Finite Group Databasebeta

← #11797614

Subgroups — #11797614

Order 1152.

175 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 175 conjugacy classes of subgroups — too many to draw. Only its 53 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#10596487C211yesmaximal, characteristic, complemented
2#10596485C211yesmaximal, characteristic, complemented
3#10593783C211yesmaximal, characteristic
4#10593271C211yesmaximal, characteristic, complemented
5#10593269C211yesmaximal, characteristic, complemented
6#10593257C211yesmaximal, characteristic, complemented
7#10593255C211yesmaximal, characteristic, complemented
8#64289C2211yescharacteristic
9#64287C2211yescharacteristic
10#64218—21no—
11C2×#3771—21no—
12#64214—21no—
13#64214C2211yescharacteristic
14#64214C2211yescharacteristic
15#64213—21no—
16#64213C2211yescharacteristic
17#64213C2211yescharacteristic
18#64125C411yescharacteristic
19#63785C411yescharacteristic
20#63783C411yescharacteristic
21#63770C411yescharacteristic
22C8×#157C2211yescharacteristic
23#3832C2×C411yescharacteristic
24#3830C2×C411yescharacteristic
25#3792—21no—
26C2×#622—21no—
27C4×#157C2×C411yescharacteristic
28#3788—21no—
29#3788C2×C411yescharacteristic
30#3788C2×C411yescharacteristic
31#3787—21no—
32#3787C2311yescharacteristic
33#3771—21no—
34#3771—21no—
35#3771—21no—
36#3771D411yescharacteristic
37#3771D411yescharacteristic
38C32×SD16C811yescharacteristic
39#3756C811yescharacteristic
40#3753C811yescharacteristic
41#3744C811yescharacteristic
42C8×C3⋊D3C2×C411yescharacteristic
43#2171—91nomaximal, Sylow
44#916—121no—
45C2×#157—21no—
46C32×Q8C2×C811yescharacteristic
47C32×D4C2×C811yescharacteristic
48#638—21no—
49C2×C3⋊Dic3—21no—
50C4⋊(C3⋊D3)—21no—
51C4⋊(C3⋊D3)C2×C811yescharacteristic
52C4×C3⋊D3—21no—
53C4×C3⋊D3C22×C411yescharacteristic
54#634C2×C811yescharacteristic
55#622—21no—
56#622—21no—
57#622C2×D411yescharacteristic
58#622#4111yescharacteristic
59C32×C8C2×C811yescharacteristic
60C3⋊(C3⋊C8)C2×C811yescharacteristic
61#504—91no—
62#504—91no—
63#443—91no—
64#364—91no—
65#350—91no—
66#350—91no—
67#346—91no—
68#239—121no—
69#237—121no—
70C3×SD16—41no—
71#216—121no—
72#213—121no—
73#204—121no—
74D3×C8—121no—
75C22×C32—21no—
76C2×C3⋊D3—21no—
77C2×C3⋊D3#13111yescharacteristic
78#157—41no—
79C32×C4—21no—
80C32×C4C22×C811yescharacteristic
81C3⋊Dic3—21no—
82C3⋊Dic3C4×D411yescharacteristic
83#135—91no—
84#131—91no—
85#131—91no—
86M32—91no—
87M32—91no—
88M32—181no—
89M32—181no—
90C2×C16—91no—
91C2×C16—91no—
92C2×C16—181no—
93C2×C16—181no—
94#108—91no—
95#104—91no—
96#104—91no—
97C4×C8—91no—
98C3×Q8—41no—
99C3×D4—41no—
100#67—241no—
101C2×Dic3—241no—
102D12—121no—
103D12—241no—
104C4×D3—121no—
105C4×D3—241no—
106Dic6—121no—
107C3×C8—41no—
108C3⋊C8—121no—
109C2×C32—41no—
110C2×C32C8×D411yescharacteristic
111C3⋊D3—21no—
112C3⋊D3—41no—
113#41—91no—
114#41—91no—
115Q16—91no—
116SD16—91no—
117SD16AGL(1,𝔽9)11yescharacteristic
118D8—91no—
119M16—91no—
120M16—91no—
121M16—181no—
122M16—181no—
123C2×C8—91no—
124C2×C8—91no—
125C2×C8—181no—
126C2×C8—181no—
127C42—91no—
128C16—91no—
129C16—91no—
130C16—181no—
131C16—181no—
132C16—181no—
133C22×C3—81no—
134C2×D3—121no—
135C2×D3—241no—
136C3×C4—41no—
137C3×C4—81no—
138Dic3—121no—
139Dic3—241no—
140C32#217111yescharacteristic, complemented, Sylow
141Q8—91no—
142Q8C2×AGL(1,𝔽9)11yescharacteristic
143D4—91no—
144D4—181no—
145D4—181no—
146D4C2×AGL(1,𝔽9)11yescharacteristic
147C2×C4—91no—
148C2×C4—181no—
149C2×C4—181no—
150C2×C4—181no—
151C8—91no—
152C8—91no—
153C8—91no—
154C8—181no—
155C8—181no—
156C8C2×AGL(1,𝔽9)11yescharacteristic
157C2×C3—41no—
158C2×C3—161no—
159D3—241no—
160D3—481no—
161C22—21no—
162C22—91no—
163C22—181no—
164C4—21no—
165C4—91no—
166C4—181no—
167C4—361no—
168C4C22×AGL(1,𝔽9)11yescharacteristic
169C3—41no—
170C2—41no—
171C2—181no—
172C2—361no—
173C2D4×AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2D4×AGL(1,𝔽9)
commutatorC32×C4C22×C8
FrattiniC4C22×AGL(1,𝔽9)
FittingC32×SD16C8
socleC2×C32C8×D4
prime radical#64125C4
cosocle#3787C23
hypercenterSD16AGL(1,𝔽9)
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #10596487C2semidirect
2. #10596485C2semidirect
4. #10593271C2semidirect
5. #10593269C2semidirect
6. #10593257C2semidirect
7. #10593255C2semidirect
140. C32#2171semidirect

Maximal subgroups

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

subgroupindex
#105964872
#105964852
#105937832
#105932712
#105932692
#105932572
#105932552
#21719