Subgroups — C₉×#5684 #13153108

Order 1728.

736 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	2	yes	maximal, complemented
3	C₉×#939	C₂	1	2	yes	maximal, complemented
4	C₉×#886	C₂	1	2	yes	maximal, complemented
5	C₉×#884	C₂	1	2	yes	maximal, complemented
6	C₉×#883	C₂	1	2	yes	maximal, complemented
7	C₉×#878	C₂	1	2	yes	maximal, complemented
8	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5684	C₃	1	1	yes	maximal, characteristic
11	C₉×#562	—	3	1	no	maximal
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	C₂²	1	2	yes	—
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₃²×#124	C₂×C₃	1	1	yes	characteristic
34	C₃×#946	C₂×C₃	1	2	yes	—
35	C₃×#939	C₂×C₃	1	2	yes	—
36	C₃×#886	C₂×C₃	1	2	yes	—
37	C₃×#884	C₂×C₃	1	2	yes	—
38	C₃×#883	C₂×C₃	1	2	yes	—
39	C₃×#878	C₂×C₃	1	2	yes	—
40	C₃×#875	C₂×C₃	1	1	yes	characteristic
41	C₃×#870	C₂×C₃	1	1	yes	characteristic
42	C₉×#125	—	3	1	no	—
43	C₉×#124	—	2	1	no	—
44	C₉×#124	—	3	1	no	—
45	C₉×#124	D₃	1	1	yes	characteristic, complemented
46	C₉×#123	—	3	2	no	—
47	C₉×#123	—	3	2	no	—
48	C₉×C₂²⋊Q₈	—	3	2	no	—
49	C₉×C₂²⋊Q₈	—	3	2	no	—
50	C₉×#121	—	3	2	no	—
51	C₉×#121	—	3	2	no	—
52	C₂³×C₃×C₉	C₂³	1	2	yes	—
53	C₂²×D₃×C₉	C₂³	1	2	yes	—
54	C₃×Q₈×C₉	—	4	1	no	—
55	C₃×D₄×C₉	—	4	1	no	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×#67	—	4	2	no	—
61	C₉×#67	—	4	2	no	—
62	C₂×C₉×Dic₃	—	4	2	no	—
63	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₉×D₁₂	—	4	1	no	—
67	C₄×D₃×C₉	—	4	2	no	—
68	C₉×Dic₆	—	4	1	no	—
69	C₃×#562	—	3	1	no	—
70	#5684	C₉	1	1	yes	characteristic, direct product factor
71	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
74	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
75	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
76	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
79	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₃×#217	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
87	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×Q₈×C₉	—	2	1	no	—
93	C₂×Q₈×C₉	—	3	1	no	—
94	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
95	C₂×D₄×C₉	—	2	1	no	—
96	C₂×D₄×C₉	—	3	2	no	—
97	C₂×D₄×C₉	—	3	2	no	—
98	C₂×D₄×C₉	—	3	1	no	—
99	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₄×C₉	—	3	2	no	—
101	C₂²×C₄×C₉	—	3	2	no	—
102	C₉×C₄⋊C₄	—	3	2	no	—
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	—	3	2	no	—
105	C₉×C₄⋊C₄	—	3	2	no	—
106	C₉×C₄⋊C₄	—	3	1	no	—
107	C₉×C₄⋊C₄	—	3	1	no	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	2	2	no	—
110	C₉×C₂²⋊C₄	—	3	2	no	—
111	C₉×C₂²⋊C₄	—	3	2	no	—
112	C₉×C₂²⋊C₄	—	3	2	no	—
113	C₉×C₂²⋊C₄	—	3	2	no	—
114	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
115	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
116	C₄²×C₉	—	2	1	no	—
117	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
118	C₂²×C₃×C₉	—	2	2	no	—
119	C₂²×C₃×C₉	—	2	2	no	—
120	C₂²×C₃×C₉	—	2	2	no	—
121	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
122	C₂×D₃×C₉	—	2	2	no	—
123	C₂×D₃×C₉	—	2	2	no	—
124	C₂×D₃×C₉	—	2	2	no	—
125	C₃×C₄×C₉	—	2	1	no	—
126	C₃×C₄×C₉	—	2	1	no	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₃×C₄×C₉	—	2	1	no	—
129	C₉×Dic₃	—	2	2	no	—
130	C₉×Dic₃	—	2	2	no	—
131	C₉×Dic₃	—	2	2	no	—
132	C₃×#125	—	3	1	no	—
133	C₃×#124	—	2	1	no	—
134	C₃×#124	—	3	1	no	—
135	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
136	C₃×#124	C₃×D₃	1	1	yes	characteristic
137	C₃×#123	—	3	2	no	—
138	C₃×#123	—	3	2	no	—
139	C₃×C₂²⋊Q₈	—	3	2	no	—
140	C₃×C₂²⋊Q₈	—	3	2	no	—
141	C₃×#121	—	3	2	no	—
142	C₃×#121	—	3	2	no	—
143	#946	C₂×C₉	1	2	yes	complemented
144	#939	C₂×C₉	1	2	yes	complemented
145	#886	C₂×C₉	1	2	yes	complemented
146	#884	C₂×C₉	1	2	yes	complemented
147	#883	C₂×C₉	1	2	yes	complemented
148	#878	C₂×C₉	1	2	yes	complemented
149	#875	C₂×C₉	1	1	yes	characteristic, complemented
150	#870	C₂×C₉	1	1	yes	characteristic, complemented
151	C₂³×C₃²	C₂³×C₃	1	2	yes	—
152	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
153	C₃²×Q₈	—	4	1	no	—
154	C₃²×D₄	—	4	1	no	—
155	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
158	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₃×#67	—	4	2	no	—
160	C₃×#67	—	4	2	no	—
161	C₂×C₃×Dic₃	—	4	2	no	—
162	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
164	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
165	C₃×D₁₂	—	4	1	no	—
166	C₃×C₄×D₃	—	4	2	no	—
167	C₃×Dic₆	—	4	1	no	—
168	C₂³×C₉	—	2	2	no	—
169	C₂³×C₉	—	3	2	no	—
170	C₂³×C₉	C₂²×D₃	1	2	yes	—
171	Q₈×C₉	—	4	1	no	—
172	Q₈×C₉	—	4	2	no	—
173	Q₈×C₉	—	12	1	no	—
174	D₄×C₉	—	4	1	no	—
175	D₄×C₉	—	4	2	no	—
176	D₄×C₉	—	12	1	no	—
177	D₄×C₉	—	12	2	no	—
178	D₄×C₉	—	12	2	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	2	no	—
183	C₂×C₄×C₉	—	3	2	no	—
184	C₂×C₄×C₉	—	3	2	no	—
185	C₂×C₄×C₉	—	3	2	no	—
186	C₂×C₄×C₉	—	12	2	no	—
187	C₂×C₄×C₉	—	12	2	no	—
188	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
192	#562	—	3	1	no	Sylow
193	C₂×C₃×C₉	—	4	2	no	—
194	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
197	D₃×C₉	—	4	2	no	—
198	C₂×C₃×Q₈	—	2	1	no	—
199	C₂×C₃×Q₈	—	3	1	no	—
200	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	—	3	2	no	—
204	C₂×C₃×D₄	—	3	2	no	—
205	C₂×C₃×D₄	—	3	1	no	—
206	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
208	C₂²×C₃×C₄	—	3	2	no	—
209	C₂²×C₃×C₄	—	3	2	no	—
210	C₂×#67	C₂²×C₉	1	2	yes	—
211	C₂×#67	C₂²×C₉	1	2	yes	—
212	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
213	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
215	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
216	C₃×C₄⋊C₄	—	3	2	no	—
217	C₃×C₄⋊C₄	—	3	2	no	—
218	C₃×C₄⋊C₄	—	3	2	no	—
219	C₃×C₄⋊C₄	—	3	2	no	—
220	C₃×C₄⋊C₄	—	3	1	no	—
221	C₃×C₄⋊C₄	—	3	1	no	—
222	C₃×C₂²⋊C₄	—	2	2	no	—
223	C₃×C₂²⋊C₄	—	2	2	no	—
224	C₃×C₂²⋊C₄	—	3	2	no	—
225	C₃×C₂²⋊C₄	—	3	2	no	—
226	C₃×C₂²⋊C₄	—	3	2	no	—
227	C₃×C₂²⋊C₄	—	3	2	no	—
228	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
230	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
231	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
232	C₃×C₄²	—	2	1	no	—
233	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
234	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
235	#217	C₂²×C₉	1	2	yes	—
236	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
239	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
240	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
241	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
242	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
243	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
244	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
245	C₂²×C₃²	—	2	2	no	—
246	C₂²×C₃²	—	2	2	no	—
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
249	C₂×C₃×D₃	—	2	2	no	—
250	C₂×C₃×D₃	—	2	2	no	—
251	C₂×C₃×D₃	—	2	2	no	—
252	C₃²×C₄	—	2	1	no	—
253	C₃²×C₄	—	2	1	no	—
254	C₃²×C₄	—	2	2	no	—
255	C₃²×C₄	—	2	1	no	—
256	C₃×Dic₃	—	2	2	no	—
257	C₃×Dic₃	—	2	2	no	—
258	C₃×Dic₃	—	2	2	no	—
259	C₂²×C₉	—	2	2	no	—
260	C₂²×C₉	—	2	2	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	2	1	no	—
263	C₂²×C₉	—	4	2	no	—
264	C₂²×C₉	—	4	2	no	—
265	C₂²×C₉	—	4	2	no	—
266	C₂²×C₉	—	6	2	no	—
267	C₂²×C₉	—	6	2	no	—
268	C₂²×C₉	—	6	2	no	—
269	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
270	C₄×C₉	—	2	2	no	—
271	C₄×C₉	—	2	2	no	—
272	C₄×C₉	—	2	1	no	—
273	C₄×C₉	—	2	1	no	—
274	C₄×C₉	—	2	1	no	—
275	C₄×C₉	—	4	1	no	—
276	C₄×C₉	—	4	1	no	—
277	C₄×C₉	—	4	2	no	—
278	C₄×C₉	—	6	2	no	—
279	C₄×C₉	—	6	2	no	—
280	C₄×C₉	—	6	2	no	—
281	#125	—	3	1	no	—
282	#124	—	3	1	no	—
283	#124	D₃×C₉	1	1	yes	characteristic, complemented
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	#121	—	3	2	no	—
289	#121	—	3	2	no	—
290	C₃×C₉	#562	1	1	yes	characteristic, complemented, Sylow
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	3	2	no	—
293	C₂³×C₃	C₂³×C₉	1	2	yes	—
294	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
295	C₂²×D₃	C₂³×C₉	1	2	yes	—
296	C₃×Q₈	—	4	1	no	—
297	C₃×Q₈	—	4	1	no	—
298	C₃×Q₈	—	4	2	no	—
299	C₃×Q₈	—	12	1	no	—
300	C₃×D₄	—	4	1	no	—
301	C₃×D₄	—	4	1	no	—
302	C₃×D₄	—	4	2	no	—
303	C₃×D₄	—	12	1	no	—
304	C₃×D₄	—	12	2	no	—
305	C₃×D₄	—	12	2	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	3	2	no	—
311	C₂×C₃×C₄	—	3	2	no	—
312	C₂×C₃×C₄	—	3	2	no	—
313	C₂×C₃×C₄	—	12	2	no	—
314	C₂×C₃×C₄	—	12	2	no	—
315	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
318	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
323	#67	—	4	2	no	—
324	#67	—	4	2	no	—
325	C₂×Dic₃	—	4	2	no	—
326	C₂×Dic₃	C₂³×C₉	1	2	yes	—
327	C₂×Dic₃	C₂³×C₉	1	2	yes	—
328	C₂×Dic₃	C₂³×C₉	1	2	yes	—
329	D₁₂	—	4	1	no	—
330	C₄×D₃	—	4	2	no	—
331	Dic₆	—	4	1	no	—
332	C₂×C₃²	—	4	2	no	—
333	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
336	C₃×D₃	—	4	2	no	—
337	C₂×C₉	—	2	1	no	—
338	C₂×C₉	—	2	1	no	—
339	C₂×C₉	—	2	1	no	—
340	C₂×C₉	—	4	2	no	—
341	C₂×C₉	—	8	2	no	—
342	C₂×C₉	—	12	2	no	—
343	C₂×C₉	#1004	1	1	yes	characteristic
344	C₂×C₉	#1009	1	1	yes	characteristic
345	C₂×C₉	#1010	1	1	yes	characteristic
346	C₂×Q₈	—	3	1	no	—
347	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
348	C₂×D₄	—	3	2	no	—
349	C₂×D₄	—	3	2	no	—
350	C₂×D₄	—	3	1	no	—
351	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
352	C₂²×C₄	—	3	2	no	—
353	C₂²×C₄	—	3	2	no	—
354	C₄⋊C₄	—	3	2	no	—
355	C₄⋊C₄	—	3	2	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	3	1	no	—
359	C₄⋊C₄	—	3	1	no	—
360	C₂²⋊C₄	—	3	2	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	2	no	—
363	C₂²⋊C₄	—	3	2	no	—
364	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
365	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
366	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	2	2	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	1	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	6	2	no	—
378	C₂²×C₃	—	6	2	no	—
379	C₂²×C₃	—	6	2	no	—
380	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
381	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
382	C₂×D₃	—	2	2	no	—
383	C₂×D₃	—	2	2	no	—
384	C₂×D₃	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	4	1	no	—
396	C₃×C₄	—	4	1	no	—
397	C₃×C₄	—	6	2	no	—
398	C₃×C₄	—	6	2	no	—
399	C₃×C₄	—	6	2	no	—
400	Dic₃	—	2	2	no	—
401	Dic₃	—	2	2	no	—
402	Dic₃	—	2	2	no	—
403	C₃²	C₃×#562	1	1	yes	characteristic
404	C₉	—	2	1	no	—
405	C₉	#5684	1	1	yes	characteristic, direct product factor
406	C₂³	—	3	2	no	—
407	C₂³	C₂²×D₃×C₉	1	2	yes	—
408	Q₈	—	4	1	no	—
409	Q₈	—	12	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	12	1	no	—
412	D₄	—	12	2	no	—
413	D₄	—	12	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	3	2	no	—
416	C₂×C₄	—	3	2	no	—
417	C₂×C₄	—	12	2	no	—
418	C₂×C₄	—	12	2	no	—
419	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
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	—	8	2	no	—
429	C₂×C₃	—	12	2	no	—
430	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂×C₃	C₃×#1004	1	1	yes	characteristic
434	C₂×C₃	C₃×#1009	1	1	yes	characteristic
435	C₂×C₃	C₃×#1010	1	1	yes	characteristic
436	D₃	—	4	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	6	2	no	—
441	C₂²	—	6	2	no	—
442	C₂²	—	6	2	no	—
443	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	6	2	no	—
449	C₄	—	6	2	no	—
450	C₄	—	6	2	no	—
451	C₃	—	2	1	no	—
452	C₃	C₉×#562	1	1	yes	characteristic, complemented
453	C₃	C₃×#5684	1	1	yes	characteristic
454	C₂	—	4	2	no	—
455	C₂	—	12	2	no	—
456	C₂	C₉×#1004	1	1	yes	characteristic
457	C₂	C₉×#1009	1	1	yes	characteristic
458	C₂	C₉×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5684	C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#124	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#939	C₂	semidirect
4. C₉×#886	C₂	semidirect
5. C₉×#884	C₂	semidirect
6. C₉×#883	C₂	semidirect
7. C₉×#878	C₂	semidirect
8. C₉×#875	C₂	semidirect
9. C₉×#870	C₂	semidirect
45. C₉×#124	D₃	semidirect
70. #5684	C₉	direct (N × H)
135. C₃×#124	C₂×C₉	semidirect
143. #946	C₂×C₉	semidirect
144. #939	C₂×C₉	semidirect
145. #886	C₂×C₉	semidirect
146. #884	C₂×C₉	semidirect
147. #883	C₂×C₉	semidirect
148. #878	C₂×C₉	semidirect
149. #875	C₂×C₉	semidirect
150. #870	C₂×C₉	semidirect
283. #124	D₃×C₉	semidirect
290. C₃×C₉	#562	semidirect
405. C₉	#5684	direct (N × H)
452. C₃	C₉×#562	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#124	2
C₉×#946	2
C₉×#939	2
C₉×#886	2
C₉×#884	2
C₉×#883	2
C₉×#878	2
C₉×#875	2
C₉×#870	2
C₃×#5684	3
C₉×#562	3

Subgroups — C9×#5684 #13153108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5684 #13153108