Subgroups — C₉×#2336 #11767057

Order 1152.

642 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₉×#389	C₂	1	2	yes	maximal
3	C₉×#387	C₂	1	2	yes	maximal
4	C₉×#387	C₂	1	2	yes	maximal
5	C₉×#387	C₂	1	2	yes	maximal
6	C₉×#387	C₂	1	2	yes	maximal
7	C₉×#383	C₂	1	1	yes	maximal, characteristic
8	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₃×#2336	C₃	1	1	yes	maximal, characteristic
11	C₉×#125	C₄	1	8	yes	complemented
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₄²×C₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₉	C₂²	1	2	yes	—
23	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
24	C₉×#95	C₂²	1	2	yes	—
25	C₉×#95	C₂²	1	2	yes	—
26	C₉×#95	C₂²	1	2	yes	—
27	C₉×#95	C₂²	1	2	yes	—
28	C₉×#95	C₂²	1	1	yes	characteristic
29	C₉×#95	C₂²	1	1	yes	characteristic
30	C₉×#95	C₂²	1	2	yes	—
31	C₉×#95	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	2	yes	—
33	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
34	C₃×#389	C₂×C₃	1	2	yes	—
35	C₃×#387	C₂×C₃	1	2	yes	—
36	C₃×#387	C₂×C₃	1	2	yes	—
37	C₃×#387	C₂×C₃	1	2	yes	—
38	C₃×#387	C₂×C₃	1	2	yes	—
39	C₃×#383	C₂×C₃	1	1	yes	characteristic
40	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
41	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
42	C₂²×C₄×C₉	C₂³	1	2	yes	—
43	C₂²×C₄×C₉	C₂³	1	2	yes	—
44	C₂²×C₄×C₉	C₂³	1	2	yes	—
45	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₉	C₂³	1	2	yes	—
47	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₉	C₂³	1	2	yes	—
49	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂²×C₄×C₉	C₂³	1	2	yes	—
51	C₉×C₄⋊C₄	—	2	4	no	—
52	C₉×C₄⋊C₄	—	2	4	no	—
53	C₉×C₄⋊C₄	—	4	2	no	—
54	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
55	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
56	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
58	C₄²×C₉	—	2	4	no	—
59	C₄²×C₉	—	4	1	no	—
60	C₄²×C₉	—	4	2	no	—
61	C₄²×C₉	—	4	1	no	—
62	C₄²×C₉	C₂×C₄	1	4	yes	—
63	#2336	C₉	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×#125	C₃×C₄	1	8	yes	—
65	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
73	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	C₃×#95	C₂²×C₃	1	2	yes	—
78	C₃×#95	C₂²×C₃	1	2	yes	—
79	C₃×#95	C₂²×C₃	1	2	yes	—
80	C₃×#95	C₂²×C₃	1	1	yes	characteristic
81	C₃×#95	C₂²×C₃	1	2	yes	—
82	C₃×#95	C₂²×C₃	1	1	yes	characteristic
83	C₃×#95	C₂²×C₃	1	2	yes	—
84	C₃×#95	C₂²×C₃	1	2	yes	—
85	C₃×#95	C₂²×C₃	1	2	yes	—
86	C₂³×C₉	C₂⁴	1	1	yes	characteristic
87	C₂×C₄×C₉	—	2	2	no	—
88	C₂×C₄×C₉	—	2	2	no	—
89	C₂×C₄×C₉	—	2	2	no	—
90	C₂×C₄×C₉	—	2	1	no	—
91	C₂×C₄×C₉	—	2	2	no	—
92	C₂×C₄×C₉	—	2	2	no	—
93	C₂×C₄×C₉	—	2	2	no	—
94	C₂×C₄×C₉	—	2	1	no	—
95	C₂×C₄×C₉	—	2	2	no	—
96	C₂×C₄×C₉	—	2	2	no	—
97	C₂×C₄×C₉	—	2	2	no	—
98	C₂×C₄×C₉	—	2	2	no	—
99	C₂×C₄×C₉	—	2	2	no	—
100	C₂×C₄×C₉	—	2	2	no	—
101	C₂×C₄×C₉	—	2	2	no	—
102	C₂×C₄×C₉	—	2	2	no	—
103	C₂×C₄×C₉	—	2	2	no	—
104	C₂×C₄×C₉	—	2	2	no	—
105	C₂×C₄×C₉	—	2	2	no	—
106	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
107	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
108	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
109	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
110	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
111	C₂×C₄×C₉	#41	1	4	yes	—
112	C₂×#125	C₂×C₉	1	1	yes	characteristic
113	#389	C₂×C₉	1	2	yes	—
114	#387	C₂×C₉	1	2	yes	—
115	#387	C₂×C₉	1	2	yes	—
116	#387	C₂×C₉	1	2	yes	—
117	#387	C₂×C₉	1	2	yes	—
118	#383	C₂×C₉	1	1	yes	characteristic
119	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	—
120	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
122	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
123	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
124	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
125	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
127	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
129	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
130	C₃×C₄⋊C₄	—	2	4	no	—
131	C₃×C₄⋊C₄	—	2	4	no	—
132	C₃×C₄⋊C₄	—	4	2	no	—
133	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
134	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
135	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
136	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
137	C₃×C₄²	—	2	4	no	—
138	C₃×C₄²	—	4	1	no	—
139	C₃×C₄²	—	4	2	no	—
140	C₃×C₄²	—	4	1	no	—
141	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
142	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₉	C₂×#41	1	2	yes	—
144	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
146	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
147	C₄×C₉	—	2	4	no	—
148	C₄×C₉	—	2	2	no	—
149	C₄×C₉	—	2	2	no	—
150	C₄×C₉	—	2	2	no	—
151	C₄×C₉	—	2	4	no	—
152	C₄×C₉	—	2	4	no	—
153	C₄×C₉	—	4	2	no	—
154	C₄×C₉	—	4	2	no	—
155	C₄×C₉	—	4	2	no	—
156	#125	C₄×C₉	1	8	yes	complemented
157	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
158	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
159	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
160	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
161	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
162	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
164	C₂×C₄²	C₂²×C₉	1	2	yes	—
165	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
166	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
167	C₂×C₄²	C₂²×C₉	1	2	yes	—
168	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
169	#95	C₂²×C₉	1	2	yes	—
170	#95	C₂²×C₉	1	2	yes	—
171	#95	C₂²×C₉	1	2	yes	—
172	#95	C₂²×C₉	1	1	yes	characteristic
173	#95	C₂²×C₉	1	2	yes	—
174	#95	C₂²×C₉	1	1	yes	characteristic
175	#95	C₂²×C₉	1	2	yes	—
176	#95	C₂²×C₉	1	2	yes	—
177	#95	C₂²×C₉	1	2	yes	—
178	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
179	C₂×C₃×C₄	—	2	2	no	—
180	C₂×C₃×C₄	—	2	2	no	—
181	C₂×C₃×C₄	—	2	2	no	—
182	C₂×C₃×C₄	—	2	1	no	—
183	C₂×C₃×C₄	—	2	2	no	—
184	C₂×C₃×C₄	—	2	2	no	—
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	2	2	no	—
189	C₂×C₃×C₄	—	2	2	no	—
190	C₂×C₃×C₄	—	2	2	no	—
191	C₂×C₃×C₄	—	2	2	no	—
192	C₂×C₃×C₄	—	2	2	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
199	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
200	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
202	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
203	C₂×C₃×C₄	C₃×#41	1	4	yes	—
204	C₂×C₉	C₄×#41	1	1	yes	characteristic
205	C₂×C₉	#519	1	1	yes	characteristic
206	C₂×C₉	#520	1	1	yes	characteristic
207	C₂×C₉	#539	1	2	yes	—
208	C₂×C₉	#541	1	2	yes	—
209	C₂²×C₄	C₂³×C₉	1	2	yes	—
210	C₂²×C₄	C₂³×C₉	1	2	yes	—
211	C₂²×C₄	C₂³×C₉	1	2	yes	—
212	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
214	C₂²×C₄	C₂³×C₉	1	2	yes	—
215	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
216	C₂²×C₄	C₂³×C₉	1	2	yes	—
217	C₂²×C₄	C₂³×C₉	1	2	yes	—
218	C₄⋊C₄	—	2	4	no	—
219	C₄⋊C₄	—	2	4	no	—
220	C₄⋊C₄	—	4	2	no	—
221	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
222	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
223	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
224	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
225	C₄²	—	2	4	no	—
226	C₄²	—	4	1	no	—
227	C₄²	—	4	2	no	—
228	C₄²	—	4	1	no	—
229	C₄²	C₂×C₄×C₉	1	4	yes	—
230	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
231	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
232	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
233	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
234	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
235	C₃×C₄	—	2	4	no	—
236	C₃×C₄	—	2	2	no	—
237	C₃×C₄	—	2	2	no	—
238	C₃×C₄	—	2	2	no	—
239	C₃×C₄	—	2	4	no	—
240	C₃×C₄	—	2	4	no	—
241	C₃×C₄	—	4	2	no	—
242	C₃×C₄	—	4	2	no	—
243	C₃×C₄	—	4	2	no	—
244	C₉	#2336	1	1	yes	characteristic, direct product factor, Sylow
245	C₂³	C₂⁴×C₉	1	1	yes	characteristic
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
266	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
267	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
268	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
269	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
270	C₂×C₄	C₉×#41	1	4	yes	—
271	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
272	C₂×C₃	C₃×#519	1	1	yes	characteristic
273	C₂×C₃	C₃×#520	1	1	yes	characteristic
274	C₂×C₃	C₃×#539	1	2	yes	—
275	C₂×C₃	C₃×#541	1	2	yes	—
276	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
277	C₂²	C₂×C₉×#41	1	2	yes	—
278	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
280	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
281	C₄	—	2	2	no	—
282	C₄	—	2	4	no	—
283	C₄	—	2	4	no	—
284	C₄	—	2	4	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	4	2	no	—
288	C₄	—	4	2	no	—
289	C₄	—	4	2	no	—
290	C₃	C₃×#2336	1	1	yes	characteristic
291	C₂	C₄×C₉×#41	1	1	yes	characteristic
292	C₂	C₉×#519	1	1	yes	characteristic
293	C₂	C₉×#520	1	1	yes	characteristic
294	C₂	C₉×#539	1	2	yes	—
295	C₂	C₉×#541	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₉×#125	C₄	semidirect
63. #2336	C₉	direct (N × H)
156. #125	C₄×C₉	semidirect
244. C₉	#2336	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#125	2
C₉×#389	2
C₉×#387	2
C₉×#383	2
C₄×C₉×C₄⋊C₄	2
C₃×#2336	3

Subgroups — C9×#2336 #11767057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2336 #11767057