Finite Group Databasebeta

← #67⋊Dic9 #11721284

Subgroups — #67⋊Dic9 #11721284

Order 864.

336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×C3⋊Dic9C211yesmaximal, characteristic, complemented
2C2×C9×#67C211yesmaximal, characteristic
3C2×D3×Dic9C211yesmaximal, characteristic, complemented
4C3×#3676C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
6Dic3⋊Dic9C211yesmaximal, characteristic, complemented
7Dic3×Dic9C211yesmaximal, characteristic, complemented
8#67⋊Dic3—31nomaximal
9D4×Dic9—31nomaximal
10C23×C3×C9C2211yescharacteristic
11C22×D3×C9C2211yescharacteristic
12C2×C3⋊Dic9—22no—
13C2×C3⋊Dic9C2211yescharacteristic
14C2×C3⋊Dic9C2211yescharacteristic
15C9×#67C414yescomplemented
16C2×C9×Dic3C2211yescharacteristic
17C2×C3×Dic9C2211yescharacteristic
18C2×C3×Dic9C2211yescharacteristic
19D3×Dic9—22no—
20C22×C3⋊Dic3—31no—
21C2×C3×#67D311yescharacteristic
22C2×D3×Dic3—31no—
23C3×#217—31no—
24Dic3⋊Dic3—31no—
25(C2×D3)⋊Dic3—31no—
26Dic32—31no—
27C2×D4×C9—31no—
28C22×Dic9—31no—
29C22×Dic9—31no—
30C22×Dic9—61no—
31#3676—31no—
32#3676D311yescharacteristic, complemented
33C4⋊Dic9—31no—
34C4×Dic9—31no—
35C22×C3×C9—21no—
36C22×C3×C9—21no—
37C22×C3×C9C2×C412yescomplemented
38C22×C3×C9C2311yescharacteristic
39C2×D3×C9—21no—
40C2×D3×C9—21no—
41C2×D3×C9C2×C412yescomplemented
42C3⋊Dic9—21no—
43C3⋊Dic9D412yescomplemented
44C9×Dic3C2×C412yescomplemented
45C3×Dic9—21no—
46C3×Dic9—21no—
47D4×Dic3—91no—
48#67⋊C4—91no—
49C23×C32C2×D311yescharacteristic
50C22×C3×D3C2×D311yescharacteristic
51C2×C3⋊Dic3—31no—
52C2×C3⋊Dic3—31no—
53C2×C3⋊Dic3—62no—
54C3×#67Dic314yes—
55C2×C3×Dic3—31no—
56C2×C3×Dic3—31no—
57C2×C3×Dic3C2×D311yescharacteristic
58D3×Dic3—62no—
59C23×C9—21no—
60C23×C9—31no—
61C23×C9C2×D311yescharacteristic
62D4×C9—34no—
63C2×C4×C9—31no—
64C2×Dic9—31no—
65C2×Dic9—31no—
66C2×Dic9—61no—
67C2×Dic9—61no—
68C2×Dic9—62no—
69C2×Dic9—62no—
70C2×Dic9—64no—
71C2×Dic9C2×D311yescharacteristic
72C2×Dic9C2×D311yescharacteristic
73C2×C3×C9—22no—
74C2×C3×C9C22×C411yescharacteristic
75C2×C3×C9C2×D411yescharacteristic
76C2×C3×C9#4111yescharacteristic
77D3×C9—22no—
78C2×C3×D4—31no—
79C2×#67D911yescharacteristic
80C22×Dic3—91no—
81C22×Dic3—91no—
82C22×Dic3—91no—
83C22×Dic3—181no—
84C2×C4×D3—91no—
85C3×C22⋊C4—91no—
86#217—31no—
87#217—91no—
88(C2×D3)⋊C4—91no—
89C4⋊Dic3—91no—
90Dic3⋊C4—91no—
91C4×Dic3—91no—
92C4×Dic3—91no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32C2×Dic312yes—
96C22×C32C22×D311yescharacteristic
97C2×C3×D3—21no—
98C2×C3×D3—21no—
99C2×C3×D3C2×Dic312yes—
100C3⋊Dic3—32no—
101C3⋊Dic3—61no—
102C3×Dic3—61no—
103C3×Dic3—61no—
104C3×Dic3C2×Dic312yes—
105C22×C9—22no—
106C22×C9—22no—
107C22×C9—21no—
108C22×C9—21no—
109C22×C9—22no—
110C22×C9—21no—
111C22×C9—32no—
112C22×C9—61no—
113C22×C9—61no—
114C22×C9C4×D312yescomplemented
115C22×C9C22×D311yescharacteristic
116C4×C9—32no—
117Dic9—21no—
118Dic9—21no—
119Dic9—32no—
120Dic9—62no—
121Dic9—62no—
122Dic9—61no—
123C4×D4—271noSylow
124C3×C9C4×D411yescharacteristic, complemented, Sylow
125C23×C3—21no—
126C23×C3—31no—
127C23×C3C2×D911yescharacteristic
128C23×C3D3211yescharacteristic
129C22×D3C2×D911yescharacteristic
130C3×D4—34no—
131C2×C3×C4—31no—
132C2×C3×C4—91no—
133C2×C3×C4—91no—
134#67Dic914yescomplemented
135C2×Dic3—31no—
136C2×Dic3—31no—
137C2×Dic3—91no—
138C2×Dic3—91no—
139C2×Dic3—91no—
140C2×Dic3—91no—
141C2×Dic3—181no—
142C2×Dic3—181no—
143C2×Dic3—182no—
144C2×Dic3—182no—
145C2×Dic3—182no—
146C2×Dic3—184no—
147C2×Dic3C2×D911yescharacteristic
148C4×D3—182no—
149C2×C32—22no—
150C2×C32D3×D411yescharacteristic
151C2×C32#23711yescharacteristic
152C2×C32C22×Dic311yescharacteristic
153C3×D3—22no—
154C2×C9—24no—
155C2×C9—22no—
156C2×C9—21no—
157C2×C9—21no—
158C2×C9—21no—
159C2×C9—62no—
160C2×C9C2×C4×D311yescharacteristic
161C2×C9D3×D411yescharacteristic
162C2×C9#23711yescharacteristic
163C2×D4—31no—
164C22×C4—271no—
165C22×C4—271no—
166C4⋊C4—271no—
167C22⋊C4—91no—
168C22⋊C4—271no—
169C42—271no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—22no—
177C22×C3—21no—
178C22×C3—32no—
179C22×C3—61no—
180C22×C3—61no—
181C22×C3C2×Dic912yescomplemented
182C22×C3C22×D911yescharacteristic
183C22×C3D3×Dic312yes—
184C22×C3C2×D3211yescharacteristic
185C2×D3—21no—
186C2×D3—21no—
187C2×D3C2×Dic912yescomplemented
188C3×C4—32no—
189C3×C4—181no—
190C3×C4—181no—
191Dic3—61no—
192Dic3—61no—
193Dic3—92no—
194Dic3—92no—
195Dic3—182no—
196Dic3—182no—
197Dic3—181no—
198Dic3—181no—
199Dic3C2×Dic912yescomplemented
200C32D4×Dic311yescharacteristic
201C9—21no—
202C9#67⋊C411yescharacteristic, complemented
203C23—31no—
204C23D3×D911yescharacteristic
205D4—34no—
206C2×C4—31no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—271no—
210C2×C4—271no—
211C2×C4—542no—
212C2×C4—542no—
213C2×C3—24no—
214C2×C3—22no—
215C2×C3—22no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—62no—
220C2×C3D4×D911yescharacteristic
221C2×C3#369911yescharacteristic
222C2×C3C22×Dic911yescharacteristic
223C2×C3C2×D3×Dic311yescharacteristic
224C2×C3#380511yescharacteristic
225C2×C3#381111yescharacteristic
226D3—22no—
227C22—21no—
228C22—21no—
229C22—32no—
230C22—61no—
231C22—61no—
232C22D3×Dic912yescomplemented
233C22C2×D3×D911yescharacteristic
234C4—32no—
235C4—181no—
236C4—181no—
237C4—272no—
238C4—541no—
239C3—21no—
240C3D4×Dic911yescharacteristic, complemented
241C3#67⋊Dic311yescharacteristic
242C2—22no—
243C2—62no—
244C2C2×D3×Dic911yescharacteristic
245C2#8866311yescharacteristic
246C2#8866811yescharacteristic
subgroupG/H
centerC22C2×D3×D9
commutatorC2×C3×C9C22×C4
FrattiniC22×C3C2×D32
FittingC23×C3×C9C22
socleC22×C32C22×D3
prime radicalC2×C3×#67D3
cosocleC22×C3×C9C23
hypercenterC23D3×D9
hypocenterC3×C9C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊Dic9C2semidirect
3. C2×D3×Dic9C2semidirect
4. C3×#3676C2semidirect
5. (C2×D3)⋊Dic9C2semidirect
6. Dic3⋊Dic9C2semidirect
7. Dic3×Dic9C2semidirect
15. C9×#67C4semidirect
32. #3676D3semidirect
37. C22×C3×C9C2×C4semidirect
41. C2×D3×C9C2×C4semidirect
43. C3⋊Dic9D4semidirect
44. C9×Dic3C2×C4semidirect
114. C22×C9C4×D3semidirect
124. C3×C9C4×D4semidirect
134. #67Dic9semidirect
181. C22×C3C2×Dic9semidirect
187. C2×D3C2×Dic9semidirect
199. Dic3C2×Dic9semidirect
202. C9#67⋊C4semidirect
232. C22D3×Dic9semidirect
240. C3D4×Dic9semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊Dic92
C2×C9×#672
C2×D3×Dic92
C3×#36762
(C2×D3)⋊Dic92
Dic3⋊Dic92
Dic3×Dic92
#67⋊Dic33
D4×Dic93