Subgroups — C₉×#4776 #13141759

Order 1728.

614 conjugacy classes of subgroups.

The subgroup lattice has 446 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
2	C₂×C₉×#214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#204	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#897	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×#4776	C₃	1	1	yes	maximal, characteristic
9	C₉×#450	—	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	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
20	C₉×#214	—	2	2	no	—
21	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₉×C₄⋊Dic₃	—	2	1	no	—
23	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₉×#204	—	2	2	no	—
25	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#214	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#204	C₂×C₃	1	1	yes	characteristic
28	C₃×#897	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×SD₁₆	—	3	1	no	—
34	C₂×C₉×SD₁₆	—	3	1	no	—
35	C₉×C₂²⋊Q₈	—	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	—	4	2	no	—
44	C₂²×D₃×C₉	—	4	2	no	—
45	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
46	C₃×D₄×C₉	—	2	1	no	—
47	C₃×D₄×C₉	D₄	1	2	yes	—
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₉×#67	—	2	4	no	—
51	C₂×C₉×Dic₃	—	2	1	no	—
52	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
53	C₉×D₁₂	—	2	1	no	—
54	C₉×D₁₂	D₄	1	2	yes	—
55	C₄×D₃×C₉	—	2	1	no	—
56	C₄×D₃×C₉	—	2	1	no	—
57	C₉×Dic₆	—	2	1	no	—
58	C₉×Dic₆	—	2	1	no	—
59	C₃×C₈×C₉	—	2	1	no	—
60	C₉×C₃⋊C₈	—	2	1	no	—
61	C₃×#450	—	3	1	no	—
62	#4776	C₉	1	1	yes	characteristic, direct product factor
63	C₂³×C₃×D₃	—	2	1	no	—
64	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×#67	—	2	1	no	—
66	C₃×D₃×D₄	—	2	2	no	—
67	C₃×D₃×D₄	—	2	2	no	—
68	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	—	6	1	no	—
72	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₃×#214	—	2	2	no	—
75	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
76	C₃×C₄⋊Dic₃	—	2	1	no	—
77	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
78	C₃×#204	—	2	2	no	—
79	C₂×Q₈×C₉	—	3	1	no	—
80	C₂×D₄×C₉	—	2	1	no	—
81	C₂×D₄×C₉	—	3	1	no	—
82	C₂×D₄×C₉	—	6	1	no	—
83	C₂×D₄×C₉	—	6	2	no	—
84	C₂×D₄×C₉	—	6	2	no	—
85	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₄×C₉	—	3	1	no	—
87	C₉×SD₁₆	—	6	2	no	—
88	C₉×SD₁₆	—	6	2	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	—	3	1	no	—
91	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	—	6	1	no	—
94	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
95	C₉×C₂²⋊C₄	—	6	1	no	—
96	C₂²×C₃×C₉	—	2	2	no	—
97	C₂²×C₃×C₉	—	4	1	no	—
98	C₂²×C₃×C₉	—	4	1	no	—
99	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
100	C₂×D₃×C₉	—	2	1	no	—
101	C₂×D₃×C₉	—	2	1	no	—
102	C₂×D₃×C₉	—	2	2	no	—
103	C₂×D₃×C₉	—	4	8	no	—
104	C₂×D₃×C₉	—	4	1	no	—
105	C₂×D₃×C₉	—	4	1	no	—
106	C₂×D₃×C₉	SD₁₆	1	2	yes	complemented
107	C₃×C₄×C₉	—	4	1	no	—
108	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
109	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
110	C₉×Dic₃	—	2	1	no	—
111	C₉×Dic₃	—	4	1	no	—
112	C₂²×C₃×D₄	—	3	1	no	—
113	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
114	C₂×C₃×SD₁₆	—	3	1	no	—
115	C₂×C₃×SD₁₆	—	3	1	no	—
116	C₃×C₂²⋊Q₈	—	3	1	no	—
117	C₂×#214	C₂×C₉	1	1	yes	characteristic, complemented
118	C₂×#204	C₂×C₉	1	1	yes	characteristic, complemented
119	#897	C₂×C₉	1	1	yes	characteristic, complemented
120	C₃×#102	—	2	1	no	—
121	C₃×#102	—	3	1	no	—
122	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
123	C₃×#102	C₃×D₃	1	1	yes	characteristic
124	C₃×C₂²⋊C₈	—	3	1	no	—
125	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
126	#809	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂³×C₃²	—	2	1	no	—
128	C₂²×C₃×D₃	—	2	4	no	—
129	C₂²×C₃×D₃	—	2	1	no	—
130	C₂²×C₃×D₃	—	4	2	no	—
131	C₂²×C₃×D₃	—	4	2	no	—
132	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
133	C₃²×D₄	—	2	1	no	—
134	C₃²×D₄	C₃×D₄	1	2	yes	—
135	C₂×C₃²×C₄	—	2	1	no	—
136	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₃×#67	—	2	4	no	—
138	C₂×C₃×Dic₃	—	2	1	no	—
139	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
140	C₃×D₁₂	—	2	1	no	—
141	C₃×D₁₂	C₃×D₄	1	2	yes	—
142	C₃×C₄×D₃	—	2	1	no	—
143	C₃×C₄×D₃	—	2	1	no	—
144	C₃×Dic₆	—	2	1	no	—
145	C₃×Dic₆	—	2	1	no	—
146	C₂³×C₉	—	2	1	no	—
147	C₂³×C₉	—	3	1	no	—
148	C₂³×C₉	—	4	1	no	—
149	C₂³×C₉	—	6	4	no	—
150	C₂³×C₉	—	6	1	no	—
151	C₂³×C₉	—	12	2	no	—
152	C₂³×C₉	—	12	2	no	—
153	C₃²×C₈	—	2	1	no	—
154	C₃×C₃⋊C₈	—	2	1	no	—
155	Q₈×C₉	—	6	1	no	—
156	Q₈×C₉	—	6	1	no	—
157	D₄×C₉	—	2	1	no	—
158	D₄×C₉	—	2	2	no	—
159	D₄×C₉	—	3	2	no	—
160	D₄×C₉	—	4	1	no	—
161	D₄×C₉	—	6	4	no	—
162	D₄×C₉	—	6	1	no	—
163	D₄×C₉	D₁₂	1	2	yes	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	3	1	no	—
167	C₂×C₄×C₉	—	4	1	no	—
168	C₂×C₄×C₉	—	6	1	no	—
169	C₂×C₄×C₉	—	6	1	no	—
170	C₂×C₄×C₉	—	6	1	no	—
171	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
172	C₈×C₉	—	2	1	no	—
173	C₈×C₉	—	4	1	no	—
174	C₈×C₉	—	6	1	no	—
175	#450	—	3	1	no	Sylow
176	C₂×C₃×C₉	—	4	2	no	—
177	C₂×C₃×C₉	#120	1	1	yes	characteristic
178	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
180	D₃×C₉	—	2	2	no	—
181	D₃×C₉	—	4	2	no	—
182	C₂⁴×C₃	—	6	1	no	—
183	C₂³×D₃	—	2	1	no	—
184	C₂×C₃×Q₈	—	3	1	no	—
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	—	3	1	no	—
187	C₂×C₃×D₄	—	6	1	no	—
188	C₂×C₃×D₄	—	6	2	no	—
189	C₂×C₃×D₄	—	6	2	no	—
190	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
191	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	3	1	no	—
193	C₂×#67	—	2	1	no	—
194	D₃×D₄	—	2	2	no	—
195	D₃×D₄	—	2	2	no	—
196	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
198	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
199	C₃×SD₁₆	—	6	2	no	—
200	C₃×SD₁₆	—	6	2	no	—
201	C₂×C₃×C₈	—	2	1	no	—
202	C₂×C₃×C₈	—	3	1	no	—
203	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
204	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
205	C₃×C₄⋊C₄	—	2	1	no	—
206	C₃×C₄⋊C₄	—	6	1	no	—
207	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
208	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
209	C₃×C₂²⋊C₄	—	6	1	no	—
210	#214	—	2	2	no	—
211	(C₂×D₃)⋊C₄	—	2	1	no	—
212	C₄⋊Dic₃	—	2	1	no	—
213	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
214	#204	—	2	2	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	—	4	1	no	—
218	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	—	2	1	no	—
221	C₂×C₃×D₃	—	2	2	no	—
222	C₂×C₃×D₃	—	4	8	no	—
223	C₂×C₃×D₃	—	4	1	no	—
224	C₂×C₃×D₃	—	4	1	no	—
225	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
226	C₃²×C₄	—	4	1	no	—
227	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
228	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
229	C₃×Dic₃	—	2	1	no	—
230	C₃×Dic₃	—	4	1	no	—
231	C₂²×C₉	—	2	2	no	—
232	C₂²×C₉	—	2	1	no	—
233	C₂²×C₉	—	3	2	no	—
234	C₂²×C₉	—	4	2	no	—
235	C₂²×C₉	—	4	1	no	—
236	C₂²×C₉	—	4	1	no	—
237	C₂²×C₉	—	6	1	no	—
238	C₂²×C₉	—	6	1	no	—
239	C₂²×C₉	—	6	2	no	—
240	C₂²×C₉	—	8	1	no	—
241	C₂²×C₉	—	8	1	no	—
242	C₂²×C₉	—	12	8	no	—
243	C₂²×C₉	—	12	1	no	—
244	C₂²×C₉	—	12	1	no	—
245	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
246	C₄×C₉	—	2	1	no	—
247	C₄×C₉	—	2	1	no	—
248	C₄×C₉	—	4	1	no	—
249	C₄×C₉	—	6	1	no	—
250	C₄×C₉	—	8	1	no	—
251	C₄×C₉	—	12	1	no	—
252	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
253	C₄×C₉	D₃×D₄	1	1	yes	characteristic
254	C₂²×D₄	—	3	1	no	—
255	C₂×SD₁₆	—	3	1	no	—
256	C₂×SD₁₆	—	3	1	no	—
257	C₂²⋊Q₈	—	3	1	no	—
258	#102	—	3	1	no	—
259	#102	D₃×C₉	1	1	yes	characteristic, complemented
260	C₂²⋊C₈	—	3	1	no	—
261	C₃×C₉	#450	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₃	—	2	1	no	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	3	1	no	—
265	C₂³×C₃	—	4	1	no	—
266	C₂³×C₃	—	6	4	no	—
267	C₂³×C₃	—	6	1	no	—
268	C₂³×C₃	—	12	2	no	—
269	C₂³×C₃	—	12	2	no	—
270	C₂²×D₃	—	2	4	no	—
271	C₂²×D₃	—	2	1	no	—
272	C₂²×D₃	—	4	2	no	—
273	C₂²×D₃	—	4	2	no	—
274	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
275	C₃×Q₈	—	6	1	no	—
276	C₃×Q₈	—	6	1	no	—
277	C₃×D₄	—	2	1	no	—
278	C₃×D₄	—	2	1	no	—
279	C₃×D₄	—	2	2	no	—
280	C₃×D₄	—	3	2	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	—	6	4	no	—
283	C₃×D₄	—	6	1	no	—
284	C₃×D₄	D₄×C₉	1	2	yes	—
285	C₃×D₄	C₃×D₁₂	1	2	yes	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	3	1	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	6	1	no	—
292	C₂×C₃×C₄	—	6	1	no	—
293	C₂×C₃×C₄	—	6	1	no	—
294	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
296	#67	—	2	4	no	—
297	C₂×Dic₃	—	2	1	no	—
298	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
299	D₁₂	—	2	1	no	—
300	D₁₂	D₄×C₉	1	2	yes	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	2	1	no	—
303	Dic₆	—	2	1	no	—
304	Dic₆	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	4	1	no	—
308	C₃×C₈	—	6	1	no	—
309	C₃⋊C₈	—	2	1	no	—
310	C₂×C₃²	—	4	2	no	—
311	C₂×C₃²	C₃×#120	1	1	yes	characteristic
312	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
313	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₃×D₃	—	2	2	no	—
315	C₃×D₃	—	4	2	no	—
316	C₂×C₉	—	2	1	no	—
317	C₂×C₉	—	2	1	no	—
318	C₂×C₉	—	2	1	no	—
319	C₂×C₉	—	4	2	no	—
320	C₂×C₉	—	6	2	no	—
321	C₂×C₉	—	8	2	no	—
322	C₂×C₉	—	12	2	no	—
323	C₂×C₉	#882	1	1	yes	characteristic
324	C₂×C₉	#911	1	1	yes	characteristic
325	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
326	C₂⁴	—	6	1	no	—
327	C₂×Q₈	—	3	1	no	—
328	C₂×D₄	—	3	1	no	—
329	C₂×D₄	—	6	1	no	—
330	C₂×D₄	—	6	2	no	—
331	C₂×D₄	—	6	2	no	—
332	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
333	C₂²×C₄	—	3	1	no	—
334	SD₁₆	—	6	2	no	—
335	SD₁₆	—	6	2	no	—
336	C₂×C₈	—	3	1	no	—
337	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
338	C₄⋊C₄	—	6	1	no	—
339	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
340	C₂²⋊C₄	—	6	1	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	3	2	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	6	1	no	—
351	C₂²×C₃	—	6	1	no	—
352	C₂²×C₃	—	6	2	no	—
353	C₂²×C₃	—	8	1	no	—
354	C₂²×C₃	—	8	1	no	—
355	C₂²×C₃	—	12	8	no	—
356	C₂²×C₃	—	12	1	no	—
357	C₂²×C₃	—	12	1	no	—
358	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
359	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	2	1	no	—
362	C₂×D₃	—	2	2	no	—
363	C₂×D₃	—	4	8	no	—
364	C₂×D₃	—	4	1	no	—
365	C₂×D₃	—	4	1	no	—
366	C₂×D₃	C₉×SD₁₆	1	2	yes	complemented
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	—	6	1	no	—
372	C₃×C₄	—	8	1	no	—
373	C₃×C₄	—	12	1	no	—
374	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
375	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
376	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
377	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
378	Dic₃	—	2	1	no	—
379	Dic₃	—	4	1	no	—
380	C₃²	C₃×#450	1	1	yes	characteristic
381	C₉	—	2	1	no	—
382	C₉	#4776	1	1	yes	characteristic, direct product factor
383	C₂³	—	2	1	no	—
384	C₂³	—	3	1	no	—
385	C₂³	—	6	4	no	—
386	C₂³	—	6	1	no	—
387	C₂³	—	12	2	no	—
388	C₂³	—	12	2	no	—
389	Q₈	—	6	1	no	—
390	Q₈	—	6	1	no	—
391	D₄	—	2	1	no	—
392	D₄	—	3	2	no	—
393	D₄	—	6	4	no	—
394	D₄	—	6	1	no	—
395	D₄	C₉×D₁₂	1	2	yes	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	6	1	no	—
399	C₂×C₄	—	6	1	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	6	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	2	1	no	—
406	C₂×C₃	—	2	1	no	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	—	4	2	no	—
409	C₂×C₃	—	6	2	no	—
410	C₂×C₃	—	8	2	no	—
411	C₂×C₃	—	12	2	no	—
412	C₂×C₃	C₉×#120	1	1	yes	characteristic
413	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
414	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂×C₃	C₃×#882	1	1	yes	characteristic
416	C₂×C₃	C₃×#911	1	1	yes	characteristic
417	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
418	D₃	—	2	2	no	—
419	D₃	—	4	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	3	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	6	1	no	—
425	C₂²	—	6	1	no	—
426	C₂²	—	6	2	no	—
427	C₂²	—	12	8	no	—
428	C₂²	—	12	1	no	—
429	C₂²	—	12	1	no	—
430	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
431	C₄	—	4	1	no	—
432	C₄	—	6	1	no	—
433	C₄	—	12	1	no	—
434	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
435	C₄	D₃×D₄×C₉	1	1	yes	characteristic
436	C₃	—	2	1	no	—
437	C₃	C₉×#450	1	1	yes	characteristic, complemented
438	C₃	C₃×#4776	1	1	yes	characteristic
439	C₂	—	4	2	no	—
440	C₂	—	6	2	no	—
441	C₂	—	12	2	no	—
442	C₂	C₉×#882	1	1	yes	characteristic
443	C₂	C₉×#911	1	1	yes	characteristic
444	C₂	D₃×C₉×SD₁₆	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	C₂×C₃×D₃×D₄	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#450
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
2. C₂×C₉×#214	C₂	semidirect
3. C₂×C₉×#204	C₂	semidirect
4. C₉×#897	C₂	semidirect
5. C₃×C₉×#102	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×#809	C₂	semidirect
17. C₂×C₉×Dic₆	C₂²	semidirect
18. C₂×C₃×C₈×C₉	C₂²	semidirect
19. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₂×C₉×C₃⋊C₈	C₂²	semidirect
38. C₉×#102	D₃	semidirect
62. #4776	C₉	direct (N × H)
91. C₂×C₈×C₉	C₂×D₃	semidirect
94. C₉×C₄⋊C₄	C₂×D₃	semidirect
106. C₂×D₃×C₉	SD₁₆	semidirect
117. C₂×#214	C₂×C₉	semidirect
118. C₂×#204	C₂×C₉	semidirect
119. #897	C₂×C₉	semidirect
122. C₃×#102	C₂×C₉	semidirect
125. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
126. #809	C₂×C₉	semidirect
198. C₂×Dic₆	C₂²×C₉	semidirect
203. C₂×C₃×C₈	C₂²×C₉	semidirect
207. C₃×C₄⋊C₄	C₂²×C₉	semidirect
213. C₂×C₃⋊C₈	C₂²×C₉	semidirect
259. #102	D₃×C₉	semidirect
261. C₃×C₉	#450	semidirect
337. C₂×C₈	C₂×D₃×C₉	semidirect
339. C₄⋊C₄	C₂×D₃×C₉	semidirect
366. C₂×D₃	C₉×SD₁₆	semidirect
382. C₉	#4776	direct (N × H)
437. C₃	C₉×#450	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×#214	2
C₂×C₉×#204	2
C₉×#897	2
C₃×C₉×#102	2
C₉×(C₂×D₃)⋊C₈	2
C₉×#809	2
C₃×#4776	3
C₉×#450	3

Subgroups — C9×#4776 #13141759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4776 #13141759