Finite Group Databasebeta

← #11800604

Subgroups — #11800604

Order 1152.

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

normal subgroups only

This group has 240 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
1#10590244C211yesmaximal, characteristic, complemented
2#10590234C211yesmaximal, characteristic, complemented
3#10589313C211yesmaximal, characteristic, complemented
4C3×#4449C211yesmaximal, characteristic, complemented
5C3×D96C211yesmaximal, characteristic, complemented
6#10589072C211yesmaximal, characteristic, complemented
7#10589070C211yesmaximal, characteristic, complemented
8#69380—31nomaximal
9#69377—31nomaximal
10#63810—21no—
11#63797—21no—
12C16×C3⋊D3C2211yescharacteristic
13C3×Dic24C2211yescharacteristic, complemented
14C3×D48C2211yescharacteristic
15C3×D48C2211yescharacteristic
16C3×D48C2211yescharacteristic, complemented
17#63547—21no—
18#63545—21no—
19C32×C32C2211yescharacteristic, complemented
20C3⋊(C3⋊C32)C2211yescharacteristic, complemented
21#4919—31no—
22#4912—31no—
23D3×D16—31no—
24D3×D16—31no—
25C3×SD64—31no—
26C3×D32—31no—
27#4521—31no—
28#4520—31no—
29#4519—31no—
30#4519—31no—
31#4449D311yescharacteristic, complemented
32D96D311yescharacteristic, complemented
33#4447—31no—
34#4447—31no—
35#4447—61no—
36#3802—41no—
37#3796—41no—
38C8×C3⋊D3D411yescharacteristic
39C3×Dic12—21no—
40C3×D24—21no—
41C3×D24—21no—
42C3×D24—21no—
43#3715—41no—
44#3713—41no—
45C32×C16C2311yescharacteristic
46C3⋊(C3⋊C16)D411yescharacteristic
47#2263—91noSylow
48#919—61no—
49#912—61no—
50D3×D8—61no—
51D3×D8—61no—
52C3×Q32—31no—
53C3×D16—31no—
54C3×D16—31no—
55C3×D16—31no—
56#828—61no—
57#827—61no—
58#826—61no—
59#826—61no—
60Dic24C2×D311yescharacteristic, complemented
61D48C2×D311yescharacteristic
62D48C2×D311yescharacteristic
63D48C2×D311yescharacteristic, complemented
64D3×C16—31no—
65D3×C16—31no—
66D3×C16—61no—
67C3×C32—21no—
68C3×C32C2×D311yescharacteristic, complemented
69C3×C32C2×D311yescharacteristic, complemented
70C3⋊C32—31no—
71C3⋊C32—31no—
72C3⋊C32—61no—
73C2×D32—81no—
74C4×C3⋊D3D811yescharacteristic
75C3×D12—41no—
76C3×D12—41no—
77C3×D12—41no—
78C3×Dic6—41no—
79#626—81no—
80#625—81no—
81D3×Dic3—81no—
82C32×C8C2×D411yescharacteristic
83C3⋊(C3⋊C8)D811yescharacteristic
84#508—91no—
85C2×D16—91no—
86SD64—31no—
87SD64—91no—
88D32—31no—
89D32—91no—
90M64—91no—
91#239—121no—
92#237—121no—
93D3×D4—121no—
94D3×D4—121no—
95C3×Q16—61no—
96C3×D8—61no—
97C3×D8—61no—
98C3×D8—61no—
99#215—121no—
100#214—121no—
101#213—121no—
102#213—121no—
103Dic12—21no—
104D24—21no—
105D24—21no—
106D24—21no—
107D3×C8—31no—
108D3×C8—31no—
109D3×C8—61no—
110C3×C16—21no—
111C3×C16C22×D311yescharacteristic
112C3×C16C22×D311yescharacteristic
113C3⋊C16—31no—
114C3⋊C16—31no—
115C3⋊C16—61no—
116C2×C3⋊D3D1611yescharacteristic
117C2×C3×D3—81no—
118C2×C3×D3—81no—
119C2×C3×D3—81no—
120D32—162no—
121C32×C4C2×D811yescharacteristic
122C3⋊Dic3D1611yescharacteristic
123C3×Dic3—81no—
124#135—181no—
125C2×D8—181no—
126Q32—31no—
127SD32—181no—
128D16—31no—
129D16—31no—
130D16—31no—
131D16—181no—
132C2×C16—91no—
133C32—91no—
134C32D3211yescharacteristic, complemented
135C22×D3—241no—
136C22×D3—241no—
137C3×Q8—121no—
138C3×D4—121no—
139C3×D4—121no—
140C3×D4—121no—
141#67—241no—
142#67—241no—
143#67—241no—
144C2×Dic3—241no—
145D12—41no—
146D12—41no—
147D12—41no—
148D12—241no—
149C4×D3—31no—
150C4×D3—31no—
151C4×D3—61no—
152C4×D3—241no—
153Dic6—41no—
154C3×C8—21no—
155C3×C8D3×D411yescharacteristic
156C3×C8D3×D411yescharacteristic
157C3⋊C8—31no—
158C3⋊C8—31no—
159C3⋊C8—61no—
160C2×C32C2×D1611yescharacteristic
161C3⋊D3—21no—
162C3×D3—161no—
163C3×D3—161no—
164C3×D3—161no—
165#41—361no—
166C2×D4—361no—
167Q16—61no—
168SD16—361no—
169D8—61no—
170D8—61no—
171D8—61no—
172D8—361no—
173C2×C8—91no—
174C16—91no—
175C16C2×D3211yescharacteristic
176C22×C3—241no—
177C22×C3—241no—
178C22×C3—241no—
179C2×D3—31no—
180C2×D3—31no—
181C2×D3—61no—
182C2×D3—81no—
183C2×D3—81no—
184C2×D3—81no—
185C2×D3—482no—
186C2×D3—482no—
187C3×C4—21no—
188C3×C4—241no—
189C3×C4D3×D811yescharacteristic
190C3×C4D3×D811yescharacteristic
191Dic3—31no—
192Dic3—31no—
193Dic3—61no—
194Dic3—81no—
195C32#226311yescharacteristic, complemented, Sylow
196C23—721no—
197Q8—121no—
198D4—121no—
199D4—121no—
200D4—121no—
201D4—721no—
202D4—721no—
203C2×C4—91no—
204C2×C4—721no—
205C8—91no—
206C8#380211yescharacteristic
207C2×C3—21no—
208C2×C3—481no—
209C2×C3—481no—
210C2×C3—481no—
211C2×C3D3×D1611yescharacteristic
212C2×C3D3×D1611yescharacteristic
213D3—61no—
214D3—61no—
215D3—121no—
216D3—161no—
217D3—161no—
218D3—161no—
219C22—91no—
220C22—241no—
221C22—241no—
222C22—241no—
223C22—1442no—
224C4—91no—
225C4—241no—
226C4#6379711yescharacteristic
227C3—21no—
228C3#6937711yescharacteristic, complemented
229C3#6938011yescharacteristic, complemented
230C2—181no—
231C2—481no—
232C2—481no—
233C2—481no—
234C2#1059023411yescharacteristic
subgroupG/H
centerC2#10590234
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. #10590244C2semidirect
2. #10590234C2semidirect
3. #10589313C2semidirect
4. C3×#4449C2semidirect
5. C3×D96C2semidirect
6. #10589072C2semidirect
7. #10589070C2semidirect
13. C3×Dic24C22semidirect
16. C3×D48C22semidirect
19. C32×C32C22semidirect
20. C3⋊(C3⋊C32)C22semidirect
31. #4449D3semidirect
32. D96D3semidirect
60. Dic24C2×D3semidirect
63. D48C2×D3semidirect
68. C3×C32C2×D3semidirect
69. C3×C32C2×D3semidirect
134. C32D32semidirect
195. C32#2263semidirect
228. C3#69377semidirect
229. C3#69380semidirect

Maximal subgroups

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

subgroupindex
#105902442
#105902342
#105893132
C3×#44492
C3×D962
#105890722
#105890702
#693803
#693773