Subgroups — C₂×C₉×#884 #13152349

Order 1728.

1410 conjugacy classes of subgroups.

The subgroup lattice has 540 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, complemented
2	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₉×C₂²⋊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×#884	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#884	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#121	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂³×D₃×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	C₂×C₉×#67	—	2	4	no	—
17	C₂×C₉×#67	—	2	4	no	—
18	C₂×C₉×#67	C₂²	1	4	yes	complemented
19	C₂×C₉×#67	C₂²	1	4	yes	complemented
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₉×D₁₂	—	2	4	no	—
23	C₂×C₉×D₁₂	C₂²	1	4	yes	complemented
24	C₂×C₄×D₃×C₉	—	2	4	no	—
25	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
26	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
28	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
29	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
31	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
36	C₃×#884	C₂×C₃	1	8	yes	—
37	C₂²×D₄×C₉	—	3	1	no	—
38	C₂²×D₄×C₉	—	3	1	no	—
39	C₂²×D₄×C₉	—	3	1	no	—
40	C₂³×C₄×C₉	—	3	1	no	—
41	C₉×#121	—	3	8	no	—
42	C₂×C₉×C₄⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
44	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
45	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
46	C₂³×C₃×C₉	—	2	2	no	—
47	C₂³×C₃×C₉	—	2	2	no	—
48	C₂³×C₃×C₉	—	2	2	no	—
49	C₂³×C₃×C₉	C₂³	1	2	yes	—
50	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
51	C₂²×D₃×C₉	—	2	2	no	—
52	C₂²×D₃×C₉	—	2	2	no	—
53	C₂²×D₃×C₉	—	2	2	no	—
54	C₂²×D₃×C₉	—	2	2	no	—
55	C₂²×D₃×C₉	—	2	2	no	—
56	C₂²×D₃×C₉	D₄	1	4	yes	complemented
57	C₂²×D₃×C₉	C₂³	1	2	yes	—
58	C₂²×D₃×C₉	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₉	—	2	2	no	—
60	C₂×C₃×C₄×C₉	—	2	2	no	—
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
63	C₉×#67	—	2	8	no	—
64	C₉×#67	—	2	8	no	—
65	C₂×C₉×Dic₃	—	2	2	no	—
66	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₉×D₁₂	—	2	8	no	—
70	C₄×D₃×C₉	—	2	8	no	—
71	C₂×C₃×#121	—	3	1	no	—
72	C₂×#884	C₉	1	1	yes	characteristic, direct product factor
73	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×#67	—	2	4	no	—
79	C₂×C₃×#67	—	2	4	no	—
80	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
81	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
82	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×D₁₂	—	2	4	no	—
85	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
86	C₂×C₃×C₄×D₃	—	2	4	no	—
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
88	C₂⁴×C₉	—	2	1	no	—
89	C₂⁴×C₉	—	3	1	no	—
90	C₂⁴×C₉	—	3	1	no	—
91	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
92	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
95	C₂×D₄×C₉	—	3	4	no	—
96	C₂×D₄×C₉	—	3	4	no	—
97	C₂×D₄×C₉	—	3	4	no	—
98	C₂×D₄×C₉	—	6	4	no	—
99	C₂×D₄×C₉	—	6	4	no	—
100	C₂×D₄×C₉	—	6	4	no	—
101	C₂²×C₄×C₉	—	2	1	no	—
102	C₂²×C₄×C₉	—	2	1	no	—
103	C₂²×C₄×C₉	—	3	1	no	—
104	C₂²×C₄×C₉	—	3	1	no	—
105	C₂²×C₄×C₉	—	3	4	no	—
106	C₂²×C₄×C₉	—	6	4	no	—
107	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
109	C₉×C₄⋊C₄	—	3	4	no	—
110	C₉×C₂²⋊C₄	—	2	4	no	—
111	C₉×C₂²⋊C₄	—	3	4	no	—
112	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
113	C₂²×C₃×C₉	—	2	2	no	—
114	C₂²×C₃×C₉	—	2	2	no	—
115	C₂²×C₃×C₉	—	2	2	no	—
116	C₂²×C₃×C₉	—	4	4	no	—
117	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
118	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
119	C₂²×C₃×C₉	#41	1	2	yes	—
120	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
121	C₂×D₃×C₉	—	2	8	no	—
122	C₂×D₃×C₉	—	2	2	no	—
123	C₂×D₃×C₉	—	2	2	no	—
124	C₂×D₃×C₉	—	2	2	no	—
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	2	2	no	—
127	C₂×D₃×C₉	—	4	4	no	—
128	C₂×D₃×C₉	C₂×D₄	1	4	yes	complemented
129	C₃×C₄×C₉	—	2	2	no	—
130	C₃×C₄×C₉	—	2	2	no	—
131	C₉×Dic₃	—	2	2	no	—
132	C₉×Dic₃	C₂×D₄	1	4	yes	complemented
133	C₂²×C₃×D₄	—	3	1	no	—
134	C₂²×C₃×D₄	—	3	1	no	—
135	C₂²×C₃×D₄	—	3	1	no	—
136	C₂³×C₃×C₄	—	3	1	no	—
137	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
139	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
140	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
141	C₃×#121	—	3	8	no	—
142	C₂×C₃×C₄⋊C₄	—	3	1	no	—
143	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
144	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
145	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
146	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
147	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
149	#884	C₂×C₉	1	8	yes	direct product factor
150	C₂³×C₃²	—	2	2	no	—
151	C₂³×C₃²	—	2	2	no	—
152	C₂³×C₃²	—	2	2	no	—
153	C₂³×C₃²	C₂³×C₃	1	2	yes	—
154	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×D₃	—	2	2	no	—
156	C₂²×C₃×D₃	—	2	2	no	—
157	C₂²×C₃×D₃	—	2	2	no	—
158	C₂²×C₃×D₃	—	2	2	no	—
159	C₂²×C₃×D₃	—	2	2	no	—
160	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
161	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
162	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
163	C₂×C₃²×C₄	—	2	2	no	—
164	C₂×C₃²×C₄	—	2	2	no	—
165	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
166	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
167	C₃×#67	—	2	8	no	—
168	C₃×#67	—	2	8	no	—
169	C₂×C₃×Dic₃	—	2	2	no	—
170	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
171	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
172	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
173	C₃×D₁₂	—	2	8	no	—
174	C₃×C₄×D₃	—	2	8	no	—
175	C₂³×C₉	—	2	4	no	—
176	C₂³×C₉	—	2	2	no	—
177	C₂³×C₉	—	2	2	no	—
178	C₂³×C₉	—	2	2	no	—
179	C₂³×C₉	—	2	1	no	—
180	C₂³×C₉	—	2	2	no	—
181	C₂³×C₉	—	3	4	no	—
182	C₂³×C₉	—	3	2	no	—
183	C₂³×C₉	—	3	2	no	—
184	C₂³×C₉	—	4	2	no	—
185	C₂³×C₉	—	4	2	no	—
186	C₂³×C₉	—	6	2	no	—
187	C₂³×C₉	—	6	2	no	—
188	C₂³×C₉	—	6	2	no	—
189	C₂³×C₉	—	6	2	no	—
190	C₂³×C₉	—	6	2	no	—
191	C₂³×C₉	C₂²×D₃	1	2	yes	—
192	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
193	D₄×C₉	—	6	8	no	—
194	D₄×C₉	—	6	8	no	—
195	D₄×C₉	—	6	8	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	2	no	—
199	C₂×C₄×C₉	—	2	2	no	—
200	C₂×C₄×C₉	—	3	4	no	—
201	C₂×C₄×C₉	—	3	2	no	—
202	C₂×C₄×C₉	—	3	2	no	—
203	C₂×C₄×C₉	—	4	2	no	—
204	C₂×C₄×C₉	—	4	2	no	—
205	C₂×C₄×C₉	—	6	8	no	—
206	C₂×C₄×C₉	—	6	2	no	—
207	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
208	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
209	C₂×#121	—	3	1	no	Sylow
210	C₂×C₃×C₉	—	4	2	no	—
211	C₂×C₃×C₉	#121	1	4	yes	complemented
212	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
215	D₃×C₉	—	2	4	no	—
216	D₃×C₉	—	4	2	no	—
217	C₂⁴×C₃	—	2	1	no	—
218	C₂⁴×C₃	—	3	1	no	—
219	C₂⁴×C₃	—	3	1	no	—
220	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
221	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
222	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
223	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
224	C₂×C₃×D₄	—	3	4	no	—
225	C₂×C₃×D₄	—	3	4	no	—
226	C₂×C₃×D₄	—	3	4	no	—
227	C₂×C₃×D₄	—	6	4	no	—
228	C₂×C₃×D₄	—	6	4	no	—
229	C₂×C₃×D₄	—	6	4	no	—
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	3	1	no	—
233	C₂²×C₃×C₄	—	3	1	no	—
234	C₂²×C₃×C₄	—	3	4	no	—
235	C₂²×C₃×C₄	—	6	4	no	—
236	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₂×#67	—	2	4	no	—
241	C₂×#67	—	2	4	no	—
242	C₂×#67	C₂²×C₉	1	4	yes	complemented
243	C₂×#67	C₂²×C₉	1	4	yes	complemented
244	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
245	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
246	C₂×D₁₂	—	2	4	no	—
247	C₂×D₁₂	C₂²×C₉	1	4	yes	complemented
248	C₂×C₄×D₃	—	2	4	no	—
249	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
250	C₃×C₄⋊C₄	—	3	4	no	—
251	C₃×C₂²⋊C₄	—	2	4	no	—
252	C₃×C₂²⋊C₄	—	3	4	no	—
253	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
254	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
255	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
256	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
257	C₂²×C₃²	—	2	2	no	—
258	C₂²×C₃²	—	2	2	no	—
259	C₂²×C₃²	—	2	2	no	—
260	C₂²×C₃²	—	4	4	no	—
261	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
262	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
263	C₂²×C₃²	C₃×#41	1	2	yes	—
264	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
265	C₂×C₃×D₃	—	2	8	no	—
266	C₂×C₃×D₃	—	2	2	no	—
267	C₂×C₃×D₃	—	2	2	no	—
268	C₂×C₃×D₃	—	2	2	no	—
269	C₂×C₃×D₃	—	2	2	no	—
270	C₂×C₃×D₃	—	2	2	no	—
271	C₂×C₃×D₃	—	4	4	no	—
272	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃×Dic₃	—	2	2	no	—
276	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
277	C₂²×C₉	—	2	4	no	—
278	C₂²×C₉	—	2	2	no	—
279	C₂²×C₉	—	2	2	no	—
280	C₂²×C₉	—	2	2	no	—
281	C₂²×C₉	—	2	1	no	—
282	C₂²×C₉	—	2	2	no	—
283	C₂²×C₉	—	2	2	no	—
284	C₂²×C₉	—	2	2	no	—
285	C₂²×C₉	—	3	4	no	—
286	C₂²×C₉	—	4	2	no	—
287	C₂²×C₉	—	4	2	no	—
288	C₂²×C₉	—	4	8	no	—
289	C₂²×C₉	—	4	4	no	—
290	C₂²×C₉	—	6	8	no	—
291	C₂²×C₉	—	6	2	no	—
292	C₂²×C₉	—	6	2	no	—
293	C₂²×C₉	—	6	2	no	—
294	C₂²×C₉	—	6	2	no	—
295	C₂²×C₉	—	6	2	no	—
296	C₂²×C₉	—	12	4	no	—
297	C₂²×C₉	#235	1	2	yes	—
298	C₂²×C₉	D₃×D₄	1	2	yes	—
299	C₂²×C₉	D₃×D₄	1	2	yes	—
300	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
301	C₄×C₉	—	2	2	no	—
302	C₄×C₉	—	2	2	no	—
303	C₄×C₉	—	3	4	no	—
304	C₄×C₉	—	4	2	no	—
305	C₄×C₉	—	4	2	no	—
306	C₄×C₉	—	6	2	no	—
307	C₂²×D₄	—	3	1	no	—
308	C₂²×D₄	—	3	1	no	—
309	C₂²×D₄	—	3	1	no	—
310	C₂³×C₄	—	3	1	no	—
311	#121	—	3	8	no	—
312	C₂×C₄⋊C₄	—	3	1	no	—
313	C₂×C₂²⋊C₄	—	3	1	no	—
314	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
315	C₃×C₉	C₂×#121	1	1	yes	characteristic, complemented, Sylow
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	2	2	no	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	2	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂³×C₃	—	2	1	no	—
324	C₂³×C₃	—	2	2	no	—
325	C₂³×C₃	—	3	2	no	—
326	C₂³×C₃	—	3	4	no	—
327	C₂³×C₃	—	3	2	no	—
328	C₂³×C₃	—	4	2	no	—
329	C₂³×C₃	—	4	2	no	—
330	C₂³×C₃	—	6	2	no	—
331	C₂³×C₃	—	6	2	no	—
332	C₂³×C₃	—	6	2	no	—
333	C₂³×C₃	—	6	2	no	—
334	C₂³×C₃	—	6	2	no	—
335	C₂³×C₃	C₂³×C₉	1	2	yes	—
336	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
337	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
338	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂²×D₃	—	2	2	no	—
340	C₂²×D₃	—	2	2	no	—
341	C₂²×D₃	—	2	2	no	—
342	C₂²×D₃	—	2	2	no	—
343	C₂²×D₃	—	2	2	no	—
344	C₂²×D₃	D₄×C₉	1	4	yes	complemented
345	C₂²×D₃	C₂³×C₉	1	2	yes	—
346	C₂²×D₃	C₂³×C₉	1	2	yes	—
347	C₃×D₄	—	6	8	no	—
348	C₃×D₄	—	6	8	no	—
349	C₃×D₄	—	6	8	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	3	2	no	—
357	C₂×C₃×C₄	—	3	4	no	—
358	C₂×C₃×C₄	—	3	2	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	—	4	2	no	—
361	C₂×C₃×C₄	—	6	8	no	—
362	C₂×C₃×C₄	—	6	2	no	—
363	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
364	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
365	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
366	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
367	#67	—	2	8	no	—
368	#67	—	2	8	no	—
369	C₂×Dic₃	—	2	2	no	—
370	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
371	C₂×Dic₃	C₂³×C₉	1	2	yes	—
372	C₂×Dic₃	C₂³×C₉	1	2	yes	—
373	D₁₂	—	2	8	no	—
374	C₄×D₃	—	2	8	no	—
375	C₂×C₃²	—	4	2	no	—
376	C₂×C₃²	C₃×#121	1	4	yes	—
377	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
378	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
380	C₃×D₃	—	2	4	no	—
381	C₃×D₃	—	4	2	no	—
382	C₂×C₉	—	2	4	no	—
383	C₂×C₉	—	2	1	no	—
384	C₂×C₉	—	2	1	no	—
385	C₂×C₉	—	2	1	no	—
386	C₂×C₉	—	4	4	no	—
387	C₂×C₉	—	4	2	no	—
388	C₂×C₉	—	6	4	no	—
389	C₂×C₉	—	12	2	no	—
390	C₂×C₉	#884	1	4	yes	direct product factor
391	C₂×C₉	C₂×#235	1	1	yes	characteristic
392	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
393	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
394	C₂⁴	—	3	1	no	—
395	C₂⁴	—	3	1	no	—
396	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
397	C₂×D₄	—	3	4	no	—
398	C₂×D₄	—	3	4	no	—
399	C₂×D₄	—	3	4	no	—
400	C₂×D₄	—	6	4	no	—
401	C₂×D₄	—	6	4	no	—
402	C₂×D₄	—	6	4	no	—
403	C₂²×C₄	—	3	1	no	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	—	3	4	no	—
406	C₂²×C₄	—	6	4	no	—
407	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
409	C₄⋊C₄	—	3	4	no	—
410	C₂²⋊C₄	—	3	4	no	—
411	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
412	C₂²×C₃	—	2	4	no	—
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	2	2	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	2	2	no	—
423	C₂²×C₃	—	3	4	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	4	2	no	—
426	C₂²×C₃	—	4	8	no	—
427	C₂²×C₃	—	4	4	no	—
428	C₂²×C₃	—	4	4	no	—
429	C₂²×C₃	—	6	8	no	—
430	C₂²×C₃	—	6	2	no	—
431	C₂²×C₃	—	6	2	no	—
432	C₂²×C₃	—	6	2	no	—
433	C₂²×C₃	—	6	2	no	—
434	C₂²×C₃	—	6	2	no	—
435	C₂²×C₃	—	12	4	no	—
436	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
437	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
438	C₂²×C₃	C₉×#41	1	2	yes	—
439	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
440	C₂²×C₃	C₃×#235	1	2	yes	—
441	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
442	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
443	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
444	C₂×D₃	—	2	8	no	—
445	C₂×D₃	—	2	2	no	—
446	C₂×D₃	—	2	2	no	—
447	C₂×D₃	—	2	2	no	—
448	C₂×D₃	—	2	2	no	—
449	C₂×D₃	—	2	2	no	—
450	C₂×D₃	—	4	4	no	—
451	C₂×D₃	C₂×D₄×C₉	1	4	yes	complemented
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	2	2	no	—
456	C₃×C₄	—	3	4	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	—	4	2	no	—
459	C₃×C₄	—	6	2	no	—
460	Dic₃	—	2	2	no	—
461	Dic₃	C₂×D₄×C₉	1	4	yes	complemented
462	C₃²	C₂×C₃×#121	1	1	yes	characteristic
463	C₉	—	2	1	no	—
464	C₉	C₂×#884	1	1	yes	characteristic, direct product factor
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	3	2	no	—
469	C₂³	—	3	4	no	—
470	C₂³	—	3	2	no	—
471	C₂³	—	6	2	no	—
472	C₂³	—	6	2	no	—
473	C₂³	—	6	2	no	—
474	C₂³	—	6	2	no	—
475	C₂³	—	6	2	no	—
476	C₂³	C₂²×D₃×C₉	1	2	yes	—
477	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
478	D₄	—	6	8	no	—
479	D₄	—	6	8	no	—
480	D₄	—	6	8	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	3	2	no	—
484	C₂×C₄	—	3	4	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	6	8	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
489	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
490	C₂×C₃	—	2	1	no	—
491	C₂×C₃	—	2	1	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	4	no	—
494	C₂×C₃	—	4	4	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	—	4	2	no	—
497	C₂×C₃	—	6	4	no	—
498	C₂×C₃	—	12	2	no	—
499	C₂×C₃	C₉×#121	1	4	yes	complemented
500	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
501	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
502	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
503	C₂×C₃	C₃×#884	1	4	yes	—
504	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
505	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
506	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
507	D₃	—	2	4	no	—
508	D₃	—	4	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	3	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	6	2	no	—
515	C₂²	—	6	2	no	—
516	C₂²	—	6	8	no	—
517	C₂²	—	6	2	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	6	2	no	—
520	C₂²	—	12	4	no	—
521	C₂²	C₉×#235	1	2	yes	—
522	C₂²	D₃×D₄×C₉	1	2	yes	—
523	C₂²	D₃×D₄×C₉	1	2	yes	—
524	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	3	4	no	—
528	C₄	—	6	2	no	—
529	C₃	—	2	1	no	—
530	C₃	C₂×C₉×#121	1	1	yes	characteristic, complemented
531	C₃	C₂×C₃×#884	1	1	yes	characteristic
532	C₂	—	4	2	no	—
533	C₂	—	6	4	no	—
534	C₂	—	12	2	no	—
535	C₂	C₉×#884	1	4	yes	direct product factor
536	C₂	C₂×C₉×#235	1	1	yes	characteristic
537	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
538	C₂	C₂×D₃×D₄×C₉	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	C₂×C₃×#884	C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#121
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
1. C₂²×C₉×#67	C₂	semidirect
2. C₂²×C₉×#67	C₂	semidirect
3. C₂²×C₉×D₁₂	C₂	semidirect
4. C₂²×C₄×D₃×C₉	C₂	semidirect
5. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
6. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₉×#884	C₂	direct (N × H)
18. C₂×C₉×#67	C₂²	semidirect
19. C₂×C₉×#67	C₂²	semidirect
23. C₂×C₉×D₁₂	C₂²	semidirect
25. C₂×C₄×D₃×C₉	C₂²	semidirect
26. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
27. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₉×Dic₃⋊C₄	C₂²	semidirect
45. C₂×C₉×C₂²⋊C₄	D₃	semidirect
56. C₂²×D₃×C₉	D₄	semidirect
66. C₂×C₉×Dic₃	D₄	semidirect
72. C₂×#884	C₉	direct (N × H)
112. C₉×C₂²⋊C₄	C₂×D₃	semidirect
128. C₂×D₃×C₉	C₂×D₄	semidirect
132. C₉×Dic₃	C₂×D₄	semidirect
137. C₂²×#67	C₂×C₉	semidirect
138. C₂²×#67	C₂×C₉	semidirect
139. C₂²×D₁₂	C₂×C₉	semidirect
140. C₂²×C₄×D₃	C₂×C₉	semidirect
145. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
147. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
148. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
149. #884	C₂×C₉	direct (N × H)
211. C₂×C₃×C₉	#121	semidirect
242. C₂×#67	C₂²×C₉	semidirect
243. C₂×#67	C₂²×C₉	semidirect
247. C₂×D₁₂	C₂²×C₉	semidirect
249. C₂×C₄×D₃	C₂²×C₉	semidirect
253. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
255. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
256. Dic₃⋊C₄	C₂²×C₉	semidirect
314. C₂×C₂²⋊C₄	D₃×C₉	semidirect
315. C₃×C₉	C₂×#121	semidirect
344. C₂²×D₃	D₄×C₉	semidirect
370. C₂×Dic₃	D₄×C₉	semidirect
390. C₂×C₉	#884	direct (N × H)
411. C₂²⋊C₄	C₂×D₃×C₉	semidirect
451. C₂×D₃	C₂×D₄×C₉	semidirect
461. Dic₃	C₂×D₄×C₉	semidirect
464. C₉	C₂×#884	direct (N × H)
499. C₂×C₃	C₉×#121	semidirect
530. C₃	C₂×C₉×#121	semidirect
535. C₂	C₉×#884	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×C₉×D₁₂	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#884	2
C₂×C₃×#884	3
C₂×C₉×#121	3

Subgroups — C2×C9×#884 #13152349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#884 #13152349