Finite Group Databasebeta

← #11797649

Subgroups — #11797649

Order 1152.

486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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
1Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#63655C211yesmaximal, characteristic
3#10592571C211yesmaximal, characteristic
4C32×#358C211yesmaximal, characteristic, complemented
5#10589375C211yesmaximal, characteristic
6C16×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10589356C211yesmaximal, characteristic, complemented
8#69206—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10Q8×C3⋊Dic3—21no—
11C2×#3745C2211yescharacteristic
12#64102—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15#63662—21no—
16#63655C414yescomplemented
17#63645C2211yescharacteristic
18C8×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20#63636—21no—
21Dic3×Q16—34no—
22C2×#828—34no—
23#4872—34no—
24C3×#358D314yescomplemented
25#4509—34no—
26Dic3×C16—34no—
27#4490—34no—
28C2×C32×Q8—21no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4×C3⋊D3—41no—
31C32×Q16—21no—
32C32×Q16C2×C412yescomplemented
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—41no—
38C4×C3⋊Dic3—41no—
39C4×C3⋊Dic3D411yescharacteristic
40C2×C3⋊(C3⋊C8)D411yescharacteristic
41#3745—21no—
42#3745C2×C412yes—
43C32×C16—21no—
44C3⋊(C3⋊C16)C2×C412yescomplemented
45C4×SD32—91noSylow
46C2×C3×Q16C2×D314yes—
47Q8×Dic3—64no—
48C2×D24—34no—
49#893—64no—
50C2×C3×C16C2×D314yes—
51C3×#107C2×D314yes—
52#835—64no—
53#828—316no—
54#818—34no—
55C8×Dic3—34no—
56C2×C3⋊C16—34no—
57#809—64no—
58C22×C3⋊D3—41no—
59C32×Q8—22no—
60C32×Q8—41no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3D811yescharacteristic
66C2×C3⋊Dic3D811yescharacteristic
67C4⋊(C3⋊D3)—22no—
68C4⋊(C3⋊D3)—41no—
69C4×C3⋊D3—82no—
70C32×C8C22×C411yescharacteristic
71C32×C8#4111yescharacteristic
72C3⋊(C3⋊C8)—21no—
73C2×SD32—91no—
74C4×Q16—91no—
75C4×D8—91no—
76#367—91no—
77#358C3⋊D311yescharacteristic, complemented
78#357—91no—
79C4×C16—91no—
80C2×C3×Q8—24no—
81C2×D12—64no—
82C2×C4×D3—124no—
83C3×Q16—24no—
84C3×Q16C4×D318yescomplemented
85C2×C3×C8C22×D314yes—
86C3×C4⋊C4—24no—
87(C2×D3)⋊C4—124no—
88C4⋊Dic3—64no—
89C4⋊Dic3—124no—
90C4×Dic3—34no—
91C4×Dic3—124no—
92C2×C3⋊C8—34no—
93D24—38no—
94D24—64no—
95C3×C16—24no—
96C3⋊C16—38no—
97C22×C32C2×D811yescharacteristic
98C2×C3⋊D3—42no—
99C2×C3⋊D3—81no—
100C2×C3⋊D3—81no—
101C32×C4—42no—
102C32×C4—81no—
103C32×C4C4×D411yescharacteristic
104C32×C4#13511yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3—81no—
107C3⋊Dic3SD3212yescomplemented
108C2×Q16C2×C3⋊D311yescharacteristic
109C2×D8—91no—
110C4×Q8—181no—
111C4×D4—181no—
112SD32—94no—
113C2×C16—91no—
114C2×C16C2×C3⋊D311yescharacteristic
115#107—91no—
116#107C2×C3⋊D311yescharacteristic
117#103—181no—
118#102—181no—
119C4×C8—91no—
120C22×D3—124no—
121C3×Q8—28no—
122C3×Q8—44no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4D3×D414yes—
126C2×Dic3—34no—
127C2×Dic3—34no—
128C2×Dic3—124no—
129D12—68no—
130D12—124no—
131C4×D3—248no—
132C3×C8C2×C4×D314yes—
133C3×C8#23714yes—
134C3⋊C8—64no—
135C2×C32C4×D811yescharacteristic
136C2×C32C2×SD3211yescharacteristic
137C2×C32#50811yescharacteristic
138C3⋊D3—82no—
139C2×Q8—21no—
140C2×D4—181no—
141C22×C4—361no—
142Q16—21no—
143Q16C4×C3⋊D312yescomplemented
144D8—92no—
145D8—181no—
146C2×C8—91no—
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—21no—
149C4⋊C4—181no—
150C4⋊C4—361no—
151C22⋊C4—361no—
152C42—91no—
153C42—361no—
154C16—21no—
155C16—92no—
156C22×C3D3×D814yes—
157C2×D3—128no—
158C2×D3—244no—
159C2×D3—244no—
160C3×C4—48no—
161C3×C4—84no—
162C3×C4#67⋊C414yes—
163C3×C4#91614yes—
164Dic3—38no—
165Dic3—64no—
166Dic3—244no—
167C32C4×SD3211yescharacteristic, complemented, Sylow
168C23—361no—
169Q8—22no—
170Q8—41no—
171D4—182no—
172D4—361no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—361no—
178C2×C4—722no—
179C2×C4D4×C3⋊D311yescharacteristic
180C8—181no—
181C8C2×C4×C3⋊D311yescharacteristic
182C8#383011yescharacteristic
183C2×C3#475614yes—
184C2×C3D3×SD3214yes—
185C2×C3#491914yes—
186D3—248no—
187C22—362no—
188C22—721no—
189C22—721no—
190C22D8×C3⋊D311yescharacteristic
191C4—42no—
192C4—81no—
193C4—92no—
194C4—181no—
195C4—721no—
196C4#6409011yescharacteristic
197C4#6412511yescharacteristic
198C3#6920614yescomplemented
199C2—722no—
200C2#1059245511yescharacteristic
201C2C3⋊D3×SD3211yescharacteristic
202C2#1059261811yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
cosocleC2×C32×C8C23
hypercenter#358C3⋊D3
hypocenterC32C4×SD32
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. Q16×C3⋊Dic3C2semidirect
4. C32×#358C2semidirect
6. C16×C3⋊Dic3C2semidirect
7. #10589356C2semidirect
16. #63655C4semidirect
24. C3×#358D3semidirect
32. C32×Q16C2×C4semidirect
44. C3⋊(C3⋊C16)C2×C4semidirect
77. #358C3⋊D3semidirect
84. C3×Q16C4×D3semidirect
107. C3⋊Dic3SD32semidirect
143. Q16C4×C3⋊D3semidirect
167. C32C4×SD32semidirect
198. C3#69206semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
C2×#636552
#105925712
C32×#3582
#105893752
C16×C3⋊Dic32
#105893562
#692063