Finite Group Databasebeta

← #11799720

Subgroups — #11799720

Order 1152.

281 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 70 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#10590917C211yesmaximal, characteristic
2#10590889C211yesmaximal, characteristic, complemented
3#10589384C211yesmaximal, characteristic
4C3×#4513C211yesmaximal, characteristic, complemented
5C3×#4511C211yesmaximal, characteristic, complemented
6#10589137C211yesmaximal, characteristic, complemented
7#10589125C211yesmaximal, characteristic
8#69315—31nomaximal
9#69307—31nomaximal
10#64113C2211yescharacteristic
11#63918—21no—
12#63817—21no—
13C32×M32C2211yescharacteristic
14#63644C2211yescharacteristic
15C3×#819C2211yescharacteristic
16C3×#817C2211yescharacteristic
17C3×C8×Dic3C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63573—21no—
20#63570—21no—
21#4895—31no—
22#4855—31no—
23#4700—31no—
24#4680—31no—
25C3×#365—31no—
26C3×#364—31no—
27#4518—31no—
28#4518—31no—
29#4518—31no—
30#4518—61no—
31#4513—31no—
32#4513D311yescharacteristic, complemented
33#4511D311yescharacteristic, complemented
34#4494—31no—
35#4488—31no—
36#3828—21no—
37C2×#627—41no—
38C2×C32×C8C2311yescharacteristic
39C4⋊(C3⋊Dic3)—21no—
40#3746Q811yescharacteristic, complemented
41#3745Q811yescharacteristic, complemented
42#3744—21no—
43C3×C4⋊Dic3—21no—
44C3×C4×Dic3D411yescharacteristic
45C3×#208—21no—
46C2×C3×C3⋊C8D411yescharacteristic
47Dic3⋊Dic3—41no—
48#3712—41no—
49#3710—41no—
50C32×C16—21no—
51C3×C3⋊C16—21no—
52#2230—91noSylow
53#907—61no—
54#904—31no—
55#904—31no—
56#904—61no—
57#901—61no—
58#888—61no—
59#869—61no—
60C3×M32—21no—
61C3×M32—31no—
62C3×M32C2×D311yescharacteristic
63C3×M32C2×D311yescharacteristic
64C3×#108—31no—
65C3×#106—31no—
66C3×C4×C8—31no—
67#825—61no—
68#819C2×D311yescharacteristic
69#817—31no—
70#817—31no—
71#817—61no—
72#817—61no—
73#817C2×D311yescharacteristic
74C8×Dic3C2×D311yescharacteristic
75#812C2×D311yescharacteristic
76#808—61no—
77#805—61no—
78C2×C32×C4C2×D411yescharacteristic
79#638—41no—
80C2×C3⋊Dic3—41no—
81C4⋊(C3⋊D3)—21no—
82C4×C3⋊D3—41no—
83#634—21no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—41no—
86#627—82no—
87C32×C8C2×Q811yescharacteristic
88C32×C8#4111yescharacteristic
89C3×C3⋊C8—41no—
90C3×C3⋊C8SD1611yescharacteristic
91C3×C3⋊C8SD1611yescharacteristic
92#498—91no—
93#443—91no—
94#365—31no—
95#365—91no—
96#364—31no—
97#360—91no—
98#360—91no—
99#235—61no—
100#235—61no—
101#235—121no—
102C2×Dic6—121no—
103C2×Dic6—121no—
104C3×M16—61no—
105C2×C3×C8—21no—
106C2×C3×C8—31no—
107C2×C3×C8C22×D311yescharacteristic
108C2×C3×C8C22×D311yescharacteristic
109C3×C4⋊C4—61no—
110C3×C42—31no—
111C4⋊Dic3—21no—
112C4⋊Dic3—61no—
113C4⋊Dic3—61no—
114C4⋊Dic3—121no—
115C4⋊Dic3—121no—
116Dic3⋊C4—121no—
117C4×Dic3D1211yescharacteristic
118#208—21no—
119C2×C3⋊C8D1211yescharacteristic
120Dic12—31no—
121Dic12—31no—
122Dic12—61no—
123D24—31no—
124D24—31no—
125D24—61no—
126#204—61no—
127#204—61no—
128#204—121no—
129ΓL(1,𝔽25)—121no—
130ΓL(1,𝔽25)—121no—
131D3×C8—121no—
132D3×C8—121no—
133C3×C16—21no—
134C3×C16—21no—
135C3×C16—41no—
136C3×C16—61no—
137C3⋊C16—21no—
138C22×C32AGL(1,ℤ/8)11yescharacteristic
139C2×C3⋊D3—41no—
140C32×C4C22⋊Q811yescharacteristic
141C32×C4C2×SD1611yescharacteristic
142C3⋊Dic3—41no—
143C3⋊Dic3—81no—
144C3×Dic3—22no—
145C3×Dic3—81no—
146#135—91no—
147#131—181no—
148C4⋊Q8—181no—
149M32—31no—
150M32D3211yescharacteristic
151#108—31no—
152#106—31no—
153#106—91no—
154#106—181no—
155#104—181no—
156C4×C8—31no—
157C2×C3×C4—21no—
158C2×C3×C4—61no—
159C2×C3×C4—121no—
160C2×C3×C4C2×D1211yescharacteristic
161C2×C3×C4D3×D411yescharacteristic
162#67—121no—
163#67—121no—
164#67—241no—
165C2×Dic3—21no—
166C2×Dic3—41no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—241no—
170D12—61no—
171D12—61no—
172D12—121no—
173C4×D3—121no—
174C4×D3—121no—
175C4×D3—241no—
176Dic6—61no—
177Dic6—61no—
178Dic6—121no—
179Dic6—242no—
180Dic6—242no—
181C3×C8—21no—
182C3×C8—21no—
183C3×C8—31no—
184C3×C8—31no—
185C3×C8—121no—
186C3×C8#23511yescharacteristic
187C3×C8#23711yescharacteristic
188C3×C8D3×Q811yescharacteristic
189C3×C8D3×Q811yescharacteristic
190C3⋊C8—41no—
191C3⋊C8#20411yescharacteristic
192C3⋊C8#20411yescharacteristic
193C2×C32—21no—
194C2×C32#47611yescharacteristic
195C3⋊D3—81no—
196#41—181no—
197C2×Q8—361no—
198Q16—91no—
199SD16—181no—
200D8—91no—
201M16—61no—
202M16—361no—
203C2×C8—31no—
204C2×C8—361no—
205C2×C8C2×D3211yescharacteristic
206C4⋊C4—61no—
207C4⋊C4—181no—
208C4⋊C4—361no—
209C42—31no—
210C16—21no—
211C16—61no—
212C22×C3—21no—
213C22×C3#90811yescharacteristic
214C22×C3#91411yescharacteristic
215C2×D3—121no—
216C2×D3—121no—
217C2×D3—241no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—62no—
221C3×C4—241no—
222C3×C4#89611yescharacteristic
223C3×C4#89711yescharacteristic
224C3×C4C2×#20411yescharacteristic
225C3×C4D3×SD1611yescharacteristic
226Dic3—22no—
227Dic3—81no—
228Dic3—121no—
229Dic3—121no—
230Dic3—241no—
231Dic3—241no—
232Dic3—241no—
233Dic3—481no—
234C32#223011yescharacteristic, complemented, Sylow
235Q8—181no—
236Q8—722no—
237D4—181no—
238D4—361no—
239C2×C4—61no—
240C2×C4—121no—
241C2×C4—361no—
242C2×C4—361no—
243C2×C4D3×D1211yescharacteristic
244C8—31no—
245C8—31no—
246C8—121no—
247C8#379711yescharacteristic
248C8#380411yescharacteristic
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3#484211yescharacteristic
254C2×C3#487011yescharacteristic
255D3—241no—
256D3—241no—
257D3—481no—
258C22—361no—
259C22#6379411yescharacteristic
260C4—62no—
261C4—241no—
262C4—361no—
263C4—721no—
264C4D3×#20411yescharacteristic
265C4#6389511yescharacteristic
266C3—21no—
267C3#6930711yescharacteristic, complemented
268C3#6931511yescharacteristic, complemented
269C2—21no—
270C2—721no—
271C2#1059075911yescharacteristic
subgroupG/H
centerC2#10590759
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#476
prime radical#64113C22
hypercenterM32D32
hypocenterC32#2230
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. #10590889C2semidirect
4. C3×#4513C2semidirect
5. C3×#4511C2semidirect
6. #10589137C2semidirect
32. #4513D3semidirect
33. #4511D3semidirect
40. #3746Q8semidirect
41. #3745Q8semidirect
234. C32#2230semidirect
267. C3#69307semidirect
268. C3#69315semidirect

Maximal subgroups

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

subgroupindex
#105909172
#105908892
#105893842
C3×#45132
C3×#45112
#105891372
#105891252
#693153
#693073