Finite Group Databasebeta

← #11799998

Subgroups — #11799998

Order 1152.

299 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 68 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#10590912C211yesmaximal, characteristic, complemented
2#10590835C211yesmaximal, characteristic
3#10589382C211yesmaximal, characteristic, complemented
4C3×#4514C211yesmaximal, characteristic, complemented
5C3×#4513C211yesmaximal, characteristic, complemented
6#10589136C211yesmaximal, characteristic, complemented
7#10589128C211yesmaximal, characteristic, complemented
8#69313—31nomaximal
9#69116—31nomaximal
10C2×#3745C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
12#63909—21no—
13D3×#208—21no—
14C32×M32C2211yescharacteristic
15#63646C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63577—21no—
20#63564—21no—
21#5135—31no—
22#5125—31no—
23#4893—31no—
24#4865—31no—
25C3×#365—31no—
26C3×#349—31no—
27#4516—31no—
28#4516—31no—
29#4516—31no—
30#4516—61no—
31#4514D311yescharacteristic, complemented
32#4513—31no—
33#4513D311yescharacteristic, complemented
34#4495—31no—
35#4487—31no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C3×C4×D3D411yescharacteristic
38C2×#626—41no—
39C2×C32×C8C2311yescharacteristic
40#3748—21no—
41#3745—21no—
42#3745—21no—
43C3×C4⋊Dic3—21no—
44C3×#208—21no—
45C2×C3×C3⋊C8D411yescharacteristic
46C3×ΓL(1,𝔽25)—21no—
47C3×ΓL(1,𝔽25)—21no—
48#3722—41no—
49#3711—41no—
50D3×C3⋊C8—41no—
51C32×C16—21no—
52C3×C3⋊C16—21no—
53#2238—91noSylow
54C2×C3×M16—31no—
55#930—61no—
56C2×#208—61no—
57D3×M16—61no—
58C2×D24—31no—
59C2×D24—31no—
60C2×D24—61no—
61C2×ΓL(1,𝔽25)C2×D311yescharacteristic
62#895—61no—
63C3×M32—21no—
64C3×M32—31no—
65C3×M32C2×D311yescharacteristic
66C3×M32C2×D311yescharacteristic
67C3×#108—31no—
68C3×#106—31no—
69#822—61no—
70#821—61no—
71#819—31no—
72#819—31no—
73#819—61no—
74#819—61no—
75#819C2×D311yescharacteristic
76#817C2×D311yescharacteristic
77#812C2×D311yescharacteristic
78#809—61no—
79C22×C3⋊D3—41no—
80C22×C3×D3SD1611yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C4⋊(C3⋊D3)—41no—
83C4⋊(C3⋊D3)—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3SD1611yescharacteristic
86C3×C4×D3—21no—
87C3×C4×D3—21no—
88#626—82no—
89C32×C8#4111yescharacteristic
90C32×C8#4111yescharacteristic
91C3⋊(C3⋊C8)—41no—
92C3×C3⋊C8—21no—
93C3×C3⋊C8—41no—
94#469—91no—
95#430—91no—
96#365—31no—
97#365—91no—
98#361—91no—
99#361—91no—
100#349—31no—
101C22×C3×C4—31no—
102C2×#67—121no—
103C2×D12—61no—
104C2×D12—61no—
105C2×D12—121no—
106C2×D12—121no—
107C2×C4×D3D1211yescharacteristic
108C3×M16—61no—
109C3×M16—61no—
110C3×M16—61no—
111C2×C3×C8—21no—
112C2×C3×C8—31no—
113C2×C3×C8C22×D311yescharacteristic
114C2×C3×C8C22×D311yescharacteristic
115C3×C4⋊C4—61no—
116(C2×D3)⋊C4—121no—
117(C2×D3)⋊C4—121no—
118C4⋊Dic3—21no—
119#208—21no—
120#208—61no—
121#208—61no—
122#208—121no—
123#208—121no—
124C2×C3⋊C8—121no—
125C2×C3⋊C8D1211yescharacteristic
126D24—62no—
127D24—61no—
128D24—61no—
129D24—61no—
130D24—61no—
131D24—121no—
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—21no—
134ΓL(1,𝔽25)—121no—
135D3×C8—121no—
136C3×C16—21no—
137C3×C16—21no—
138C3×C16—41no—
139C3×C16—61no—
140C3⋊C16—21no—
141C22×C32C2×SD1611yescharacteristic
142C2×C3⋊D3—81no—
143C2×C3⋊D3—81no—
144C2×C3⋊D3—81no—
145C2×C3×D3—21no—
146C2×C3×D3—41no—
147C32×C4#12311yescharacteristic
148C32×C4AGL(1,ℤ/8)11yescharacteristic
149C3×Dic3—21no—
150C3×Dic3—81no—
151C2×D8—91no—
152C2×M16—31no—
153C2×M16—181no—
154#121—181no—
155M32—31no—
156M32D3211yescharacteristic
157#108—31no—
158#108—91no—
159#108—181no—
160#106—31no—
161#102—181no—
162C23×C3—31no—
163C22×D3—121no—
164C22×D3—121no—
165C22×D3—241no—
166C22×D3#20411yescharacteristic
167C2×C3×C4—21no—
168C2×C3×C4—31no—
169C2×C3×C4—61no—
170C2×C3×C4—61no—
171C2×C3×C4—121no—
172C2×C3×C4C2×D1211yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174#67—242no—
175C2×Dic3—41no—
176C2×Dic3#20411yescharacteristic
177D12—122no—
178D12—121no—
179D12—121no—
180D12—121no—
181D12—121no—
182D12—241no—
183D12—242no—
184C4×D3—21no—
185C4×D3—21no—
186C3×C8—21no—
187C3×C8—21no—
188C3×C8—61no—
189C3×C8—121no—
190C3×C8#23511yescharacteristic
191C3×C8#23711yescharacteristic
192C3×C8#23711yescharacteristic
193C3×C8#23911yescharacteristic
194C3⋊C8—21no—
195C3⋊C8—41no—
196C3⋊C8—121no—
197C3⋊C8—121no—
198C3⋊C8—241no—
199C2×C32—21no—
200C2×C32#48111yescharacteristic
201C3⋊D3—161no—
202C3×D3—41no—
203C2×D4—181no—
204C2×D4—361no—
205C22×C4—31no—
206D8—181no—
207D8—181no—
208M16—61no—
209M16—61no—
210M16—61no—
211M16—181no—
212M16—361no—
213C2×C8—31no—
214C2×C8—361no—
215C2×C8C2×D3211yescharacteristic
216C4⋊C4—61no—
217C22⋊C4—361no—
218C16—21no—
219C16—61no—
220C22×C3—21no—
221C22×C3—61no—
222C22×C3—121no—
223C22×C3C2×#20411yescharacteristic
224C22×C3D3×SD1611yescharacteristic
225C2×D3—21no—
226C2×D3—41no—
227C2×D3—242no—
228C2×D3—241no—
229C2×D3—241no—
230C2×D3—241no—
231C2×D3—241no—
232C2×D3—241no—
233C2×D3—241no—
234C2×D3—481no—
235C2×D3—481no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—61no—
239C3×C4—241no—
240C3×C4#88611yescharacteristic
241C3×C4#89411yescharacteristic
242C3×C4#90811yescharacteristic
243C3×C4#91411yescharacteristic
244Dic3—21no—
245Dic3—81no—
246C32#223811yescharacteristic, complemented, Sylow
247C23—31no—
248C23—361no—
249D4—361no—
250D4—361no—
251D4—722no—
252C2×C4—31no—
253C2×C4—61no—
254C2×C4—61no—
255C2×C4—121no—
256C2×C4D3×D1211yescharacteristic
257C8—61no—
258C8—121no—
259C8—361no—
260C8#379611yescharacteristic
261C8#380411yescharacteristic
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—41no—
266C2×C3—121no—
267C2×C3#473511yescharacteristic
268C2×C3#486311yescharacteristic
269D3—41no—
270D3—482no—
271D3—481no—
272D3—481no—
273C22—61no—
274C22—121no—
275C22—721no—
276C22—721no—
277C22—721no—
278C22D3×#20411yescharacteristic
279C4—61no—
280C4—241no—
281C4#6379411yescharacteristic
282C4#6389011yescharacteristic
283C3—21no—
284C3#6911611yescharacteristic, complemented
285C3#6931311yescharacteristic, complemented
286C2—21no—
287C2—121no—
288C2—1441no—
289C2#1059067711yescharacteristic
subgroupG/H
centerC2#10590677
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#481
prime radical#10590835C2
hypercenterM32D32
hypocenterC32#2238
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
1. #10590912C2semidirect
3. #10589382C2semidirect
4. C3×#4514C2semidirect
5. C3×#4513C2semidirect
6. #10589136C2semidirect
7. #10589128C2semidirect
31. #4514D3semidirect
33. #4513D3semidirect
246. C32#2238semidirect
284. C3#69116semidirect
285. C3#69313semidirect

Maximal subgroups

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

subgroupindex
#105909122
#105908352
#105893822
C3×#45142
C3×#45132
#105891362
#105891282
#693133
#691163