q8—222no—
119C2×Q8—221no—
120C2×Q8—221no—
121C2×Q8—441no—
122Q16—112no—
123Q16—111no—
124Q16—222no—
125Q16—221no—
126Q16—221no—
127Q16—221no—
128Q16—441no—
129SD16—222no—
130SD16—221no—
131SD16—441no—
132D8—111no—
133M16—21no—
134M16—221no—
135M16D4411yescharacteristic
136C2×C8—21no—
137C2×C8C22×D1111yescharacteristic
138C16—21no—
139C16—21no—
140C11#219511yescharacteristic, complemented, Sylow
141Q8—222no—
142Q8—221no—
143Q8—442no—
144Q8—441no—
145Q8—441no—
146Q8—441no—
147Q8D8811yescharacteristic
148D4—21no—
149D4—221no—
150D4—442no—
151D4—441no—
152D4D8811yescharacteristic
153C2×C4—21no—
154C2×C4—442no—
155C2×C4—442no—
156C2×C4—441no—
157C2×C4—441no—
158C2×C4—441no—
159C2×C4C2×D4411yescharacteristic
160C8—21no—
161C8—441no—
162C8D4×D1111yescharacteristic
163C8D4×D1111yescharacteristic
164C22—21no—
165C22—441no—
166C22#6696111yescharacteristic
167C4—21no—
168C4—442no—
169C4—441no—
170C4—881no—
171C4#6693511yescharacteristic
172C4C2×D8811yescharacteristic
173C2—21no—
174C2—41no—
175C2—881no—
176C2#1062234511yescharacteristic
subgroupG/H
centerC2#10622345
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#350C2
socleC2×C11#447
prime radical#10623284C2
hypercenter#350D11
hypocenterC11#2195
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #10622756C2semidirect
3. #10622522C2semidirect
4. C2×Dic88C2semidirect
5. C11×#350C2semidirect
6. #10622155C2semidirect
7. #10622148C2semidirect
82. #350D11semidirect
140. C11#2195semidirect

Maximal subgroups

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

subgroupindex
#106232842
#106227562
#106225222
C2×Dic882
C11×#3502
#106221552
#106221482
#219511