Subgroups — C₂×C₉×#894 #13152417

Order 1728.

1118 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#894	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#894	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#123	—	3	1	no	maximal
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₉×D₁₂	—	2	4	no	—
19	C₂×C₉×D₁₂	C₂²	1	4	yes	—
20	C₂×C₄×D₃×C₉	—	2	4	no	—
21	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
22	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₃×#894	C₂×C₃	1	8	yes	—
35	C₂²×D₄×C₉	—	3	1	no	—
36	C₂³×C₄×C₉	—	3	1	no	—
37	C₉×#123	—	3	8	no	—
38	C₂×C₉×C₄⋊C₄	—	2	1	no	—
39	C₂×C₉×C₄⋊C₄	—	3	1	no	—
40	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
41	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
42	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
44	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
45	C₂²×D₃×C₉	—	2	2	no	—
46	C₂²×D₃×C₉	—	2	2	no	—
47	C₂²×D₃×C₉	—	2	2	no	—
48	C₂²×D₃×C₉	—	2	2	no	—
49	C₂²×D₃×C₉	—	2	2	no	—
50	C₂²×D₃×C₉	D₄	1	4	yes	—
51	C₂²×D₃×C₉	C₂³	1	2	yes	—
52	C₂²×D₃×C₉	C₂³	1	2	yes	—
53	C₂×C₃×C₄×C₉	—	2	2	no	—
54	C₂×C₃×C₄×C₉	—	2	2	no	—
55	C₂×C₃×C₄×C₉	—	2	2	no	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
59	C₂×C₉×Dic₃	—	2	2	no	—
60	C₂×C₉×Dic₃	—	2	2	no	—
61	C₂×C₉×Dic₃	C₂³	1	2	yes	—
62	C₂×C₉×Dic₃	C₂³	1	2	yes	—
63	C₉×D₁₂	—	2	8	no	—
64	C₄×D₃×C₉	—	2	8	no	—
65	C₂×C₃×#123	—	3	1	no	—
66	C₂×#894	C₉	1	1	yes	characteristic, direct product factor
67	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×D₁₂	—	2	4	no	—
75	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
76	C₂×C₃×C₄×D₃	—	2	4	no	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
78	C₂⁴×C₉	—	3	1	no	—
79	C₂⁴×C₉	—	3	1	no	—
80	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
81	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
82	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
84	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
85	C₂×D₄×C₉	—	3	4	no	—
86	C₂×D₄×C₉	—	6	4	no	—
87	C₂²×C₄×C₉	—	2	1	no	—
88	C₂²×C₄×C₉	—	2	1	no	—
89	C₂²×C₄×C₉	—	2	1	no	—
90	C₂²×C₄×C₉	—	3	1	no	—
91	C₂²×C₄×C₉	—	3	1	no	—
92	C₂²×C₄×C₉	—	3	4	no	—
93	C₂²×C₄×C₉	—	6	4	no	—
94	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
95	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
97	C₉×C₄⋊C₄	—	2	4	no	—
98	C₉×C₄⋊C₄	—	3	4	no	—
99	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
100	C₉×C₂²⋊C₄	—	3	4	no	—
101	C₉×C₂²⋊C₄	—	3	4	no	—
102	C₉×C₂²⋊C₄	—	3	4	no	—
103	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
104	C₂²×C₃×C₉	#41	1	2	yes	—
105	C₂²×C₃×C₉	#41	1	2	yes	—
106	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
107	C₂×D₃×C₉	—	2	8	no	—
108	C₂×D₃×C₉	—	2	2	no	—
109	C₂×D₃×C₉	—	2	2	no	—
110	C₂×D₃×C₉	—	2	2	no	—
111	C₂×D₃×C₉	—	2	2	no	—
112	C₂×D₃×C₉	—	2	2	no	—
113	C₂×D₃×C₉	—	4	4	no	—
114	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
115	C₃×C₄×C₉	—	2	2	no	—
116	C₃×C₄×C₉	—	2	2	no	—
117	C₃×C₄×C₉	—	2	2	no	—
118	C₉×Dic₃	—	2	2	no	—
119	C₉×Dic₃	—	2	2	no	—
120	C₂²×C₃×D₄	—	3	1	no	—
121	C₂³×C₃×C₄	—	3	1	no	—
122	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic
123	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
124	C₃×#123	—	3	8	no	—
125	C₂×C₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₃×C₄⋊C₄	—	3	1	no	—
127	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
129	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
130	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
131	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
132	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
133	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
134	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
135	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
136	#894	C₂×C₉	1	8	yes	direct product factor
137	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
138	C₂²×C₃×D₃	—	2	2	no	—
139	C₂²×C₃×D₃	—	2	2	no	—
140	C₂²×C₃×D₃	—	2	2	no	—
141	C₂²×C₃×D₃	—	2	2	no	—
142	C₂²×C₃×D₃	—	2	2	no	—
143	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
144	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
145	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
146	C₂×C₃²×C₄	—	2	2	no	—
147	C₂×C₃²×C₄	—	2	2	no	—
148	C₂×C₃²×C₄	—	2	2	no	—
149	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
151	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
152	C₂×C₃×Dic₃	—	2	2	no	—
153	C₂×C₃×Dic₃	—	2	2	no	—
154	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
155	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
156	C₃×D₁₂	—	2	8	no	—
157	C₃×C₄×D₃	—	2	8	no	—
158	C₂³×C₉	—	2	1	no	—
159	C₂³×C₉	—	3	4	no	—
160	C₂³×C₉	—	3	2	no	—
161	C₂³×C₉	—	3	2	no	—
162	C₂³×C₉	—	6	2	no	—
163	C₂³×C₉	—	6	2	no	—
164	C₂³×C₉	—	6	2	no	—
165	C₂³×C₉	—	6	2	no	—
166	C₂³×C₉	—	6	2	no	—
167	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
168	D₄×C₉	—	6	8	no	—
169	C₂×C₄×C₉	—	2	4	no	—
170	C₂×C₄×C₉	—	2	2	no	—
171	C₂×C₄×C₉	—	2	2	no	—
172	C₂×C₄×C₉	—	2	2	no	—
173	C₂×C₄×C₉	—	2	2	no	—
174	C₂×C₄×C₉	—	2	2	no	—
175	C₂×C₄×C₉	—	2	2	no	—
176	C₂×C₄×C₉	—	3	2	no	—
177	C₂×C₄×C₉	—	3	2	no	—
178	C₂×C₄×C₉	—	4	2	no	—
179	C₂×C₄×C₉	—	4	2	no	—
180	C₂×C₄×C₉	—	6	8	no	—
181	C₂×C₄×C₉	—	6	2	no	—
182	C₂×C₄×C₉	—	6	2	no	—
183	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
184	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
185	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
186	C₂×#123	—	3	1	no	Sylow
187	C₂×C₃×C₉	#123	1	4	yes	complemented
188	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
191	D₃×C₉	—	2	4	no	—
192	D₃×C₉	—	4	2	no	—
193	C₂⁴×C₃	—	3	1	no	—
194	C₂⁴×C₃	—	3	1	no	—
195	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
196	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
197	C₂×C₃×D₄	—	3	4	no	—
198	C₂×C₃×D₄	—	6	4	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	1	no	—
204	C₂²×C₃×C₄	—	3	4	no	—
205	C₂²×C₃×C₄	—	6	4	no	—
206	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
213	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
214	C₂×D₁₂	—	2	4	no	—
215	C₂×D₁₂	C₂²×C₉	1	4	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
218	C₃×C₄⋊C₄	—	2	4	no	—
219	C₃×C₄⋊C₄	—	3	4	no	—
220	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
221	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
222	C₃×C₂²⋊C₄	—	3	4	no	—
223	C₃×C₂²⋊C₄	—	3	4	no	—
224	C₃×C₂²⋊C₄	—	3	4	no	—
225	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
226	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
227	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
228	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
229	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
230	C₂²×C₃²	C₃×#41	1	2	yes	—
231	C₂²×C₃²	C₃×#41	1	2	yes	—
232	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
233	C₂×C₃×D₃	—	2	8	no	—
234	C₂×C₃×D₃	—	2	2	no	—
235	C₂×C₃×D₃	—	2	2	no	—
236	C₂×C₃×D₃	—	2	2	no	—
237	C₂×C₃×D₃	—	2	2	no	—
238	C₂×C₃×D₃	—	2	2	no	—
239	C₂×C₃×D₃	—	4	4	no	—
240	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
241	C₃²×C₄	—	2	2	no	—
242	C₃²×C₄	—	2	2	no	—
243	C₃²×C₄	—	2	2	no	—
244	C₃×Dic₃	—	2	2	no	—
245	C₃×Dic₃	—	2	2	no	—
246	C₂²×C₉	—	2	1	no	—
247	C₂²×C₉	—	2	2	no	—
248	C₂²×C₉	—	2	2	no	—
249	C₂²×C₉	—	2	2	no	—
250	C₂²×C₉	—	3	4	no	—
251	C₂²×C₉	—	6	8	no	—
252	C₂²×C₉	—	6	2	no	—
253	C₂²×C₉	—	6	2	no	—
254	C₂²×C₉	—	6	2	no	—
255	C₂²×C₉	—	6	2	no	—
256	C₂²×C₉	—	6	2	no	—
257	C₂²×C₉	—	12	4	no	—
258	C₂²×C₉	#235	1	2	yes	—
259	C₂²×C₉	D₃×D₄	1	2	yes	—
260	C₂²×C₉	#239	1	2	yes	—
261	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
262	C₄×C₉	—	2	4	no	—
263	C₄×C₉	—	2	2	no	—
264	C₄×C₉	—	2	2	no	—
265	C₄×C₉	—	2	2	no	—
266	C₄×C₉	—	4	2	no	—
267	C₄×C₉	—	4	2	no	—
268	C₄×C₉	—	6	2	no	—
269	C₄×C₉	—	6	2	no	—
270	C₂²×D₄	—	3	1	no	—
271	C₂³×C₄	—	3	1	no	—
272	#123	—	3	8	no	—
273	C₂×C₄⋊C₄	—	3	1	no	—
274	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	3	1	no	—
276	C₂×C₂²⋊C₄	—	3	1	no	—
277	C₂×C₂²⋊C₄	—	3	1	no	—
278	C₃×C₉	C₂×#123	1	1	yes	characteristic, complemented, Sylow
279	C₂³×C₃	—	2	1	no	—
280	C₂³×C₃	—	3	2	no	—
281	C₂³×C₃	—	3	4	no	—
282	C₂³×C₃	—	3	2	no	—
283	C₂³×C₃	—	6	2	no	—
284	C₂³×C₃	—	6	2	no	—
285	C₂³×C₃	—	6	2	no	—
286	C₂³×C₃	—	6	2	no	—
287	C₂³×C₃	—	6	2	no	—
288	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
289	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	2	2	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	—	2	2	no	—
295	C₂²×D₃	D₄×C₉	1	4	yes	—
296	C₂²×D₃	C₂³×C₉	1	2	yes	—
297	C₂²×D₃	C₂³×C₉	1	2	yes	—
298	C₃×D₄	—	6	8	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	3	2	no	—
310	C₂×C₃×C₄	—	3	2	no	—
311	C₂×C₃×C₄	—	4	2	no	—
312	C₂×C₃×C₄	—	4	2	no	—
313	C₂×C₃×C₄	—	6	8	no	—
314	C₂×C₃×C₄	—	6	2	no	—
315	C₂×C₃×C₄	—	6	2	no	—
316	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
317	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
318	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	C₂³×C₉	1	2	yes	—
325	C₂×Dic₃	C₂³×C₉	1	2	yes	—
326	D₁₂	—	2	8	no	—
327	C₄×D₃	—	2	8	no	—
328	C₂×C₃²	C₃×#123	1	4	yes	—
329	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
331	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
332	C₃×D₃	—	2	4	no	—
333	C₃×D₃	—	4	2	no	—
334	C₂×C₉	—	2	4	no	—
335	C₂×C₉	—	2	1	no	—
336	C₂×C₉	—	2	1	no	—
337	C₂×C₉	—	2	1	no	—
338	C₂×C₉	—	6	4	no	—
339	C₂×C₉	—	12	2	no	—
340	C₂×C₉	#894	1	4	yes	direct product factor
341	C₂×C₉	C₂×#235	1	1	yes	characteristic
342	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
343	C₂×C₉	C₂×#239	1	1	yes	characteristic
344	C₂⁴	—	3	1	no	—
345	C₂⁴	—	3	1	no	—
346	C₂×D₄	—	3	4	no	—
347	C₂×D₄	—	6	4	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	4	no	—
351	C₂²×C₄	—	6	4	no	—
352	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
355	C₄⋊C₄	—	3	4	no	—
356	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
357	C₂²⋊C₄	—	3	4	no	—
358	C₂²⋊C₄	—	3	4	no	—
359	C₂²⋊C₄	—	3	4	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	3	4	no	—
365	C₂²×C₃	—	6	8	no	—
366	C₂²×C₃	—	6	2	no	—
367	C₂²×C₃	—	6	2	no	—
368	C₂²×C₃	—	6	2	no	—
369	C₂²×C₃	—	6	2	no	—
370	C₂²×C₃	—	6	2	no	—
371	C₂²×C₃	—	12	4	no	—
372	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
373	C₂²×C₃	C₉×#41	1	2	yes	—
374	C₂²×C₃	C₉×#41	1	2	yes	—
375	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
376	C₂²×C₃	C₃×#235	1	2	yes	—
377	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
378	C₂²×C₃	C₃×#239	1	2	yes	—
379	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
380	C₂×D₃	—	2	8	no	—
381	C₂×D₃	—	2	2	no	—
382	C₂×D₃	—	2	2	no	—
383	C₂×D₃	—	2	2	no	—
384	C₂×D₃	—	2	2	no	—
385	C₂×D₃	—	2	2	no	—
386	C₂×D₃	—	4	4	no	—
387	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
388	C₃×C₄	—	2	4	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	—	6	2	no	—
398	C₃×C₄	—	6	2	no	—
399	Dic₃	—	2	2	no	—
400	Dic₃	—	2	2	no	—
401	C₃²	C₂×C₃×#123	1	1	yes	characteristic
402	C₉	—	2	1	no	—
403	C₉	C₂×#894	1	1	yes	characteristic, direct product factor
404	C₂³	—	3	2	no	—
405	C₂³	—	3	4	no	—
406	C₂³	—	3	2	no	—
407	C₂³	—	6	2	no	—
408	C₂³	—	6	2	no	—
409	C₂³	—	6	2	no	—
410	C₂³	—	6	2	no	—
411	C₂³	—	6	2	no	—
412	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
413	D₄	—	6	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	3	2	no	—
418	C₂×C₄	—	3	2	no	—
419	C₂×C₄	—	6	8	no	—
420	C₂×C₄	—	6	2	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
423	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
424	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	—	6	4	no	—
430	C₂×C₃	—	12	2	no	—
431	C₂×C₃	C₉×#123	1	4	yes	complemented
432	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
433	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
434	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
435	C₂×C₃	C₃×#894	1	4	yes	—
436	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
437	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
438	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
439	D₃	—	2	4	no	—
440	D₃	—	4	2	no	—
441	C₂²	—	3	4	no	—
442	C₂²	—	6	2	no	—
443	C₂²	—	6	2	no	—
444	C₂²	—	6	8	no	—
445	C₂²	—	6	2	no	—
446	C₂²	—	6	2	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	12	4	no	—
449	C₂²	C₉×#235	1	2	yes	—
450	C₂²	D₃×D₄×C₉	1	2	yes	—
451	C₂²	C₉×#239	1	2	yes	—
452	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	6	2	no	—
457	C₄	—	6	2	no	—
458	C₃	—	2	1	no	—
459	C₃	C₂×C₉×#123	1	1	yes	characteristic, complemented
460	C₃	C₂×C₃×#894	1	1	yes	characteristic
461	C₂	—	6	4	no	—
462	C₂	—	12	2	no	—
463	C₂	C₉×#894	1	4	yes	direct product factor
464	C₂	C₂×C₉×#235	1	1	yes	characteristic
465	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
466	C₂	C₂×C₉×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×D₁₂	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₉×#894	C₂	direct (N × H)
21. C₂×C₄×D₃×C₉	C₂²	semidirect
22. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
40. C₂×C₉×C₄⋊C₄	D₃	semidirect
66. C₂×#894	C₉	direct (N × H)
99. C₉×C₄⋊C₄	C₂×D₃	semidirect
123. C₂²×C₄×D₃	C₂×C₉	semidirect
127. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
132. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
133. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
134. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
135. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
136. #894	C₂×C₉	direct (N × H)
187. C₂×C₃×C₉	#123	semidirect
217. C₂×C₄×D₃	C₂²×C₉	semidirect
220. C₃×C₄⋊C₄	C₂²×C₉	semidirect
225. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
226. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
227. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
228. Dic₃⋊C₄	C₂²×C₉	semidirect
274. C₂×C₄⋊C₄	D₃×C₉	semidirect
278. C₃×C₉	C₂×#123	semidirect
340. C₂×C₉	#894	direct (N × H)
356. C₄⋊C₄	C₂×D₃×C₉	semidirect
403. C₉	C₂×#894	direct (N × H)
431. C₂×C₃	C₉×#123	semidirect
459. C₃	C₂×C₉×#123	semidirect
463. C₂	C₉×#894	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×D₁₂	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#894	2
C₂×C₃×#894	3
C₂×C₉×#123	3

Subgroups — C2×C9×#894 #13152417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#894 #13152417