Finite Group Databasebeta

← #11797938

Subgroups — #11797938

Order 1152.

325 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 325 conjugacy classes of subgroups — too many to draw. Only its 80 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#10592608C211yesmaximal, characteristic
2#10590918C211yesmaximal, characteristic
3#10590810C211yesmaximal, characteristic, complemented
4C3×#4513C211yesmaximal, characteristic, complemented
5C3×#4512C211yesmaximal, characteristic, complemented
6#10589131C211yesmaximal, characteristic, complemented
7#10589125C211yesmaximal, characteristic
8#69309—31nomaximal
9#69090—31nomaximal
10C2×#3746C2211yescharacteristic
11#64113C2211yescharacteristic
12#63844—21no—
13#63817—21no—
14C32×M32C2211yescharacteristic
15#63628C412yescomplemented
16#63627C412yescomplemented
17C3×#819C2211yescharacteristic
18C3×#817C2211yescharacteristic
19C3×#815C2211yescharacteristic
20C3×#812C2211yescharacteristic
21#63570—21no—
22#63567—21no—
23#4909—31no—
24#4909—31no—
25#4909—61no—
26#4894—31no—
27#4853—31no—
28#4717—31no—
29#4716—31no—
30C3×#365—31no—
31C3×#347—31no—
32#4518—31no—
33#4517—31no—
34#4513D311yescharacteristic, complemented
35#4512D311yescharacteristic, complemented
36#4496—31no—
37#4488—31no—
38#3828—21no—
39C2×#634—21no—
40C2×C32×C8C2311yescharacteristic
41#3746—21no—
42#3746C2×C411yescharacteristic
43#3746C2×C412yes—
44#3745C2×C411yescharacteristic
45#3744—21no—
46C3×C4⋊Dic3—21no—
47C3×C4×Dic3D411yescharacteristic
48C3×#208—21no—
49C2×C3×C3⋊C8D411yescharacteristic
50#3724—41no—
51Dic32—41no—
52#3712—41no—
53#3710—41no—
54C32×C16C2×C412yes—
55C3×C3⋊C16—21no—
56#2180—91noSylow
57#907—61no—
58C2×Dic12—31no—
59C2×Dic12—31no—
60C2×Dic12—61no—
61#904—31no—
62#904—31no—
63#904—61no—
64#901—61no—
65#887—61no—
66C4×Dic6—61no—
67C3×M32—21no—
68C3×M32—31no—
69C3×M32C2×D311yescharacteristic
70C3×M32C2×D311yescharacteristic
71C3×#108—31no—
72C3×#106—31no—
73C3×#97—31no—
74#825—61no—
75#819C2×D311yescharacteristic
76#817C2×D311yescharacteristic
77#816—61no—
78#815C2×D311yescharacteristic
79#812C2×D311yescharacteristic
80#810—61no—
81#805—61no—
82Dic24—32no—
83Dic24—32no—
84Dic24—62no—
85#800—32no—
86#800—32no—
87#800—62no—
88C2×C32×C4C2×D411yescharacteristic
89#638—41no—
90C2×C3⋊Dic3—41no—
91C4⋊(C3⋊D3)—21no—
92C4×C3⋊D3—41no—
93#634—21no—
94#634—22no—
95#634—41no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3×C3⋊C8—21no—
101C3×C3⋊C8—41no—
102#510—91no—
103#444—91no—
104#441—91no—
105#365—31no—
106#362—91no—
107#360—91no—
108#347—31no—
109#235—61no—
110#235—61no—
111#235—121no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—121no—
115C3×M16—61no—
116C2×C3×C8—21no—
117C2×C3×C8—31no—
118C2×C3×C8C22×D311yescharacteristic
119C2×C3×C8C22×D311yescharacteristic
120C3×C4⋊C4—61no—
121C3×C42—31no—
122C4⋊Dic3—21no—
123Dic3⋊C4—121no—
124Dic3⋊C4—121no—
125C4×Dic3—121no—
126C4×Dic3—121no—
127C4×Dic3D1211yescharacteristic
128#208—21no—
129C2×C3⋊C8D1211yescharacteristic
130Dic12—32no—
131Dic12—32no—
132Dic12—31no—
133Dic12—31no—
134Dic12—62no—
135Dic12—61no—
136Dic12—61no—
137Dic12—61no—
138Dic12—121no—
139D24—31no—
140D24—31no—
141D24—61no—
142#204—61no—
143#204—61no—
144#204—121no—
145ΓL(1,𝔽25)—121no—
146ΓL(1,𝔽25)—121no—
147D3×C8—121no—
148D3×C8—121no—
149C3×C16—22no—
150C3×C16—61no—
151C3×C16C4×D312yes—
152C3×C16C4×D312yes—
153C3⋊C16—21no—
154C22×C32AGL(1,ℤ/8)11yescharacteristic
155C2×C3⋊D3—41no—
156C32×C4C4×D411yescharacteristic
157C32×C4AGL(1,ℤ/8)11yescharacteristic
158C3⋊Dic3—42no—
159C3⋊Dic3—41no—
160C3×Dic3—41no—
161C3×Dic3—81no—
162#135—91no—
163C2×Q16—91no—
164#131—181no—
165C4×Q8—181no—
166Q32—92no—
167SD32—92no—
168M32—31no—
169M32D3211yescharacteristic
170#108—31no—
171#106—31no—
172#104—181no—
173#103—181no—
174#97—31no—
175C2×C3×C4—21no—
176C2×C3×C4—61no—
177C2×C3×C4—121no—
178C2×C3×C4C2×D1211yescharacteristic
179C2×C3×C4D3×D411yescharacteristic
180#67—121no—
181#67—121no—
182#67—241no—
183C2×Dic3—21no—
184C2×Dic3—41no—
185C2×Dic3—121no—
186C2×Dic3—121no—
187C2×Dic3—241no—
188D12—61no—
189D12—61no—
190D12—121no—
191C4×D3—121no—
192C4×D3—121no—
193C4×D3—241no—
194Dic6—61no—
195Dic6—62no—
196Dic6—61no—
197Dic6—62no—
198Dic6—121no—
199Dic6—122no—
200Dic6—121no—
201Dic6—121no—
202Dic6—241no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—61no—
206C3×C8—121no—
207C3×C8C2×C4×D311yescharacteristic
208C3×C8C2×C4×D311yescharacteristic
209C3×C8#23511yescharacteristic
210C3×C8#23911yescharacteristic
211C3⋊C8—21no—
212C3⋊C8—41no—
213C2×C32—21no—
214C2×C32#44211yescharacteristic
215C3⋊D3—81no—
216#41—181no—
217C2×Q8—181no—
218Q16—92no—
219Q16—91no—
220Q16—181no—
221SD16—181no—
222D8—91no—
223M16—61no—
224M16—361no—
225C2×C8—31no—
226C2×C8—361no—
227C2×C8C2×D3211yescharacteristic
228C4⋊C4—61no—
229C4⋊C4—361no—
230C42—31no—
231C42—361no—
232C16—61no—
233C16#62412yes—
234C22×C3—21no—
235C22×C3#90811yescharacteristic
236C22×C3#91411yescharacteristic
237C2×D3—121no—
238C2×D3—121no—
239C2×D3—241no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—121no—
243C3×C4—241no—
244C3×C4C4×D1211yescharacteristic
245C3×C4#89311yescharacteristic
246C3×C4#90811yescharacteristic
247C3×C4#91411yescharacteristic
248Dic3—41no—
249Dic3—81no—
250Dic3—122no—
251Dic3—121no—
252Dic3—122no—
253Dic3—121no—
254Dic3—242no—
255Dic3—241no—
256C32#218011yescharacteristic, complemented, Sylow
257Q8—181no—
258Q8—182no—
259Q8—361no—
260D4—181no—
261D4—361no—
262C2×C4—61no—
263C2×C4—121no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4D3×D1211yescharacteristic
267C8—61no—
268C8—121no—
269C8#379911yescharacteristic
270C8C2×#62411yescharacteristic
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—41no—
275C2×C3#471111yescharacteristic
276C2×C3#486911yescharacteristic
277D3—241no—
278D3—241no—
279D3—481no—
280C22—361no—
281C22#6379411yescharacteristic
282C4—121no—
283C4—241no—
284C4—361no—
285C4—362no—
286C4#6379411yescharacteristic
287C4#6389411yescharacteristic
288C3—21no—
289C3#6909011yescharacteristic, complemented
290C3#6930911yescharacteristic, complemented
291C2—21no—
292C2—721no—
293C2#1059076811yescharacteristic
subgroupG/H
centerC2#10590768
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32#2180
LCSG ▷ 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
3. #10590810C2semidirect
4. C3×#4513C2semidirect
5. C3×#4512C2semidirect
6. #10589131C2semidirect
15. #63628C4semidirect
16. #63627C4semidirect
34. #4513D3semidirect
35. #4512D3semidirect
256. C32#2180semidirect
289. C3#69090semidirect
290. C3#69309semidirect

Maximal subgroups

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

subgroupindex
#105926082
#105909182
#105908102
C3×#45132
C3×#45122
#105891312
#105891252
#693093
#690903