Finite Group Databasebeta

← #11798903

Subgroups — #11798903

Order 1152.

498 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 109 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#10592882C211yesmaximal, characteristic, complemented
2C2×#63655C211yesmaximal, characteristic
3C2×#63627C211yesmaximal, characteristic
4#10592571C211yesmaximal, characteristic
5C32×#358C211yesmaximal, characteristic, complemented
6#10589367C211yesmaximal, characteristic, complemented
7#10589358C211yesmaximal, characteristic, complemented
8#69234—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10#64153—21no—
11C2×#3756—21no—
12C2×#3746C2211yescharacteristic
13C2×#3745C2211yescharacteristic
14#64102—21no—
15C2×C32×C16C2211yescharacteristic
16C32×#107C2211yescharacteristic
17#63655—22no—
18C8×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20#63636—21no—
21#63627—22no—
22#5183—34no—
23C2×#828—34no—
24C2×#800—34no—
25#4872—34no—
26C3×#358D314yescomplemented
27Dic3⋊C16—34no—
28#4492—34no—
29C2×C32×Q8—21no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4×C3⋊D3—41no—
32C2×#634—21no—
33C32×Q16—21no—
34C32×Q16—21no—
35C2×C32×C8C2311yescharacteristic
36C32×C4⋊C4—21no—
37#3756—42no—
38#3752—41no—
39#3750—41no—
40#3750—41no—
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746—21no—
44#3746—21no—
45#3745—21no—
46#3745D412yes—
47C32×C16—21no—
48C3⋊(C3⋊C16)—21no—
49#2208—91noSylow
50C2×C3×Q16C2×D314yes—
51#944—64no—
52C2×#216—64no—
53C2×Dic12—34no—
54C2×D24—34no—
55#893—64no—
56C2×C3×C16C2×D314yes—
57C3×#107C2×D314yes—
58#828—68no—
59C8×Dic3—34no—
60C2×C3⋊C16—34no—
61#809—64no—
62#800—68no—
63C22×C3⋊D3—41no—
64C32×Q8—41no—
65C32×Q8—41no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3D811yescharacteristic
71C2×C3⋊Dic3D811yescharacteristic
72C4⋊(C3⋊D3)—22no—
73C4⋊(C3⋊D3)—41no—
74C4×C3⋊D3—82no—
75#634—41no—
76#634—41no—
77C32×C8C2×D411yescharacteristic
78C32×C8#4111yescharacteristic
79C3⋊(C3⋊C8)—21no—
80C2×SD32—91no—
81C2×SD32—91no—
82#494—91no—
83C4×D8—91no—
84C4⋊C16—91no—
85#358—91no—
86#358C3⋊D311yescharacteristic, complemented
87C2×C3×Q8—24no—
88C2×D12—64no—
89C2×C4×D3—124no—
90C2×Dic6—64no—
91C3×Q16—24no—
92C3×Q16—24no—
93C2×C3×C8C22×D314yes—
94C3×C4⋊C4—24no—
95#216—128no—
96(C2×D3)⋊C4—124no—
97Dic3⋊C4—124no—
98Dic3⋊C4—124no—
99C4×Dic3—34no—
100C2×C3⋊C8—34no—
101Dic12—64no—
102Dic12—64no—
103D24—38no—
104D24—64no—
105C3×C16—24no—
106C3⋊C16—64no—
107C22×C32C2×D811yescharacteristic
108C2×C3⋊D3—42no—
109C2×C3⋊D3—81no—
110C2×C3⋊D3—81no—
111C32×C4—81no—
112C32×C4—81no—
113C32×C4#12111yescharacteristic
114C32×C4AGL(1,ℤ/8)11yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3—81no—
117C3⋊Dic3SD3212yescomplemented
118C2×Q16—91no—
119C2×Q16—181no—
120C2×Q16C2×C3⋊D311yescharacteristic
121C2×D8—91no—
122C4⋊Q8—181no—
123C4×D4—181no—
124SD32—182no—
125SD32—182no—
126C2×C16—91no—
127C2×C16C2×C3⋊D311yescharacteristic
128#107C2×C3⋊D311yescharacteristic
129#102—181no—
130C4×C8—91no—
131C22×D3—124no—
132C3×Q8—44no—
133C3×Q8—44no—
134C2×C3×C4—44no—
135C2×C3×C4—44no—
136C2×C3×C4D3×D414yes—
137C2×Dic3—34no—
138C2×Dic3—34no—
139C2×Dic3—124no—
140D12—68no—
141D12—124no—
142C4×D3—248no—
143Dic6—124no—
144Dic6—124no—
145C3×C8#23514yes—
146C3×C8D3×D414yes—
147C3⋊C8—64no—
148C2×C32#45911yescharacteristic
149C2×C32C2×SD3211yescharacteristic
150C2×C32#51011yescharacteristic
151C3⋊D3—82no—
152C2×Q8—21no—
153C2×Q8—181no—
154C2×D4—181no—
155C22×C4—361no—
156Q16—21no—
157Q16—21no—
158Q16—181no—
159Q16—181no—
160Q16—362no—
161D8—92no—
162D8—181no—
163C2×C8—91no—
164C2×C8C22×C3⋊D311yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—361no—
167C4⋊C4—361no—
168C22⋊C4—361no—
169C42—91no—
170C16—21no—
171C16—181no—
172C22×C3D3×D814yes—
173C2×D3—128no—
174C2×D3—244no—
175C2×D3—244no—
176C3×C4—84no—
177C3×C4—84no—
178C3×C4#88414yes—
179C3×C4#91414yes—
180Dic3—38no—
181Dic3—64no—
182Dic3—244no—
183C32#220811yescharacteristic, complemented, Sylow
184C23—361no—
185Q8—41no—
186Q8—41no—
187Q8—361no—
188Q8—361no—
189D4—182no—
190D4—361no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—361no—
196C2×C4—722no—
197C2×C4D4×C3⋊D311yescharacteristic
198C8—181no—
199C8#382811yescharacteristic
200C8D4×C3⋊D311yescharacteristic
201C2×C3#478614yes—
202C2×C3D3×SD3214yes—
203C2×C3#491814yes—
204D3—248no—
205C22—362no—
206C22—721no—
207C22—721no—
208C22D8×C3⋊D311yescharacteristic
209C4—81no—
210C4—81no—
211C4—92no—
212C4—181no—
213C4—721no—
214C4#6409311yescharacteristic
215C4#6412311yescharacteristic
216C3#6923414yescomplemented
217C2—722no—
218C2#1059248511yescharacteristic
219C2C3⋊D3×SD3211yescharacteristic
220C2#1059261711yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#358C3⋊D3
hypocenterC32#2208
LCSG ▷ C2×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. #10592882C2semidirect
5. C32×#358C2semidirect
6. #10589367C2semidirect
7. #10589358C2semidirect
26. C3×#358D3semidirect
86. #358C3⋊D3semidirect
117. C3⋊Dic3SD32semidirect
183. C32#2208semidirect
216. C3#69234semidirect

Maximal subgroups

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

subgroupindex
#105928822
C2×#636552
C2×#636272
#105925712
C32×#3582
#105893672
#105893582
#692343