Subgroups — C₉×#4773 #13141756

Order 1728.

644 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4773	C₃	1	1	yes	maximal, characteristic
9	C₉×#447	—	3	1	no	maximal
10	C₂³×D₃×C₉	—	2	1	no	—
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	—	2	1	no	—
13	D₃×D₄×C₉	—	2	2	no	—
14	D₃×D₄×C₉	—	2	2	no	—
15	C₂×C₉×D₁₂	—	2	1	no	—
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
21	C₉×#213	—	2	2	no	—
22	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
23	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₉×D₂₄	—	2	2	no	—
25	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×D₂₄	C₂×C₃	1	1	yes	characteristic
28	C₃×#895	C₂×C₃	1	1	yes	characteristic
29	C₂²×D₄×C₉	—	3	1	no	—
30	C₃²×#102	C₂×C₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₃×#809	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×D₈	—	3	1	no	—
34	C₂×C₉×D₈	—	3	1	no	—
35	C₉×#121	—	3	1	no	—
36	C₉×#102	—	2	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	D₃	1	1	yes	characteristic, complemented
39	C₉×C₂²⋊C₈	—	3	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	2	1	no	—
43	C₂²×D₃×C₉	—	2	1	no	—
44	C₂²×D₃×C₉	—	4	2	no	—
45	C₂²×D₃×C₉	—	4	2	no	—
46	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
47	C₃×D₄×C₉	—	2	1	no	—
48	C₃×D₄×C₉	D₄	1	2	yes	complemented
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₉×#67	—	2	4	no	—
52	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
53	C₉×D₁₂	—	2	1	no	—
54	C₉×D₁₂	—	2	1	no	—
55	C₉×D₁₂	—	2	1	no	—
56	C₉×D₁₂	—	4	2	no	—
57	C₉×D₁₂	D₄	1	2	yes	complemented
58	C₄×D₃×C₉	—	2	1	no	—
59	C₄×D₃×C₉	—	2	1	no	—
60	C₃×C₈×C₉	—	2	1	no	—
61	C₉×C₃⋊C₈	—	2	1	no	—
62	C₃×#447	—	3	1	no	—
63	#4773	C₉	1	1	yes	characteristic, direct product factor
64	C₂³×C₃×D₃	—	2	1	no	—
65	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×#67	—	2	1	no	—
67	C₃×D₃×D₄	—	2	2	no	—
68	C₃×D₃×D₄	—	2	2	no	—
69	C₂×C₃×D₁₂	—	2	1	no	—
70	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
73	C₂⁴×C₉	—	6	1	no	—
74	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₃×#213	—	2	2	no	—
77	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
78	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
79	C₃×D₂₄	—	2	2	no	—
80	C₂×D₄×C₉	—	2	1	no	—
81	C₂×D₄×C₉	—	3	1	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	6	1	no	—
84	C₂×D₄×C₉	—	6	1	no	—
85	C₂×D₄×C₉	—	6	2	no	—
86	C₂×D₄×C₉	—	6	2	no	—
87	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₄×C₉	—	3	1	no	—
89	C₉×D₈	—	6	2	no	—
90	C₉×D₈	—	6	2	no	—
91	C₂×C₈×C₉	—	2	1	no	—
92	C₂×C₈×C₉	—	3	1	no	—
93	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
94	C₉×C₄⋊C₄	—	2	1	no	—
95	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
96	C₉×C₂²⋊C₄	—	6	1	no	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	—	4	1	no	—
99	C₂²×C₃×C₉	—	4	1	no	—
100	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
101	C₂×D₃×C₉	—	2	1	no	—
102	C₂×D₃×C₉	—	2	1	no	—
103	C₂×D₃×C₉	—	2	2	no	—
104	C₂×D₃×C₉	—	4	8	no	—
105	C₂×D₃×C₉	—	4	1	no	—
106	C₂×D₃×C₉	—	4	1	no	—
107	C₂×D₃×C₉	—	4	1	no	—
108	C₂×D₃×C₉	—	4	1	no	—
109	C₂×D₃×C₉	—	4	1	no	—
110	C₂×D₃×C₉	D₈	1	2	yes	complemented
111	C₃×C₄×C₉	—	4	1	no	—
112	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
113	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
114	C₉×Dic₃	—	2	1	no	—
115	C₂²×C₃×D₄	—	3	1	no	—
116	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
117	C₂×C₃×D₈	—	3	1	no	—
118	C₂×C₃×D₈	—	3	1	no	—
119	C₃×#121	—	3	1	no	—
120	C₂×#213	C₂×C₉	1	1	yes	characteristic, complemented
121	C₂×D₂₄	C₂×C₉	1	1	yes	characteristic, complemented
122	#895	C₂×C₉	1	1	yes	characteristic, complemented
123	C₃×#102	—	2	1	no	—
124	C₃×#102	—	3	1	no	—
125	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
126	C₃×#102	C₃×D₃	1	1	yes	characteristic
127	C₃×C₂²⋊C₈	—	3	1	no	—
128	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
129	#809	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂³×C₃²	—	2	1	no	—
131	C₂²×C₃×D₃	—	2	4	no	—
132	C₂²×C₃×D₃	—	2	1	no	—
133	C₂²×C₃×D₃	—	2	1	no	—
134	C₂²×C₃×D₃	—	4	2	no	—
135	C₂²×C₃×D₃	—	4	2	no	—
136	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
137	C₃²×D₄	—	2	1	no	—
138	C₃²×D₄	C₃×D₄	1	2	yes	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₃×#67	—	2	4	no	—
142	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
143	C₃×D₁₂	—	2	1	no	—
144	C₃×D₁₂	—	2	1	no	—
145	C₃×D₁₂	—	2	1	no	—
146	C₃×D₁₂	—	4	2	no	—
147	C₃×D₁₂	C₃×D₄	1	2	yes	—
148	C₃×C₄×D₃	—	2	1	no	—
149	C₃×C₄×D₃	—	2	1	no	—
150	C₂³×C₉	—	2	1	no	—
151	C₂³×C₉	—	3	1	no	—
152	C₂³×C₉	—	4	1	no	—
153	C₂³×C₉	—	6	4	no	—
154	C₂³×C₉	—	6	1	no	—
155	C₂³×C₉	—	6	1	no	—
156	C₂³×C₉	—	12	2	no	—
157	C₂³×C₉	—	12	2	no	—
158	C₃²×C₈	—	2	1	no	—
159	C₃×C₃⋊C₈	—	2	1	no	—
160	D₄×C₉	—	2	1	no	—
161	D₄×C₉	—	2	2	no	—
162	D₄×C₉	—	3	2	no	—
163	D₄×C₉	—	4	1	no	—
164	D₄×C₉	—	6	4	no	—
165	D₄×C₉	—	6	1	no	—
166	D₄×C₉	—	6	1	no	—
167	D₄×C₉	—	6	1	no	—
168	D₄×C₉	—	12	2	no	—
169	D₄×C₉	D₁₂	1	2	yes	complemented
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	3	1	no	—
173	C₂×C₄×C₉	—	4	1	no	—
174	C₂×C₄×C₉	—	6	1	no	—
175	C₂×C₄×C₉	—	6	1	no	—
176	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
177	C₈×C₉	—	2	1	no	—
178	C₈×C₉	—	4	1	no	—
179	C₈×C₉	—	6	1	no	—
180	#447	—	3	1	no	Sylow
181	C₂×C₃×C₉	—	4	2	no	—
182	C₂×C₃×C₉	#120	1	1	yes	characteristic
183	C₂×C₃×C₉	C₂×D₈	1	1	yes	characteristic
184	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	D₃×C₉	—	2	2	no	—
186	D₃×C₉	—	4	2	no	—
187	D₃×C₉	—	8	1	no	—
188	C₂⁴×C₃	—	6	1	no	—
189	C₂³×D₃	—	2	1	no	—
190	C₂×C₃×D₄	—	2	1	no	—
191	C₂×C₃×D₄	—	3	1	no	—
192	C₂×C₃×D₄	—	3	1	no	—
193	C₂×C₃×D₄	—	6	1	no	—
194	C₂×C₃×D₄	—	6	1	no	—
195	C₂×C₃×D₄	—	6	2	no	—
196	C₂×C₃×D₄	—	6	2	no	—
197	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
198	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	—	3	1	no	—
200	C₂×#67	—	2	1	no	—
201	D₃×D₄	—	2	2	no	—
202	D₃×D₄	—	2	2	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
205	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
206	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
207	C₃×D₈	—	6	2	no	—
208	C₃×D₈	—	6	2	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	3	1	no	—
211	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
212	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
215	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
216	C₃×C₂²⋊C₄	—	6	1	no	—
217	#213	—	2	2	no	—
218	(C₂×D₃)⋊C₄	—	2	1	no	—
219	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
220	D₂₄	—	2	2	no	—
221	C₂²×C₃²	—	2	2	no	—
222	C₂²×C₃²	—	4	1	no	—
223	C₂²×C₃²	—	4	1	no	—
224	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂×C₃×D₃	—	2	1	no	—
226	C₂×C₃×D₃	—	2	1	no	—
227	C₂×C₃×D₃	—	2	2	no	—
228	C₂×C₃×D₃	—	4	8	no	—
229	C₂×C₃×D₃	—	4	1	no	—
230	C₂×C₃×D₃	—	4	1	no	—
231	C₂×C₃×D₃	—	4	1	no	—
232	C₂×C₃×D₃	—	4	1	no	—
233	C₂×C₃×D₃	—	4	1	no	—
234	C₂×C₃×D₃	C₃×D₈	1	2	yes	—
235	C₃²×C₄	—	4	1	no	—
236	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₃×Dic₃	—	2	1	no	—
239	C₂²×C₉	—	2	2	no	—
240	C₂²×C₉	—	2	1	no	—
241	C₂²×C₉	—	3	2	no	—
242	C₂²×C₉	—	4	2	no	—
243	C₂²×C₉	—	4	1	no	—
244	C₂²×C₉	—	4	1	no	—
245	C₂²×C₉	—	6	1	no	—
246	C₂²×C₉	—	6	1	no	—
247	C₂²×C₉	—	6	2	no	—
248	C₂²×C₉	—	8	1	no	—
249	C₂²×C₉	—	8	1	no	—
250	C₂²×C₉	—	12	8	no	—
251	C₂²×C₉	—	12	1	no	—
252	C₂²×C₉	—	12	1	no	—
253	C₂²×C₉	—	12	1	no	—
254	C₂²×C₉	—	12	1	no	—
255	C₂²×C₉	—	12	1	no	—
256	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
257	C₄×C₉	—	2	1	no	—
258	C₄×C₉	—	2	1	no	—
259	C₄×C₉	—	4	1	no	—
260	C₄×C₉	—	6	1	no	—
261	C₄×C₉	—	8	1	no	—
262	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
263	C₄×C₉	D₃×D₄	1	1	yes	characteristic
264	C₂²×D₄	—	3	1	no	—
265	C₂×D₈	—	3	1	no	—
266	C₂×D₈	—	3	1	no	—
267	#121	—	3	1	no	—
268	#102	—	3	1	no	—
269	#102	D₃×C₉	1	1	yes	characteristic, complemented
270	C₂²⋊C₈	—	3	1	no	—
271	C₃×C₉	#447	1	1	yes	characteristic, complemented, Sylow
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	—	3	1	no	—
275	C₂³×C₃	—	4	1	no	—
276	C₂³×C₃	—	6	4	no	—
277	C₂³×C₃	—	6	1	no	—
278	C₂³×C₃	—	6	1	no	—
279	C₂³×C₃	—	12	2	no	—
280	C₂³×C₃	—	12	2	no	—
281	C₂²×D₃	—	2	4	no	—
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	—	2	1	no	—
284	C₂²×D₃	—	4	2	no	—
285	C₂²×D₃	—	4	2	no	—
286	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
287	C₃×D₄	—	2	1	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	—	3	2	no	—
291	C₃×D₄	—	4	1	no	—
292	C₃×D₄	—	6	4	no	—
293	C₃×D₄	—	6	1	no	—
294	C₃×D₄	—	6	1	no	—
295	C₃×D₄	—	6	1	no	—
296	C₃×D₄	—	12	2	no	—
297	C₃×D₄	D₄×C₉	1	2	yes	complemented
298	C₃×D₄	C₃×D₁₂	1	2	yes	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	1	no	—
302	C₂×C₃×C₄	—	3	1	no	—
303	C₂×C₃×C₄	—	4	1	no	—
304	C₂×C₃×C₄	—	6	1	no	—
305	C₂×C₃×C₄	—	6	1	no	—
306	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
308	#67	—	2	4	no	—
309	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
310	D₁₂	—	2	1	no	—
311	D₁₂	—	2	1	no	—
312	D₁₂	—	2	1	no	—
313	D₁₂	—	4	2	no	—
314	D₁₂	D₄×C₉	1	2	yes	complemented
315	C₄×D₃	—	2	1	no	—
316	C₄×D₃	—	2	1	no	—
317	C₃×C₈	—	2	1	no	—
318	C₃×C₈	—	2	1	no	—
319	C₃×C₈	—	4	1	no	—
320	C₃×C₈	—	6	1	no	—
321	C₃⋊C₈	—	2	1	no	—
322	C₂×C₃²	—	4	2	no	—
323	C₂×C₃²	C₃×#120	1	1	yes	characteristic
324	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
325	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₃×D₃	—	2	2	no	—
327	C₃×D₃	—	4	2	no	—
328	C₃×D₃	—	8	1	no	—
329	C₂×C₉	—	2	1	no	—
330	C₂×C₉	—	2	1	no	—
331	C₂×C₉	—	2	1	no	—
332	C₂×C₉	—	4	2	no	—
333	C₂×C₉	—	6	2	no	—
334	C₂×C₉	—	8	2	no	—
335	C₂×C₉	—	12	2	no	—
336	C₂×C₉	—	24	1	no	—
337	C₂×C₉	#882	1	1	yes	characteristic
338	C₂×C₉	D₃×D₈	1	1	yes	characteristic
339	C₂×C₉	#914	1	1	yes	characteristic
340	C₂⁴	—	6	1	no	—
341	C₂×D₄	—	3	1	no	—
342	C₂×D₄	—	3	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂×D₄	—	6	1	no	—
345	C₂×D₄	—	6	2	no	—
346	C₂×D₄	—	6	2	no	—
347	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
348	C₂²×C₄	—	3	1	no	—
349	D₈	—	6	2	no	—
350	D₈	—	6	2	no	—
351	C₂×C₈	—	3	1	no	—
352	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
353	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
354	C₂²⋊C₄	—	6	1	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	3	2	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	1	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	—	6	1	no	—
365	C₂²×C₃	—	6	1	no	—
366	C₂²×C₃	—	6	2	no	—
367	C₂²×C₃	—	8	1	no	—
368	C₂²×C₃	—	8	1	no	—
369	C₂²×C₃	—	12	8	no	—
370	C₂²×C₃	—	12	1	no	—
371	C₂²×C₃	—	12	1	no	—
372	C₂²×C₃	—	12	1	no	—
373	C₂²×C₃	—	12	1	no	—
374	C₂²×C₃	—	12	1	no	—
375	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
376	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
377	C₂×D₃	—	2	1	no	—
378	C₂×D₃	—	2	1	no	—
379	C₂×D₃	—	2	2	no	—
380	C₂×D₃	—	4	8	no	—
381	C₂×D₃	—	4	1	no	—
382	C₂×D₃	—	4	1	no	—
383	C₂×D₃	—	4	1	no	—
384	C₂×D₃	—	4	1	no	—
385	C₂×D₃	—	4	1	no	—
386	C₂×D₃	C₉×D₈	1	2	yes	complemented
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	4	1	no	—
390	C₃×C₄	—	4	1	no	—
391	C₃×C₄	—	6	1	no	—
392	C₃×C₄	—	8	1	no	—
393	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
394	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
395	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
396	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
397	Dic₃	—	2	1	no	—
398	C₃²	C₃×#447	1	1	yes	characteristic
399	C₉	—	2	1	no	—
400	C₉	#4773	1	1	yes	characteristic, direct product factor
401	C₂³	—	2	1	no	—
402	C₂³	—	3	1	no	—
403	C₂³	—	6	4	no	—
404	C₂³	—	6	1	no	—
405	C₂³	—	6	1	no	—
406	C₂³	—	12	2	no	—
407	C₂³	—	12	2	no	—
408	D₄	—	2	1	no	—
409	D₄	—	3	2	no	—
410	D₄	—	6	4	no	—
411	D₄	—	6	1	no	—
412	D₄	—	6	1	no	—
413	D₄	—	6	1	no	—
414	D₄	—	12	2	no	—
415	D₄	C₉×D₁₂	1	2	yes	complemented
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	6	1	no	—
419	C₂×C₄	—	6	1	no	—
420	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	6	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	2	1	no	—
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	—	4	2	no	—
428	C₂×C₃	—	6	2	no	—
429	C₂×C₃	—	8	2	no	—
430	C₂×C₃	—	12	2	no	—
431	C₂×C₃	—	24	1	no	—
432	C₂×C₃	C₉×#120	1	1	yes	characteristic
433	C₂×C₃	C₂×C₉×D₈	1	1	yes	characteristic
434	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂×C₃	C₃×#882	1	1	yes	characteristic
436	C₂×C₃	C₃×D₃×D₈	1	1	yes	characteristic
437	C₂×C₃	C₃×#914	1	1	yes	characteristic
438	D₃	—	2	2	no	—
439	D₃	—	4	2	no	—
440	D₃	—	8	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	3	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	6	1	no	—
446	C₂²	—	6	1	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	12	8	no	—
449	C₂²	—	12	1	no	—
450	C₂²	—	12	1	no	—
451	C₂²	—	12	1	no	—
452	C₂²	—	12	1	no	—
453	C₂²	—	12	1	no	—
454	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
455	C₄	—	4	1	no	—
456	C₄	—	6	1	no	—
457	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
458	C₄	D₃×D₄×C₉	1	1	yes	characteristic
459	C₃	—	2	1	no	—
460	C₃	C₉×#447	1	1	yes	characteristic, complemented
461	C₃	C₃×#4773	1	1	yes	characteristic
462	C₂	—	4	2	no	—
463	C₂	—	6	2	no	—
464	C₂	—	12	2	no	—
465	C₂	—	24	1	no	—
466	C₂	C₉×#882	1	1	yes	characteristic
467	C₂	D₃×C₉×D₈	1	1	yes	characteristic
468	C₂	C₉×#914	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃×#4773	C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#447
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×C₉×#213	C₂	semidirect
3. C₂×C₉×D₂₄	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₃×C₉×#102	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×#809	C₂	semidirect
17. C₂×C₉×D₁₂	C₂²	semidirect
19. C₂×C₃×C₈×C₉	C₂²	semidirect
20. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₂×C₉×C₃⋊C₈	C₂²	semidirect
38. C₉×#102	D₃	semidirect
48. C₃×D₄×C₉	D₄	semidirect
57. C₉×D₁₂	D₄	semidirect
63. #4773	C₉	direct (N × H)
93. C₂×C₈×C₉	C₂×D₃	semidirect
95. C₉×C₄⋊C₄	C₂×D₃	semidirect
110. C₂×D₃×C₉	D₈	semidirect
116. C₂×D₃×D₄	C₂×C₉	semidirect
120. C₂×#213	C₂×C₉	semidirect
121. C₂×D₂₄	C₂×C₉	semidirect
122. #895	C₂×C₉	semidirect
125. C₃×#102	C₂×C₉	semidirect
128. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
129. #809	C₂×C₉	semidirect
169. D₄×C₉	D₁₂	semidirect
205. C₂×D₁₂	C₂²×C₉	semidirect
211. C₂×C₃×C₈	C₂²×C₉	semidirect
214. C₃×C₄⋊C₄	C₂²×C₉	semidirect
219. C₂×C₃⋊C₈	C₂²×C₉	semidirect
269. #102	D₃×C₉	semidirect
271. C₃×C₉	#447	semidirect
297. C₃×D₄	D₄×C₉	semidirect
314. D₁₂	D₄×C₉	semidirect
352. C₂×C₈	C₂×D₃×C₉	semidirect
353. C₄⋊C₄	C₂×D₃×C₉	semidirect
386. C₂×D₃	C₉×D₈	semidirect
400. C₉	#4773	direct (N × H)
415. D₄	C₉×D₁₂	semidirect
460. C₃	C₉×#447	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂×C₉×#213	2
C₂×C₉×D₂₄	2
C₉×#895	2
C₃×C₉×#102	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#809	2
C₃×#4773	3
C₉×#447	3

Subgroups — C9×#4773 #13141756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4773 #13141756