Finite Group Databasebeta

← #11797573

Subgroups — #11797573

Order 1152.

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

normal subgroups only

This group has 321 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
1#10590921C211yesmaximal, characteristic
2#10590622C212yesmaximal, complemented
3C16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4508C212yesmaximal, complemented
5#10589135C211yesmaximal, characteristic, complemented
6#69122—32nomaximal
7C3×#901C2212yes—
8#63822C411yescharacteristic
9C2×C32×C16C2211yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C3×#812C2212yes—
13#63578C411yescharacteristic
14#63568C412yes—
15#63543—22no—
16D3×C3⋊C16—22no—
17#5144—32no—
18#5140—32no—
19#4907—32no—
20C3×#350—32no—
21#4511—32no—
22#4508D312yescomplemented
23Dic3×C16—32no—
24Dic3×C16—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×C16—21no—
36C3⋊(C3⋊C16)D411yescharacteristic
37C3⋊(C3⋊C16)D411yescharacteristic
38C3×C3⋊C16—22no—
39#2170—91noSylow
40C3×#131—32no—
41#950—32no—
42#901C2×D312yes—
43C3×M32—32no—
44C2×C3×C16—21no—
45C2×C3×C16C2×D312yes—
46#837—32no—
47#825—32no—
48#822—32no—
49C8×Dic3—32no—
50C8×Dic3—61no—
51#812—62no—
52#812C2×D312yes—
53C2×C3⋊C16—32no—
54C2×C3⋊C16—61no—
55C2×C3⋊C16—62no—
56#798—62no—
57D3×C16—62no—
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3—21no—
60C3×#67—22no—
61C3×D12C2×C812yes—
62C3×C4×D3—22no—
63C3×Dic6C2×C812yes—
64C32×C8C2×D411yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)C2×C811yescharacteristic
67C3⋊(C3⋊C8)C2×C811yescharacteristic
68C3×C3⋊C8—22no—
69#504—92no—
70#443—91no—
71#364—91no—
72#350—32no—
73C4×C16—91no—
74C3×#41—32no—
75#235C4×D312yes—
76C3×M16—32no—
77C3×M16—62no—
78C2×C3×C8—21no—
79C2×C3×C8—62no—
80C2×C3×C8C22×D312yes—
81#216—32no—
82#215—32no—
83#214—32no—
84#213—32no—
85C4×Dic3—32no—
86C4×Dic3—61no—
87#208C4×D312yes—
88C2×C3⋊C8—32no—
89C2×C3⋊C8—61no—
90ΓL(1,𝔽25)—22no—
91D3×C8—22no—
92C3×C16—22no—
93C3×C16—22no—
94C3×C16—62no—
95C3⋊C16—22no—
96C3⋊C16—32no—
97C3⋊C16—32no—
98C3⋊C16—61no—
99C3⋊C16—61no—
100C22×C32#13111yescharacteristic
101C2×C3×D3—22no—
102C32×C4C4×D411yescharacteristic
103C32×C4C22×C811yescharacteristic
104C3⋊Dic3—22no—
105C3×Dic3—22no—
106#135—91no—
107#131—32no—
108M32—32no—
109M32—182no—
110C2×C16—91no—
111C2×C16—182no—
112C2×C16D3211yescharacteristic
113#108—91no—
114#104—92no—
115C4×C8—91no—
116C3×Q8—32no—
117C3×D4—32no—
118C3×D4—62no—
119C2×C3×C4—21no—
120C2×C3×C4—62no—
121C2×C3×C4C2×C4×D312yes—
122#67—22no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125D12D3×C812yes—
126C4×D3—22no—
127Dic6D3×C812yes—
128C3×C8—21no—
129C3×C8—21no—
130C3×C8—62no—
131C3×C8D3×D412yes—
132C3×C8#23712yes—
133C3⋊C8—22no—
134C3⋊C8—32no—
135C3⋊C8—32no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C2×C32—21no—
139C2×C32C8×D411yescharacteristic
140C3×D3—42no—
141#41—32no—
142Q16—91no—
143SD16—92no—
144D8—91no—
145M16—32no—
146M16—62no—
147C2×C8—62no—
148C2×C8—91no—
149C2×C8C2×D3211yescharacteristic
150C42—91no—
151C16—21no—
152C16—62no—
153C16—91no—
154C16—91no—
155C22×C3—21no—
156C22×C3—62no—
157C22×C3#90712yes—
158C2×D3—22no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—62no—
162C3×C4#67⋊C412yes—
163C3×C4C2×D3×C812yes—
164Dic3—22no—
165Dic3—64no—
166Dic3—64no—
167C32#217011yescharacteristic, complemented, Sylow
168Q8—32no—
169D4—32no—
170D4—62no—
171C2×C4—62no—
172C2×C4—181no—
173C2×C4C4×D3211yescharacteristic
174C8—62no—
175C8—91no—
176C8—91no—
177C8#380211yescharacteristic
178C8#380511yescharacteristic
179C2×C3—22no—
180C2×C3—22no—
181C2×C3—21no—
182C2×C3—122no—
183C2×C3#67⋊C812yes—
184D3—42no—
185C22—62no—
186C22#6380511yescharacteristic
187C4—62no—
188C4—182no—
189C4D32×C811yescharacteristic
190C4#6390211yescharacteristic
191C3—21no—
192C3#6912212yescomplemented
193C2—21no—
194C2—122no—
195C2#1059071811yescharacteristic
subgroupG/H
centerC8#3802
commutatorC32×C4C22×C8
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32C8×D4
prime radical#63822C4
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2170
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #10590622C2semidirect
3. C16×C3⋊Dic3C2semidirect
4. C3×#4508C2semidirect
5. #10589135C2semidirect
22. #4508D3semidirect
167. C32#2170semidirect
192. C3#69122semidirect

Maximal subgroups

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

subgroupindex
#105909212
#105906222
C16×C3⋊Dic32
C3×#45082
#105891352
#691223