Finite Group Databasebeta

← #11797607

Subgroups — #11797607

Order 1152.

315 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#4901C212yesmaximal, complemented
2#10590921C211yesmaximal, characteristic
3#10589368C211yesmaximal, characteristic, complemented
4#10589135C211yesmaximal, characteristic, complemented
5#10589111C212yesmaximal, complemented
6#71453—32nomaximal
7C3×#901C2212yes—
8#63822C411yescharacteristic
9C2×C32×C16C2211yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C3×#812C2212yes—
13C3×#798—22no—
14C3×D3×C16—22no—
15#63578C411yescharacteristic
16#63568C412yes—
17C3×#504—32no—
18#5144—32no—
19#4901D312yescomplemented
20#4561—32no—
21#4515—32no—
22#4511—32no—
23#4502—32no—
24#4502—61no—
25C3×#235C2×C412yes—
26C2×C32×C8C2311yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
29C3×#208C2×C412yes—
30C3×ΓL(1,𝔽25)—22no—
31C3×D3×C8—22no—
32#3718C811yescharacteristic
33#3715C812yes—
34#3713C811yescharacteristic
35C32×C16D412yes—
36C3⋊(C3⋊C16)—21no—
37C3×C3⋊C16—22no—
38#2171—91noSylow
39C3×#131—32no—
40#950—32no—
41#901C2×D312yes—
42C3×M32—32no—
43C3×M32—62no—
44C2×C3×C16—21no—
45C2×C3×C16—62no—
46C2×C3×C16C2×D312yes—
47#837—32no—
48#825—32no—
49#822—32no—
50C8×Dic3—32no—
51C8×Dic3—61no—
52#812C2×D312yes—
53C2×C3⋊C16—32no—
54C2×C3⋊C16—61no—
55#798—22no—
56D3×C16—22no—
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—21no—
59C3×#67—22no—
60C3×D12C2×C812yes—
61C3×C4×D3—22no—
62C3×Dic6C2×C812yes—
63C32×C8C2×D411yescharacteristic
64C32×C8#4111yescharacteristic
65C3⋊(C3⋊C8)C2×C811yescharacteristic
66C3⋊(C3⋊C8)C2×C811yescharacteristic
67C3×C3⋊C8—22no—
68#504—32no—
69#443—91no—
70#364—91no—
71#350—92no—
72#346—91no—
73C3×#41—32no—
74#235C4×D312yes—
75C3×M16—32no—
76C3×M16—62no—
77C2×C3×C8—21no—
78C2×C3×C8—62no—
79C2×C3×C8C22×D312yes—
80#216—32no—
81#215—32no—
82#214—32no—
83#213—32no—
84C4×Dic3—32no—
85C4×Dic3—61no—
86#208C4×D312yes—
87C2×C3⋊C8—32no—
88C2×C3⋊C8—61no—
89ΓL(1,𝔽25)—22no—
90D3×C8—22no—
91C3×C16—22no—
92C3×C16—62no—
93C3×C16#6712yes—
94C3×C16#6712yes—
95C3⋊C16—22no—
96C3⋊C16—62no—
97C3⋊C16—62no—
98C22×C32#13111yescharacteristic
99C2×C3×D3—22no—
100C32×C4C4×D411yescharacteristic
101C32×C4C22×C811yescharacteristic
102C3⋊Dic3—41no—
103C3×Dic3—22no—
104#135—91no—
105#131—32no—
106M32—32no—
107M32—62no—
108C2×C16—62no—
109C2×C16—91no—
110C2×C16D3211yescharacteristic
111#108—91no—
112#104—92no—
113C4×C8—91no—
114C3×Q8—32no—
115C3×D4—32no—
116C3×D4—62no—
117C2×C3×C4—21no—
118C2×C3×C4—62no—
119C2×C3×C4C2×C4×D312yes—
120#67—22no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123D12D3×C812yes—
124C4×D3—22no—
125Dic6D3×C812yes—
126C3×C8—21no—
127C3×C8—21no—
128C3×C8—62no—
129C3×C8#23512yes—
130C3×C8C2×#6712yes—
131C3⋊C8—22no—
132C3⋊C8—32no—
133C3⋊C8—32no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C2×C32—21no—
137C2×C32C8×D411yescharacteristic
138C3×D3—42no—
139#41—32no—
140Q16—91no—
141SD16—92no—
142D8—91no—
143M16—32no—
144M16—62no—
145C2×C8—62no—
146C2×C8—91no—
147C2×C8C2×D3211yescharacteristic
148C42—91no—
149C16—62no—
150C16—181no—
151C16#62512yes—
152C22×C3—21no—
153C22×C3—62no—
154C22×C3#90112yes—
155C2×D3—22no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—62no—
159C3×C4C2×D3×C812yes—
160C3×C4C4×#6712yes—
161Dic3—22no—
162Dic3—122no—
163Dic3—122no—
164C32#217111yescharacteristic, complemented, Sylow
165Q8—32no—
166D4—32no—
167D4—62no—
168C2×C4—62no—
169C2×C4—181no—
170C2×C4C4×D3211yescharacteristic
171C8—62no—
172C8—91no—
173C8—91no—
174C8#379811yescharacteristic
175C8C2×#62511yescharacteristic
176C2×C3—22no—
177C2×C3—22no—
178C2×C3—21no—
179C2×C3—122no—
180C2×C3C8×#6712yes—
181D3—42no—
182C22—62no—
183C22#6380311yescharacteristic
184C4—62no—
185C4—361no—
186C4D32×C811yescharacteristic
187C4C4×#62511yescharacteristic
188C3—21no—
189C3#7145312yescomplemented
190C2—21no—
191C2—122no—
192C2C8×#62511yescharacteristic
subgroupG/H
centerC8C2×#625
commutatorC32×C4C22×C8
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32C8×D4
prime radical#63822C4
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C3×#4901C2semidirect
3. #10589368C2semidirect
4. #10589135C2semidirect
5. #10589111C2semidirect
19. #4901D3semidirect
164. C32#2171semidirect
189. C3#71453semidirect

Maximal subgroups

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

subgroupindex
C3×#49012
#105909212
#105893682
#105891352
#105891112
#714533