Finite Group Databasebeta

← #11798923

Subgroups — #11798923

Order 1152.

399 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592571C211yesmaximal, characteristic
2#10590905C211yesmaximal, characteristic, complemented
3C2×#63549C212yesmaximal
4C3×#4492C212yesmaximal, complemented
5#10589133C211yesmaximal, characteristic, complemented
6#69234—32nomaximal
7C2×#3745C2211yescharacteristic
8#64102—21no—
9C2×C3×Dic12C2212yes—
10#63873—21no—
11C2×#3718—21no—
12C32×#107C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63636—21no—
15C2×C3×C3⋊C16C2212yes—
16#63549—24no—
17#5183—32no—
18C2×#828—32no—
19C2×#800—32no—
20#4872—32no—
21#4872—61no—
22C3×#358—32no—
23Dic3⋊C16—32no—
24#4492D312yescomplemented
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4×C3⋊D3—41no—
27C2×C3×Dic6—22no—
28C2×C32×C8C2311yescharacteristic
29C32×C4⋊C4—21no—
30#3752—41no—
31C4×C3⋊Dic3D411yescharacteristic
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33#3745—21no—
34#3745D412yes—
35C3×Dic12—22no—
36C3×Dic12—22no—
37#3724—41no—
38#3724—41no—
39#3718—42no—
40C3×C3⋊C16—22no—
41#2208—91noSylow
42C2×C3×Q16—32no—
43#944—62no—
44C2×#216—62no—
45C2×Dic12C2×D312yes—
46C2×D24—32no—
47C2×D24—61no—
48#893—62no—
49#893—62no—
50C2×C3×C16—32no—
51C3×#107—21no—
52C3×#107C2×D312yes—
53#828—64no—
54C8×Dic3—32no—
55C8×Dic3—61no—
56C2×C3⋊C16C2×D312yes—
57#809—62no—
58#809—62no—
59#800—64no—
60C22×C3⋊D3—41no—
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3D811yescharacteristic
64C2×C3⋊Dic3D811yescharacteristic
65C4⋊(C3⋊D3)—22no—
66C4⋊(C3⋊D3)—41no—
67C4×C3⋊D3—82no—
68C2×C3×Dic3—42no—
69C3×Dic6—42no—
70C3×Dic6—42no—
71C32×C8C2×D411yescharacteristic
72C32×C8#4111yescharacteristic
73C3⋊(C3⋊C8)—21no—
74C2×SD32—92no—
75#494—91no—
76C4×D8—91no—
77C4⋊C16—91no—
78#358—32no—
79C2×C3×Q8—62no—
80C2×D12—62no—
81C2×D12—62no—
82C2×C4×D3—122no—
83C2×C4×D3—122no—
84C2×Dic6—22no—
85C3×Q16—62no—
86C3×Q16—62no—
87C2×C3×C8—21no—
88C2×C3×C8C22×D312yes—
89C3×C4⋊C4—22no—
90C3×C4⋊C4—22no—
91#216—124no—
92(C2×D3)⋊C4—122no—
93(C2×D3)⋊C4—122no—
94Dic3⋊C4—122no—
95Dic3⋊C4—122no—
96C4×Dic3—32no—
97C4×Dic3—61no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—61no—
100Dic12—22no—
101Dic12—22no—
102D24—34no—
103D24—62no—
104D24—62no—
105D24—62no—
106C3×C16—62no—
107C3⋊C16—22no—
108C22×C32C2×D811yescharacteristic
109C2×C3⋊D3—42no—
110C2×C3⋊D3—81no—
111C2×C3⋊D3—81no—
112C32×C4—81no—
113C32×C4#12111yescharacteristic
114C32×C4AGL(1,ℤ/8)11yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3SD3212yescomplemented
117C3×Dic3—82no—
118C2×Q16—32no—
119C2×Q16—181no—
120C2×D8—91no—
121C4⋊Q8—181no—
122C4×D4—181no—
123SD32—184no—
124C2×C16—32no—
125#107D3211yescharacteristic
126#102—181no—
127C4×C8—91no—
128C22×D3—122no—
129C22×D3—122no—
130C3×Q8—122no—
131C3×Q8—122no—
132C2×C3×C4—21no—
133C2×C3×C4—42no—
134C2×C3×C4—42no—
135C2×C3×C4—122no—
136C2×C3×C4D3×D412yes—
137C2×Dic3—32no—
138C2×Dic3—32no—
139C2×Dic3—42no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142D12—64no—
143D12—64no—
144D12—122no—
145D12—122no—
146C4×D3—244no—
147C4×D3—244no—
148Dic6—42no—
149Dic6—42no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8#23512yes—
153C3×C8D3×D412yes—
154C3⋊C8—62no—
155C3⋊C8—121no—
156C2×C32#45911yescharacteristic
157C2×C32C2×SD3211yescharacteristic
158C2×C32#51011yescharacteristic
159C3⋊D3—82no—
160C2×Q8—62no—
161C2×D4—181no—
162C22×C4—361no—
163Q16—62no—
164Q16—62no—
165Q16—362no—
166D8—92no—
167D8—181no—
168C2×C8—91no—
169C2×C8C2×D3211yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—361no—
172C4⋊C4—361no—
173C22⋊C4—361no—
174C42—91no—
175C16—62no—
176C22×C3—21no—
177C22×C3D3×D812yes—
178C2×D3—124no—
179C2×D3—124no—
180C2×D3—242no—
181C2×D3—242no—
182C2×D3—242no—
183C2×D3—242no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—82no—
187C3×C4—82no—
188C3×C4—242no—
189C3×C4#88412yes—
190C3×C4#91412yes—
191Dic3—34no—
192Dic3—62no—
193Dic3—62no—
194Dic3—82no—
195Dic3—121no—
196C32#220811yescharacteristic, complemented, Sylow
197C23—361no—
198Q8—122no—
199Q8—122no—
200D4—182no—
201D4—361no—
202C2×C4—41no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—122no—
206C2×C4—722no—
207C2×C4#381111yescharacteristic
208C8—181no—
209C8#379811yescharacteristic
210C8#380211yescharacteristic
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3#478612yes—
215C2×C3D3×SD3212yes—
216C2×C3#491812yes—
217D3—244no—
218D3—244no—
219C22—362no—
220C22—721no—
221C22—721no—
222C22#6392611yescharacteristic
223C4—81no—
224C4—92no—
225C4—181no—
226C4—242no—
227C4#6391211yescharacteristic
228C4#6394111yescharacteristic
229C3—21no—
230C3#6923412yescomplemented
231C2—722no—
232C2#1059055111yescharacteristic
233C2#1059102911yescharacteristic
234C2#1059104411yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#107D32
hypocenterC32#2208
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10590905C2semidirect
4. C3×#4492C2semidirect
5. #10589133C2semidirect
24. #4492D3semidirect
116. C3⋊Dic3SD32semidirect
196. C32#2208semidirect
230. C3#69234semidirect

Maximal subgroups

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

subgroupindex
#105925712
#105909052
C2×#635492
C3×#44922
#105891332
#692343