Finite Group Databasebeta

← #11797977

Subgroups — #11797977

Order 1152.

339 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 78 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#10590916C211yesmaximal, characteristic, complemented
2#10590768C211yesmaximal, characteristic, complemented
3#10590634C211yesmaximal, characteristic
4#10589382C211yesmaximal, characteristic, complemented
5C3×#4518C211yesmaximal, characteristic, complemented
6C3×#4512C211yesmaximal, characteristic, complemented
7#10589136C211yesmaximal, characteristic, complemented
8#69249—31nomaximal
9#69091—31nomaximal
10C2×#3745C2211yescharacteristic
11C3×#904C2211yescharacteristic
12#63894—21no—
13#63814—21no—
14C32×M32C2211yescharacteristic
15#63646C2211yescharacteristic
16C3×#817C2211yescharacteristic
17C3×#815C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63569—21no—
20#63564—21no—
21#63549C412yescomplemented
22#63546C412yescomplemented
23#5197—31no—
24#5193—31no—
25#4908—31no—
26#4869—31no—
27#4717—31no—
28#4711—31no—
29C3×#360—31no—
30C3×#347—31no—
31#4518D311yescharacteristic, complemented
32#4516—31no—
33#4516—31no—
34#4516—61no—
35#4513—31no—
36#4512D311yescharacteristic, complemented
37#4487—31no—
38C2×C4⋊(C3⋊D3)—21no—
39C3×#235—21no—
40C2×#624—41no—
41C2×C32×C8C2311yescharacteristic
42#3748—21no—
43#3745—21no—
44#3745C2×C412yes—
45C3×C4⋊Dic3—21no—
46C3×C4×Dic3D411yescharacteristic
47C2×C3×C3⋊C8D411yescharacteristic
48C3×Dic12C2×C411yescharacteristic, complemented
49C3×D24C2×C411yescharacteristic, complemented
50C3×#204—21no—
51#3722—41no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C32×C16—21no—
55C3×C3⋊C16C2×C412yescomplemented
56AGL(1,ℤ/16)—91noSylow
57C3×#135—31no—
58#948—61no—
59#904C2×D311yescharacteristic
60C2×D24—31no—
61C2×D24—31no—
62C2×D24—61no—
63#901—61no—
64#893—61no—
65C4×D12—61no—
66C3×M32—21no—
67C3×M32—31no—
68C3×M32C2×D311yescharacteristic
69C3×M32C2×D311yescharacteristic
70C3×#106—31no—
71C3×#97—31no—
72#837—61no—
73#828—32no—
74#826—32no—
75#821—61no—
76#819—31no—
77#819—31no—
78#819—61no—
79#817C2×D311yescharacteristic
80#815C2×D311yescharacteristic
81#812C2×D311yescharacteristic
82#809—61no—
83#805—61no—
84#800—32no—
85D48—32no—
86C22×C3⋊D3—41no—
87C2×C32×C4C2×D411yescharacteristic
88C4⋊(C3⋊D3)—22no—
89C4⋊(C3⋊D3)—41no—
90C3×#67—41no—
91C2×C3×Dic3—21no—
92C2×C3×Dic3—41no—
93C3×D12—21no—
94C3×C4×D3—41no—
95C3×Dic6—21no—
96#624—82no—
97C32×C8C22×C411yescharacteristic
98C32×C8#4111yescharacteristic
99C3⋊(C3⋊C8)—41no—
100C3×C3⋊C8—21no—
101#509—91no—
102#444—91no—
103#442—91no—
104#365—91no—
105#361—91no—
106#360—31no—
107#347—31no—
108C3×#41—61no—
109#235—21no—
110C2×D12—61no—
111C2×D12—61no—
112C2×D12—121no—
113C2×C4×D3—121no—
114C2×C4×D3—121no—
115C3×Q16—31no—
116C3×SD16—61no—
117C3×D8—31no—
118C2×C3×C8—21no—
119C2×C3×C8—31no—
120C2×C3×C8C22×D311yescharacteristic
121C2×C3×C8C22×D311yescharacteristic
122C3×C4⋊C4—61no—
123C3×C42—31no—
124(C2×D3)⋊C4—121no—
125(C2×D3)⋊C4—121no—
126C4⋊Dic3—21no—
127C4×Dic3D1211yescharacteristic
128#208—61no—
129#208—61no—
130#208—121no—
131#208—121no—
132C2×C3⋊C8—121no—
133C2×C3⋊C8D1211yescharacteristic
134Dic12C4×D311yescharacteristic, complemented
135D24—32no—
136D24—32no—
137D24—62no—
138D24—61no—
139D24—61no—
140D24—121no—
141D24C4×D311yescharacteristic, complemented
142#204—21no—
143ΓL(1,𝔽25)—121no—
144D3×C8—121no—
145C3×C16—21no—
146C3×C16—21no—
147C3×C16—32no—
148C3×C16—41no—
149C3⋊C16C4×D312yescomplemented
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C2×C3⋊D3—42no—
152C2×C3⋊D3—81no—
153C2×C3⋊D3—81no—
154C2×C3×D3—41no—
155C32×C4C4×D411yescharacteristic
156C32×C4AGL(1,ℤ/8)11yescharacteristic
157C3×Dic3—41no—
158C3×Dic3—41no—
159C3×Dic3—81no—
160#135—31no—
161C2×D8—91no—
162#131—181no—
163C4×D4—181no—
164SD32—92no—
165D16—92no—
166M32—31no—
167M32D3211yescharacteristic
168#108—91no—
169#106—31no—
170#104—181no—
171#102—181no—
172#97—31no—
173C22×D3—121no—
174C22×D3—121no—
175C22×D3—241no—
176C3×Q8—61no—
177C3×D4—61no—
178C3×D4—121no—
179C2×C3×C4—21no—
180C2×C3×C4—61no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4C2×D1211yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185#67—41no—
186C2×Dic3—21no—
187C2×Dic3—41no—
188D12—21no—
189D12—62no—
190D12—62no—
191D12—122no—
192D12—121no—
193D12—121no—
194D12—241no—
195C4×D3—41no—
196C4×D3—242no—
197C4×D3—242no—
198Dic6—21no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—61no—
202C3×C8C2×C4×D311yescharacteristic
203C3×C8C2×C4×D311yescharacteristic
204C3×C8#23511yescharacteristic
205C3×C8#23711yescharacteristic
206C3⋊C8—21no—
207C3⋊C8—121no—
208C3⋊C8—121no—
209C3⋊C8—241no—
210C2×C32—21no—
211C2×C32#44211yescharacteristic
212C3⋊D3—82no—
213C3×D3—81no—
214#41—61no—
215C2×D4—181no—
216C22×C4—361no—
217Q16—31no—
218SD16—61no—
219D8—31no—
220D8—92no—
221D8—181no—
222M16—181no—
223M16—361no—
224C2×C8—31no—
225C2×C8—361no—
226C2×C8C2×D3211yescharacteristic
227C4⋊C4—61no—
228C22⋊C4—361no—
229C42—31no—
230C16—21no—
231C16—32no—
232C22×C3—21no—
233C22×C3—121no—
234C22×C3#90811yescharacteristic
235C22×C3#91111yescharacteristic
236C2×D3—41no—
237C2×D3—122no—
238C2×D3—122no—
239C2×D3—242no—
240C2×D3—241no—
241C2×D3—241no—
242C2×D3—241no—
243C2×D3—241no—
244C2×D3—481no—
245C2×D3—481no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—121no—
249C3×C4—121no—
250C3×C4—241no—
251C3×C4C4×D1211yescharacteristic
252C3×C4#67⋊C411yescharacteristic
253C3×C4#90811yescharacteristic
254C3×C4#91411yescharacteristic
255Dic3—41no—
256Dic3—41no—
257Dic3—81no—
258C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
259C23—361no—
260Q8—61no—
261D4—61no—
262D4—121no—
263D4—182no—
264D4—361no—
265C2×C4—61no—
266C2×C4—121no—
267C2×C4—121no—
268C2×C4—722no—
269C2×C4D3×D1211yescharacteristic
270C8—61no—
271C8—361no—
272C8C4×D3211yescharacteristic
273C8#380411yescharacteristic
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—41no—
278C2×C3—241no—
279C2×C3#471111yescharacteristic
280C2×C3#478511yescharacteristic
281D3—81no—
282D3—242no—
283D3—242no—
284D3—482no—
285C22—121no—
286C22—362no—
287C22—721no—
288C22—721no—
289C22#6379511yescharacteristic
290C4—121no—
291C4—121no—
292C4—241no—
293C4#6379411yescharacteristic
294C4#6388011yescharacteristic
295C3—21no—
296C3#6909111yescharacteristic, complemented
297C3#6924911yescharacteristic, complemented
298C2—21no—
299C2—241no—
300C2—722no—
301C2#1059074611yescharacteristic
subgroupG/H
centerC2#10590746
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#442
prime radical#10590634C2
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32AGL(1,ℤ/16)
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
1. #10590916C2semidirect
2. #10590768C2semidirect
4. #10589382C2semidirect
5. C3×#4518C2semidirect
6. C3×#4512C2semidirect
7. #10589136C2semidirect
21. #63549C4semidirect
22. #63546C4semidirect
31. #4518D3semidirect
36. #4512D3semidirect
48. C3×Dic12C2×C4semidirect
49. C3×D24C2×C4semidirect
55. C3×C3⋊C16C2×C4semidirect
134. Dic12C4×D3semidirect
141. D24C4×D3semidirect
149. C3⋊C16C4×D3semidirect
258. C32AGL(1,ℤ/16)semidirect
296. C3#69091semidirect
297. C3#69249semidirect

Maximal subgroups

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

subgroupindex
#105909162
#105907682
#105906342
#105893822
C3×#45182
C3×#45122
#105891362
#692493
#690913