Finite Group Databasebeta

← #11797976

Subgroups — #11797976

Order 1152.

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

normal subgroups only

This group has 331 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#10590920C211yesmaximal, characteristic, complemented
2#10590781C211yesmaximal, characteristic, complemented
3#10590630C211yesmaximal, characteristic
4#10589378C211yesmaximal, characteristic, complemented
5C3×#4518C211yesmaximal, characteristic, complemented
6C3×#4516C211yesmaximal, characteristic, complemented
7#10589138C211yesmaximal, characteristic, complemented
8#69254—31nomaximal
9#69249—31nomaximal
10C3×#904C2211yescharacteristic
11C2×C3×D24C2211yescharacteristic
12#63898—21no—
13#63815—21no—
14C32×M32C2211yescharacteristic
15#63642C2211yescharacteristic
16#63639C2211yescharacteristic
17C3×#819C2211yescharacteristic
18C3×#817C2211yescharacteristic
19#63568—21no—
20#63562—21no—
21#63547C412yescomplemented
22#63545C412yescomplemented
23#5197—31no—
24#5193—31no—
25#5152—31no—
26#5147—31no—
27#4894—31no—
28#4869—31no—
29C3×#361—31no—
30C3×#360—31no—
31#4518D311yescharacteristic, complemented
32#4516D311yescharacteristic, complemented
33#4512—31no—
34#4512—31no—
35#4512—61no—
36#4494—31no—
37#4487—31no—
38C3×#235—21no—
39C2×C3×D12—21no—
40C2×D3×Dic3—41no—
41C2×C32×C8C2311yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C2×C3⋊(C3⋊C8)D411yescharacteristic
44C3×C4⋊Dic3—21no—
45C3×#208—21no—
46C3×Dic12C2×C411yescharacteristic, complemented
47C3×D24—21no—
48C3×D24C2×C412yes—
49C3×D24C2×C411yescharacteristic, complemented
50C3×#204—21no—
51(C2×D3)⋊Dic3—41no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C32×C16—21no—
55C3⋊(C3⋊C16)C2×C412yescomplemented
56AGL(1,ℤ/16)—91noSylow
57C3×#135—31no—
58C2×C3×D8—31no—
59#948—61no—
60D4×Dic3—61no—
61#907—61no—
62#904C2×D311yescharacteristic
63C2×D24C2×D311yescharacteristic
64#893—61no—
65C3×M32—21no—
66C3×M32C2×D311yescharacteristic
67C3×M32C2×D311yescharacteristic
68C3×#108—31no—
69C3×#106—31no—
70#837—61no—
71#832—61no—
72#828—32no—
73#827—32no—
74#826—32no—
75#826—32no—
76#825—61no—
77#819C2×D311yescharacteristic
78#817C2×D311yescharacteristic
79#815—31no—
80#815—31no—
81#815—61no—
82#812—31no—
83#812—31no—
84#812—61no—
85#809—61no—
86C22×C3×D3—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—21no—
89C3×#67—41no—
90C2×C3×Dic3—41no—
91C3×D12—21no—
92C3×D12—22no—
93C3×D12—41no—
94C3×C4×D3—41no—
95C3×Dic6—21no—
96D3×Dic3—82no—
97C32×C8C22×C411yescharacteristic
98C32×C8#4111yescharacteristic
99C3⋊(C3⋊C8)—21no—
100C3×C3⋊C8—41no—
101#509—91no—
102#444—91no—
103#442—91no—
104#365—91no—
105#361—31no—
106#360—31no—
107#347—91no—
108C3×#41—61no—
109C2×C3×D4—61no—
110C22×Dic3—121no—
111#235—21no—
112C2×D12—21no—
113C2×C4×D3—121no—
114C3×Q16—31no—
115C3×SD16—61no—
116C3×D8—31no—
117C3×D8—32no—
118C3×D8—61no—
119C3×M16—61no—
120C2×C3×C8—21no—
121C2×C3×C8C22×D311yescharacteristic
122C2×C3×C8C22×D311yescharacteristic
123C3×C4⋊C4—61no—
124#217—121no—
125(C2×D3)⋊C4—121no—
126C4⋊Dic3—21no—
127C4×Dic3—31no—
128C4×Dic3—31no—
129C4×Dic3—61no—
130#208—21no—
131#208—121no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—31no—
134C2×C3⋊C8—61no—
135C2×C3⋊C8—121no—
136Dic12C4×D311yescharacteristic, complemented
137D24—21no—
138D24C4×D312yes—
139D24C4×D311yescharacteristic, complemented
140#204—21no—
141ΓL(1,𝔽25)—121no—
142D3×C8—121no—
143C3×C16—22no—
144C3×C16—21no—
145C3×C16—21no—
146C3⋊C16—32no—
147C3⋊C16—32no—
148C3⋊C16—62no—
149C22×C32AGL(1,ℤ/8)11yescharacteristic
150C2×C3×D3—41no—
151C2×C3×D3—42no—
152C2×C3×D3—81no—
153C2×C3×D3—81no—
154C32×C4C4×D411yescharacteristic
155C32×C4AGL(1,ℤ/8)11yescharacteristic
156C3⋊Dic3—41no—
157C3×Dic3—41no—
158C3×Dic3—81no—
159#135—31no—
160C2×D8—31no—
161#131—181no—
162C4×D4—181no—
163SD32—92no—
164D16—92no—
165M32—91no—
166M32D3211yescharacteristic
167#108—31no—
168#106—31no—
169#104—181no—
170#102—181no—
171#97—91no—
172C23×C3—121no—
173C22×D3—41no—
174C3×Q8—61no—
175C3×D4—62no—
176C3×D4—61no—
177C3×D4—121no—
178C3×D4—121no—
179C2×C3×C4—21no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4D3×D411yescharacteristic
183C2×C3×C4D3×D411yescharacteristic
184#67—41no—
185C2×Dic3—41no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—121no—
189C2×Dic3—242no—
190D12—21no—
191D12—22no—
192D12—41no—
193C4×D3—41no—
194C4×D3—242no—
195Dic6—21no—
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—121no—
199C3×C8C2×C4×D311yescharacteristic
200C3×C8C2×C4×D311yescharacteristic
201C3×C8#23711yescharacteristic
202C3×C8#23711yescharacteristic
203C3⋊C8—41no—
204C3⋊C8—61no—
205C3⋊C8—61no—
206C3⋊C8—121no—
207C2×C32—21no—
208C2×C32#44211yescharacteristic
209C3×D3—81no—
210C3×D3—82no—
211#41—61no—
212C2×D4—61no—
213C22×C4—361no—
214Q16—31no—
215SD16—61no—
216D8—31no—
217D8—32no—
218D8—61no—
219M16—61no—
220M16—361no—
221C2×C8—91no—
222C2×C8—361no—
223C2×C8C2×D3211yescharacteristic
224C4⋊C4—61no—
225C22⋊C4—361no—
226C42—91no—
227C16—21no—
228C16—92no—
229C22×C3—21no—
230C22×C3—121no—
231C22×C3—122no—
232C22×C3—241no—
233C22×C3—241no—
234C22×C3#91111yescharacteristic
235C22×C3#91411yescharacteristic
236C2×D3—41no—
237C2×D3—42no—
238C2×D3—81no—
239C2×D3—81no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—121no—
243C3×C4—241no—
244C3×C4#67⋊C411yescharacteristic
245C3×C4#67⋊C411yescharacteristic
246C3×C4#91111yescharacteristic
247C3×C4#91411yescharacteristic
248Dic3—41no—
249Dic3—81no—
250Dic3—121no—
251Dic3—121no—
252Dic3—241no—
253C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
254C23—121no—
255Q8—61no—
256D4—62no—
257D4—61no—
258D4—121no—
259D4—121no—
260C2×C4—121no—
261C2×C4—121no—
262C2×C4—181no—
263C2×C4—722no—
264C2×C4#380211yescharacteristic
265C8—121no—
266C8—181no—
267C8C4×D3211yescharacteristic
268C8#380511yescharacteristic
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—41no—
273C2×C3—242no—
274C2×C3—241no—
275C2×C3#478511yescharacteristic
276C2×C3#478511yescharacteristic
277D3—81no—
278D3—82no—
279C22—121no—
280C22—122no—
281C22—241no—
282C22—241no—
283C22#6379811yescharacteristic
284C4—121no—
285C4—241no—
286C4—361no—
287C4#6379811yescharacteristic
288C4#6390211yescharacteristic
289C3—21no—
290C3#6924911yescharacteristic, complemented
291C3#6925411yescharacteristic, complemented
292C2—21no—
293C2—242no—
294C2—241no—
295C2#1059074111yescharacteristic
subgroupG/H
centerC2#10590741
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#442
prime radical#10590630C2
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. #10590920C2semidirect
2. #10590781C2semidirect
4. #10589378C2semidirect
5. C3×#4518C2semidirect
6. C3×#4516C2semidirect
7. #10589138C2semidirect
21. #63547C4semidirect
22. #63545C4semidirect
31. #4518D3semidirect
32. #4516D3semidirect
46. C3×Dic12C2×C4semidirect
49. C3×D24C2×C4semidirect
55. C3⋊(C3⋊C16)C2×C4semidirect
136. Dic12C4×D3semidirect
139. D24C4×D3semidirect
253. C32AGL(1,ℤ/16)semidirect
290. C3#69249semidirect
291. C3#69254semidirect

Maximal subgroups

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

subgroupindex
#105909202
#105907812
#105906302
#105893782
C3×#45182
C3×#45162
#105891382
#692543
#692493