Finite Group Databasebeta

← #11800603

Subgroups — #11800603

Order 1152.

241 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 56 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#10590243C211yesmaximal, characteristic, complemented
2D3×D48C211yesmaximal, characteristic, complemented
3#10589314C211yesmaximal, characteristic, complemented
4C3×#4449C211yesmaximal, characteristic, complemented
5C3×#4447C211yesmaximal, characteristic, complemented
6#10589074C211yesmaximal, characteristic, complemented
7#10589071C211yesmaximal, characteristic, complemented
8#69380—31nomaximal
9#69373—31nomaximal
10#63808—21no—
11D3×D24—21no—
12#63626C2211yescharacteristic
13#63626C2211yescharacteristic, complemented
14C3×Dic24C2211yescharacteristic, complemented
15C3×D48C2211yescharacteristic
16C3×D3×C16C2211yescharacteristic
17#63549—21no—
18#63546—21no—
19C32×C32C2211yescharacteristic, complemented
20C3×C3⋊C32C2211yescharacteristic, complemented
21#4919—31no—
22D3×D16—31no—
23#4904—31no—
24C2×D48—31no—
25C3×SD64—31no—
26C3×M64—31no—
27#4521—31no—
28#4519—31no—
29#4449—31no—
30#4449D311yescharacteristic, complemented
31D96—31no—
32D96—31no—
33D96—31no—
34D96—61no—
35#4447D311yescharacteristic, complemented
36D3×D12—41no—
37#3799—41no—
38#3745—21no—
39#3745—21no—
40C3×Dic12—21no—
41C3×D24—21no—
42C3×D3×C8D411yescharacteristic
43#3717—41no—
44#3714—41no—
45C32×C16C2311yescharacteristic
46C3×C3⋊C16D411yescharacteristic
47#2263—91noSylow
48#919—61no—
49D3×D8—61no—
50#904—61no—
51C2×D24—61no—
52C3×Q32—31no—
53C3×D16—31no—
54C2×C3×C16—31no—
55#828—61no—
56#826—61no—
57Dic24C2×D311yescharacteristic, complemented
58#800—61no—
59D48—31no—
60D48—31no—
61D48—31no—
62D48—31no—
63D48—61no—
64D48—61no—
65D48—61no—
66D48C2×D311yescharacteristic
67D3×C16C2×D311yescharacteristic
68C3×C32—21no—
69C3×C32—31no—
70C3×C32C2×D311yescharacteristic, complemented
71C3×C32C2×D311yescharacteristic, complemented
72C3⋊C32C2×D311yescharacteristic, complemented
73C2×D32—81no—
74C4⋊(C3⋊D3)—41no—
75C4⋊(C3⋊D3)—41no—
76C3×D12—41no—
77C3×C4×D3D811yescharacteristic
78C3×Dic6—41no—
79#626—81no—
80#626—81no—
81#624—81no—
82C32×C8C2×D411yescharacteristic
83C3×C3⋊C8D811yescharacteristic
84#508—91no—
85C2×D16—91no—
86SD64—31no—
87SD64—91no—
88D32—91no—
89D32—91no—
90M64—31no—
91#239—121no—
92D3×D4—121no—
93#235—121no—
94C2×D12—121no—
95C3×Q16—61no—
96C3×D8—61no—
97C2×C3×C8—31no—
98#215—121no—
99#213—121no—
100Dic12—21no—
101D24—21no—
102D24—61no—
103D24—61no—
104D24—61no—
105D24—61no—
106D24—121no—
107D24—121no—
108D24—121no—
109#204—121no—
110D3×C8D1211yescharacteristic
111C3×C16—21no—
112C3×C16—31no—
113C3×C16C22×D311yescharacteristic
114C3×C16C22×D311yescharacteristic
115C3⋊C16D1211yescharacteristic
116C2×C3⋊D3—81no—
117C2×C3⋊D3—81no—
118C2×C3×D3—81no—
119C2×C3×D3D1611yescharacteristic
120D32—162no—
121C32×C4C2×D811yescharacteristic
122C3×Dic3—81no—
123C3×Dic3D1611yescharacteristic
124#135—181no—
125C2×D8—181no—
126Q32—31no—
127SD32—181no—
128D16—31no—
129D16—91no—
130D16—91no—
131D16—181no—
132C2×C16—31no—
133C32—31no—
134C32D3211yescharacteristic, complemented
135C22×D3—241no—
136C22×D3—241no—
137C3×Q8—121no—
138C3×D4—121no—
139C2×C3×C4—31no—
140#67—241no—
141#67—241no—
142D12—41no—
143D12—121no—
144D12—121no—
145D12—121no—
146D12—121no—
147D12—241no—
148D12—241no—
149D12—241no—
150D12—241no—
151C4×D3—241no—
152C4×D3—241no—
153C4×D3D2411yescharacteristic
154Dic6—41no—
155C3×C8—21no—
156C3×C8—31no—
157C3×C8C2×D1211yescharacteristic
158C3×C8D3×D411yescharacteristic
159C3⋊C8D2411yescharacteristic
160C2×C32C2×D1611yescharacteristic
161C3⋊D3—161no—
162C3⋊D3—161no—
163C3×D3—21no—
164C3×D3—161no—
165#41—361no—
166C2×D4—361no—
167Q16—61no—
168SD16—361no—
169D8—61no—
170D8—181no—
171D8—181no—
172D8—361no—
173C2×C8—31no—
174C16—31no—
175C16C2×D3211yescharacteristic
176C22×C3—31no—
177C22×C3—241no—
178C2×D3—81no—
179C2×D3—241no—
180C2×D3—241no—
181C2×D3—241no—
182C2×D3—241no—
183C2×D3—481no—
184C2×D3—481no—
185C2×D3—482no—
186C2×D3—482no—
187C2×D3D4811yescharacteristic
188C3×C4—21no—
189C3×C4—31no—
190C3×C4—241no—
191C3×C4C2×D2411yescharacteristic
192C3×C4D3×D811yescharacteristic
193Dic3—81no—
194Dic3D4811yescharacteristic
195C32#226311yescharacteristic, complemented, Sylow
196C23—721no—
197Q8—121no—
198D4—121no—
199D4—361no—
200D4—361no—
201D4—721no—
202D4—721no—
203C2×C4—31no—
204C2×C4—721no—
205C8—31no—
206C8D3×D1211yescharacteristic
207C2×C3—21no—
208C2×C3—61no—
209C2×C3—481no—
210C2×C3C2×D4811yescharacteristic
211C2×C3D3×D1611yescharacteristic
212D3—21no—
213D3—161no—
214D3—481no—
215D3—481no—
216D3—481no—
217D3—481no—
218D3—961no—
219D3—961no—
220C22—31no—
221C22—241no—
222C22—721no—
223C22—721no—
224C22—1442no—
225C4—31no—
226C4—241no—
227C4D3×D2411yescharacteristic
228C3—21no—
229C3#6937311yescharacteristic, complemented
230C3#6938011yescharacteristic, complemented
231C2—61no—
232C2—481no—
233C2—1441no—
234C2—1441no—
235C2D3×D4811yescharacteristic
subgroupG/H
centerC2D3×D48
commutator, cosocleC32×C16C23
FrattiniC16C2×D32
FittingC32×C32C22
socleC2×C32C2×D16
hypercenterC32D32
hypocenterC32#2263
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32

Complements

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

NH ≅ G/Ntype
1. #10590243C2semidirect
2. D3×D48C2semidirect
3. #10589314C2semidirect
4. C3×#4449C2semidirect
5. C3×#4447C2semidirect
6. #10589074C2semidirect
7. #10589071C2semidirect
13. #63626C22semidirect
14. C3×Dic24C22semidirect
19. C32×C32C22semidirect
20. C3×C3⋊C32C22semidirect
30. #4449D3semidirect
35. #4447D3semidirect
57. Dic24C2×D3semidirect
70. C3×C32C2×D3semidirect
71. C3×C32C2×D3semidirect
72. C3⋊C32C2×D3semidirect
134. C32D32semidirect
195. C32#2263semidirect
229. C3#69373semidirect
230. C3#69380semidirect

Maximal subgroups

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

subgroupindex
#105902432
D3×D482
#105893142
C3×#44492
C3×#44472
#105890742
#105890712
#693803
#693733