Finite Group Databasebeta

← #11799787

Subgroups — #11799787

Order 1152.

367 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 367 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592582C211yesmaximal, characteristic
2#10590687C211yesmaximal, characteristic, complemented
3C3×#4489C212yesmaximal, complemented
4#10589116C212yesmaximal, complemented
5#10589108C211yesmaximal, characteristic, complemented
6#69330—32nomaximal
7C2×#3745C2211yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9#64104—21no—
10#63900—21no—
11C32×#107C2211yescharacteristic
12#63636—21no—
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16#4883—32no—
17#4883—61no—
18D3×#107—32no—
19C3×#366—32no—
20#4509—32no—
21(C2×D3)⋊C16—32no—
22#4491—32no—
23#4489D312yescomplemented
24C2×C4⋊(C3⋊D3)—21no—
25C2×C4⋊(C3⋊D3)—41no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×#624—41no—
28C2×C32×C8C2311yescharacteristic
29C32×C4⋊C4—21no—
30#3752—41no—
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3745—22no—
33C8×C3⋊D3—22no—
34C3×C4⋊Dic3—22no—
35#3724—41no—
36C3×C3⋊C16—22no—
37#2232—91noSylow
38C2×D24—32no—
39C2×D24—61no—
40C2×D3×C8—32no—
41C2×D3×C8—61no—
42#895—62no—
43#895—62no—
44D3×C4⋊C4—62no—
45C2×C3×C16—32no—
46C3×#107—21no—
47C3×#107—32no—
48C3×#107C2×D312yes—
49#818C2×D312yes—
50C2×C3⋊C16C2×D312yes—
51#809—62no—
52#809—62no—
53#807—62no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3D811yescharacteristic
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3D811yescharacteristic
59C4⋊(C3⋊D3)—41no—
60C4⋊(C3⋊D3)—41no—
61C4⋊(C3⋊D3)—82no—
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C2×C3×Dic3—42no—
65#624—82no—
66C32×C8#4112yes—
67C3⋊(C3⋊C8)—21no—
68#466—91no—
69C2×#107—91no—
70#366—32no—
71#357—92no—
72C22⋊C16—91no—
73C2×D12—62no—
74C2×D12—62no—
75C2×D12—122no—
76C2×D12—122no—
77C2×C4×D3—32no—
78C2×C4×D3—61no—
79C2×C4×D3—122no—
80C2×C3×C8—21no—
81C2×C3×C8C22×D312yes—
82C3×C4⋊C4—22no—
83C3×C4⋊C4—22no—
84C3×C4⋊C4—62no—
85(C2×D3)⋊C4—122no—
86(C2×D3)⋊C4—122no—
87C4⋊Dic3—22no—
88Dic3⋊C4—122no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—61no—
91D24—62no—
92D24—62no—
93D24—122no—
94D3×C8—62no—
95D3×C8—62no—
96D3×C8—122no—
97C3×C16—62no—
98C3⋊C16—22no—
99C22×C32C2×D811yescharacteristic
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3—81no—
103C2×C3⋊D3—81no—
104C2×C3⋊D3—81no—
105C2×C3⋊D3D1612yes—
106C32×C4—81no—
107C32×C4#12311yescharacteristic
108C32×C4#13711yescharacteristic
109C3⋊Dic3—21no—
110C3×Dic3—82no—
111C2×D8—91no—
112C22×C8—91no—
113#121—181no—
114C2×C4⋊C4—181no—
115C2×C16—32no—
116#107—32no—
117#107—181no—
118#107D3211yescharacteristic
119#102—181no—
120C22×D3—32no—
121C22×D3—61no—
122C22×D3—122no—
123C22×D3—122no—
124C2×C3×C4—21no—
125C2×C3×C4—42no—
126C2×C3×C4—42no—
127C2×C3×C4—122no—
128C2×C3×C4D3×D412yes—
129C2×Dic3—32no—
130C2×Dic3—42no—
131C2×Dic3—61no—
132D12—122no—
133D12—122no—
134D12—122no—
135D12—122no—
136D12—244no—
137D12—244no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—121no—
141C4×D3—121no—
142C4×D3—244no—
143C3×C8—22no—
144C3×C8#23512yes—
145C3×C8#23912yes—
146C3⋊C8—62no—
147C3⋊C8—121no—
148C2×C32#48011yescharacteristic
149C2×C32C2×D1611yescharacteristic
150C2×C32#51011yescharacteristic
151C3⋊D3—22no—
152C3⋊D3—161no—
153C2×D4—181no—
154C2×D4—361no—
155C22×C4—91no—
156C22×C4—361no—
157D8—182no—
158C2×C8—91no—
159C2×C8—182no—
160C2×C8C2×D3211yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—62no—
163C4⋊C4—361no—
164C22⋊C4—361no—
165C16—62no—
166C22×C3—21no—
167C22×C3D3×D812yes—
168C2×D3—34no—
169C2×D3—62no—
170C2×D3—62no—
171C2×D3—62no—
172C2×D3—121no—
173C2×D3—121no—
174C2×D3—242no—
175C2×D3—242no—
176C2×D3—242no—
177C2×D3—242no—
178C2×D3—242no—
179C2×D3—242no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—82no—
183C3×C4—82no—
184C3×C4—242no—
185C3×C4#89412yes—
186C3×C4#91812yes—
187Dic3—62no—
188Dic3—82no—
189Dic3—121no—
190C32#223211yescharacteristic, complemented, Sylow
191C23—91no—
192C23—361no—
193D4—361no—
194D4—361no—
195D4—722no—
196C2×C4—41no—
197C2×C4—91no—
198C2×C4—122no—
199C2×C4—181no—
200C2×C4—181no—
201C2×C4—722no—
202C2×C4#381111yescharacteristic
203C8—181no—
204C8#379912yes—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3#488212yes—
209C2×C3D3×D1612yes—
210C2×C3#491812yes—
211D3—64no—
212D3—122no—
213D3—482no—
214D3—482no—
215C22—92no—
216C22—181no—
217C22—181no—
218C22—721no—
219C22—721no—
220C22—721no—
221C22#6392611yescharacteristic
222C4—81no—
223C4—181no—
224C4—242no—
225C4#6389711yescharacteristic
226C4#6394511yescharacteristic
227C3—21no—
228C3#6933012yescomplemented
229C2—182no—
230C2—1441no—
231C2#1059044211yescharacteristic
232C2#1059102511yescharacteristic
233C2#1059104411yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radical#10592582C2
hypercenter#107D32
hypocenterC32#2232
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. #10590687C2semidirect
3. C3×#4489C2semidirect
4. #10589116C2semidirect
5. #10589108C2semidirect
23. #4489D3semidirect
190. C32#2232semidirect
228. C3#69330semidirect

Maximal subgroups

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

subgroupindex
#105925822
#105906872
C3×#44892
#105891162
#105891082
#693303