Subgroups — C₉×#5630 #13152929

Order 1728.

1076 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#895	C₂	1	2	yes	maximal, complemented
8	C₉×#894	C₂	1	2	yes	maximal, complemented
9	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#882	C₂	1	2	yes	maximal, complemented
11	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5630	C₃	1	1	yes	maximal, characteristic
13	C₉×#546	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₉×#239	—	2	4	no	—
19	C₂×C₉×D₁₂	—	2	4	no	—
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₉×D₁₂	C₂²	1	2	yes	—
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
24	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₉×#217	C₂²	1	1	yes	characteristic
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#947	C₂×C₃	1	1	yes	characteristic
43	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
44	C₃×#895	C₂×C₃	1	1	yes	characteristic
45	C₃×#895	C₂×C₃	1	2	yes	—
46	C₃×#894	C₂×C₃	1	2	yes	—
47	C₃×#893	C₂×C₃	1	1	yes	characteristic
48	C₃×#882	C₂×C₃	1	2	yes	—
49	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×#123	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	2	1	no	—
55	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	2	no	—
58	C₉×#120	—	3	2	no	—
59	C₄×D₄×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	1	no	—
61	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	—	2	4	no	—
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	4	2	no	—
66	C₂²×D₃×C₉	C₂³	1	2	yes	—
67	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
68	C₂²×D₃×C₉	C₂³	1	2	yes	—
69	C₃×Q₈×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	—	2	2	no	—
71	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
72	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×#67	—	2	2	no	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₉×D₁₂	—	2	4	no	—
80	C₉×D₁₂	—	2	4	no	—
81	C₉×D₁₂	—	2	2	no	—
82	C₉×D₁₂	—	4	2	no	—
83	C₉×D₁₂	D₄	1	4	yes	complemented
84	C₄×D₃×C₉	—	2	4	no	—
85	C₄×D₃×C₉	—	2	2	no	—
86	C₄×D₃×C₉	—	4	2	no	—
87	C₃×#546	—	3	1	no	—
88	#5630	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
90	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
93	C₃×#239	—	2	4	no	—
94	C₂×C₃×D₁₂	—	2	4	no	—
95	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
98	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
99	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
103	C₂⁴×C₉	—	3	2	no	—
104	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×#217	C₂²×C₃	1	1	yes	characteristic
108	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	2	1	no	—
117	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	2	no	—
122	C₂×D₄×C₉	—	3	1	no	—
123	C₂×D₄×C₉	—	3	2	no	—
124	C₂×D₄×C₉	—	6	4	no	—
125	C₂²×C₄×C₉	—	2	1	no	—
126	C₂²×C₄×C₉	—	3	2	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	3	2	no	—
129	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
130	C₉×C₄⋊C₄	—	2	1	no	—
131	C₉×C₄⋊C₄	—	2	2	no	—
132	C₉×C₄⋊C₄	—	3	1	no	—
133	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
134	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
135	C₉×C₂²⋊C₄	—	2	2	no	—
136	C₉×C₂²⋊C₄	—	3	1	no	—
137	C₉×C₂²⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	2	no	—
140	C₉×C₂²⋊C₄	—	3	1	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
143	C₄²×C₉	—	3	1	no	—
144	C₂²×C₃×C₉	—	2	1	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	#41	1	2	yes	complemented
147	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
148	C₂×D₃×C₉	—	2	2	no	—
149	C₂×D₃×C₉	—	2	2	no	—
150	C₂×D₃×C₉	—	2	1	no	—
151	C₂×D₃×C₉	—	2	2	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	2	no	—
154	C₂×D₃×C₉	—	2	1	no	—
155	C₂×D₃×C₉	—	2	2	no	—
156	C₂×D₃×C₉	—	4	8	no	—
157	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
158	C₃×C₄×C₉	—	2	2	no	—
159	C₃×C₄×C₉	—	2	1	no	—
160	C₃×C₄×C₉	—	2	2	no	—
161	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
162	C₉×Dic₃	—	2	1	no	—
163	C₉×Dic₃	—	2	1	no	—
164	C₉×Dic₃	—	2	1	no	—
165	C₂×C₃×#41	—	3	1	no	—
166	C₂²×C₃×D₄	—	3	1	no	—
167	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#124	—	3	1	no	—
170	C₃×#123	—	3	2	no	—
171	C₃×C₂²⋊Q₈	—	2	1	no	—
172	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
173	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
174	C₃×#121	—	3	1	no	—
175	C₃×#121	—	3	2	no	—
176	C₃×#120	—	3	2	no	—
177	C₃×C₄×D₄	—	3	1	no	—
178	C₃×C₄×D₄	—	3	1	no	—
179	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
180	#947	C₂×C₉	1	1	yes	characteristic, complemented
181	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
182	#895	C₂×C₉	1	1	yes	characteristic, complemented
183	#895	C₂×C₉	1	2	yes	complemented
184	#894	C₂×C₉	1	2	yes	complemented
185	#893	C₂×C₉	1	1	yes	characteristic, complemented
186	#882	C₂×C₉	1	2	yes	complemented
187	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
188	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₃×D₃	—	2	4	no	—
190	C₂²×C₃×D₃	—	2	4	no	—
191	C₂²×C₃×D₃	—	4	2	no	—
192	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
193	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
195	C₃²×Q₈	—	2	2	no	—
196	C₂×C₃²×C₄	—	2	2	no	—
197	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
199	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
200	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₃×#67	—	2	2	no	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
205	C₃×D₁₂	—	2	4	no	—
206	C₃×D₁₂	—	2	4	no	—
207	C₃×D₁₂	—	2	2	no	—
208	C₃×D₁₂	—	4	2	no	—
209	C₃×D₁₂	C₃×D₄	1	4	yes	—
210	C₃×C₄×D₃	—	2	4	no	—
211	C₃×C₄×D₃	—	2	2	no	—
212	C₃×C₄×D₃	—	4	2	no	—
213	C₂³×C₉	—	2	1	no	—
214	C₂³×C₉	—	3	2	no	—
215	C₂³×C₉	—	3	2	no	—
216	C₂³×C₉	—	3	1	no	—
217	C₂³×C₉	—	6	4	no	—
218	C₂³×C₉	—	6	4	no	—
219	C₂³×C₉	—	12	2	no	—
220	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
221	Q₈×C₉	—	2	2	no	—
222	Q₈×C₉	—	4	2	no	—
223	D₄×C₉	—	3	4	no	—
224	D₄×C₉	—	6	4	no	—
225	D₄×C₉	—	6	4	no	—
226	D₄×C₉	—	6	2	no	—
227	D₄×C₉	—	6	2	no	—
228	D₄×C₉	—	12	2	no	—
229	C₂×C₄×C₉	—	2	2	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	2	2	no	—
232	C₂×C₄×C₉	—	2	2	no	—
233	C₂×C₄×C₉	—	2	1	no	—
234	C₂×C₄×C₉	—	3	1	no	—
235	C₂×C₄×C₉	—	3	1	no	—
236	C₂×C₄×C₉	—	3	1	no	—
237	C₂×C₄×C₉	—	4	2	no	—
238	C₂×C₄×C₉	—	6	4	no	—
239	C₂×C₄×C₉	—	6	2	no	—
240	C₂×C₄×C₉	—	12	2	no	—
241	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
242	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
243	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
245	#546	—	3	1	no	Sylow
246	C₂×C₃×C₉	—	2	2	no	—
247	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
250	D₃×C₉	—	2	4	no	—
251	D₃×C₉	—	4	1	no	—
252	D₃×C₉	—	4	2	no	—
253	C₂⁴×C₃	—	3	2	no	—
254	C₂³×D₃	C₂²×C₉	1	2	yes	—
255	C₃×#41	—	6	4	no	—
256	C₂×C₃×Q₈	—	2	1	no	—
257	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
258	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
259	C₂×C₃×D₄	—	3	1	no	—
260	C₂×C₃×D₄	—	3	1	no	—
261	C₂×C₃×D₄	—	3	2	no	—
262	C₂×C₃×D₄	—	3	2	no	—
263	C₂×C₃×D₄	—	3	1	no	—
264	C₂×C₃×D₄	—	3	2	no	—
265	C₂×C₃×D₄	—	6	4	no	—
266	C₂²×C₃×C₄	—	2	1	no	—
267	C₂²×C₃×C₄	—	3	2	no	—
268	C₂²×C₃×C₄	—	3	1	no	—
269	C₂²×C₃×C₄	—	3	2	no	—
270	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
272	C₂×#67	C₂²×C₉	1	1	yes	characteristic
273	#239	—	2	4	no	—
274	C₂×D₁₂	—	2	4	no	—
275	C₂×D₁₂	C₂²×C₉	1	2	yes	—
276	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
277	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
278	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
279	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
280	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
281	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
282	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
283	C₃×C₄⋊C₄	—	2	1	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	3	1	no	—
286	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
287	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
288	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	—	3	1	no	—
292	C₃×C₂²⋊C₄	—	3	2	no	—
293	C₃×C₂²⋊C₄	—	3	2	no	—
294	C₃×C₂²⋊C₄	—	3	2	no	—
295	C₃×C₂²⋊C₄	—	3	1	no	—
296	C₃×C₂²⋊C₄	—	3	2	no	—
297	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
298	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
299	C₃×C₄²	—	3	1	no	—
300	#217	C₂²×C₉	1	1	yes	characteristic
301	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
302	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
303	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
304	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
305	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
306	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
307	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
308	C₂²×C₃²	—	2	1	no	—
309	C₂²×C₃²	—	2	1	no	—
310	C₂²×C₃²	C₃×#41	1	2	yes	—
311	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
312	C₂×C₃×D₃	—	2	2	no	—
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	—	2	1	no	—
315	C₂×C₃×D₃	—	2	2	no	—
316	C₂×C₃×D₃	—	2	1	no	—
317	C₂×C₃×D₃	—	2	2	no	—
318	C₂×C₃×D₃	—	2	1	no	—
319	C₂×C₃×D₃	—	2	2	no	—
320	C₂×C₃×D₃	—	4	8	no	—
321	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
322	C₃²×C₄	—	2	2	no	—
323	C₃²×C₄	—	2	1	no	—
324	C₃²×C₄	—	2	2	no	—
325	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
326	C₃×Dic₃	—	2	1	no	—
327	C₃×Dic₃	—	2	1	no	—
328	C₃×Dic₃	—	2	1	no	—
329	C₂²×C₉	—	2	1	no	—
330	C₂²×C₉	—	2	1	no	—
331	C₂²×C₉	—	2	1	no	—
332	C₂²×C₉	—	2	2	no	—
333	C₂²×C₉	—	3	4	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	4	1	no	—
336	C₂²×C₉	—	6	2	no	—
337	C₂²×C₉	—	6	2	no	—
338	C₂²×C₉	—	6	1	no	—
339	C₂²×C₉	—	6	2	no	—
340	C₂²×C₉	—	6	1	no	—
341	C₂²×C₉	—	6	2	no	—
342	C₂²×C₉	—	6	1	no	—
343	C₂²×C₉	—	6	2	no	—
344	C₂²×C₉	—	12	8	no	—
345	C₂²×C₉	#239	1	2	yes	complemented
346	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
347	C₄×C₉	—	2	1	no	—
348	C₄×C₉	—	2	2	no	—
349	C₄×C₉	—	2	2	no	—
350	C₄×C₉	—	2	2	no	—
351	C₄×C₉	—	4	2	no	—
352	C₄×C₉	—	4	1	no	—
353	C₄×C₉	—	4	2	no	—
354	C₄×C₉	—	6	1	no	—
355	C₄×C₉	—	6	1	no	—
356	C₄×C₉	—	6	1	no	—
357	C₄×C₉	D₃×D₄	1	2	yes	—
358	C₂×#41	—	3	1	no	—
359	C₂²×D₄	—	3	1	no	—
360	#124	—	3	1	no	—
361	#123	—	3	2	no	—
362	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
363	#121	—	3	1	no	—
364	#121	—	3	2	no	—
365	#120	—	3	2	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	C₂×C₂²⋊C₄	—	3	2	no	—
369	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
370	C₂³×C₃	—	2	1	no	—
371	C₂³×C₃	—	3	2	no	—
372	C₂³×C₃	—	3	2	no	—
373	C₂³×C₃	—	3	1	no	—
374	C₂³×C₃	—	6	4	no	—
375	C₂³×C₃	—	6	4	no	—
376	C₂³×C₃	—	12	2	no	—
377	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
378	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
379	C₂²×D₃	—	2	4	no	—
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	4	2	no	—
382	C₂²×D₃	C₂³×C₉	1	2	yes	—
383	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
384	C₂²×D₃	C₂³×C₉	1	2	yes	—
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×Q₈	—	4	2	no	—
388	C₃×D₄	—	3	4	no	—
389	C₃×D₄	—	6	4	no	—
390	C₃×D₄	—	6	4	no	—
391	C₃×D₄	—	6	2	no	—
392	C₃×D₄	—	6	2	no	—
393	C₃×D₄	—	12	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	3	1	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	1	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	—	6	4	no	—
405	C₂×C₃×C₄	—	6	2	no	—
406	C₂×C₃×C₄	—	12	2	no	—
407	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
409	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
410	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
412	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
413	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
415	#67	—	2	2	no	—
416	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
417	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
418	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
419	D₁₂	—	2	4	no	—
420	D₁₂	—	2	4	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	—	4	2	no	—
423	D₁₂	D₄×C₉	1	4	yes	complemented
424	C₄×D₃	—	2	4	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	4	2	no	—
427	C₂×C₃²	—	2	2	no	—
428	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
429	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
430	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
431	C₃×D₃	—	2	4	no	—
432	C₃×D₃	—	4	1	no	—
433	C₃×D₃	—	4	2	no	—
434	C₂×C₉	—	2	2	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	2	1	no	—
438	C₂×C₉	—	4	2	no	—
439	C₂×C₉	—	6	4	no	—
440	C₂×C₉	—	12	1	no	—
441	C₂×C₉	—	12	2	no	—
442	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
443	C₂×C₉	C₂×#239	1	1	yes	characteristic
444	C₂×C₉	#1009	1	1	yes	characteristic
445	C₂⁴	—	3	2	no	—
446	#41	—	6	4	no	—
447	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	2	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	1	no	—
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	6	4	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
461	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
462	C₂²⋊C₄	—	3	1	no	—
463	C₂²⋊C₄	—	3	2	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
469	C₄²	—	3	1	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	3	4	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	—	6	2	no	—
480	C₂²×C₃	—	6	2	no	—
481	C₂²×C₃	—	6	1	no	—
482	C₂²×C₃	—	6	2	no	—
483	C₂²×C₃	—	6	1	no	—
484	C₂²×C₃	—	6	2	no	—
485	C₂²×C₃	—	6	1	no	—
486	C₂²×C₃	—	6	2	no	—
487	C₂²×C₃	—	12	8	no	—
488	C₂²×C₃	C₉×#41	1	2	yes	complemented
489	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
490	C₂²×C₃	C₃×#239	1	2	yes	—
491	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	2	2	no	—
494	C₂×D₃	—	2	1	no	—
495	C₂×D₃	—	2	2	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	2	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	2	no	—
500	C₂×D₃	—	4	8	no	—
501	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	2	2	no	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	4	1	no	—
510	C₃×C₄	—	4	2	no	—
511	C₃×C₄	—	4	2	no	—
512	C₃×C₄	—	6	1	no	—
513	C₃×C₄	—	6	1	no	—
514	C₃×C₄	—	6	1	no	—
515	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
516	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
517	Dic₃	—	2	1	no	—
518	Dic₃	—	2	1	no	—
519	Dic₃	—	2	1	no	—
520	C₃²	C₃×#546	1	1	yes	characteristic
521	C₉	—	2	1	no	—
522	C₉	#5630	1	1	yes	characteristic, direct product factor
523	C₂³	—	3	2	no	—
524	C₂³	—	3	2	no	—
525	C₂³	—	3	1	no	—
526	C₂³	—	6	4	no	—
527	C₂³	—	6	4	no	—
528	C₂³	—	12	2	no	—
529	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	D₄	—	3	4	no	—
532	D₄	—	6	4	no	—
533	D₄	—	6	4	no	—
534	D₄	—	6	2	no	—
535	D₄	—	6	2	no	—
536	D₄	—	12	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	3	1	no	—
539	C₂×C₄	—	3	1	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	6	4	no	—
542	C₂×C₄	—	6	2	no	—
543	C₂×C₄	—	12	2	no	—
544	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
545	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
546	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
548	C₂×C₃	—	2	2	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	2	1	no	—
552	C₂×C₃	—	2	1	no	—
553	C₂×C₃	—	4	2	no	—
554	C₂×C₃	—	6	4	no	—
555	C₂×C₃	—	12	2	no	—
556	C₂×C₃	—	12	1	no	—
557	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
558	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
559	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
561	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
562	C₂×C₃	C₃×#1009	1	1	yes	characteristic
563	D₃	—	2	4	no	—
564	D₃	—	4	2	no	—
565	D₃	—	4	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	3	4	no	—
569	C₂²	—	6	2	no	—
570	C₂²	—	6	2	no	—
571	C₂²	—	6	1	no	—
572	C₂²	—	6	2	no	—
573	C₂²	—	6	1	no	—
574	C₂²	—	6	2	no	—
575	C₂²	—	6	1	no	—
576	C₂²	—	6	2	no	—
577	C₂²	—	12	8	no	—
578	C₂²	C₉×#239	1	2	yes	complemented
579	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	6	1	no	—
584	C₄	—	6	1	no	—
585	C₄	—	6	1	no	—
586	C₄	D₃×D₄×C₉	1	2	yes	—
587	C₃	—	2	1	no	—
588	C₃	C₉×#546	1	1	yes	characteristic, complemented
589	C₃	C₃×#5630	1	1	yes	characteristic
590	C₂	—	2	2	no	—
591	C₂	—	6	4	no	—
592	C₂	—	12	2	no	—
593	C₂	—	12	1	no	—
594	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
595	C₂	C₂×C₉×#239	1	1	yes	characteristic
596	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×#5630	C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#546
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. C₂×C₉×#239	C₂	semidirect
2. C₂²×C₉×D₁₂	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#947	C₂	semidirect
5. C₄×C₉×#67	C₂	semidirect
6. C₉×#895	C₂	semidirect
7. C₉×#895	C₂	semidirect
8. C₉×#894	C₂	semidirect
9. C₉×#893	C₂	semidirect
10. C₉×#882	C₂	semidirect
11. D₃×C₉×C₂²⋊C₄	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
23. C₂×C₉×D₁₂	C₂²	semidirect
24. C₂×C₉×D₁₂	C₂²	semidirect
25. C₂×C₄×D₃×C₉	C₂²	semidirect
26. C₂×C₄×D₃×C₉	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
32. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
55. C₉×C₂²⋊Q₈	D₃	semidirect
83. C₉×D₁₂	D₄	semidirect
88. #5630	C₉	direct (N × H)
117. C₂×Q₈×C₉	C₂×D₃	semidirect
133. C₉×C₄⋊C₄	C₂×D₃	semidirect
134. C₉×C₄⋊C₄	C₂×D₃	semidirect
146. C₂²×C₃×C₉	#41	semidirect
167. C₂×#239	C₂×C₉	semidirect
168. C₂²×D₁₂	C₂×C₉	semidirect
172. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
180. #947	C₂×C₉	semidirect
181. C₄×#67	C₂×C₉	semidirect
182. #895	C₂×C₉	semidirect
183. #895	C₂×C₉	semidirect
184. #894	C₂×C₉	semidirect
185. #893	C₂×C₉	semidirect
186. #882	C₂×C₉	semidirect
187. D₃×C₂²⋊C₄	C₂×C₉	semidirect
257. C₂×C₃×Q₈	C₂²×C₉	semidirect
278. C₂×D₁₂	C₂²×C₉	semidirect
279. C₂×D₁₂	C₂²×C₉	semidirect
280. C₂×C₄×D₃	C₂²×C₉	semidirect
281. C₂×C₄×D₃	C₂²×C₉	semidirect
282. C₂×C₄×D₃	C₂²×C₉	semidirect
286. C₃×C₄⋊C₄	C₂²×C₉	semidirect
287. C₃×C₄⋊C₄	C₂²×C₉	semidirect
301. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
302. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
303. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
304. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
305. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
306. Dic₃⋊C₄	C₂²×C₉	semidirect
307. C₄×Dic₃	C₂²×C₉	semidirect
345. C₂²×C₉	#239	semidirect
362. C₂²⋊Q₈	D₃×C₉	semidirect
369. C₃×C₉	#546	semidirect
423. D₁₂	D₄×C₉	semidirect
447. C₂×Q₈	C₂×D₃×C₉	semidirect
460. C₄⋊C₄	C₂×D₃×C₉	semidirect
461. C₄⋊C₄	C₂×D₃×C₉	semidirect
488. C₂²×C₃	C₉×#41	semidirect
522. C₉	#5630	direct (N × H)
578. C₂²	C₉×#239	semidirect
588. C₃	C₉×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂²×C₉×D₁₂	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#947	2
C₄×C₉×#67	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
C₉×#882	2
D₃×C₉×C₂²⋊C₄	2
C₃×#5630	3
C₉×#546	3

Subgroups — C9×#5630 #13152929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5630 #13152929