Finite Group Databasebeta

← #11798418

Subgroups — #11798418

Order 1152.

324 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 62 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#10589871C211yesmaximal, characteristic
2C9×#510C211yesmaximal, characteristic, complemented
3#10588872C211yesmaximal, characteristic, complemented
4C2×#63387C211yesmaximal, characteristic, complemented
5#10588244C211yesmaximal, characteristic, complemented
6#10588193C211yesmaximal, characteristic, complemented
7#10588192C211yesmaximal, characteristic, complemented
8#71523—31nomaximal
9#63715—21no—
10C9×#135C2211yescharacteristic
11C2×C9×Q16C2211yescharacteristic, complemented
12#63512—21no—
13#63505—21no—
14#63481—21no—
15#63476—22no—
16D8×D9—21no—
17C2×D72C2211yescharacteristic
18#63464C2211yescharacteristic
19C9×Q32—21no—
20C9×SD32—21no—
21C9×M32C2211yescharacteristic, complemented
22#63394—21no—
23#63387—22no—
24#63372C2211yescharacteristic, complemented
25C2×C9⋊C16C2211yescharacteristic, complemented
26#5769—31no—
27C3×#510D311yescharacteristic
28#5192—31no—
29C2×#828—31no—
30#4567—31no—
31#4516—31no—
32#4515—31no—
33C9×#41—21no—
34C2×Q8×C9—21no—
35#3701—22no—
36D4×D9—22no—
37D4×D9—42no—
38#3697—41no—
39#3697D411yescharacteristic
40C2×D36—21no—
41C2×D36—41no—
42C9×Q16—21no—
43C9×Q16—21no—
44C9×Q16D411yescharacteristic
45C9×SD16—21no—
46C9×D8D411yescharacteristic
47C2×C8×C9C2311yescharacteristic
48#3675—22no—
49#3675—41no—
50#3674—41no—
51#3673—22no—
52#3667—21no—
53#3667D411yescharacteristic
54D72—21no—
55D72D412yes—
56#3663—21no—
57C8×D9—21no—
58C9×C16—21no—
59C9⋊C16—21no—
60#2194—91noSylow
61#1009—61no—
62C3×#135C2×D311yescharacteristic
63C2×C3×Q16C2×D311yescharacteristic
64#949—61no—
65#942—61no—
66#919—61no—
67#914—62no—
68D3×D8—61no—
69C2×D24—31no—
70#901—31no—
71C3×Q32—21no—
72C3×SD32—21no—
73C3×M32C2×D311yescharacteristic
74#836—61no—
75#828—62no—
76#819—31no—
77C2×C3⋊C16—31no—
78C22×D9—42no—
79C22×D9—41no—
80Q8×C9—21no—
81Q8×C9—41no—
82Q8×C9—41no—
83D4×C9—21no—
84D4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9—41no—
87C2×C4×C9C2×D411yescharacteristic
88#611—21no—
89#611—42no—
90D36—22no—
91D36—42no—
92D36—41no—
93D36D811yescharacteristic
94C4×D9—21no—
95C4×D9—42no—
96Dic18D811yescharacteristic
97C8×C9C2×D411yescharacteristic
98C8×C9C2×D411yescharacteristic
99C9⋊C8—21no—
100C9⋊C8—41no—
101#576—91no—
102#510D911yescharacteristic, complemented
103C2×SD32—91no—
104#473—91no—
105#361—91no—
106#359—91no—
107#350—91no—
108C3×#41—21no—
109C2×C3×Q8—21no—
110#239—62no—
111D3×D4—62no—
112D3×D4—122no—
113#235—31no—
114#235—121no—
115C2×D12—61no—
116C2×D12—121no—
117C3×Q16—21no—
118C3×Q16—21no—
119C3×Q16#6711yescharacteristic
120C3×SD16—21no—
121C3×D8#6711yescharacteristic
122C2×C3×C8C22×D311yescharacteristic
123#216—121no—
124#215—62no—
125#215—121no—
126#213—62no—
127#208—31no—
128#208—61no—
129D24—32no—
130D24—61no—
131ΓL(1,𝔽25)—61no—
132D3×C8—61no—
133C3×C16—21no—
134C3⋊C16—61no—
135C22×C9—41no—
136C22×C9AGL(1,ℤ/8)11yescharacteristic
137C2×D9—21no—
138C2×D9—42no—
139C2×D9—162no—
140C2×D9—161no—
141C4×C9—41no—
142C4×C9—81no—
143C4×C9#12011yescharacteristic
144C4×C9C2×D811yescharacteristic
145Dic9—21no—
146H(5,𝔽2)—181no—
147#137—181no—
148AGL(1,ℤ/8)—181no—
149AGL(1,ℤ/8)—182no—
150#135—181no—
151#135C2×D911yescharacteristic
152C2×Q16C2×D911yescharacteristic, complemented
153C2×D8—91no—
154C2×D8—181no—
155#131—91no—
156Q32—21no—
157SD32—21no—
158SD32—182no—
159M32C2×D911yescharacteristic, complemented
160C2×C16—91no—
161#108—91no—
162#101—181no—
163C22×D3—122no—
164C22×D3—121no—
165C3×Q8—21no—
166C3×Q8—41no—
167C3×Q8—41no—
168C3×D4—21no—
169C3×D4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4D3×D411yescharacteristic
173#67—61no—
174#67—122no—
175D12—31no—
176D12—62no—
177D12—122no—
178D12—121no—
179C4×D3—61no—
180C4×D3—122no—
181Dic6—31no—
182C3×C8D3×D411yescharacteristic
183C3×C8C2×#6711yescharacteristic
184C3⋊C8—61no—
185C3⋊C8—121no—
186C2×C9—21no—
187C2×C9—81no—
188C2×C9#44711yescharacteristic
189D9—41no—
190D9—82no—
191#41—21no—
192#41—91no—
193#41—182no—
194#41—361no—
195C2×Q8—21no—
196C2×D4—182no—
197C2×D4—181no—
198C2×D4—361no—
199C2×D4—362no—
200Q16—21no—
201Q16—21no—
202Q16—361no—
203Q16#61111yescharacteristic
204SD16—21no—
205SD16—182no—
206SD16—361no—
207D8—92no—
208D8—182no—
209D8—181no—
210D8#61111yescharacteristic
211M16—91no—
212M16—181no—
213M16—181no—
214C2×C8—181no—
215C2×C8C22×D911yescharacteristic
216C16—21no—
217C16—181no—
218C22×C3—41no—
219C22×C3#91111yescharacteristic
220C2×D3—61no—
221C2×D3—122no—
222C2×D3—482no—
223C2×D3—481no—
224C3×C4—41no—
225C3×C4—81no—
226C3×C4D3×D811yescharacteristic
227C3×C4#93711yescharacteristic
228Dic3—61no—
229C9#219411yescharacteristic, complemented, Sylow
230C23—362no—
231C23—361no—
232Q8—21no—
233Q8—41no—
234Q8—41no—
235Q8—91no—
236D4—21no—
237D4—41no—
238D4—91no—
239D4—181no—
240D4—182no—
241D4—362no—
242D4—362no—
243D4—361no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—181no—
247C2×C4—362no—
248C2×C4D4×D911yescharacteristic
249C8—181no—
250C8—361no—
251C8D4×D911yescharacteristic
252C8C2×#61111yescharacteristic
253C2×C3—21no—
254C2×C3—81no—
255C2×C3#515611yescharacteristic
256D3—121no—
257D3—242no—
258C22—41no—
259C22—181no—
260C22—362no—
261C22—1441no—
262C22—1442no—
263C22#6347311yescharacteristic
264C4—41no—
265C4—81no—
266C4—181no—
267C4D8×D911yescharacteristic
268C4#6349911yescharacteristic
269C3#7152311yescharacteristic
270C2—21no—
271C2—81no—
272C2—361no—
273C2—722no—
274C2#1058883611yescharacteristic
subgroupG/H
centerC2#10588836
commutator, cosocleC2×C8×C9C23
FrattiniC2×C3×C8C22×D3
FittingC9×#510C2
socleC2×C3#5156
prime radical#10589871C2
hypercenter#510D9
hypocenterC9#2194
LCSG ▷ C2×C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C9×#510C2semidirect
3. #10588872C2semidirect
4. C2×#63387C2semidirect
5. #10588244C2semidirect
6. #10588193C2semidirect
7. #10588192C2semidirect
11. C2×C9×Q16C22semidirect
21. C9×M32C22semidirect
24. #63372C22semidirect
25. C2×C9⋊C16C22semidirect
102. #510D9semidirect
152. C2×Q16C2×D9semidirect
159. M32C2×D9semidirect
229. C9#2194semidirect

Maximal subgroups

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

subgroupindex
#105898712
C9×#5102
#105888722
C2×#633872
#105882442
#105881932
#105881922
#715233