Subgroups — C₉×#1827 #11766548

Order 1152.

393 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	C₉×#413	C₂	1	1	yes	maximal, characteristic
3	C₉×#410	C₂	1	1	yes	maximal, characteristic
4	C₉×#339	C₂	1	2	yes	maximal, complemented
5	C₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₃×#1827	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₄×Q₈×C₉	—	2	1	no	—
10	C₄×D₄×C₉	—	2	2	no	—
11	C₄×D₄×C₉	—	2	1	no	—
12	C₉×#117	C₄	1	2	yes	complemented
13	C₉×#117	C₂²	1	2	yes	—
14	C₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₉	C₄	1	2	yes	complemented
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#101	—	2	1	no	—
18	C₉×#100	—	2	1	no	—
19	C₉×#99	—	2	2	no	—
20	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
21	C₃×#413	C₂×C₃	1	1	yes	characteristic
22	C₃×#410	C₂×C₃	1	1	yes	characteristic
23	C₃×#339	C₂×C₃	1	2	yes	—
24	C₃×H(3,ℤ/4)	C₂×C₃	1	2	yes	—
25	C₉×#41	—	2	2	no	—
26	C₉×#41	—	2	2	no	—
27	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
28	C₂×D₄×C₉	D₄	1	2	yes	—
29	C₂×D₄×C₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₉	—	2	2	no	—
31	C₂²×C₄×C₉	—	2	1	no	—
32	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
34	C₉×M₁₆	—	2	2	no	—
35	C₉×M₁₆	—	2	2	no	—
36	C₂×C₈×C₉	—	2	2	no	—
37	C₉×C₄⋊C₄	—	2	2	no	—
38	C₉×C₄⋊C₄	—	2	1	no	—
39	C₉×C₄⋊C₄	—	2	2	no	—
40	C₉×C₂²⋊C₄	—	2	2	no	—
41	C₉×C₂²⋊C₄	—	2	1	no	—
42	C₉×C₂²⋊C₄	—	2	2	no	—
43	C₄²×C₉	—	2	2	no	—
44	C₄²×C₉	—	2	1	no	—
45	C₄²×C₉	—	2	2	no	—
46	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₉	C₂×C₄	1	2	yes	—
48	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
49	#1827	C₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
52	C₃×C₄×Q₈	—	2	1	no	—
53	C₃×C₄×D₄	—	2	2	no	—
54	C₃×C₄×D₄	—	2	1	no	—
55	C₃×#117	C₃×C₄	1	2	yes	—
56	C₃×#117	C₂²×C₃	1	2	yes	—
57	C₃×#117	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₃×C₄	1	2	yes	—
59	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
60	C₃×#101	—	2	1	no	—
61	C₃×#100	—	2	1	no	—
62	C₃×#99	—	2	2	no	—
63	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
64	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₉	—	2	2	no	—
66	D₄×C₉	—	2	4	no	—
67	D₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	—	2	1	no	—
69	C₂×C₄×C₉	—	2	2	no	—
70	C₂×C₄×C₉	—	2	2	no	—
71	C₂×C₄×C₉	—	2	2	no	—
72	C₂×C₄×C₉	—	2	1	no	—
73	C₂×C₄×C₉	—	4	2	no	—
74	C₂×C₄×C₉	—	4	4	no	—
75	C₂×C₄×C₉	—	4	2	no	—
76	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
77	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₉	#41	1	2	yes	—
80	C₂×C₄×C₉	#41	1	2	yes	—
81	C₈×C₉	—	4	2	no	—
82	C₄×#41	C₂×C₉	1	1	yes	characteristic
83	#413	C₂×C₉	1	1	yes	characteristic
84	#410	C₂×C₉	1	1	yes	characteristic
85	#339	C₂×C₉	1	2	yes	complemented
86	H(3,ℤ/4)	C₂×C₉	1	2	yes	complemented
87	C₃×#41	—	2	2	no	—
88	C₃×#41	—	2	2	no	—
89	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
90	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
91	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
92	C₂²×C₃×C₄	—	2	2	no	—
93	C₂²×C₃×C₄	—	2	1	no	—
94	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
95	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
96	C₃×M₁₆	—	2	2	no	—
97	C₃×M₁₆	—	2	2	no	—
98	C₂×C₃×C₈	—	2	2	no	—
99	C₃×C₄⋊C₄	—	2	2	no	—
100	C₃×C₄⋊C₄	—	2	1	no	—
101	C₃×C₄⋊C₄	—	2	2	no	—
102	C₃×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₂²⋊C₄	—	2	2	no	—
105	C₃×C₄²	—	2	2	no	—
106	C₃×C₄²	—	2	1	no	—
107	C₃×C₄²	—	2	2	no	—
108	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
109	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
110	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
111	C₂²×C₉	—	2	2	no	—
112	C₂²×C₉	—	4	1	no	—
113	C₂²×C₉	—	4	2	no	—
114	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₉	#123	1	2	yes	—
116	C₄×C₉	—	2	2	no	—
117	C₄×C₉	—	2	2	no	—
118	C₄×C₉	—	4	2	no	—
119	C₄×C₉	—	4	1	no	—
120	C₄×C₉	—	8	2	no	—
121	C₄×C₉	#117	1	1	yes	characteristic
122	C₄×C₉	#117	1	1	yes	characteristic
123	C₄×C₉	#123	1	2	yes	—
124	C₂×#41	C₂²×C₉	1	1	yes	characteristic
125	C₂×M₁₆	C₂²×C₉	1	2	yes	—
126	C₄×Q₈	—	2	1	no	—
127	C₄×D₄	—	2	2	no	—
128	C₄×D₄	—	2	1	no	—
129	#117	C₄×C₉	1	2	yes	complemented
130	#117	C₂²×C₉	1	2	yes	—
131	#117	C₂²×C₉	1	1	yes	characteristic
132	C₂×C₄²	C₄×C₉	1	2	yes	complemented
133	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
134	#101	—	2	1	no	—
135	#100	—	2	1	no	—
136	#99	—	2	2	no	—
137	C₂³×C₃	C₃×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
139	C₃×Q₈	—	2	2	no	—
140	C₃×D₄	—	2	4	no	—
141	C₃×D₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	1	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	2	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	4	2	no	—
148	C₂×C₃×C₄	—	4	4	no	—
149	C₂×C₃×C₄	—	4	2	no	—
150	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
151	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄	C₃×#41	1	2	yes	—
154	C₂×C₃×C₄	C₃×#41	1	2	yes	—
155	C₃×C₈	—	4	2	no	—
156	C₂×C₉	—	2	1	no	—
157	C₂×C₉	—	2	2	no	—
158	C₂×C₉	—	4	2	no	—
159	C₂×C₉	#381	1	1	yes	characteristic
160	#41	—	2	2	no	—
161	#41	—	2	2	no	—
162	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
163	C₂×D₄	D₄×C₉	1	2	yes	—
164	C₂×D₄	D₄×C₉	1	1	yes	characteristic
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	1	no	—
167	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
168	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
169	M₁₆	—	2	2	no	—
170	M₁₆	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₂²⋊C₄	—	2	2	no	—
176	C₂²⋊C₄	—	2	1	no	—
177	C₂²⋊C₄	—	2	2	no	—
178	C₄²	—	2	2	no	—
179	C₄²	—	2	1	no	—
180	C₄²	—	2	2	no	—
181	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
182	C₄²	C₂×C₄×C₉	1	2	yes	—
183	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
184	C₂²×C₃	—	2	2	no	—
185	C₂²×C₃	—	4	1	no	—
186	C₂²×C₃	—	4	2	no	—
187	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₃	C₃×#123	1	2	yes	—
189	C₃×C₄	—	2	2	no	—
190	C₃×C₄	—	2	2	no	—
191	C₃×C₄	—	4	2	no	—
192	C₃×C₄	—	4	1	no	—
193	C₃×C₄	—	8	2	no	—
194	C₃×C₄	C₃×#117	1	1	yes	characteristic
195	C₃×C₄	C₃×#117	1	1	yes	characteristic
196	C₃×C₄	C₃×#123	1	2	yes	—
197	C₉	#1827	1	1	yes	characteristic, direct product factor, Sylow
198	C₂³	C₉×C₂²⋊C₄	1	2	yes	—
199	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
200	Q₈	—	2	2	no	—
201	D₄	—	2	4	no	—
202	D₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
213	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
214	C₂×C₄	C₉×#41	1	2	yes	—
215	C₂×C₄	C₉×#41	1	2	yes	—
216	C₈	—	4	2	no	—
217	C₂×C₃	—	2	1	no	—
218	C₂×C₃	—	2	2	no	—
219	C₂×C₃	—	4	2	no	—
220	C₂×C₃	C₃×#381	1	1	yes	characteristic
221	C₂²	—	2	2	no	—
222	C₂²	—	4	1	no	—
223	C₂²	—	4	2	no	—
224	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²	C₉×#123	1	2	yes	—
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	8	2	no	—
231	C₄	C₉×#117	1	1	yes	characteristic
232	C₄	C₉×#117	1	1	yes	characteristic
233	C₄	C₉×#123	1	2	yes	—
234	C₃	C₃×#1827	1	1	yes	characteristic
235	C₂	—	2	1	no	—
236	C₂	—	2	2	no	—
237	C₂	—	4	2	no	—
238	C₂	C₉×#381	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	#117
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#381
prime radical	C₂×C₃×#41	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₉×#339	C₂	semidirect
5. C₉×H(3,ℤ/4)	C₂	semidirect
12. C₉×#117	C₄	semidirect
15. C₂×C₄²×C₉	C₄	semidirect
49. #1827	C₉	direct (N × H)
85. #339	C₂×C₉	semidirect
86. H(3,ℤ/4)	C₂×C₉	semidirect
129. #117	C₄×C₉	semidirect
132. C₂×C₄²	C₄×C₉	semidirect
197. C₉	#1827	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×#41	2
C₉×#413	2
C₉×#410	2
C₉×#339	2
C₉×H(3,ℤ/4)	2
C₃×#1827	3

Subgroups — C9×#1827 #11766548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1827 #11766548