Finite Group Databasebeta

← #11797891

Subgroups — #11797891

Order 1152.

315 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 78 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#10590919C212yesmaximal, complemented
2#10590629C211yesmaximal, characteristic
3#10589368C211yesmaximal, characteristic, complemented
4C3×#4510C212yesmaximal, complemented
5#10589144C211yesmaximal, characteristic, complemented
6#69239—32nomaximal
7C3×#904C2212yes—
8#63815—22no—
9C2×C32×C16C2211yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C3×#819C2212yes—
13#63568—22no—
14#63550C411yescharacteristic, complemented
15#63547C412yescomplemented
16#63545C411yescharacteristic, complemented
17#5196—32no—
18#5194—32no—
19#4895—32no—
20C3×#359—32no—
21#4510D312yescomplemented
22#4502—32no—
23#4502—61no—
24#4493—32no—
25C3×#235—22no—
26C2×C32×C8C2311yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C3×#208—22no—
30C3×Dic12C2×C412yes—
31C3×D24C2×C412yes—
32C3×#204—22no—
33#3711—42no—
34D3×C3⋊C8—42no—
35C32×C16—21no—
36C3⋊(C3⋊C16)C2×C411yescharacteristic
37C3⋊(C3⋊C16)C2×C411yescharacteristic
38#2179—91noSylow
39C3×#135—32no—
40#948—62no—
41#907—62no—
42#904C2×D312yes—
43C2×C3×C16—21no—
44C2×C3×C16C2×D312yes—
45C3×#108—32no—
46#837—62no—
47#829—32no—
48#828—32no—
49#827—32no—
50#826—32no—
51#825—62no—
52#819C2×D312yes—
53C8×Dic3—32no—
54C8×Dic3—61no—
55C2×C3⋊C16—32no—
56C2×C3⋊C16—61no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—21no—
59C3×#67—42no—
60C3×D12—22no—
61C3×C4×D3—42no—
62C3×Dic6—22no—
63C32×C8C22×C411yescharacteristic
64C32×C8#4111yescharacteristic
65C3⋊(C3⋊C8)D812yes—
66C3×C3⋊C8—42no—
67#508—91no—
68#443—92no—
69#368—91no—
70#359—32no—
71#346—91no—
72C3×#41—62no—
73#235—22no—
74C3×Q16—32no—
75C3×SD16—62no—
76C3×D8—32no—
77C3×M16—62no—
78C2×C3×C8—21no—
79C2×C3×C8C22×D312yes—
80C4×Dic3—32no—
81C4×Dic3—61no—
82#208—22no—
83#208—122no—
84C2×C3⋊C8—32no—
85C2×C3⋊C8—61no—
86C2×C3⋊C8—122no—
87Dic12C4×D312yes—
88D24C4×D312yes—
89#204—22no—
90ΓL(1,𝔽25)—122no—
91D3×C8—122no—
92C3×C16—22no—
93C3×C16—22no—
94C3⋊C16—32no—
95C3⋊C16—32no—
96C3⋊C16—61no—
97C3⋊C16—61no—
98C22×C32#13511yescharacteristic
99C2×C3×D3—42no—
100C32×C4C4×D411yescharacteristic
101C32×C4C2×D811yescharacteristic
102C3⋊Dic3—41no—
103C3×Dic3—42no—
104#135—32no—
105#131—182no—
106Q32—91no—
107SD32—92no—
108D16—91no—
109C2×C16—91no—
110C2×C16D3211yescharacteristic
111#108—32no—
112#104—182no—
113C4×C8—91no—
114C3×Q8—62no—
115C3×D4—62no—
116C3×D4—122no—
117C2×C3×C4—21no—
118C2×C3×C4—122no—
119C2×C3×C4D3×D412yes—
120#67—42no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123D12—22no—
124C4×D3—42no—
125Dic6—22no—
126C3×C8—21no—
127C3×C8—21no—
128C3×C8—122no—
129C3×C8C2×C4×D312yes—
130C3×C8#23712yes—
131C3⋊C8—32no—
132C3⋊C8—32no—
133C3⋊C8—42no—
134C3⋊C8—62no—
135C2×C32—21no—
136C2×C32C4×D811yescharacteristic
137C3×D3—82no—
138#41—62no—
139Q16—32no—
140SD16—62no—
141D8—32no—
142M16—62no—
143M16—362no—
144C2×C8—91no—
145C2×C8—362no—
146C2×C8C2×D3211yescharacteristic
147C42—91no—
148C16—21no—
149C16—91no—
150C16—91no—
151C22×C3—21no—
152C22×C3—122no—
153C22×C3#91612yes—
154C2×D3—42no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—122no—
158C3×C4#67⋊C412yes—
159C3×C4D3×D812yes—
160Dic3—42no—
161Dic3—122no—
162Dic3—122no—
163C32#217911yescharacteristic, complemented, Sylow
164Q8—62no—
165D4—62no—
166D4—122no—
167C2×C4—122no—
168C2×C4—181no—
169C2×C4#380211yescharacteristic
170C8—92no—
171C8—122no—
172C8C4×D3211yescharacteristic
173C8#380511yescharacteristic
174C2×C3—22no—
175C2×C3—22no—
176C2×C3—21no—
177C2×C3—242no—
178C2×C3#475612yes—
179D3—82no—
180C22—122no—
181C22#6380911yescharacteristic
182C4—122no—
183C4—361no—
184C4#6379711yescharacteristic
185C4#6390211yescharacteristic
186C3—21no—
187C3#6923912yescomplemented
188C2—21no—
189C2—242no—
190C2#1059074011yescharacteristic
subgroupG/H
centerC4#63797
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32C4×D8
prime radical#10590629C2
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #10590919C2semidirect
3. #10589368C2semidirect
4. C3×#4510C2semidirect
5. #10589144C2semidirect
14. #63550C4semidirect
15. #63547C4semidirect
16. #63545C4semidirect
21. #4510D3semidirect
163. C32#2179semidirect
187. C3#69239semidirect

Maximal subgroups

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

subgroupindex
#105909192
#105906292
#105893682
C3×#45102
#105891442
#692393