Finite Group Databasebeta

← #11797982

Subgroups — #11797982

Order 1152.

360 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592593C211yesmaximal, characteristic, complemented
2#10590781C211yesmaximal, characteristic, complemented
3#10590633C211yesmaximal, characteristic
4C3×#4495C211yesmaximal, characteristic, complemented
5C3×#4494C211yesmaximal, characteristic, complemented
6#10589125C211yesmaximal, characteristic, complemented
7#10589106C211yesmaximal, characteristic, complemented
8#69310—31nomaximal
9#69254—31nomaximal
10#64116—21no—
11#64113C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63898—21no—
14C32×#108C2211yescharacteristic
15#63652—21no—
16#63642C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63562—21no—
21#63548C412yescomplemented
22#63546C412yescomplemented
23#5152—31no—
24#5147—31no—
25#4908—31no—
26#4894—31no—
27#4894—31no—
28#4894—61no—
29#4869—31no—
30C3×#365—31no—
31C3×#361—31no—
32#4518—31no—
33#4512—31no—
34#4512—31no—
35#4495D311yescharacteristic, complemented
36#4494D311yescharacteristic, complemented
37#4488—31no—
38#3828—21no—
39C2×C3×D12—21no—
40C2×D3×Dic3—41no—
41C32×M16—21no—
42C2×C32×C8C2311yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45#3746C2×C411yescharacteristic, complemented
46#3745C2×C411yescharacteristic, complemented
47#3744—21no—
48#3743—41no—
49C8×C3⋊D3—41no—
50C3×C4⋊Dic3—21no—
51C3×D24—21no—
52C3×D24C2×C412yes—
53(C2×D3)⋊Dic3—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yescomplemented
56AGL(1,ℤ/16)—91noSylow
57C2×C3×D8—31no—
58D4×Dic3—61no—
59#907—61no—
60#907—61no—
61#907—62no—
62#904—31no—
63#904—31no—
64#904—61no—
65C2×D24C2×D311yescharacteristic
66#893—61no—
67C3×M32—31no—
68C3×M32—31no—
69C3×#108—21no—
70C3×#108C2×D311yescharacteristic
71C3×#108C2×D311yescharacteristic
72C3×#106—31no—
73#832—61no—
74#827—32no—
75#826—32no—
76#825—61no—
77#825—61no—
78#825—62no—
79#817C2×D311yescharacteristic
80#815—31no—
81#815—31no—
82#815—61no—
83#812C2×D311yescharacteristic
84#812C2×D311yescharacteristic
85#809—61no—
86#800—32no—
87D48—32no—
88C22×C3×D3—41no—
89C2×C32×C4C2×D411yescharacteristic
90#638—41no—
91C2×C3⋊Dic3—21no—
92C4⋊(C3⋊D3)—21no—
93C4×C3⋊D3—41no—
94#634—21no—
95C2×C3×Dic3—41no—
96C3×D12—22no—
97C3×D12—41no—
98D3×Dic3—82no—
99C32×C8—41no—
100C32×C8C22×C411yescharacteristic
101C32×C8#4111yescharacteristic
102C3⋊(C3⋊C8)—21no—
103#509—91no—
104#444—91no—
105#442—91no—
106#365—31no—
107#361—31no—
108#360—91no—
109#347—91no—
110C2×C3×D4—61no—
111C22×Dic3—121no—
112#235—62no—
113#235—61no—
114#235—61no—
115C2×D12—21no—
116C2×C4×D3—121no—
117C3×D8—32no—
118C3×D8—61no—
119C3×M16—22no—
120C3×M16—21no—
121C3×M16—21no—
122C2×C3×C8—21no—
123C2×C3×C8C22×D311yescharacteristic
124C2×C3×C8C22×D311yescharacteristic
125C3×C4⋊C4—61no—
126#217—121no—
127(C2×D3)⋊C4—121no—
128C4⋊Dic3—21no—
129C4×Dic3—31no—
130C4×Dic3—31no—
131C4×Dic3—61no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—31no—
134C2×C3⋊C8—61no—
135Dic12—31no—
136Dic12—31no—
137Dic12—61no—
138D24—21no—
139D24—31no—
140D24—31no—
141D24—61no—
142D24C4×D312yes—
143#204—62no—
144#204—61no—
145#204—61no—
146ΓL(1,𝔽25)—122no—
147ΓL(1,𝔽25)—121no—
148ΓL(1,𝔽25)—121no—
149D3×C8—122no—
150D3×C8—121no—
151D3×C8—121no—
152C3×C16—32no—
153C3×C16—61no—
154C3⋊C16—21no—
155C3⋊C16C4×D312yescomplemented
156C22×C32AGL(1,ℤ/8)11yescharacteristic
157C2×C3⋊D3—41no—
158C2×C3×D3—42no—
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C32×C4C4×D411yescharacteristic
162C32×C4AGL(1,ℤ/8)11yescharacteristic
163C3⋊Dic3—41no—
164C3⋊Dic3—41no—
165C3×Dic3—81no—
166#135—91no—
167C2×D8—31no—
168#131—181no—
169C4×D4—181no—
170SD32—92no—
171D16—92no—
172M32—31no—
173M32—31no—
174#108D3211yescharacteristic
175#106—31no—
176#104—181no—
177#102—181no—
178#97—91no—
179C23×C3—121no—
180C22×D3—41no—
181C3×D4—62no—
182C3×D4—121no—
183C2×C3×C4—21no—
184C2×C3×C4—121no—
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4D3×D411yescharacteristic
187#67—122no—
188#67—121no—
189#67—121no—
190C2×Dic3—41no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—121no—
194C2×Dic3—242no—
195D12—22no—
196D12—41no—
197D12—62no—
198D12—61no—
199D12—61no—
200C4×D3—122no—
201C4×D3—121no—
202C4×D3—121no—
203C4×D3—242no—
204Dic6—62no—
205Dic6—61no—
206Dic6—61no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—42no—
210C3×C8—41no—
211C3×C8—41no—
212C3×C8C2×C4×D311yescharacteristic
213C3×C8C2×C4×D311yescharacteristic
214C3×C8#23711yescharacteristic
215C3×C8#23911yescharacteristic
216C3⋊C8—62no—
217C3⋊C8—61no—
218C3⋊C8—61no—
219C2×C32—21no—
220C2×C32#44211yescharacteristic
221C3⋊D3—81no—
222C3×D3—82no—
223#41—181no—
224C2×D4—61no—
225C22×C4—361no—
226Q16—91no—
227SD16—181no—
228D8—32no—
229D8—61no—
230D8—91no—
231M16—21no—
232M16—361no—
233C2×C8—91no—
234C2×C8—361no—
235C2×C8C2×D3211yescharacteristic
236C4⋊C4—61no—
237C22⋊C4—361no—
238C42—91no—
239C16—32no—
240C16—61no—
241C22×C3—21no—
242C22×C3—122no—
243C22×C3—241no—
244C22×C3—241no—
245C22×C3#91411yescharacteristic
246C22×C3#91411yescharacteristic
247C2×D3—42no—
248C2×D3—81no—
249C2×D3—81no—
250C2×D3—122no—
251C2×D3—121no—
252C2×D3—121no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—241no—
256C3×C4#67⋊C411yescharacteristic
257C3×C4#89311yescharacteristic
258C3×C4#91111yescharacteristic
259C3×C4#91411yescharacteristic
260Dic3—81no—
261Dic3—122no—
262Dic3—121no—
263Dic3—121no—
264Dic3—121no—
265Dic3—121no—
266Dic3—241no—
267C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
268C23—121no—
269Q8—181no—
270D4—62no—
271D4—121no—
272D4—181no—
273D4—361no—
274C2×C4—121no—
275C2×C4—181no—
276C2×C4—361no—
277C2×C4—722no—
278C2×C4#381111yescharacteristic
279C8—41no—
280C8—181no—
281C8#379611yescharacteristic
282C8C4×D3211yescharacteristic
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—41no—
287C2×C3—242no—
288C2×C3#478511yescharacteristic
289C2×C3#486911yescharacteristic
290D3—82no—
291D3—242no—
292D3—241no—
293D3—241no—
294C22—122no—
295C22—241no—
296C22—241no—
297C22—361no—
298C22#6394111yescharacteristic
299C4—241no—
300C4—361no—
301C4—361no—
302C4#6388111yescharacteristic
303C4#6393711yescharacteristic
304C3—21no—
305C3#6925411yescharacteristic, complemented
306C3#6931011yescharacteristic, complemented
307C2—21no—
308C2—242no—
309C2—721no—
310C2#1059046211yescharacteristic
subgroupG/H
centerC2#10590462
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#442
prime radical#10590633C2
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10592593C2semidirect
2. #10590781C2semidirect
4. C3×#4495C2semidirect
5. C3×#4494C2semidirect
6. #10589125C2semidirect
7. #10589106C2semidirect
21. #63548C4semidirect
22. #63546C4semidirect
35. #4495D3semidirect
36. #4494D3semidirect
45. #3746C2×C4semidirect
46. #3745C2×C4semidirect
55. C3×C3⋊C16C2×C4semidirect
155. C3⋊C16C4×D3semidirect
267. C32AGL(1,ℤ/16)semidirect
305. C3#69254semidirect
306. C3#69310semidirect

Maximal subgroups

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

subgroupindex
#105925932
#105907812
#105906332
C3×#44952
C3×#44942
#105891252
#105891062
#693103
#692543