Finite Group Databasebeta

← #11799019

Subgroups — #11799019

Order 1152.

474 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×C32×Q32C211yesmaximal, characteristic, complemented
2#10592890C211yesmaximal, characteristic
3Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63655C211yesmaximal, characteristic
5#10589430C211yesmaximal, characteristic, complemented
6#10589375C211yesmaximal, characteristic
7#10589367C211yesmaximal, characteristic, complemented
8#71498—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10C2×C32×Q16C2211yescharacteristic
11#64156—21no—
12Q8×C3⋊Dic3—21no—
13C2×#3755—21no—
14C2×#3745C2211yescharacteristic
15C32×Q32—22no—
16C2×C32×C16C2211yescharacteristic
17#63662—21no—
18#63655—22no—
19#63645C2211yescharacteristic
20C8×C3⋊Dic3C2211yescharacteristic
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22C2×C3×Q32D314yescomplemented
23#5191—34no—
24Dic3×Q16—34no—
25C2×#828—34no—
26#4564—34no—
27#4509—34no—
28Dic3⋊C16—34no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C4⋊(C3⋊D3)—21no—
32C32×Q16—21no—
33C32×Q16—21no—
34C32×Q16—21no—
35C32×Q16D412yes—
36C2×C32×C8C2311yescharacteristic
37#3755—42no—
38#3752—41no—
39#3752—41no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—41no—
42C4×C3⋊Dic3—41no—
43C4×C3⋊Dic3D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45#3745—21no—
46#3745—21no—
47C32×C16—21no—
48C3⋊(C3⋊C16)—21no—
49#2211—91noSylow
50C2×C3×Q16C2×D314yes—
51C2×C3×Q16C2×D314yes—
52#947—64no—
53Q8×Dic3—64no—
54C2×#215—64no—
55C2×D24—34no—
56C3×Q32—28no—
57C2×C3×C16C2×D314yes—
58#835—64no—
59#828—68no—
60#818—34no—
61C8×Dic3—34no—
62C2×C3⋊C16—34no—
63C22×C3⋊D3—41no—
64C32×Q8—22no—
65C32×Q8—41no—
66C32×Q8—41no—
67C32×Q8—41no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4C2×D411yescharacteristic
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3D811yescharacteristic
73C2×C3⋊Dic3D811yescharacteristic
74C4⋊(C3⋊D3)—41no—
75C4⋊(C3⋊D3)—41no—
76C32×C8C2×D411yescharacteristic
77C32×C8#4111yescharacteristic
78C3⋊(C3⋊C8)—21no—
79C2×Q32C3⋊D311yescharacteristic, complemented
80C2×SD32—91no—
81#495—91no—
82C4×Q16—91no—
83C4⋊C16—91no—
84#358—91no—
85#357—91no—
86C2×C3×Q8—24no—
87C2×C3×Q8—24no—
88C2×D12—64no—
89C3×Q16—24no—
90C3×Q16—24no—
91C3×Q16—24no—
92C3×Q16#6718yes—
93C2×C3×C8C22×D314yes—
94#215—128no—
95(C2×D3)⋊C4—124no—
96(C2×D3)⋊C4—124no—
97C4⋊Dic3—64no—
98C4⋊Dic3—124no—
99C4×Dic3—34no—
100C4×Dic3—124no—
101C2×C3⋊C8—34no—
102D24—64no—
103D24—64no—
104C3×C16—24no—
105C3⋊C16—64no—
106C22×C32C2×D811yescharacteristic
107C2×C3⋊D3—81no—
108C2×C3⋊D3—81no—
109C2×C3⋊D3—81no—
110C32×C4—42no—
111C32×C4—81no—
112C32×C4#12111yescharacteristic
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3—81no—
117C2×Q16C2×C3⋊D311yescharacteristic
118C2×Q16C2×C3⋊D311yescharacteristic
119C2×SD16—181no—
120C2×D8—91no—
121#124—181no—
122C4×Q8—181no—
123Q32—22no—
124SD32—182no—
125C2×C16—91no—
126C2×C16C2×C3⋊D311yescharacteristic
127#107—91no—
128#103—181no—
129C4×C8—91no—
130C22×D3—124no—
131C3×Q8—28no—
132C3×Q8—44no—
133C3×Q8—44no—
134C3×Q8—44no—
135C2×C3×C4—44no—
136C2×C3×C4—44no—
137C2×C3×C4D3×D414yes—
138C2×Dic3—34no—
139C2×Dic3—34no—
140C2×Dic3—124no—
141D12—124no—
142D12—124no—
143C3×C8#23714yes—
144C3×C8C2×#6714yes—
145C3⋊C8—64no—
146C2×C32#45911yescharacteristic
147C2×C32#50811yescharacteristic
148C2×C32#51011yescharacteristic
149C3⋊D3—161no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×D4—181no—
153Q16—21no—
154Q16—21no—
155Q16—21no—
156Q16#63812yes—
157SD16—362no—
158D8—181no—
159D8—181no—
160C2×C8—91no—
161C2×C8C22×C3⋊D311yescharacteristic
162C4⋊C4—181no—
163C4⋊C4—361no—
164C22⋊C4—361no—
165C22⋊C4—361no—
166C42—91no—
167C42—361no—
168C16—21no—
169C16—181no—
170C22×C3D3×D814yes—
171C2×D3—244no—
172C2×D3—244no—
173C2×D3—244no—
174C3×C4—48no—
175C3×C4—84no—
176C3×C4#91114yes—
177C3×C4#93914yes—
178Dic3—64no—
179Dic3—64no—
180Dic3—244no—
181C32#221111yescharacteristic, complemented, Sylow
182C23—361no—
183Q8—22no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187D4—361no—
188D4—361no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—361no—
194C2×C4D4×C3⋊D311yescharacteristic
195C8—181no—
196C8#383011yescharacteristic
197C8C2×#63811yescharacteristic
198C2×C3#491814yes—
199C2×C3#491914yes—
200C2×C3#515014yes—
201D3—484no—
202C22—721no—
203C22—721no—
204C22—721no—
205C22D8×C3⋊D311yescharacteristic
206C4—42no—
207C4—81no—
208C4—181no—
209C4—181no—
210C4—721no—
211C4#6412011yescharacteristic
212C4#6414811yescharacteristic
213C3#7149814yescomplemented
214C2—1441no—
215C2#1059261711yescharacteristic
216C2#1059261811yescharacteristic
217C2#1059284911yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC2×C32×Q32C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenterC2×Q32C3⋊D3
hypocenterC32#2211
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
1. C2×C32×Q32C2semidirect
3. Q16×C3⋊Dic3C2semidirect
5. #10589430C2semidirect
7. #10589367C2semidirect
22. C2×C3×Q32D3semidirect
79. C2×Q32C3⋊D3semidirect
181. C32#2211semidirect
213. C3#71498semidirect

Maximal subgroups

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

subgroupindex
C2×C32×Q322
#105928902
Q16×C3⋊Dic32
C2×#636552
#105894302
#105893752
#105893672
#714983