Subgroups — C₂×C₉×#883 #13152348

Order 1728.

1158 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#883	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#883	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#123	—	3	1	no	maximal
11	C₂⁴×C₃×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	C₂×C₉×#67	—	2	4	no	—
16	C₂×C₉×#67	C₂²	1	4	yes	—
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	—	2	4	no	—
21	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
23	C₉×#217	C₂²	1	4	yes	complemented
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
25	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₃×#883	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	—	3	1	no	—
39	C₂×C₉×C₄⋊C₄	—	3	1	no	—
40	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
41	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
42	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
44	C₂³×C₃×C₉	—	2	2	no	—
45	C₂³×C₃×C₉	—	2	2	no	—
46	C₂³×C₃×C₉	—	2	2	no	—
47	C₂³×C₃×C₉	C₂³	1	2	yes	—
48	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
49	C₂²×D₃×C₉	—	2	2	no	—
50	C₂²×D₃×C₉	—	2	2	no	—
51	C₂²×D₃×C₉	D₄	1	4	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	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₉×#67	—	2	8	no	—
58	C₂×C₉×Dic₃	—	2	2	no	—
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	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₄×D₃×C₉	—	2	8	no	—
65	C₂×C₃×#123	—	3	1	no	—
66	C₂×#883	C₉	1	1	yes	characteristic, direct product factor
67	C₂⁴×C₃²	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	C₂×C₃×#67	—	2	4	no	—
72	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
73	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	—	2	4	no	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
78	C₂⁴×C₉	—	2	1	no	—
79	C₂⁴×C₉	—	3	1	no	—
80	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
81	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
82	C₃×#217	C₂²×C₃	1	4	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
84	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
85	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
86	C₂×D₄×C₉	—	3	4	no	—
87	C₂×D₄×C₉	—	6	4	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	1	no	—
93	C₂²×C₄×C₉	—	3	4	no	—
94	C₂²×C₄×C₉	—	6	4	no	—
95	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
97	C₉×C₄⋊C₄	—	3	4	no	—
98	C₉×C₄⋊C₄	—	3	4	no	—
99	C₉×C₂²⋊C₄	—	2	4	no	—
100	C₉×C₂²⋊C₄	—	3	4	no	—
101	C₉×C₂²⋊C₄	—	3	4	no	—
102	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
103	C₂²×C₃×C₉	—	2	2	no	—
104	C₂²×C₃×C₉	—	2	2	no	—
105	C₂²×C₃×C₉	—	2	2	no	—
106	C₂²×C₃×C₉	—	4	4	no	—
107	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
108	C₂²×C₃×C₉	#41	1	2	yes	—
109	C₂²×C₃×C₉	#41	1	2	yes	—
110	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
111	C₂×D₃×C₉	—	2	8	no	—
112	C₂×D₃×C₉	—	2	2	no	—
113	C₂×D₃×C₉	—	2	2	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	C₉×Dic₃	—	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×#67	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	—	3	1	no	—
126	C₂×C₃×C₄⋊C₄	—	3	1	no	—
127	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
129	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
130	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
131	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
132	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
133	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
134	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
135	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
136	#883	C₂×C₉	1	8	yes	direct product factor
137	C₂³×C₃²	—	2	2	no	—
138	C₂³×C₃²	—	2	2	no	—
139	C₂³×C₃²	—	2	2	no	—
140	C₂³×C₃²	C₂³×C₃	1	2	yes	—
141	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₃×D₃	—	2	2	no	—
143	C₂²×C₃×D₃	—	2	2	no	—
144	C₂²×C₃×D₃	C₃×D₄	1	4	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	C₂³×C₃	1	2	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
150	C₃×#67	—	2	8	no	—
151	C₂×C₃×Dic₃	—	2	2	no	—
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	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
157	C₃×C₄×D₃	—	2	8	no	—
158	C₂³×C₉	—	2	4	no	—
159	C₂³×C₉	—	2	2	no	—
160	C₂³×C₉	—	2	2	no	—
161	C₂³×C₉	—	2	2	no	—
162	C₂³×C₉	—	2	1	no	—
163	C₂³×C₉	—	2	2	no	—
164	C₂³×C₉	—	3	4	no	—
165	C₂³×C₉	—	3	2	no	—
166	C₂³×C₉	—	4	2	no	—
167	C₂³×C₉	—	4	2	no	—
168	C₂³×C₉	—	6	2	no	—
169	C₂³×C₉	—	6	2	no	—
170	C₂³×C₉	C₂²×D₃	1	2	yes	—
171	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
172	D₄×C₉	—	6	8	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	—	2	2	no	—
177	C₂×C₄×C₉	—	3	2	no	—
178	C₂×C₄×C₉	—	3	2	no	—
179	C₂×C₄×C₉	—	3	2	no	—
180	C₂×C₄×C₉	—	4	2	no	—
181	C₂×C₄×C₉	—	4	2	no	—
182	C₂×C₄×C₉	—	6	8	no	—
183	C₂×C₄×C₉	—	6	2	no	—
184	C₂×C₄×C₉	—	6	2	no	—
185	C₂×C₄×C₉	—	6	2	no	—
186	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
187	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
188	C₂×#123	—	3	1	no	Sylow
189	C₂×C₃×C₉	—	4	2	no	—
190	C₂×C₃×C₉	#123	1	4	yes	complemented
191	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
194	D₃×C₉	—	2	4	no	—
195	C₂⁴×C₃	—	2	1	no	—
196	C₂⁴×C₃	—	3	1	no	—
197	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
198	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
199	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
200	C₂×C₃×D₄	—	3	4	no	—
201	C₂×C₃×D₄	—	6	4	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	3	1	no	—
205	C₂²×C₃×C₄	—	3	1	no	—
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	4	no	—
208	C₂²×C₃×C₄	—	6	4	no	—
209	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂×#67	—	2	4	no	—
214	C₂×#67	C₂²×C₉	1	4	yes	—
215	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
216	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
217	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄×D₃	—	2	4	no	—
219	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
220	C₃×C₄⋊C₄	—	3	4	no	—
221	C₃×C₄⋊C₄	—	3	4	no	—
222	C₃×C₂²⋊C₄	—	2	4	no	—
223	C₃×C₂²⋊C₄	—	3	4	no	—
224	C₃×C₂²⋊C₄	—	3	4	no	—
225	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
226	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
227	#217	C₂²×C₉	1	4	yes	complemented
228	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
229	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
230	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
231	C₂²×C₃²	—	2	2	no	—
232	C₂²×C₃²	—	2	2	no	—
233	C₂²×C₃²	—	2	2	no	—
234	C₂²×C₃²	—	4	4	no	—
235	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
236	C₂²×C₃²	C₃×#41	1	2	yes	—
237	C₂²×C₃²	C₃×#41	1	2	yes	—
238	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
239	C₂×C₃×D₃	—	2	8	no	—
240	C₂×C₃×D₃	—	2	2	no	—
241	C₂×C₃×D₃	—	2	2	no	—
242	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
243	C₃²×C₄	—	2	2	no	—
244	C₃²×C₄	—	2	2	no	—
245	C₃×Dic₃	—	2	2	no	—
246	C₃×Dic₃	—	2	2	no	—
247	C₃×Dic₃	—	2	2	no	—
248	C₂²×C₉	—	2	4	no	—
249	C₂²×C₉	—	2	2	no	—
250	C₂²×C₉	—	2	2	no	—
251	C₂²×C₉	—	2	2	no	—
252	C₂²×C₉	—	2	1	no	—
253	C₂²×C₉	—	2	2	no	—
254	C₂²×C₉	—	2	2	no	—
255	C₂²×C₉	—	2	2	no	—
256	C₂²×C₉	—	3	4	no	—
257	C₂²×C₉	—	4	2	no	—
258	C₂²×C₉	—	4	2	no	—
259	C₂²×C₉	—	4	8	no	—
260	C₂²×C₉	—	4	4	no	—
261	C₂²×C₉	—	6	8	no	—
262	C₂²×C₉	—	6	2	no	—
263	C₂²×C₉	—	6	2	no	—
264	C₂²×C₉	#235	1	2	yes	—
265	C₂²×C₉	D₃×D₄	1	2	yes	—
266	C₂²×C₉	#237	1	2	yes	—
267	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
268	C₄×C₉	—	2	2	no	—
269	C₄×C₉	—	2	2	no	—
270	C₄×C₉	—	4	2	no	—
271	C₄×C₉	—	4	2	no	—
272	C₄×C₉	—	6	2	no	—
273	C₄×C₉	—	6	2	no	—
274	C₄×C₉	—	6	2	no	—
275	C₂²×D₄	—	3	1	no	—
276	C₂³×C₄	—	3	1	no	—
277	#123	—	3	8	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₄⋊C₄	—	3	1	no	—
280	C₂×C₂²⋊C₄	—	3	1	no	—
281	C₂×C₂²⋊C₄	—	3	1	no	—
282	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
283	C₃×C₉	C₂×#123	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	2	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	—	2	1	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	3	2	no	—
294	C₂³×C₃	—	3	4	no	—
295	C₂³×C₃	—	4	2	no	—
296	C₂³×C₃	—	4	2	no	—
297	C₂³×C₃	—	6	2	no	—
298	C₂³×C₃	—	6	2	no	—
299	C₂³×C₃	C₂³×C₉	1	2	yes	—
300	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
301	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
302	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂²×D₃	—	2	2	no	—
304	C₂²×D₃	—	2	2	no	—
305	C₂²×D₃	D₄×C₉	1	4	yes	—
306	C₂²×D₃	C₂³×C₉	1	2	yes	—
307	C₃×D₄	—	6	8	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	3	2	no	—
315	C₂×C₃×C₄	—	3	2	no	—
316	C₂×C₃×C₄	—	3	2	no	—
317	C₂×C₃×C₄	—	4	2	no	—
318	C₂×C₃×C₄	—	4	2	no	—
319	C₂×C₃×C₄	—	6	8	no	—
320	C₂×C₃×C₄	—	6	2	no	—
321	C₂×C₃×C₄	—	6	2	no	—
322	C₂×C₃×C₄	—	6	2	no	—
323	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
324	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
327	#67	—	2	8	no	—
328	C₂×Dic₃	—	2	2	no	—
329	C₂×Dic₃	—	2	2	no	—
330	C₂×Dic₃	—	2	2	no	—
331	C₂×Dic₃	C₂³×C₉	1	2	yes	—
332	C₂×Dic₃	C₂³×C₉	1	2	yes	—
333	C₂×Dic₃	C₂³×C₉	1	2	yes	—
334	C₄×D₃	—	2	8	no	—
335	C₂×C₃²	—	4	2	no	—
336	C₂×C₃²	C₃×#123	1	4	yes	—
337	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
338	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
339	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
340	C₃×D₃	—	2	4	no	—
341	C₂×C₉	—	2	4	no	—
342	C₂×C₉	—	2	1	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	—	2	1	no	—
345	C₂×C₉	—	4	4	no	—
346	C₂×C₉	—	4	2	no	—
347	C₂×C₉	—	6	4	no	—
348	C₂×C₉	#883	1	4	yes	direct product factor
349	C₂×C₉	C₂×#235	1	1	yes	characteristic
350	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
351	C₂×C₉	C₂×#237	1	1	yes	characteristic
352	C₂⁴	—	3	1	no	—
353	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
354	C₂×D₄	—	3	4	no	—
355	C₂×D₄	—	6	4	no	—
356	C₂²×C₄	—	3	1	no	—
357	C₂²×C₄	—	3	1	no	—
358	C₂²×C₄	—	3	1	no	—
359	C₂²×C₄	—	3	4	no	—
360	C₂²×C₄	—	6	4	no	—
361	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
363	C₄⋊C₄	—	3	4	no	—
364	C₄⋊C₄	—	3	4	no	—
365	C₂²⋊C₄	—	3	4	no	—
366	C₂²⋊C₄	—	3	4	no	—
367	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	3	4	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	8	no	—
383	C₂²×C₃	—	4	4	no	—
384	C₂²×C₃	—	4	4	no	—
385	C₂²×C₃	—	6	8	no	—
386	C₂²×C₃	—	6	2	no	—
387	C₂²×C₃	—	6	2	no	—
388	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
389	C₂²×C₃	C₉×#41	1	2	yes	—
390	C₂²×C₃	C₉×#41	1	2	yes	—
391	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
392	C₂²×C₃	C₃×#235	1	2	yes	—
393	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
394	C₂²×C₃	C₃×#237	1	2	yes	—
395	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
396	C₂×D₃	—	2	8	no	—
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	6	2	no	—
407	C₃×C₄	—	6	2	no	—
408	C₃×C₄	—	6	2	no	—
409	Dic₃	—	2	2	no	—
410	Dic₃	—	2	2	no	—
411	Dic₃	—	2	2	no	—
412	C₃²	C₂×C₃×#123	1	1	yes	characteristic
413	C₉	—	2	1	no	—
414	C₉	C₂×#883	1	1	yes	characteristic, direct product factor
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	3	2	no	—
419	C₂³	—	3	4	no	—
420	C₂³	—	6	2	no	—
421	C₂³	—	6	2	no	—
422	C₂³	C₂²×D₃×C₉	1	2	yes	—
423	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
424	D₄	—	6	8	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	6	8	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
435	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	4	no	—
440	C₂×C₃	—	4	4	no	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	—	6	4	no	—
444	C₂×C₃	C₉×#123	1	4	yes	complemented
445	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
446	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
447	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
448	C₂×C₃	C₃×#883	1	4	yes	—
449	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
450	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
451	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
452	D₃	—	2	4	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	3	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	6	2	no	—
460	C₂²	—	6	8	no	—
461	C₂²	C₉×#235	1	2	yes	—
462	C₂²	D₃×D₄×C₉	1	2	yes	—
463	C₂²	C₉×#237	1	2	yes	—
464	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₄	—	6	2	no	—
470	C₃	—	2	1	no	—
471	C₃	C₂×C₉×#123	1	1	yes	characteristic, complemented
472	C₃	C₂×C₃×#883	1	1	yes	characteristic
473	C₂	—	4	2	no	—
474	C₂	—	6	4	no	—
475	C₂	C₉×#883	1	4	yes	direct product factor
476	C₂	C₂×C₉×#235	1	1	yes	characteristic
477	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
478	C₂	C₂×C₉×#237	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×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊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×C₂²⋊C₄	C₂	semidirect
4. C₂×C₉×#217	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₉×#883	C₂	direct (N × H)
21. C₂×C₄×D₃×C₉	C₂²	semidirect
22. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
23. C₉×#217	C₂²	semidirect
24. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₉×C₄⋊Dic₃	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
43. C₂×C₉×C₂²⋊C₄	D₃	semidirect
66. C₂×#883	C₉	direct (N × H)
102. C₉×C₂²⋊C₄	C₂×D₃	semidirect
123. C₂²×C₄×D₃	C₂×C₉	semidirect
130. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
132. C₂×#217	C₂×C₉	semidirect
133. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
134. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
135. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
136. #883	C₂×C₉	direct (N × H)
190. C₂×C₃×C₉	#123	semidirect
219. C₂×C₄×D₃	C₂²×C₉	semidirect
225. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
227. #217	C₂²×C₉	semidirect
228. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
229. C₄⋊Dic₃	C₂²×C₉	semidirect
230. Dic₃⋊C₄	C₂²×C₉	semidirect
282. C₂×C₂²⋊C₄	D₃×C₉	semidirect
283. C₃×C₉	C₂×#123	semidirect
348. C₂×C₉	#883	direct (N × H)
367. C₂²⋊C₄	C₂×D₃×C₉	semidirect
414. C₉	C₂×#883	direct (N × H)
444. C₂×C₃	C₉×#123	semidirect
471. C₃	C₂×C₉×#123	semidirect
475. C₂	C₉×#883	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×#67	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#883	2
C₂×C₃×#883	3
C₂×C₉×#123	3

Subgroups — C2×C9×#883 #13152348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#883 #13152348