Subgroups — C₉×#5617 #13152834

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#939	C₂	1	2	yes	maximal, complemented
3	C₉×#937	C₂	1	2	yes	maximal, complemented
4	D₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#898	C₂	1	2	yes	maximal, complemented
8	C₉×#886	C₂	1	2	yes	maximal, complemented
9	C₉×#885	C₂	1	2	yes	maximal, complemented
10	C₃×#5617	C₃	1	1	yes	maximal, characteristic
11	C₉×#538	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	2	yes	complemented
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, complemented
30	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
32	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
33	C₃²×#121	C₂×C₃	1	1	yes	characteristic
34	C₃×#939	C₂×C₃	1	2	yes	—
35	C₃×#937	C₂×C₃	1	2	yes	—
36	C₃×D₄×Dic₃	C₂×C₃	1	2	yes	—
37	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
38	C₃×#924	C₂×C₃	1	1	yes	characteristic
39	C₃×#898	C₂×C₃	1	2	yes	—
40	C₃×#886	C₂×C₃	1	2	yes	—
41	C₃×#885	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	—	2	1	no	—
47	C₉×#121	—	3	2	no	—
48	C₉×#121	D₃	1	1	yes	characteristic, complemented
49	C₉×#120	—	3	2	no	—
50	C₄×D₄×C₉	—	3	2	no	—
51	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
52	C₂³×C₃×C₉	C₂³	1	2	yes	—
53	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
54	C₂²×D₃×C₉	—	2	2	no	—
55	C₂²×D₃×C₉	—	4	1	no	—
56	C₂²×D₃×C₉	—	4	1	no	—
57	C₂²×D₃×C₉	C₂³	1	2	yes	—
58	C₃×D₄×C₉	—	2	4	no	—
59	C₃×D₄×C₉	—	4	1	no	—
60	C₂×C₃×C₄×C₉	—	4	1	no	—
61	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₉×#67	—	4	2	no	—
65	C₉×#67	—	4	2	no	—
66	C₂×C₉×Dic₃	—	4	1	no	—
67	C₂×C₉×Dic₃	—	4	2	no	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	2	yes	—
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₉×Dic₆	—	4	1	no	—
72	C₃×#538	—	3	1	no	—
73	#5617	C₉	1	1	yes	characteristic, direct product factor
74	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
76	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
79	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
80	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
82	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
83	C₂⁴×C₉	—	3	1	no	—
84	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃×#217	C₂²×C₃	1	2	yes	—
87	C₃×#217	C₂²×C₃	1	2	yes	—
88	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	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	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
96	C₂×Q₈×C₉	—	3	1	no	—
97	C₂×D₄×C₉	—	2	2	no	—
98	C₂×D₄×C₉	—	2	1	no	—
99	C₂×D₄×C₉	—	3	2	no	—
100	C₂×D₄×C₉	—	3	2	no	—
101	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
102	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂²×C₄×C₉	—	2	1	no	—
104	C₂²×C₄×C₉	—	3	1	no	—
105	C₂²×C₄×C₉	—	3	2	no	—
106	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₄⋊C₄	—	3	2	no	—
110	C₉×C₄⋊C₄	—	3	1	no	—
111	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	2	no	—
119	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
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	#41	1	2	yes	—
127	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
128	C₂×D₃×C₉	—	2	2	no	—
129	C₂×D₃×C₉	—	2	2	no	—
130	C₂×D₃×C₉	—	2	2	no	—
131	C₂×D₃×C₉	—	4	4	no	—
132	C₃×C₄×C₉	—	2	2	no	—
133	C₃×C₄×C₉	—	2	1	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	—	2	1	no	—
143	C₃×#121	—	3	2	no	—
144	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
145	C₃×#121	C₃×D₃	1	1	yes	characteristic
146	C₃×#120	—	3	2	no	—
147	C₃×C₄×D₄	—	3	2	no	—
148	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
149	#939	C₂×C₉	1	2	yes	complemented
150	#937	C₂×C₉	1	2	yes	complemented
151	D₄×Dic₃	C₂×C₉	1	2	yes	complemented
152	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
153	#924	C₂×C₉	1	1	yes	characteristic, complemented
154	#898	C₂×C₉	1	2	yes	complemented
155	#886	C₂×C₉	1	2	yes	complemented
156	#885	C₂×C₉	1	2	yes	complemented
157	C₂³×C₃²	C₂³×C₃	1	2	yes	—
158	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×D₃	—	2	2	no	—
160	C₂²×C₃×D₃	—	4	1	no	—
161	C₂²×C₃×D₃	—	4	1	no	—
162	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
163	C₃²×D₄	—	2	4	no	—
164	C₃²×D₄	—	4	1	no	—
165	C₂×C₃²×C₄	—	4	1	no	—
166	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
167	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₃×#67	—	4	2	no	—
170	C₃×#67	—	4	2	no	—
171	C₂×C₃×Dic₃	—	4	1	no	—
172	C₂×C₃×Dic₃	—	4	2	no	—
173	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
174	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
175	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
176	C₃×Dic₆	—	4	1	no	—
177	C₂³×C₉	—	2	1	no	—
178	C₂³×C₉	—	2	2	no	—
179	C₂³×C₉	—	3	2	no	—
180	C₂³×C₉	—	6	2	no	—
181	C₂³×C₉	—	12	1	no	—
182	C₂³×C₉	—	12	1	no	—
183	C₂³×C₉	C₂²×D₃	1	2	yes	—
184	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
185	Q₈×C₉	—	12	1	no	—
186	D₄×C₉	—	2	4	no	—
187	D₄×C₉	—	4	4	no	—
188	D₄×C₉	—	4	1	no	—
189	D₄×C₉	—	4	2	no	—
190	D₄×C₉	—	12	2	no	—
191	D₄×C₉	—	12	2	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	2	no	—
195	C₂×C₄×C₉	—	3	2	no	—
196	C₂×C₄×C₉	—	3	2	no	—
197	C₂×C₄×C₉	—	3	2	no	—
198	C₂×C₄×C₉	—	4	1	no	—
199	C₂×C₄×C₉	—	4	2	no	—
200	C₂×C₄×C₉	—	12	1	no	—
201	C₂×C₄×C₉	—	12	2	no	—
202	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
203	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	#538	—	3	1	no	Sylow
206	C₂×C₃×C₉	—	2	2	no	—
207	C₂×C₃×C₉	—	4	2	no	—
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
211	D₃×C₉	—	4	2	no	—
212	C₂⁴×C₃	—	3	1	no	—
213	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₃×Q₈	—	3	1	no	—
215	C₂×C₃×D₄	—	2	2	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	—	3	2	no	—
218	C₂×C₃×D₄	—	3	2	no	—
219	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
220	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
221	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
222	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	3	1	no	—
225	C₂²×C₃×C₄	—	3	2	no	—
226	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
228	C₂×#67	C₂²×C₉	1	2	yes	—
229	C₂×#67	C₂²×C₉	1	2	yes	—
230	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
231	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
232	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	—	3	1	no	—
237	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	—	3	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	complemented
247	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
248	C₃×C₄²	—	3	2	no	—
249	#217	C₂²×C₉	1	2	yes	—
250	#217	C₂²×C₉	1	2	yes	complemented
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
253	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
254	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
255	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
256	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
257	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
258	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
259	C₂²×C₃²	—	2	1	no	—
260	C₂²×C₃²	—	2	1	no	—
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	2	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	C₃×#41	1	2	yes	—
265	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
266	C₂×C₃×D₃	—	2	2	no	—
267	C₂×C₃×D₃	—	2	2	no	—
268	C₂×C₃×D₃	—	2	2	no	—
269	C₂×C₃×D₃	—	4	4	no	—
270	C₃²×C₄	—	2	1	no	—
271	C₃²×C₄	—	2	2	no	—
272	C₃²×C₄	—	2	1	no	—
273	C₃×Dic₃	—	2	2	no	—
274	C₃×Dic₃	—	2	2	no	—
275	C₃×Dic₃	—	2	2	no	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	—	2	1	no	—
278	C₂²×C₉	—	2	2	no	—
279	C₂²×C₉	—	2	2	no	—
280	C₂²×C₉	—	2	2	no	—
281	C₂²×C₉	—	2	1	no	—
282	C₂²×C₉	—	2	2	no	—
283	C₂²×C₉	—	4	1	no	—
284	C₂²×C₉	—	4	1	no	—
285	C₂²×C₉	—	4	2	no	—
286	C₂²×C₉	—	4	2	no	—
287	C₂²×C₉	—	4	2	no	—
288	C₂²×C₉	—	6	2	no	—
289	C₂²×C₉	—	6	2	no	—
290	C₂²×C₉	—	6	2	no	—
291	C₂²×C₉	—	12	4	no	—
292	C₂²×C₉	#237	1	2	yes	—
293	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
294	C₄×C₉	—	2	2	no	—
295	C₄×C₉	—	2	2	no	—
296	C₄×C₉	—	2	1	no	—
297	C₄×C₉	—	2	1	no	—
298	C₄×C₉	—	4	1	no	—
299	C₄×C₉	—	4	2	no	—
300	C₄×C₉	—	6	2	no	—
301	C₄×C₉	—	6	2	no	—
302	C₄×C₉	—	6	2	no	—
303	#126	—	3	2	no	—
304	#124	—	3	2	no	—
305	#123	—	3	2	no	—
306	C₂²⋊Q₈	—	3	1	no	—
307	#121	—	3	2	no	—
308	#121	D₃×C₉	1	1	yes	characteristic, complemented
309	#120	—	3	2	no	—
310	C₄×D₄	—	3	2	no	—
311	C₂×C₂²⋊C₄	—	3	1	no	—
312	C₃×C₉	#538	1	1	yes	characteristic, complemented, Sylow
313	C₂³×C₃	—	2	1	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	3	2	no	—
316	C₂³×C₃	—	6	2	no	—
317	C₂³×C₃	—	12	1	no	—
318	C₂³×C₃	—	12	1	no	—
319	C₂³×C₃	C₂³×C₉	1	2	yes	—
320	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
321	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
322	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂²×D₃	—	2	2	no	—
324	C₂²×D₃	—	4	1	no	—
325	C₂²×D₃	—	4	1	no	—
326	C₂²×D₃	C₂³×C₉	1	2	yes	—
327	C₃×Q₈	—	12	1	no	—
328	C₃×D₄	—	2	4	no	—
329	C₃×D₄	—	2	4	no	—
330	C₃×D₄	—	4	4	no	—
331	C₃×D₄	—	4	1	no	—
332	C₃×D₄	—	4	1	no	—
333	C₃×D₄	—	4	2	no	—
334	C₃×D₄	—	12	2	no	—
335	C₃×D₄	—	12	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	3	2	no	—
340	C₂×C₃×C₄	—	3	2	no	—
341	C₂×C₃×C₄	—	3	2	no	—
342	C₂×C₃×C₄	—	4	1	no	—
343	C₂×C₃×C₄	—	4	1	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	12	1	no	—
346	C₂×C₃×C₄	—	12	2	no	—
347	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
348	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
351	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
353	#67	—	4	2	no	—
354	#67	—	4	2	no	—
355	C₂×Dic₃	—	4	1	no	—
356	C₂×Dic₃	—	4	2	no	—
357	C₂×Dic₃	C₂³×C₉	1	2	yes	—
358	C₂×Dic₃	C₂³×C₉	1	2	yes	—
359	C₂×Dic₃	C₂³×C₉	1	2	yes	—
360	Dic₆	—	4	1	no	—
361	C₂×C₃²	—	2	2	no	—
362	C₂×C₃²	—	4	2	no	—
363	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
364	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₃×D₃	—	4	2	no	—
367	C₂×C₉	—	2	2	no	—
368	C₂×C₉	—	2	1	no	—
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	4	2	no	—
372	C₂×C₉	—	4	2	no	—
373	C₂×C₉	—	8	2	no	—
374	C₂×C₉	—	12	2	no	—
375	C₂×C₉	C₂×#237	1	1	yes	characteristic
376	C₂×C₉	#1004	1	1	yes	characteristic
377	C₂×C₉	#1009	1	1	yes	characteristic
378	C₂⁴	—	3	1	no	—
379	C₂×Q₈	—	3	1	no	—
380	C₂×D₄	—	3	2	no	—
381	C₂×D₄	—	3	2	no	—
382	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
383	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	3	2	no	—
386	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
387	C₄⋊C₄	—	3	2	no	—
388	C₄⋊C₄	—	3	2	no	—
389	C₄⋊C₄	—	3	1	no	—
390	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
391	C₂²⋊C₄	—	3	2	no	—
392	C₂²⋊C₄	—	3	2	no	—
393	C₂²⋊C₄	—	3	2	no	—
394	C₂²⋊C₄	—	3	2	no	—
395	C₂²⋊C₄	—	3	2	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
398	C₄²	—	3	2	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	2	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	4	1	no	—
412	C₂²×C₃	—	4	1	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	6	2	no	—
417	C₂²×C₃	—	6	2	no	—
418	C₂²×C₃	—	6	2	no	—
419	C₂²×C₃	—	12	4	no	—
420	C₂²×C₃	C₉×#41	1	2	yes	—
421	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
422	C₂²×C₃	C₃×#237	1	2	yes	—
423	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	4	4	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	2	1	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	—	6	2	no	—
438	C₃×C₄	—	6	2	no	—
439	C₃×C₄	—	6	2	no	—
440	Dic₃	—	2	2	no	—
441	Dic₃	—	2	2	no	—
442	Dic₃	—	2	2	no	—
443	C₃²	C₃×#538	1	1	yes	characteristic
444	C₉	—	2	1	no	—
445	C₉	#5617	1	1	yes	characteristic, direct product factor
446	C₂³	—	3	2	no	—
447	C₂³	—	6	2	no	—
448	C₂³	—	12	1	no	—
449	C₂³	—	12	1	no	—
450	C₂³	C₂²×D₃×C₉	1	2	yes	—
451	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
452	Q₈	—	12	1	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	1	no	—
455	D₄	—	12	2	no	—
456	D₄	—	12	2	no	—
457	C₂×C₄	—	3	2	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	12	1	no	—
462	C₂×C₄	—	12	2	no	—
463	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
464	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
466	C₂×C₃	—	2	2	no	—
467	C₂×C₃	—	2	2	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	4	2	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	—	4	2	no	—
474	C₂×C₃	—	8	2	no	—
475	C₂×C₃	—	12	2	no	—
476	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
477	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
480	C₂×C₃	C₃×#1004	1	1	yes	characteristic
481	C₂×C₃	C₃×#1009	1	1	yes	characteristic
482	D₃	—	4	2	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	6	2	no	—
489	C₂²	—	6	2	no	—
490	C₂²	—	6	2	no	—
491	C₂²	—	12	4	no	—
492	C₂²	C₉×#237	1	2	yes	—
493	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	6	2	no	—
498	C₄	—	6	2	no	—
499	C₄	—	6	2	no	—
500	C₃	—	2	1	no	—
501	C₃	C₉×#538	1	1	yes	characteristic, complemented
502	C₃	C₃×#5617	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	12	2	no	—
506	C₂	C₂×C₉×#237	1	1	yes	characteristic
507	C₂	C₉×#1004	1	1	yes	characteristic
508	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×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5617	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#121	C₂	semidirect
2. C₉×#939	C₂	semidirect
3. C₉×#937	C₂	semidirect
4. D₄×C₉×Dic₃	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₉×#924	C₂	semidirect
7. C₉×#898	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#885	C₂	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
19. C₂²×C₉×Dic₃	C₂²	semidirect
20. C₂×C₉×Dic₆	C₂²	semidirect
21. C₃×C₉×C₄⋊C₄	C₂²	semidirect
22. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
24. C₉×#217	C₂²	semidirect
29. C₉×C₄⋊Dic₃	C₂²	semidirect
30. C₉×C₄⋊Dic₃	C₂²	semidirect
31. C₉×Dic₃⋊C₄	C₂²	semidirect
32. C₄×C₉×Dic₃	C₂²	semidirect
48. C₉×#121	D₃	semidirect
73. #5617	C₉	direct (N × H)
102. C₂×D₄×C₉	C₂×D₃	semidirect
111. C₉×C₄⋊C₄	C₂×D₃	semidirect
119. C₉×C₂²⋊C₄	C₂×D₃	semidirect
144. C₃×#121	C₂×C₉	semidirect
149. #939	C₂×C₉	semidirect
150. #937	C₂×C₉	semidirect
151. D₄×Dic₃	C₂×C₉	semidirect
152. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
153. #924	C₂×C₉	semidirect
154. #898	C₂×C₉	semidirect
155. #886	C₂×C₉	semidirect
156. #885	C₂×C₉	semidirect
220. C₂×C₃×D₄	C₂²×C₉	semidirect
231. C₂²×Dic₃	C₂²×C₉	semidirect
232. C₂×Dic₆	C₂²×C₉	semidirect
237. C₃×C₄⋊C₄	C₂²×C₉	semidirect
246. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
250. #217	C₂²×C₉	semidirect
255. C₄⋊Dic₃	C₂²×C₉	semidirect
256. C₄⋊Dic₃	C₂²×C₉	semidirect
257. Dic₃⋊C₄	C₂²×C₉	semidirect
258. C₄×Dic₃	C₂²×C₉	semidirect
308. #121	D₃×C₉	semidirect
312. C₃×C₉	#538	semidirect
383. C₂×D₄	C₂×D₃×C₉	semidirect
390. C₄⋊C₄	C₂×D₃×C₉	semidirect
397. C₂²⋊C₄	C₂×D₃×C₉	semidirect
445. C₉	#5617	direct (N × H)
501. 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
C₃×C₉×#121	2
C₉×#939	2
C₉×#937	2
D₄×C₉×Dic₃	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#924	2
C₉×#898	2
C₉×#886	2
C₉×#885	2
C₃×#5617	3
C₉×#538	3

Subgroups — C9×#5617 #13152834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5617 #13152834