Finite Group Databasebeta

← #11778779

Subgroups — #11778779

Order 1152.

369 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589612C211yesmaximal, characteristic
2#10588666C211yesmaximal, characteristic, complemented
3#10588417C212yesmaximal, complemented
4C9×#324C211yesmaximal, characteristic, complemented
5#10588147C212yesmaximal, complemented
6#68137—31nomaximal
7C2×#3697—21no—
8C2×C9×C4⋊C4C2211yescharacteristic
9#63492—21no—
10#63492C2212yes—
11C2×C4⋊Dic9C2211yescharacteristic
12#63459—22no—
13#63457—22no—
14C9×C22⋊C8C2212yes—
15C9⋊#95—21no—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63380—22no—
19#63377—22no—
20#5510—31no—
21#4986—31no—
22#4735—32no—
23C3×#324D311yescharacteristic
24#4470—32no—
25C22×C4×C9D411yescharacteristic
26C22×C4×C9D411yescharacteristic
27C22×C4×C9C2311yescharacteristic
28C2×#611—22no—
29C22×Dic9—21no—
30C22×Dic9—21no—
31#3697—42no—
32#3697—42no—
33C2×D36—21no—
34C2×D36—21no—
35C2×D36D412yes—
36C2×C4×D9—22no—
37C2×Dic18—21no—
38C2×C8×C9—22no—
39C9×C4⋊C4—22no—
40(C2×D9)⋊C4—22no—
41(C2×D9)⋊C4—22no—
42C4⋊Dic9—21no—
43C4⋊Dic9—22no—
44C4⋊Dic9D412yes—
45#1616—91noSylow
46C2×#235—61no—
47C2×C3×C4⋊C4C2×D311yescharacteristic
48#930—32no—
49#930—61no—
50C2×C4⋊Dic3—31no—
51#897—62no—
52#895—62no—
53C3×C22⋊C8C2×D312yes—
54C3⋊#95—31no—
55C3⋊#95—61no—
56C3⋊#95—61no—
57#821—62no—
58#817—62no—
59C23×C9C2×D411yescharacteristic
60C22×D9—22no—
61C2×C4×C9—21no—
62C2×C4×C9—21no—
63C2×C4×C9—21no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×C4×C9SD1612yes—
67C2×C4×C9C2×D412yes—
68#611—42no—
69#611—42no—
70C2×Dic9—22no—
71C2×Dic9—41no—
72C2×Dic9—41no—
73C2×Dic9—42no—
74C2×Dic9—41no—
75C2×Dic9—41no—
76D36—42no—
77D36—42no—
78D36—81no—
79C4×D9—44no—
80Dic18—42no—
81C8×C9—42no—
82#537—91no—
83#481—92no—
84#400—91no—
85#327—92no—
86#324D911yescharacteristic, complemented
87C22×C3×C4D1211yescharacteristic
88C22×C3×C4D1211yescharacteristic
89C22×C3×C4C22×D311yescharacteristic
90C2×#67—62no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93#235—122no—
94#235—122no—
95C2×D12—32no—
96C2×D12—61no—
97C2×D12—61no—
98C2×C4×D3—62no—
99C2×Dic6—61no—
100C2×C3×C8—22no—
101C3×C4⋊C4—22no—
102(C2×D3)⋊C4—62no—
103(C2×D3)⋊C4—62no—
104C4⋊Dic3—32no—
105C4⋊Dic3—61no—
106C4⋊Dic3—62no—
107C22×C9—21no—
108C22×C9—21no—
109C22×C9#12011yescharacteristic
110C22×C9C2×SD1611yescharacteristic
111C22×C9AGL(1,ℤ/8)11yescharacteristic
112C2×D9—42no—
113C2×D9—42no—
114C2×D9—42no—
115C4×C9—22no—
116C4×C9—22no—
117C4×C9—41no—
118Dic9—42no—
119Dic9—81no—
120Dic9—81no—
121C2×#41—181no—
122C22⋊Q8—182no—
123#121—92no—
124#121—182no—
125#121—181no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4C2×D911yescharacteristic
128#106—182no—
129#102—182no—
130C22⋊C8C2×D912yes—
131#95—91no—
132#95—181no—
133#95—181no—
134C23×C3C2×D1211yescharacteristic
135C22×D3—62no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—41no—
140C2×C3×C4—41no—
141C2×C3×C4#20412yes—
142C2×C3×C4D3×D412yes—
143#67—122no—
144#67—122no—
145C2×Dic3—62no—
146C2×Dic3—121no—
147C2×Dic3—121no—
148C2×Dic3—122no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151D12—122no—
152D12—122no—
153D12—241no—
154C4×D3—124no—
155Dic6—122no—
156C3×C8—42no—
157C2×C9—21no—
158C2×C9—21no—
159C2×C9#45011yescharacteristic
160C2×C9#45411yescharacteristic
161C2×C9#45811yescharacteristic
162D9—82no—
163#41—362no—
164#41—362no—
165C2×Q8—181no—
166C2×D4—92no—
167C2×D4—181no—
168C2×D4—181no—
169C2×D4—182no—
170C22×C4—182no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4D3611yescharacteristic
174C22×C4D3611yescharacteristic
175C22×C4C22×D911yescharacteristic
176C2×C8—22no—
177C4⋊C4—22no—
178C4⋊C4—92no—
179C4⋊C4—181no—
180C4⋊C4—182no—
181C22⋊C4—182no—
182C22⋊C4—182no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3#88211yescharacteristic
186C22×C3C2×#20411yescharacteristic
187C22×C3#90811yescharacteristic
188C2×D3—122no—
189C2×D3—122no—
190C2×D3—122no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—41no—
194Dic3—122no—
195Dic3—241no—
196Dic3—241no—
197C9#161611yescharacteristic, complemented, Sylow
198C23—182no—
199C23C2×D3611yescharacteristic
200Q8—362no—
201D4—362no—
202D4—362no—
203D4—362no—
204D4—362no—
205D4—721no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—182no—
212C2×C4—364no—
213C2×C4—361no—
214C2×C4—361no—
215C2×C4—362no—
216C2×C4—361no—
217C2×C4—361no—
218C2×C4#366412yes—
219C2×C4D4×D912yes—
220C8—42no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3#473111yescharacteristic
224C2×C3#474211yescharacteristic
225C2×C3#475311yescharacteristic
226D3—242no—
227C22—21no—
228C22—21no—
229C22—362no—
230C22—362no—
231C22—362no—
232C22#6344411yescharacteristic
233C22C2×#366411yescharacteristic
234C22#6347011yescharacteristic
235C4—22no—
236C4—22no—
237C4—41no—
238C4—362no—
239C4—721no—
240C4—721no—
241C3#6813711yescharacteristic
242C2—21no—
243C2—21no—
244C2—722no—
245C2#1058841311yescharacteristic
246C2#1058842211yescharacteristic
247C2#1058843311yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3#882
prime radical#10589612C2
hypercenter#324D9
hypocenterC9#1616
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #10588666C2semidirect
3. #10588417C2semidirect
4. C9×#324C2semidirect
5. #10588147C2semidirect
86. #324D9semidirect
197. C9#1616semidirect

Maximal subgroups

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

subgroupindex
#105896122
#105886662
#105884172
C9×#3242
#105881472
#681373