Subgroups — C₉×#5494 #13152353

Order 1728.

882 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#953	C₂	1	2	yes	maximal, complemented
3	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#67	C₂	1	2	yes	maximal, complemented
5	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#885	C₂	1	2	yes	maximal, complemented
7	C₉×#884	C₂	1	2	yes	maximal, complemented
8	C₉×#883	C₂	1	2	yes	maximal, complemented
9	C₉×#879	C₂	1	2	yes	maximal, complemented
10	C₃×#5494	C₃	1	1	yes	maximal, characteristic
11	C₉×#538	—	3	1	no	maximal
12	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×#217	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
32	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
33	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₃×#953	C₂×C₃	1	2	yes	—
35	C₃×#930	C₂×C₃	1	1	yes	characteristic
36	C₃×C₄×#67	C₂×C₃	1	2	yes	—
37	C₃×#924	C₂×C₃	1	1	yes	characteristic
38	C₃×#885	C₂×C₃	1	2	yes	—
39	C₃×#884	C₂×C₃	1	2	yes	—
40	C₃×#883	C₂×C₃	1	2	yes	—
41	C₃×#879	C₂×C₃	1	2	yes	—
42	C₉×#126	—	3	2	no	—
43	C₉×#124	—	3	2	no	—
44	C₉×#123	—	3	2	no	—
45	C₉×C₂²⋊Q₈	—	3	1	no	—
46	C₉×#121	—	3	1	no	—
47	C₉×#121	—	3	2	no	—
48	C₉×#120	—	3	2	no	—
49	C₄×D₄×C₉	—	3	2	no	—
50	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
52	C₂³×C₃×C₉	—	2	2	no	—
53	C₂³×C₃×C₉	—	4	1	no	—
54	C₂³×C₃×C₉	—	4	1	no	—
55	C₂³×C₃×C₉	C₂³	1	2	yes	—
56	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
57	C₂²×D₃×C₉	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₉	—	4	1	no	—
59	C₂×C₃×C₄×C₉	—	4	1	no	—
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₉×#67	—	2	4	no	—
64	C₉×#67	—	4	2	no	—
65	C₉×#67	—	4	2	no	—
66	C₂×C₉×Dic₃	C₂³	1	2	yes	—
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₉×D₁₂	—	4	1	no	—
70	C₄×D₃×C₉	—	4	2	no	—
71	C₉×Dic₆	—	4	1	no	—
72	C₃×#538	—	3	1	no	—
73	#5494	C₉	1	1	yes	characteristic, direct product factor
74	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
78	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
79	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
80	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
82	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
83	C₂⁴×C₉	—	2	1	no	—
84	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃×#217	C₂²×C₃	1	2	yes	—
88	C₃×#217	C₂²×C₃	1	2	yes	—
89	C₃×#217	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
97	C₂×Q₈×C₉	—	3	1	no	—
98	C₂×D₄×C₉	—	3	2	no	—
99	C₂×D₄×C₉	—	3	2	no	—
100	C₂×D₄×C₉	—	3	2	no	—
101	C₂×D₄×C₉	—	3	1	no	—
102	C₂²×C₄×C₉	—	2	1	no	—
103	C₂²×C₄×C₉	—	2	1	no	—
104	C₂²×C₄×C₉	—	3	2	no	—
105	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₉×C₄⋊C₄	—	3	2	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₄⋊C₄	—	3	1	no	—
110	C₉×C₄⋊C₄	—	3	1	no	—
111	C₉×C₂²⋊C₄	—	2	2	no	—
112	C₉×C₂²⋊C₄	—	2	2	no	—
113	C₉×C₂²⋊C₄	—	3	2	no	—
114	C₉×C₂²⋊C₄	—	3	2	no	—
115	C₉×C₂²⋊C₄	—	3	2	no	—
116	C₉×C₂²⋊C₄	—	3	2	no	—
117	C₉×C₂²⋊C₄	—	3	2	no	—
118	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
120	C₄²×C₉	—	3	2	no	—
121	C₂²×C₃×C₉	—	2	1	no	—
122	C₂²×C₃×C₉	—	2	1	no	—
123	C₂²×C₃×C₉	—	2	2	no	—
124	C₂²×C₃×C₉	—	2	2	no	—
125	C₂²×C₃×C₉	—	2	2	no	—
126	C₂²×C₃×C₉	—	4	4	no	—
127	C₂²×C₃×C₉	#41	1	2	yes	—
128	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
129	C₂×D₃×C₉	—	2	2	no	—
130	C₂×D₃×C₉	—	2	2	no	—
131	C₂×D₃×C₉	—	2	2	no	—
132	C₃×C₄×C₉	—	2	1	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	—	2	1	no	—
135	C₉×Dic₃	—	2	2	no	—
136	C₉×Dic₃	—	2	2	no	—
137	C₉×Dic₃	—	2	2	no	—
138	C₃×#126	—	3	2	no	—
139	C₃×#124	—	3	2	no	—
140	C₃×#123	—	3	2	no	—
141	C₃×C₂²⋊Q₈	—	3	1	no	—
142	C₃×#121	—	3	1	no	—
143	C₃×#121	—	3	2	no	—
144	C₃×#120	—	3	2	no	—
145	C₃×C₄×D₄	—	3	2	no	—
146	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
149	#953	C₂×C₉	1	2	yes	complemented
150	#930	C₂×C₉	1	1	yes	characteristic, complemented
151	C₄×#67	C₂×C₉	1	2	yes	complemented
152	#924	C₂×C₉	1	1	yes	characteristic, complemented
153	#885	C₂×C₉	1	2	yes	complemented
154	#884	C₂×C₉	1	2	yes	complemented
155	#883	C₂×C₉	1	2	yes	complemented
156	#879	C₂×C₉	1	2	yes	complemented
157	C₂³×C₃²	—	2	2	no	—
158	C₂³×C₃²	—	4	1	no	—
159	C₂³×C₃²	—	4	1	no	—
160	C₂³×C₃²	C₂³×C₃	1	2	yes	—
161	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
163	C₂×C₃²×C₄	—	4	1	no	—
164	C₂×C₃²×C₄	—	4	1	no	—
165	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
166	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₃×#67	—	2	4	no	—
169	C₃×#67	—	4	2	no	—
170	C₃×#67	—	4	2	no	—
171	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
172	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
173	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
174	C₃×D₁₂	—	4	1	no	—
175	C₃×C₄×D₃	—	4	2	no	—
176	C₃×Dic₆	—	4	1	no	—
177	C₂³×C₉	—	2	4	no	—
178	C₂³×C₉	—	2	2	no	—
179	C₂³×C₉	—	2	1	no	—
180	C₂³×C₉	—	2	2	no	—
181	C₂³×C₉	—	3	2	no	—
182	C₂³×C₉	—	4	1	no	—
183	C₂³×C₉	—	4	1	no	—
184	C₂³×C₉	—	4	2	no	—
185	C₂³×C₉	—	4	2	no	—
186	C₂³×C₉	C₂²×D₃	1	2	yes	—
187	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
188	Q₈×C₉	—	12	1	no	—
189	D₄×C₉	—	6	4	no	—
190	D₄×C₉	—	12	1	no	—
191	D₄×C₉	—	12	2	no	—
192	D₄×C₉	—	12	2	no	—
193	C₂×C₄×C₉	—	2	2	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	3	2	no	—
197	C₂×C₄×C₉	—	3	2	no	—
198	C₂×C₄×C₉	—	3	2	no	—
199	C₂×C₄×C₉	—	4	1	no	—
200	C₂×C₄×C₉	—	4	1	no	—
201	C₂×C₄×C₉	—	4	2	no	—
202	C₂×C₄×C₉	—	4	2	no	—
203	C₂×C₄×C₉	—	12	2	no	—
204	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
205	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
207	#538	—	3	1	no	Sylow
208	C₂×C₃×C₉	—	2	2	no	—
209	C₂×C₃×C₉	—	4	2	no	—
210	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
213	D₃×C₉	—	4	2	no	—
214	C₂⁴×C₃	—	2	1	no	—
215	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
216	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
217	C₂×C₃×Q₈	—	3	1	no	—
218	C₂×C₃×D₄	—	3	2	no	—
219	C₂×C₃×D₄	—	3	2	no	—
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	—	2	1	no	—
224	C₂²×C₃×C₄	—	3	2	no	—
225	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₂×#67	C₂²×C₉	1	2	yes	—
230	C₂×#67	C₂²×C₉	1	2	yes	—
231	C₂×#67	C₂²×C₉	1	2	yes	—
232	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
233	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
234	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	—	3	2	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	3	1	no	—
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	—	2	2	no	—
241	C₃×C₂²⋊C₄	—	3	2	no	—
242	C₃×C₂²⋊C₄	—	3	2	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
247	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
248	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
250	C₃×C₄²	—	3	2	no	—
251	#217	C₂²×C₉	1	2	yes	—
252	#217	C₂²×C₉	1	2	yes	—
253	#217	C₂²×C₉	1	2	yes	—
254	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
255	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
256	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
257	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
258	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
259	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
260	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
261	C₂²×C₃²	—	2	1	no	—
262	C₂²×C₃²	—	2	1	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	—	2	2	no	—
265	C₂²×C₃²	—	2	2	no	—
266	C₂²×C₃²	—	4	4	no	—
267	C₂²×C₃²	C₃×#41	1	2	yes	—
268	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
269	C₂×C₃×D₃	—	2	2	no	—
270	C₂×C₃×D₃	—	2	2	no	—
271	C₂×C₃×D₃	—	2	2	no	—
272	C₃²×C₄	—	2	1	no	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃×Dic₃	—	2	2	no	—
276	C₃×Dic₃	—	2	2	no	—
277	C₃×Dic₃	—	2	2	no	—
278	C₂²×C₉	—	2	2	no	—
279	C₂²×C₉	—	2	2	no	—
280	C₂²×C₉	—	2	1	no	—
281	C₂²×C₉	—	2	1	no	—
282	C₂²×C₉	—	2	4	no	—
283	C₂²×C₉	—	2	2	no	—
284	C₂²×C₉	—	2	2	no	—
285	C₂²×C₉	—	2	2	no	—
286	C₂²×C₉	—	2	1	no	—
287	C₂²×C₉	—	2	2	no	—
288	C₂²×C₉	—	4	2	no	—
289	C₂²×C₉	—	4	2	no	—
290	C₂²×C₉	—	4	8	no	—
291	C₂²×C₉	—	4	4	no	—
292	C₂²×C₉	—	6	2	no	—
293	C₂²×C₉	—	6	2	no	—
294	C₂²×C₉	—	6	2	no	—
295	C₂²×C₉	#235	1	2	yes	—
296	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
297	C₄×C₉	—	2	2	no	—
298	C₄×C₉	—	2	1	no	—
299	C₄×C₉	—	2	1	no	—
300	C₄×C₉	—	4	2	no	—
301	C₄×C₉	—	4	1	no	—
302	C₄×C₉	—	4	1	no	—
303	C₄×C₉	—	6	2	no	—
304	C₄×C₉	—	6	2	no	—
305	C₄×C₉	—	6	2	no	—
306	#126	—	3	2	no	—
307	#124	—	3	2	no	—
308	#123	—	3	2	no	—
309	C₂²⋊Q₈	—	3	1	no	—
310	#121	—	3	1	no	—
311	#121	—	3	2	no	—
312	#120	—	3	2	no	—
313	C₄×D₄	—	3	2	no	—
314	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
315	C₃×C₉	#538	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	1	no	—
320	C₂³×C₃	—	2	2	no	—
321	C₂³×C₃	—	3	2	no	—
322	C₂³×C₃	—	4	1	no	—
323	C₂³×C₃	—	4	1	no	—
324	C₂³×C₃	—	4	1	no	—
325	C₂³×C₃	—	4	1	no	—
326	C₂³×C₃	—	4	2	no	—
327	C₂³×C₃	—	4	2	no	—
328	C₂³×C₃	C₂³×C₉	1	2	yes	—
329	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
330	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
331	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂²×D₃	C₂³×C₉	1	2	yes	—
333	C₃×Q₈	—	12	1	no	—
334	C₃×D₄	—	6	4	no	—
335	C₃×D₄	—	12	1	no	—
336	C₃×D₄	—	12	2	no	—
337	C₃×D₄	—	12	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	3	2	no	—
342	C₂×C₃×C₄	—	3	2	no	—
343	C₂×C₃×C₄	—	3	2	no	—
344	C₂×C₃×C₄	—	4	1	no	—
345	C₂×C₃×C₄	—	4	1	no	—
346	C₂×C₃×C₄	—	4	1	no	—
347	C₂×C₃×C₄	—	4	1	no	—
348	C₂×C₃×C₄	—	4	2	no	—
349	C₂×C₃×C₄	—	4	2	no	—
350	C₂×C₃×C₄	—	12	2	no	—
351	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
352	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
355	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	#67	—	2	4	no	—
358	#67	—	4	2	no	—
359	#67	—	4	2	no	—
360	C₂×Dic₃	C₂³×C₉	1	2	yes	—
361	C₂×Dic₃	C₂³×C₉	1	2	yes	—
362	C₂×Dic₃	C₂³×C₉	1	2	yes	—
363	D₁₂	—	4	1	no	—
364	C₄×D₃	—	4	2	no	—
365	Dic₆	—	4	1	no	—
366	C₂×C₃²	—	2	2	no	—
367	C₂×C₃²	—	4	2	no	—
368	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
369	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
371	C₃×D₃	—	4	2	no	—
372	C₂×C₉	—	2	4	no	—
373	C₂×C₉	—	2	2	no	—
374	C₂×C₉	—	2	1	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	2	1	no	—
377	C₂×C₉	—	4	4	no	—
378	C₂×C₉	—	4	2	no	—
379	C₂×C₉	—	12	2	no	—
380	C₂×C₉	C₂×#235	1	1	yes	characteristic
381	C₂×C₉	#1004	1	1	yes	characteristic
382	C₂×C₉	#1004	1	1	yes	characteristic
383	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
384	C₂×Q₈	—	3	1	no	—
385	C₂×D₄	—	3	2	no	—
386	C₂×D₄	—	3	2	no	—
387	C₂×D₄	—	3	2	no	—
388	C₂×D₄	—	3	1	no	—
389	C₂²×C₄	—	3	2	no	—
390	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₄⋊C₄	—	3	1	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	2	no	—
400	C₂²⋊C₄	—	3	2	no	—
401	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
402	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
403	C₄²	—	3	2	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	4	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	2	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	1	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	4	no	—
422	C₂²×C₃	—	4	8	no	—
423	C₂²×C₃	—	4	4	no	—
424	C₂²×C₃	—	6	2	no	—
425	C₂²×C₃	—	6	2	no	—
426	C₂²×C₃	—	6	2	no	—
427	C₂²×C₃	C₉×#41	1	2	yes	—
428	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
429	C₂²×C₃	C₃×#235	1	2	yes	—
430	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
431	C₂×D₃	—	2	2	no	—
432	C₂×D₃	—	2	2	no	—
433	C₂×D₃	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	—	6	2	no	—
444	C₃×C₄	—	6	2	no	—
445	C₃×C₄	—	6	2	no	—
446	Dic₃	—	2	2	no	—
447	Dic₃	—	2	2	no	—
448	Dic₃	—	2	2	no	—
449	C₃²	C₃×#538	1	1	yes	characteristic
450	C₉	—	2	1	no	—
451	C₉	#5494	1	1	yes	characteristic, direct product factor
452	C₂³	—	2	2	no	—
453	C₂³	—	3	2	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	C₂²×D₃×C₉	1	2	yes	—
457	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
458	Q₈	—	12	1	no	—
459	D₄	—	6	4	no	—
460	D₄	—	12	1	no	—
461	D₄	—	12	2	no	—
462	D₄	—	12	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	3	2	no	—
465	C₂×C₄	—	3	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	12	2	no	—
469	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
470	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
472	C₂×C₃	—	2	4	no	—
473	C₂×C₃	—	2	2	no	—
474	C₂×C₃	—	2	2	no	—
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	2	1	no	—
477	C₂×C₃	—	2	1	no	—
478	C₂×C₃	—	4	4	no	—
479	C₂×C₃	—	4	2	no	—
480	C₂×C₃	—	4	2	no	—
481	C₂×C₃	—	12	2	no	—
482	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
483	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
486	C₂×C₃	C₃×#1004	1	1	yes	characteristic
487	C₂×C₃	C₃×#1004	1	1	yes	characteristic
488	D₃	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	6	2	no	—
496	C₂²	—	6	2	no	—
497	C₂²	—	6	2	no	—
498	C₂²	C₉×#235	1	2	yes	—
499	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	6	2	no	—
504	C₄	—	6	2	no	—
505	C₄	—	6	2	no	—
506	C₃	—	2	1	no	—
507	C₃	C₉×#538	1	1	yes	characteristic, complemented
508	C₃	C₃×#5494	1	1	yes	characteristic
509	C₂	—	2	2	no	—
510	C₂	—	4	2	no	—
511	C₂	—	12	2	no	—
512	C₂	C₂×C₉×#235	1	1	yes	characteristic
513	C₂	C₉×#1004	1	1	yes	characteristic
514	C₂	C₉×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5494	C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
2. C₉×#953	C₂	semidirect
3. C₉×#930	C₂	semidirect
4. C₄×C₉×#67	C₂	semidirect
5. C₉×#924	C₂	semidirect
6. C₉×#885	C₂	semidirect
7. C₉×#884	C₂	semidirect
8. C₉×#883	C₂	semidirect
9. C₉×#879	C₂	semidirect
18. C₂×C₉×D₁₂	C₂²	semidirect
19. C₂×C₄×D₃×C₉	C₂²	semidirect
20. C₂×C₉×Dic₆	C₂²	semidirect
26. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
27. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₉×C₄⋊Dic₃	C₂²	semidirect
29. C₉×C₄⋊Dic₃	C₂²	semidirect
30. C₉×Dic₃⋊C₄	C₂²	semidirect
31. C₉×Dic₃⋊C₄	C₂²	semidirect
32. C₄×C₉×Dic₃	C₂²	semidirect
51. C₂×C₉×C₂²⋊C₄	D₃	semidirect
73. #5494	C₉	direct (N × H)
147. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
149. #953	C₂×C₉	semidirect
150. #930	C₂×C₉	semidirect
151. C₄×#67	C₂×C₉	semidirect
152. #924	C₂×C₉	semidirect
153. #885	C₂×C₉	semidirect
154. #884	C₂×C₉	semidirect
155. #883	C₂×C₉	semidirect
156. #879	C₂×C₉	semidirect
232. C₂×D₁₂	C₂²×C₉	semidirect
233. C₂×C₄×D₃	C₂²×C₉	semidirect
234. C₂×Dic₆	C₂²×C₉	semidirect
254. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
255. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
256. C₄⋊Dic₃	C₂²×C₉	semidirect
257. C₄⋊Dic₃	C₂²×C₉	semidirect
258. Dic₃⋊C₄	C₂²×C₉	semidirect
259. Dic₃⋊C₄	C₂²×C₉	semidirect
260. C₄×Dic₃	C₂²×C₉	semidirect
314. C₂×C₂²⋊C₄	D₃×C₉	semidirect
315. C₃×C₉	#538	semidirect
451. C₉	#5494	direct (N × H)
507. C₃	C₉×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×C₂²⋊C₄	2
C₉×#953	2
C₉×#930	2
C₄×C₉×#67	2
C₉×#924	2
C₉×#885	2
C₉×#884	2
C₉×#883	2
C₉×#879	2
C₃×#5494	3
C₉×#538	3

Subgroups — C9×#5494 #13152353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5494 #13152353