Finite Group Databasebeta

← #10589931

Subgroups — #10589931

Order 576.

501 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×C9×#41C211yesmaximal, characteristic, complemented
2C2×D4×D9C211yesmaximal, characteristic, complemented
3#63509C211yesmaximal, characteristic, complemented
4#63508C211yesmaximal, characteristic, complemented
5#63501C212yesmaximal, complemented
6#63499C212yesmaximal, complemented
7D4×Dic9C211yesmaximal, characteristic, complemented
8#63492C211yesmaximal, characteristic, complemented
9#63491C212yesmaximal, complemented
10C4×#611C211yesmaximal, characteristic, complemented
11C2×(C2×D9)⋊C4C212yesmaximal, complemented
12#5829—31nomaximal
13C23×D9C2212yes—
14C9×#41—24no—
15C2×Q8×C9C2211yescharacteristic, complemented
16C2×D4×C9C2211yescharacteristic
17C2×D4×C9C2212yescomplemented
18C22×C4×C9C2212yescomplemented
19C22×C4×C9C2211yescharacteristic, complemented
20C2×#611C2211yescharacteristic
21C2×#611C2212yes—
22C2×#611C2212yescomplemented
23C22×Dic9C2212yescomplemented
24D4×D9—24no—
25C2×D36C2211yescharacteristic
26C2×C4×D9C2211yescharacteristic
27#3676C2211yescharacteristic, complemented
28#3676C2212yescomplemented
29(C2×D9)⋊C4C2211yescharacteristic
30(C2×D9)⋊C4C2212yes—
31(C2×D9)⋊C4C2212yescomplemented
32(C2×D9)⋊C4C2212yescomplemented
33(C2×D9)⋊C4C2212yescomplemented
34C4⋊Dic9C2211yescharacteristic, complemented
35Dic9⋊C4C2211yescharacteristic, complemented
36Dic9⋊C4C2212yescomplemented
37C4×Dic9C2211yescharacteristic, complemented
38C2×C3×#41D311yescharacteristic
39C2×D3×D4—31no—
40#947—31no—
41#946—31no—
42#939—32no—
43#937—32no—
44D4×Dic3—31no—
45#930—31no—
46#929—32no—
47C4×#67—31no—
48C2×(C2×D3)⋊C4—32no—
49C23×C9C2311yescharacteristic
50C23×C9C2312yes—
51C22×D9—24no—
52C22×D9—24no—
53C22×D9—42no—
54C22×D9C2312yes—
55C22×D9C2311yescharacteristic
56Q8×C9—22no—
57D4×C9—24no—
58D4×C9D414yescomplemented
59C2×C4×C9—24no—
60C2×C4×C9—22no—
61C2×C4×C9C2311yescharacteristic
62C2×C4×C9C2312yes—
63C2×C4×C9C2311yescharacteristic
64#611—24no—
65#611—22no—
66#611—42no—
67C2×Dic9—42no—
68C2×Dic9C2311yescharacteristic
69C2×Dic9C2311yescharacteristic
70C2×Dic9C2311yescharacteristic
71C2×Dic9C2312yes—
72D36—22no—
73C4×D9—22no—
74#546—91noSylow
75C23×D3—32no—
76C3×#41—24no—
77C2×C3×Q8C2×D311yescharacteristic
78C2×C3×D4C2×D311yescharacteristic
79C2×C3×D4C2×D312yes—
80C22×C3×C4C2×D312yes—
81C22×C3×C4C2×D311yescharacteristic
82C2×#67—31no—
83C2×#67—32no—
84C2×#67—32no—
85C22×Dic3—32no—
86D3×D4—64no—
87C2×D12—31no—
88C2×C4×D3—31no—
89#217—31no—
90#217—32no—
91(C2×D3)⋊C4—31no—
92(C2×D3)⋊C4—32no—
93(C2×D3)⋊C4—32no—
94(C2×D3)⋊C4—32no—
95(C2×D3)⋊C4—32no—
96C4⋊Dic3—31no—
97Dic3⋊C4—31no—
98Dic3⋊C4—32no—
99C4×Dic3—31no—
100C22×C9—22no—
101C22×C9—22no—
102C22×C9—21no—
103C22×C9—21no—
104C22×C9—21no—
105C22×C9C2×D414yes—
106C22×C9C2411yescharacteristic
107C2×D9—21no—
108C2×D9—21no—
109C2×D9—22no—
110C2×D9—22no—
111C2×D9—22no—
112C2×D9—48no—
113C2×D9#4112yescomplemented
114C4×C9—21no—
115C4×C9—22no—
116C4×C9C2×D412yes—
117Dic9—21no—
118Dic9—21no—
119Dic9—21no—
120Dic9—22no—
121C2×#41D911yescharacteristic, complemented
122C22×D4—91no—
123#124—91no—
124#123—92no—
125C22⋊Q8—91no—
126#121—92no—
127#121—91no—
128#120—92no—
129C4×D4—91no—
130C4×D4—91no—
131C2×C22⋊C4—92no—
132C23×C3C22×D311yescharacteristic
133C23×C3C22×D312yes—
134C22×D3—31no—
135C22×D3—32no—
136C22×D3—64no—
137C22×D3—64no—
138C22×D3—122no—
139C3×Q8—22no—
140C3×D4—24no—
141C3×D4#6714yes—
142C2×C3×C4—24no—
143C2×C3×C4—22no—
144C2×C3×C4C22×D311yescharacteristic
145C2×C3×C4C22×D312yes—
146C2×C3×C4C22×D311yescharacteristic
147#67—62no—
148#67—64no—
149#67—122no—
150C2×Dic3—31no—
151C2×Dic3—31no—
152C2×Dic3—31no—
153C2×Dic3—32no—
154C2×Dic3—122no—
155D12—62no—
156C4×D3—62no—
157C2×C9—24no—
158C2×C9—41no—
159C2×C9C22×D411yescharacteristic
160C2×C9C2×#4111yescharacteristic
161C2×C9H(5,𝔽2)11yescharacteristic
162D9—22no—
163D9—42no—
164C24—92no—
165#41—24no—
166C2×Q8C2×D911yescharacteristic, complemented
167C2×D4—91no—
168C2×D4—92no—
169C2×D4—92no—
170C2×D4—91no—
171C2×D4—184no—
172C2×D4C2×D911yescharacteristic
173C2×D4C2×D912yescomplemented
174C22×C4—92no—
175C22×C4—91no—
176C22×C4C2×D912yescomplemented
177C22×C4C2×D911yescharacteristic, complemented
178C4⋊C4—91no—
179C4⋊C4—91no—
180C4⋊C4—92no—
181C22⋊C4—92no—
182C22⋊C4—91no—
183C22⋊C4—91no—
184C22⋊C4—92no—
185C22⋊C4—92no—
186C22⋊C4—92no—
187C22⋊C4—92no—
188C42—91no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3C2×#6714yes—
195C22×C3C23×D311yescharacteristic
196C2×D3—32no—
197C2×D3—61no—
198C2×D3—61no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—128no—
203C3×C4—21no—
204C3×C4—22no—
205C3×C4C2×#6712yes—
206Dic3—61no—
207Dic3—61no—
208Dic3—62no—
209Dic3—61no—
210C9#54611yescharacteristic, complemented, Sylow
211C23—91no—
212C23—92no—
213C23—184no—
214C23—184no—
215C23—362no—
216C23C22×D911yescharacteristic
217C23C22×D912yes—
218Q8—22no—
219D4—24no—
220D4—182no—
221D4—184no—
222D4—182no—
223D4—362no—
224D4#61114yescomplemented
225C2×C4—24no—
226C2×C4—22no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—92no—
230C2×C4—91no—
231C2×C4—182no—
232C2×C4—362no—
233C2×C4C22×D911yescharacteristic
234C2×C4C22×D912yes—
235C2×C4C22×D911yescharacteristic
236C2×C3—24no—
237C2×C3—41no—
238C2×C3D3×#4111yescharacteristic
239C2×C3#100911yescharacteristic
240C2×C3C22×#6711yescharacteristic
241D3—62no—
242D3—122no—
243C22—22no—
244C22—22no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—92no—
249C22—181no—
250C22—181no—
251C22—182no—
252C22—182no—
253C22—182no—
254C22—368no—
255C22C2×#61114yes—
256C22C23×D911yescharacteristic
257C4—21no—
258C4—22no—
259C4—181no—
260C4—181no—
261C4—182no—
262C4—181no—
263C4C2×#61112yes—
264C3#582911yescharacteristic
265C2—24no—
266C2—41no—
267C2—182no—
268C2—362no—
269C2#41×D911yescharacteristic
270C2#6371511yescharacteristic
271C2C22×#61111yescharacteristic
subgroupG/H
centerC22C23×D9
commutator, cosocleC22×C9C24
Frattini, socleC22×C3C23×D3
FittingC2×C9×#41C2
hypercenterC2×#41D9
hypocenterC9#546
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C9×#41C2semidirect
2. C2×D4×D9C2semidirect
3. #63509C2semidirect
4. #63508C2semidirect
5. #63501C2semidirect
6. #63499C2semidirect
7. D4×Dic9C2semidirect
8. #63492C2semidirect
9. #63491C2semidirect
10. C4×#611C2semidirect
11. C2×(C2×D9)⋊C4C2semidirect
15. C2×Q8×C9C22semidirect
17. C2×D4×C9C22semidirect
18. C22×C4×C9C22semidirect
19. C22×C4×C9C22semidirect
22. C2×#611C22semidirect
23. C22×Dic9C22semidirect
27. #3676C22semidirect
28. #3676C22semidirect
31. (C2×D9)⋊C4C22semidirect
32. (C2×D9)⋊C4C22semidirect
33. (C2×D9)⋊C4C22semidirect
34. C4⋊Dic9C22semidirect
35. Dic9⋊C4C22semidirect
36. Dic9⋊C4C22semidirect
37. C4×Dic9C22semidirect
58. D4×C9D4semidirect
113. C2×D9#41semidirect
121. C2×#41D9semidirect
166. C2×Q8C2×D9semidirect
173. C2×D4C2×D9semidirect
176. C22×C4C2×D9semidirect
177. C22×C4C2×D9semidirect
210. C9#546semidirect
224. D4#611semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#412
C2×D4×D92
#635092
#635082
#635012
#634992
D4×Dic92
#634922
#634912
C4×#6112
C2×(C2×D9)⋊C42
#58293