Finite Group Databasebeta

← #11778327

Subgroups — #11778327

Order 1152.

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

normal subgroups only

This group has 423 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#10588659C211yesmaximal, characteristic, complemented
3#10588404C212yesmaximal, complemented
4C9×#324C211yesmaximal, characteristic, complemented
5#10588147C212yesmaximal, complemented
6#68133—31nomaximal
7C2×#3697—21no—
8C22×Dic18C2211yescharacteristic
9C2×C9×C4⋊C4C2211yescharacteristic
10#63492—21no—
11#63492C2212yes—
12C2×Dic9⋊C4—21no—
13C2×#3664—22no—
14#63459—22no—
15#63457—22no—
16C9×C22⋊C8C2212yes—
17C9⋊#95—21no—
18C9⋊#95C2211yescharacteristic
19#63376—22no—
20#5510—31no—
21#4979—31no—
22#4738—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—22no—
38C2×Dic18—21no—
39C2×Dic18—42no—
40C2×C8×C9—22no—
41C9×C4⋊C4—22no—
42(C2×D9)⋊C4—22no—
43(C2×D9)⋊C4—22no—
44C4⋊Dic9—21no—
45C4⋊Dic9D412yes—
46Dic9⋊C4—42no—
47#3664—44no—
48#1604—91noSylow
49C2×#235—61no—
50C22×Dic6—31no—
51C2×C3×C4⋊C4C2×D311yescharacteristic
52#930—32no—
53#930—61no—
54C2×Dic3⋊C4—61no—
55C2×#204—62no—
56#897—62no—
57#895—62no—
58C3×C22⋊C8C2×D312yes—
59C3⋊#95—31no—
60C3⋊#95—61no—
61#816—62no—
62C23×C9C2×D411yescharacteristic
63C22×D9—22no—
64C2×C4×C9—21no—
65C2×C4×C9—21no—
66C2×C4×C9—21no—
67C2×C4×C9—41no—
68C2×C4×C9—41no—
69C2×C4×C9SD1612yescomplemented
70C2×C4×C9C2×D412yes—
71#611—42no—
72#611—42no—
73C2×Dic9—22no—
74C2×Dic9—22no—
75C2×Dic9—22no—
76C2×Dic9—41no—
77C2×Dic9—41no—
78C2×Dic9—41no—
79C2×Dic9—41no—
80D36—42no—
81D36—42no—
82D36—81no—
83C4×D9—44no—
84Dic18—24no—
85Dic18—42no—
86Dic18—42no—
87C8×C9—42no—
88#537—91no—
89#448—92no—
90#395—91no—
91#327—92no—
92#324D911yescharacteristic, complemented
93C22×C3×C4D1211yescharacteristic
94C22×C3×C4D1211yescharacteristic
95C22×C3×C4C22×D311yescharacteristic
96C2×#67—62no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99#235—122no—
100#235—122no—
101C2×D12—32no—
102C2×D12—61no—
103C2×D12—61no—
104C2×C4×D3—62no—
105C2×Dic6—62no—
106C2×Dic6—61no—
107C2×Dic6—122no—
108C2×C3×C8—22no—
109C3×C4⋊C4—22no—
110(C2×D3)⋊C4—62no—
111(C2×D3)⋊C4—62no—
112C4⋊Dic3—32no—
113C4⋊Dic3—61no—
114Dic3⋊C4—122no—
115#204—124no—
116C22×C9—21no—
117C22×C9—21no—
118C22×C9#12011yescharacteristic
119C22×C9C2×SD1611yescharacteristic
120C22×C9AGL(1,ℤ/8)11yescharacteristic
121C2×D9—42no—
122C2×D9—42no—
123C2×D9—42no—
124C4×C9—22no—
125C4×C9—22no—
126C4×C9—41no—
127Dic9—42no—
128Dic9—42no—
129Dic9—42no—
130C2×#41—181no—
131C22×Q8—91no—
132C2×SD16—182no—
133C22⋊Q8—182no—
134#121—92no—
135#121—182no—
136#121—181no—
137C2×C4⋊C4—181no—
138C2×C4⋊C4C2×D911yescharacteristic
139#103—182no—
140C22⋊C8C2×D912yes—
141#95—91no—
142#95—181no—
143C23×C3C2×D1211yescharacteristic
144C22×D3—62no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4#20412yes—
151C2×C3×C4D3×D412yes—
152#67—122no—
153#67—122no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C2×Dic3—121no—
160C2×Dic3—121no—
161D12—122no—
162D12—122no—
163D12—241no—
164C4×D3—124no—
165Dic6—64no—
166Dic6—122no—
167Dic6—122no—
168C3×C8—42no—
169C2×C9—21no—
170C2×C9—21no—
171C2×C9#45011yescharacteristic
172C2×C9#45611yescharacteristic
173C2×C9B(4,𝔽2)11yescharacteristic
174D9—82no—
175#41—362no—
176#41—362no—
177C2×Q8—181no—
178C2×Q8—182no—
179C2×Q8—362no—
180C2×D4—92no—
181C2×D4—181no—
182C2×D4—181no—
183C2×D4—182no—
184C22×C4—182no—
185C22×C4—181no—
186C22×C4—181no—
187C22×C4D3611yescharacteristic
188C22×C4D3611yescharacteristic
189C22×C4C22×D911yescharacteristic
190SD16—364no—
191C2×C8—22no—
192C4⋊C4—22no—
193C4⋊C4—92no—
194C4⋊C4—181no—
195C4⋊C4—362no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3#88211yescharacteristic
201C22×C3C2×#20411yescharacteristic
202C22×C3#90811yescharacteristic
203C2×D3—122no—
204C2×D3—122no—
205C2×D3—122no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—41no—
209Dic3—122no—
210Dic3—122no—
211Dic3—122no—
212C9#160411yescharacteristic, complemented, Sylow
213C23—182no—
214C23C2×D3611yescharacteristic
215Q8—184no—
216Q8—362no—
217Q8—362no—
218D4—362no—
219D4—362no—
220D4—362no—
221D4—362no—
222D4—721no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4—182no—
231C2×C4—364no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4#366412yescomplemented
237C2×C4D4×D912yes—
238C8—42no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3#473111yescharacteristic
242C2×C3#474111yescharacteristic
243C2×C3#475211yescharacteristic
244D3—242no—
245C22—21no—
246C22—21no—
247C22—362no—
248C22—362no—
249C22—362no—
250C22#6344411yescharacteristic
251C22C2×#366411yescharacteristic
252C22#6347011yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—362no—
257C4—362no—
258C4—362no—
259C3#6813311yescharacteristic
260C2—21no—
261C2—21no—
262C2—722no—
263C2#1058841311yescharacteristic
264C2#1058842111yescharacteristic
265C2#1058843211yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3#882
prime radical#10589612C2
hypercenter#324D9
hypocenterC9#1604
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. #10588659C2semidirect
3. #10588404C2semidirect
4. C9×#324C2semidirect
5. #10588147C2semidirect
69. C2×C4×C9SD16semidirect
92. #324D9semidirect
212. C9#1604semidirect
236. C2×C4#3664semidirect

Maximal subgroups

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

subgroupindex
#105896122
#105886592
#105884042
C9×#3242
#105881472
#681333