Finite Group Databasebeta

← #11797889

Subgroups — #11797889

Order 1152.

315 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4700C212yesmaximal, complemented
2#10590629C211yesmaximal, characteristic
3#10589327C211yesmaximal, characteristic, complemented
4#10589144C211yesmaximal, characteristic, complemented
5#10589120C212yesmaximal, complemented
6#70922—32nomaximal
7C3×#904C2212yes—
8C3×#901—22no—
9C32×C4×C8C2211yescharacteristic
10C2×C3⋊(C3⋊C16)C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C3×#819C2212yes—
13C3×#805—22no—
14#63550C411yescharacteristic, complemented
15#63547C412yescomplemented
16#63545C411yescharacteristic, complemented
17C3×#443—32no—
18#5194—32no—
19#4700D312yescomplemented
20#4567—32no—
21#4497—32no—
22#4493—32no—
23#4461—32no—
24#4461—61no—
25C3×#235—22no—
26C2×C32×C8D411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28C32×C42D411yescharacteristic
29C3×#208—22no—
30C3×Dic12C2×C412yes—
31C3×D24C2×C412yes—
32C3×#204—22no—
33C3×ΓL(1,𝔽25)—42no—
34C3×D3×C8—42no—
35C3⋊(C3⋊C16)—21no—
36C3⋊(C3⋊C16)C2×C411yescharacteristic
37C3⋊(C3⋊C16)C2×C411yescharacteristic
38#2179—91noSylow
39C3×#135—32no—
40C3×#131—62no—
41#904C2×D312yes—
42#901—22no—
43C3×#108—32no—
44C3×#104—62no—
45C3×C4×C8—21no—
46C3×C4×C8C2×D312yes—
47#829—32no—
48#828—32no—
49#827—32no—
50#826—32no—
51#819C2×D312yes—
52C2×C3⋊C16—32no—
53C2×C3⋊C16—32no—
54C2×C3⋊C16—61no—
55C2×C3⋊C16—61no—
56#805—22no—
57C2×C32×C4—21no—
58C2×C32×C4C2×D411yescharacteristic
59C3×#67—42no—
60C3×D12—22no—
61C3×C4×D3—42no—
62C3×Dic6—22no—
63C32×C8D812yes—
64C32×C8C22×C411yescharacteristic
65C32×C8#4111yescharacteristic
66C3×C3⋊C8—42no—
67#508—91no—
68#443—32no—
69#368—91no—
70#359—92no—
71#346—91no—
72C3×#41—62no—
73#235—22no—
74C3×Q16—32no—
75C3×SD16—62no—
76C3×D8—32no—
77C3×M16—62no—
78C3×M16—122no—
79C2×C3×C8—21no—
80C2×C3×C8—21no—
81C2×C3×C8—122no—
82C2×C3×C8#6712yes—
83C2×C3×C8C22×D312yes—
84C3×C42—21no—
85C3×C42#6712yes—
86#208—22no—
87Dic12C4×D312yes—
88D24C4×D312yes—
89#204—22no—
90ΓL(1,𝔽25)—42no—
91D3×C8—42no—
92C3⋊C16—32no—
93C3⋊C16—32no—
94C3⋊C16—61no—
95C3⋊C16—61no—
96C3⋊C16—62no—
97C3⋊C16—62no—
98C22×C32#13511yescharacteristic
99C2×C3×D3—42no—
100C32×C4—41no—
101C32×C4C4×D411yescharacteristic
102C32×C4C2×D811yescharacteristic
103C3×Dic3—42no—
104#135—32no—
105#131—62no—
106Q32—91no—
107SD32—92no—
108D16—91no—
109C2×C16—91no—
110C2×C16—91no—
111#108—32no—
112#104—62no—
113C4×C8D3211yescharacteristic
114C3×Q8—62no—
115C3×D4—62no—
116C3×D4—122no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—21no—
120C2×C3×C4—122no—
121C2×C3×C4C2×#6712yes—
122#67—42no—
123D12—22no—
124C4×D3—42no—
125Dic6—22no—
126C3×C8—22no—
127C3×C8—21no—
128C3×C8—21no—
129C3×C8—122no—
130C3×C8#21312yes—
131C3×C8#21312yes—
132C3×C8C2×C4×D312yes—
133C3×C8#23512yes—
134C3⋊C8—42no—
135C2×C32—21no—
136C2×C32C4×D811yescharacteristic
137C3×D3—82no—
138#41—62no—
139Q16—32no—
140SD16—62no—
141D8—32no—
142M16—62no—
143M16—122no—
144C2×C8—122no—
145C2×C8#62511yescharacteristic
146C2×C8C2×D3211yescharacteristic
147C42#62511yescharacteristic
148C16—91no—
149C16—91no—
150C16—181no—
151C22×C3—21no—
152C22×C3—122no—
153C22×C3#95012yes—
154C2×D3—42no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—42no—
158C3×C4—42no—
159C3×C4—122no—
160C3×C4C4×#6712yes—
161C3×C4C2×#21312yes—
162Dic3—42no—
163C32#217911yescharacteristic, complemented, Sylow
164Q8—62no—
165D4—62no—
166D4—122no—
167C2×C4—21no—
168C2×C4—122no—
169C2×C4C2×#62511yescharacteristic
170C8—122no—
171C8#371312yes—
172C8#379811yescharacteristic
173C8C4×D3211yescharacteristic
174C2×C3—22no—
175C2×C3—22no—
176C2×C3—21no—
177C2×C3—242no—
178C2×C3C4×#21312yes—
179D3—82no—
180C22—122no—
181C22#6382211yescharacteristic
182C4—41no—
183C4—122no—
184C4C2×#371311yescharacteristic
185C4C4×#62511yescharacteristic
186C3—21no—
187C3#7092212yescomplemented
188C2—21no—
189C2—242no—
190C2C4×#371311yescharacteristic
subgroupG/H
centerC4C2×#3713
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×C4×C8C22
socleC2×C32C4×D8
prime radical#10590629C2
cosocleC2×C32×C8C23
hypercenterC4×C8D32
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C3×#4700C2semidirect
3. #10589327C2semidirect
4. #10589144C2semidirect
5. #10589120C2semidirect
14. #63550C4semidirect
15. #63547C4semidirect
16. #63545C4semidirect
19. #4700D3semidirect
163. C32#2179semidirect
187. C3#70922semidirect

Maximal subgroups

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

subgroupindex
C3×#47002
#105906292
#105893272
#105891442
#105891202
#709223