Finite Group Databasebeta

← #11800598

Subgroups — #11800598

Order 1152.

273 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3⋊D3×D16C211yesmaximal, characteristic, complemented
2#10590244C211yesmaximal, characteristic, complemented
3C3×#4520C211yesmaximal, characteristic, complemented
4C3×#4519C211yesmaximal, characteristic, complemented
5#10589074C211yesmaximal, characteristic, complemented
6#10589071C211yesmaximal, characteristic, complemented
7#10589069C211yesmaximal, characteristic, complemented
8#69380—31nomaximal
9#69377—31nomaximal
10D8×C3⋊D3—21no—
11#63810—21no—
12C32×D16C2211yescharacteristic
13#63653—21no—
14#63626C2211yescharacteristic
15C16×C3⋊D3C2211yescharacteristic
16C3×Dic24C2211yescharacteristic, complemented
17C3×D48C2211yescharacteristic, complemented
18#63547—21no—
19C3×C3⋊C32C2211yescharacteristic, complemented
20C3×C3⋊C32C2211yescharacteristic, complemented
21#4919—31no—
22#4912—31no—
23D3×D16—31no—
24D3×D16—31no—
25D3×D16—61no—
26C3×SD64—31no—
27C3×D32—31no—
28#4521—31no—
29#4520D311yescharacteristic, complemented
30#4519—31no—
31#4519D311yescharacteristic, complemented
32#4449—31no—
33D96—31no—
34#4447—31no—
35#4447—31no—
36D4×C3⋊D3—41no—
37#3796—41no—
38C32×D8—21no—
39#3753—41no—
40#3745—21no—
41C8×C3⋊D3D411yescharacteristic
42C3×Dic12—21no—
43C3×D24—21no—
44#3715—41no—
45C32×C16C2311yescharacteristic
46C3⋊(C3⋊C16)D411yescharacteristic
47#2263—91noSylow
48#919—61no—
49#912—61no—
50D3×D8—61no—
51D3×D8—61no—
52D3×D8—62no—
53C3×Q32—31no—
54C3×D16—21no—
55C3×D16—31no—
56C3×D16C2×D311yescharacteristic
57C3×D16C2×D311yescharacteristic
58#828—61no—
59#827—61no—
60#826—61no—
61#826—61no—
62#826—62no—
63Dic24C2×D311yescharacteristic, complemented
64D48—31no—
65D48—31no—
66D48—61no—
67D48C2×D311yescharacteristic, complemented
68D3×C16—31no—
69D3×C16—31no—
70D3×C16—61no—
71C3×C32—31no—
72C3×C32—31no—
73C3⋊C32C2×D311yescharacteristic, complemented
74C3⋊C32C2×D311yescharacteristic, complemented
75C22×C3⋊D3—81no—
76C32×D4—41no—
77#638—81no—
78C4⋊(C3⋊D3)—41no—
79C4×C3⋊D3D811yescharacteristic
80C3×D12—41no—
81C3×Dic6—41no—
82#626—81no—
83D3×Dic3—81no—
84C32×C8C2×D411yescharacteristic
85C3⋊(C3⋊C8)D811yescharacteristic
86#508—91no—
87C2×D16—91no—
88SD64—31no—
89SD64—91no—
90D32—31no—
91D32—91no—
92M64—91no—
93#239—121no—
94#237—121no—
95D3×D4—121no—
96D3×D4—121no—
97D3×D4—122no—
98C3×Q16—61no—
99C3×D8—22no—
100C3×D8—21no—
101C3×D8—21no—
102C3×D8—61no—
103#215—121no—
104#214—121no—
105#213—121no—
106#213—121no—
107#213—122no—
108Dic12—21no—
109D24—21no—
110D24—62no—
111D24—61no—
112D24—61no—
113D3×C8—31no—
114D3×C8—31no—
115D3×C8—61no—
116C3×C16—21no—
117C3×C16C22×D311yescharacteristic
118C3×C16C22×D311yescharacteristic
119C3⋊C16—31no—
120C3⋊C16—31no—
121C3⋊C16—61no—
122C22×C32—81no—
123C2×C3⋊D3—81no—
124C2×C3⋊D3—162no—
125C2×C3⋊D3D1611yescharacteristic
126C2×C3×D3—81no—
127C32×C4C2×D811yescharacteristic
128C3⋊Dic3D1611yescharacteristic
129C3×Dic3—81no—
130#135—181no—
131C2×D8—181no—
132Q32—31no—
133SD32—181no—
134D16—31no—
135D16—91no—
136D16—181no—
137D16D3211yescharacteristic
138C2×C16—91no—
139C32—31no—
140C32—31no—
141C22×D3—241no—
142C22×D3—241no—
143C22×D3—242no—
144C3×Q8—121no—
145C3×D4—42no—
146C3×D4—41no—
147C3×D4—41no—
148C3×D4—121no—
149#67—241no—
150#67—241no—
151#67—242no—
152#67—241no—
153C2×Dic3—241no—
154D12—41no—
155D12—122no—
156D12—121no—
157D12—121no—
158D12—241no—
159C4×D3—31no—
160C4×D3—31no—
161C4×D3—61no—
162C4×D3—241no—
163Dic6—41no—
164C3×C8—21no—
165C3×C8D3×D411yescharacteristic
166C3×C8D3×D411yescharacteristic
167C3⋊C8—31no—
168C3⋊C8—31no—
169C3⋊C8—61no—
170C2×C32—161no—
171C2×C32C2×D1611yescharacteristic
172C3⋊D3—21no—
173C3⋊D3—161no—
174C3×D3—161no—
175#41—361no—
176C2×D4—361no—
177Q16—61no—
178SD16—361no—
179D8—21no—
180D8—61no—
181D8—181no—
182D8—361no—
183C2×C8—91no—
184C16—91no—
185C16C2×D3211yescharacteristic
186C22×C3—82no—
187C22×C3—81no—
188C22×C3—81no—
189C22×C3—241no—
190C2×D3—31no—
191C2×D3—31no—
192C2×D3—61no—
193C2×D3—81no—
194C2×D3—242no—
195C2×D3—241no—
196C2×D3—241no—
197C2×D3—484no—
198C2×D3—482no—
199C2×D3—482no—
200C3×C4—21no—
201C3×C4—241no—
202C3×C4D3×D811yescharacteristic
203C3×C4D3×D811yescharacteristic
204Dic3—31no—
205Dic3—31no—
206Dic3—61no—
207Dic3—81no—
208C32#226311yescharacteristic, complemented, Sylow
209C23—721no—
210Q8—121no—
211D4—41no—
212D4—121no—
213D4—361no—
214D4—721no—
215D4—721no—
216C2×C4—91no—
217C2×C4—721no—
218C8—91no—
219C8#381111yescharacteristic
220C2×C3—21no—
221C2×C3—162no—
222C2×C3—161no—
223C2×C3—161no—
224C2×C3—481no—
225C2×C3D3×D1611yescharacteristic
226C2×C3D3×D1611yescharacteristic
227D3—62no—
228D3—61no—
229D3—61no—
230D3—161no—
231D3—482no—
232D3—481no—
233D3—481no—
234C22—81no—
235C22—91no—
236C22—241no—
237C22—721no—
238C22—1442no—
239C4—91no—
240C4—241no—
241C4#6392611yescharacteristic
242C3—21no—
243C3#6937711yescharacteristic, complemented
244C3#6938011yescharacteristic, complemented
245C2—161no—
246C2—181no—
247C2—481no—
248C2—1441no—
249C2#1059102511yescharacteristic
subgroupG/H
centerC2#10591025
commutator, cosocleC32×C16C23
FrattiniC16C2×D32
FittingC32×D16C22
socleC2×C32C2×D16
hypercenterD16D32
hypocenterC32#2263
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D16

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×D16C2semidirect
2. #10590244C2semidirect
3. C3×#4520C2semidirect
4. C3×#4519C2semidirect
5. #10589074C2semidirect
6. #10589071C2semidirect
7. #10589069C2semidirect
16. C3×Dic24C22semidirect
17. C3×D48C22semidirect
19. C3×C3⋊C32C22semidirect
20. C3×C3⋊C32C22semidirect
29. #4520D3semidirect
31. #4519D3semidirect
63. Dic24C2×D3semidirect
67. D48C2×D3semidirect
73. C3⋊C32C2×D3semidirect
74. C3⋊C32C2×D3semidirect
208. C32#2263semidirect
243. C3#69377semidirect
244. C3#69380semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×D162
#105902442
C3×#45202
C3×#45192
#105890742
#105890712
#105890692
#693803
#693773