Subgroups — C₉×#5643 #13152938

Order 1728.

722 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#930	C₂	1	1	yes	maximal, characteristic
5	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#898	C₂	1	2	yes	maximal, complemented
7	C₉×#897	C₂	1	2	yes	maximal, complemented
8	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#883	C₂	1	2	yes	maximal, complemented
12	C₃×#5643	C₃	1	1	yes	maximal, characteristic
13	C₉×#542	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	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	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	1	yes	characteristic
24	C₉×#217	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#947	C₂×C₃	1	1	yes	characteristic
39	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
40	C₃×#930	C₂×C₃	1	1	yes	characteristic
41	C₃×#926	C₂×C₃	1	1	yes	characteristic
42	C₃×#898	C₂×C₃	1	2	yes	—
43	C₃×#897	C₂×C₃	1	2	yes	—
44	C₃×#893	C₂×C₃	1	1	yes	characteristic
45	C₃×#888	C₂×C₃	1	1	yes	characteristic
46	C₃×#885	C₂×C₃	1	2	yes	—
47	C₃×#883	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#124	—	3	1	no	—
51	C₉×#124	—	3	2	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	2	1	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
56	C₉×#121	—	3	1	no	—
57	C₄×Q₈×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₉×#117	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₃×Q₈×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×#67	—	4	2	no	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₉×D₁₂	—	2	2	no	—
75	C₄×D₃×C₉	—	4	2	no	—
76	C₉×Dic₆	—	4	2	no	—
77	C₃×#542	—	3	1	no	—
78	#5643	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
82	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
84	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×#217	C₂²×C₃	1	1	yes	characteristic
89	C₃×#217	C₂²×C₃	1	1	yes	characteristic
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
95	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
105	C₂×D₄×C₉	—	3	2	no	—
106	C₂×D₄×C₉	—	3	1	no	—
107	C₂²×C₄×C₉	—	2	1	no	—
108	C₂²×C₄×C₉	—	3	2	no	—
109	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	3	1	no	—
121	C₉×C₂²⋊C₄	—	3	1	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	1	no	—
129	C₄²×C₉	—	3	2	no	—
130	C₂²×C₃×C₉	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	1	no	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
134	C₂×D₃×C₉	—	2	2	no	—
135	C₂×D₃×C₉	—	2	2	no	—
136	C₂×D₃×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	2	no	—
140	C₃×C₄×C₉	#41	1	2	yes	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	—	2	2	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	1	no	—
145	C₉×Dic₃	—	2	1	no	—
146	C₃×C₄⋊Q₈	—	3	1	no	—
147	C₃×#126	—	3	2	no	—
148	C₃×#124	—	3	1	no	—
149	C₃×#124	—	3	2	no	—
150	C₃×#123	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	3	2	no	—
153	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
154	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
155	C₃×#121	—	3	1	no	—
156	C₃×C₄×Q₈	—	3	1	no	—
157	C₃×C₄×D₄	—	3	1	no	—
158	C₃×#117	—	3	1	no	—
159	#947	C₂×C₉	1	1	yes	characteristic, complemented
160	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
161	#930	C₂×C₉	1	1	yes	characteristic
162	#926	C₂×C₉	1	1	yes	characteristic, complemented
163	#898	C₂×C₉	1	2	yes	complemented
164	#897	C₂×C₉	1	2	yes	complemented
165	#893	C₂×C₉	1	1	yes	characteristic, complemented
166	#888	C₂×C₉	1	1	yes	characteristic, complemented
167	#885	C₂×C₉	1	2	yes	complemented
168	#883	C₂×C₉	1	2	yes	complemented
169	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
171	C₃²×Q₈	—	2	2	no	—
172	C₂×C₃²×C₄	—	2	2	no	—
173	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
174	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₃×#67	—	4	2	no	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
181	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
183	C₃×D₁₂	—	2	2	no	—
184	C₃×C₄×D₃	—	4	2	no	—
185	C₃×Dic₆	—	4	2	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	3	2	no	—
188	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
189	Q₈×C₉	—	2	2	no	—
190	Q₈×C₉	—	4	2	no	—
191	Q₈×C₉	—	12	2	no	—
192	D₄×C₉	—	6	2	no	—
193	D₄×C₉	—	12	2	no	—
194	C₂×C₄×C₉	—	2	2	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	3	1	no	—
200	C₂×C₄×C₉	—	3	1	no	—
201	C₂×C₄×C₉	—	3	1	no	—
202	C₂×C₄×C₉	—	3	1	no	—
203	C₂×C₄×C₉	—	3	2	no	—
204	C₂×C₄×C₉	—	4	2	no	—
205	C₂×C₄×C₉	—	12	2	no	—
206	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
207	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
209	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
210	#542	—	3	1	no	Sylow
211	C₂×C₃×C₉	—	4	1	no	—
212	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
215	D₃×C₉	—	4	2	no	—
216	C₂×C₃×Q₈	—	2	1	no	—
217	C₂×C₃×Q₈	—	3	2	no	—
218	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂×C₃×D₄	—	3	2	no	—
221	C₂×C₃×D₄	—	3	1	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	3	2	no	—
224	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×#67	C₂²×C₉	1	2	yes	—
227	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
228	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
229	C₂×Dic₆	C₂²×C₉	1	2	yes	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₃×C₄⋊C₄	—	2	2	no	—
232	C₃×C₄⋊C₄	—	3	2	no	—
233	C₃×C₄⋊C₄	—	3	1	no	—
234	C₃×C₄⋊C₄	—	3	1	no	—
235	C₃×C₄⋊C₄	—	3	1	no	—
236	C₃×C₄⋊C₄	—	3	2	no	—
237	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
238	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
241	C₃×C₂²⋊C₄	—	2	2	no	—
242	C₃×C₂²⋊C₄	—	3	1	no	—
243	C₃×C₂²⋊C₄	—	3	1	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	1	no	—
252	C₃×C₄²	—	3	2	no	—
253	#217	C₂²×C₉	1	1	yes	characteristic
254	#217	C₂²×C₉	1	1	yes	characteristic
255	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
256	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
257	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
259	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
260	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
261	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
262	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
263	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
264	C₄×Dic₃	C₂²×C₉	1	2	yes	—
265	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
266	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₂²×C₃²	—	2	1	no	—
268	C₂²×C₃²	—	2	1	no	—
269	C₂²×C₃²	—	2	1	no	—
270	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
271	C₂×C₃×D₃	—	2	2	no	—
272	C₂×C₃×D₃	—	2	2	no	—
273	C₂×C₃×D₃	—	2	2	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	C₃×#41	1	2	yes	—
278	C₃×Dic₃	—	2	1	no	—
279	C₃×Dic₃	—	2	2	no	—
280	C₃×Dic₃	—	2	1	no	—
281	C₃×Dic₃	—	2	1	no	—
282	C₃×Dic₃	—	2	1	no	—
283	C₂²×C₉	—	2	2	no	—
284	C₂²×C₉	—	2	1	no	—
285	C₂²×C₉	—	2	1	no	—
286	C₂²×C₉	—	2	1	no	—
287	C₂²×C₉	—	2	1	no	—
288	C₂²×C₉	—	4	1	no	—
289	C₂²×C₉	—	4	1	no	—
290	C₂²×C₉	—	6	2	no	—
291	C₂²×C₉	—	6	2	no	—
292	C₂²×C₉	—	6	2	no	—
293	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
294	C₄×C₉	—	2	1	no	—
295	C₄×C₉	—	2	2	no	—
296	C₄×C₉	—	2	2	no	—
297	C₄×C₉	—	2	2	no	—
298	C₄×C₉	—	4	2	no	—
299	C₄×C₉	—	4	1	no	—
300	C₄×C₉	—	4	2	no	—
301	C₄×C₉	—	6	1	no	—
302	C₄×C₉	—	6	1	no	—
303	C₄×C₉	—	6	1	no	—
304	C₄×C₉	—	6	2	no	—
305	C₄×C₉	—	6	1	no	—
306	C₄×C₉	#237	1	2	yes	—
307	C₄⋊Q₈	—	3	1	no	—
308	#126	—	3	2	no	—
309	#124	—	3	1	no	—
310	#124	—	3	2	no	—
311	#123	—	3	2	no	—
312	C₂²⋊Q₈	—	3	2	no	—
313	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
314	#121	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×D₄	—	3	1	no	—
317	#117	—	3	1	no	—
318	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
319	C₂³×C₃	—	2	1	no	—
320	C₂³×C₃	—	3	2	no	—
321	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
322	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂²×D₃	C₂³×C₉	1	2	yes	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×Q₈	—	4	2	no	—
327	C₃×Q₈	—	12	2	no	—
328	C₃×D₄	—	6	2	no	—
329	C₃×D₄	—	12	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	3	1	no	—
337	C₂×C₃×C₄	—	3	1	no	—
338	C₂×C₃×C₄	—	3	1	no	—
339	C₂×C₃×C₄	—	3	1	no	—
340	C₂×C₃×C₄	—	3	2	no	—
341	C₂×C₃×C₄	—	4	2	no	—
342	C₂×C₃×C₄	—	12	2	no	—
343	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
345	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
351	#67	—	4	2	no	—
352	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
353	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
354	C₂×Dic₃	C₂³×C₉	1	2	yes	—
355	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
356	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
357	D₁₂	—	2	2	no	—
358	C₄×D₃	—	4	2	no	—
359	Dic₆	—	4	2	no	—
360	C₂×C₃²	—	4	1	no	—
361	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
362	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
364	C₃×D₃	—	4	2	no	—
365	C₂×C₉	—	2	1	no	—
366	C₂×C₉	—	2	1	no	—
367	C₂×C₉	—	2	1	no	—
368	C₂×C₉	—	4	2	no	—
369	C₂×C₉	—	4	1	no	—
370	C₂×C₉	—	12	2	no	—
371	C₂×C₉	C₂×#237	1	1	yes	characteristic
372	C₂×C₉	#1007	1	1	yes	characteristic
373	C₂×C₉	#1009	1	1	yes	characteristic
374	C₂×Q₈	—	3	2	no	—
375	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
376	C₂×D₄	—	3	2	no	—
377	C₂×D₄	—	3	1	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
380	C₄⋊C₄	—	3	1	no	—
381	C₄⋊C₄	—	3	1	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
386	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
387	C₂²⋊C₄	—	3	1	no	—
388	C₂²⋊C₄	—	3	1	no	—
389	C₂²⋊C₄	—	3	2	no	—
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	—	3	2	no	—
392	C₂²⋊C₄	—	3	2	no	—
393	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
394	C₄²	—	3	1	no	—
395	C₄²	—	3	1	no	—
396	C₄²	—	3	2	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	1	no	—
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	4	1	no	—
406	C₂²×C₃	—	4	1	no	—
407	C₂²×C₃	—	6	2	no	—
408	C₂²×C₃	—	6	2	no	—
409	C₂²×C₃	—	6	2	no	—
410	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
411	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
412	C₂×D₃	—	2	2	no	—
413	C₂×D₃	—	2	2	no	—
414	C₂×D₃	—	2	2	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	4	1	no	—
423	C₃×C₄	—	4	2	no	—
424	C₃×C₄	—	4	2	no	—
425	C₃×C₄	—	6	1	no	—
426	C₃×C₄	—	6	1	no	—
427	C₃×C₄	—	6	1	no	—
428	C₃×C₄	—	6	2	no	—
429	C₃×C₄	—	6	1	no	—
430	C₃×C₄	C₉×#41	1	2	yes	—
431	C₃×C₄	C₃×#237	1	2	yes	—
432	Dic₃	—	2	1	no	—
433	Dic₃	—	2	2	no	—
434	Dic₃	—	2	1	no	—
435	Dic₃	—	2	1	no	—
436	Dic₃	—	2	1	no	—
437	C₃²	C₃×#542	1	1	yes	characteristic
438	C₉	—	2	1	no	—
439	C₉	#5643	1	1	yes	characteristic, direct product factor
440	C₂³	—	3	2	no	—
441	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	12	2	no	—
444	D₄	—	6	2	no	—
445	D₄	—	12	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	12	2	no	—
453	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
454	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
456	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	4	2	no	—
461	C₂×C₃	—	4	1	no	—
462	C₂×C₃	—	4	1	no	—
463	C₂×C₃	—	12	2	no	—
464	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
465	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
468	C₂×C₃	C₃×#1007	1	1	yes	characteristic
469	C₂×C₃	C₃×#1009	1	1	yes	characteristic
470	D₃	—	4	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	6	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	—	6	2	no	—
477	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	6	1	no	—
482	C₄	—	6	1	no	—
483	C₄	—	6	1	no	—
484	C₄	—	6	2	no	—
485	C₄	—	6	1	no	—
486	C₄	C₉×#237	1	2	yes	—
487	C₃	—	2	1	no	—
488	C₃	C₉×#542	1	1	yes	characteristic, complemented
489	C₃	C₃×#5643	1	1	yes	characteristic
490	C₂	—	4	1	no	—
491	C₂	—	12	2	no	—
492	C₂	C₂×C₉×#237	1	1	yes	characteristic
493	C₂	C₉×#1007	1	1	yes	characteristic
494	C₂	C₉×#1009	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×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#930	C₂×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. Q₈×C₉×Dic₃	C₂	semidirect
5. C₉×#926	C₂	semidirect
6. C₉×#898	C₂	semidirect
7. C₉×#897	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#883	C₂	semidirect
55. C₉×C₂²⋊Q₈	D₃	semidirect
78. #5643	C₉	direct (N × H)
153. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
159. #947	C₂×C₉	semidirect
160. Q₈×Dic₃	C₂×C₉	semidirect
162. #926	C₂×C₉	semidirect
163. #898	C₂×C₉	semidirect
164. #897	C₂×C₉	semidirect
165. #893	C₂×C₉	semidirect
166. #888	C₂×C₉	semidirect
167. #885	C₂×C₉	semidirect
168. #883	C₂×C₉	semidirect
313. C₂²⋊Q₈	D₃×C₉	semidirect
318. C₃×C₉	#542	semidirect
439. C₉	#5643	direct (N × H)
488. C₃	C₉×#542	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂²⋊Q₈	2
C₉×#947	2
Q₈×C₉×Dic₃	2
C₉×#930	2
C₉×#926	2
C₉×#898	2
C₉×#897	2
C₉×#893	2
C₉×#888	2
C₉×#885	2
C₉×#883	2
C₃×#5643	3
C₉×#542	3

Subgroups — C9×#5643 #13152938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5643 #13152938