Finite Group Databasebeta

← #11797858

Subgroups — #11797858

Order 1152.

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

normal subgroups only

This group has 321 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
3C16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4510C212yesmaximal, complemented
5#10589144C211yesmaximal, characteristic, complemented
6#69238—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
22Dic3×C16—32no—
23Dic3×C16—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#2178—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)D811yescharacteristic
66C3⋊(C3⋊C8)D811yescharacteristic
67C3×C3⋊C8—42no—
68#508—91no—
69#443—92no—
70#368—91no—
71#359—32no—
72C4×C16—91no—
73C3×#41—62no—
74#235—22no—
75C3×Q16—32no—
76C3×SD16—62no—
77C3×D8—32no—
78C3×M16—62no—
79C2×C3×C8—21no—
80C2×C3×C8C22×D312yes—
81C4×Dic3—32no—
82C4×Dic3—61no—
83#208—22no—
84#208—122no—
85C2×C3⋊C8—32no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—122no—
88Dic12C4×D312yes—
89D24C4×D312yes—
90#204—22no—
91ΓL(1,𝔽25)—122no—
92D3×C8—122no—
93C3×C16—22no—
94C3×C16—22no—
95C3⋊C16—32no—
96C3⋊C16—32no—
97C3⋊C16—61no—
98C3⋊C16—61no—
99C22×C32#13511yescharacteristic
100C2×C3×D3—42no—
101C32×C4C4×D411yescharacteristic
102C32×C4C2×D811yescharacteristic
103C3⋊Dic3—22no—
104C3×Dic3—42no—
105#135—32no—
106#131—182no—
107Q32—91no—
108SD32—92no—
109D16—91no—
110C2×C16—91no—
111C2×C16D3211yescharacteristic
112#108—32no—
113#104—182no—
114C4×C8—91no—
115C3×Q8—62no—
116C3×D4—62no—
117C3×D4—122no—
118C2×C3×C4—21no—
119C2×C3×C4—122no—
120C2×C3×C4D3×D412yes—
121#67—42no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124D12—22no—
125C4×D3—42no—
126Dic6—22no—
127C3×C8—21no—
128C3×C8—21no—
129C3×C8—122no—
130C3×C8C2×C4×D312yes—
131C3×C8#23712yes—
132C3⋊C8—32no—
133C3⋊C8—32no—
134C3⋊C8—42no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C2×C32—21no—
138C2×C32C4×D811yescharacteristic
139C3×D3—82no—
140#41—62no—
141Q16—32no—
142SD16—62no—
143D8—32no—
144M16—62no—
145M16—362no—
146C2×C8—91no—
147C2×C8—362no—
148C2×C8C2×D3211yescharacteristic
149C42—91no—
150C16—21no—
151C16—91no—
152C16—91no—
153C22×C3—21no—
154C22×C3—122no—
155C22×C3#91612yes—
156C2×D3—42no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—122no—
160C3×C4#67⋊C412yes—
161C3×C4D3×D812yes—
162Dic3—42no—
163Dic3—64no—
164Dic3—64no—
165C32#217811yescharacteristic, complemented, Sylow
166Q8—62no—
167D4—62no—
168D4—122no—
169C2×C4—122no—
170C2×C4—181no—
171C2×C4#380211yescharacteristic
172C8—91no—
173C8—91no—
174C8—122no—
175C8C4×D3211yescharacteristic
176C8#380511yescharacteristic
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—21no—
180C2×C3—242no—
181C2×C3#475612yes—
182D3—82no—
183C22—122no—
184C22#6380911yescharacteristic
185C4—122no—
186C4—182no—
187C4#6379711yescharacteristic
188C4#6390211yescharacteristic
189C3—21no—
190C3#6923812yescomplemented
191C2—21no—
192C2—242no—
193C2#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#2178
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. C16×C3⋊Dic3C2semidirect
4. C3×#4510C2semidirect
5. #10589144C2semidirect
14. #63550C4semidirect
15. #63547C4semidirect
16. #63545C4semidirect
21. #4510D3semidirect
165. C32#2178semidirect
190. C3#69238semidirect

Maximal subgroups

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

subgroupindex
#105909192
#105906292
C16×C3⋊Dic32
C3×#45102
#105891442
#692383