Subgroups — C₉×#5629 #13152928

Order 1728.

956 conjugacy classes of subgroups.

The subgroup lattice has 592 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	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	2	yes	maximal, complemented
7	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#895	C₂	1	2	yes	maximal, complemented
9	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#884	C₂	1	2	yes	maximal, complemented
11	C₉×#884	C₂	1	2	yes	maximal, complemented
12	C₃×#5629	C₃	1	1	yes	maximal, characteristic
13	C₉×#537	—	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	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₉×#239	—	2	4	no	—
20	C₉×#235	—	2	4	no	—
21	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₉×D₁₂	C₂²	1	2	yes	—
24	C₂×C₉×D₁₂	C₂²	1	2	yes	—
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
32	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
36	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#930	C₂×C₃	1	1	yes	characteristic
44	C₃×#896	C₂×C₃	1	2	yes	—
45	C₃×#895	C₂×C₃	1	1	yes	characteristic
46	C₃×#895	C₂×C₃	1	2	yes	—
47	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×#884	C₂×C₃	1	2	yes	—
49	C₃×#884	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂×C₉×#41	—	3	1	no	—
52	C₉×C₂²⋊Q₈	—	2	1	no	—
53	C₉×C₂²⋊Q₈	—	3	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	C₉×#121	—	3	1	no	—
58	C₉×#121	—	3	2	no	—
59	C₉×#121	—	3	2	no	—
60	C₉×#121	—	3	2	no	—
61	C₂×C₉×C₄⋊C₄	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	C₂³	1	2	yes	—
64	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
65	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
66	C₃×Q₈×C₉	—	2	2	no	—
67	C₂×C₃×C₄×C₉	—	2	2	no	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
70	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
71	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₉×#67	—	2	2	no	—
73	C₉×#67	—	2	2	no	—
74	C₉×#67	—	4	2	no	—
75	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₉×Dic₃	C₂³	1	2	yes	—
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₉×D₁₂	—	2	2	no	—
79	C₉×D₁₂	—	2	4	no	—
80	C₉×D₁₂	—	2	2	no	—
81	C₉×D₁₂	—	4	2	no	—
82	C₄×D₃×C₉	—	2	2	no	—
83	C₄×D₃×C₉	—	2	4	no	—
84	C₄×D₃×C₉	—	4	2	no	—
85	C₄×D₃×C₉	D₄	1	4	yes	complemented
86	C₉×Dic₆	—	2	2	no	—
87	C₃×#537	—	3	1	no	—
88	#5629	C₉	1	1	yes	characteristic, direct product factor
89	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₃×#239	—	2	4	no	—
95	C₃×#235	—	2	4	no	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
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	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
112	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
114	C₉×#41	—	6	4	no	—
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	2	1	no	—
117	C₂×Q₈×C₉	—	3	1	no	—
118	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	1	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	—	3	1	no	—
125	C₂×D₄×C₉	—	3	2	no	—
126	C₂²×C₄×C₉	—	2	1	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	3	2	no	—
129	C₂²×C₄×C₉	—	3	1	no	—
130	C₂²×C₄×C₉	—	3	2	no	—
131	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
132	C₉×C₄⋊C₄	—	2	1	no	—
133	C₉×C₄⋊C₄	—	2	2	no	—
134	C₉×C₄⋊C₄	—	3	2	no	—
135	C₉×C₄⋊C₄	—	3	1	no	—
136	C₉×C₄⋊C₄	—	3	2	no	—
137	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
139	C₉×C₂²⋊C₄	—	2	2	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
144	C₂²×C₃×C₉	—	2	1	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	—	2	1	no	—
147	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
148	C₂×D₃×C₉	—	2	1	no	—
149	C₂×D₃×C₉	—	2	1	no	—
150	C₂×D₃×C₉	—	2	2	no	—
151	C₂×D₃×C₉	—	2	1	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	2	no	—
154	C₂×D₃×C₉	—	2	2	no	—
155	C₂×D₃×C₉	—	2	1	no	—
156	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
157	C₃×C₄×C₉	—	2	1	no	—
158	C₃×C₄×C₉	—	2	2	no	—
159	C₃×C₄×C₉	—	2	2	no	—
160	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₉×Dic₃	—	2	1	no	—
162	C₉×Dic₃	—	2	2	no	—
163	C₉×Dic₃	C₂×D₄	1	2	yes	—
164	C₂×C₃×#41	—	3	1	no	—
165	C₂×C₃×#41	—	3	1	no	—
166	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
168	C₃×C₂²⋊Q₈	—	2	1	no	—
169	C₃×C₂²⋊Q₈	—	3	1	no	—
170	C₃×C₂²⋊Q₈	—	3	2	no	—
171	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
172	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
173	C₃×#121	—	3	1	no	—
174	C₃×#121	—	3	1	no	—
175	C₃×#121	—	3	2	no	—
176	C₃×#121	—	3	2	no	—
177	C₃×#121	—	3	2	no	—
178	C₂×C₃×C₄⋊C₄	—	3	1	no	—
179	#946	C₂×C₉	1	1	yes	characteristic, complemented
180	#930	C₂×C₉	1	1	yes	characteristic, complemented
181	#896	C₂×C₉	1	2	yes	complemented
182	#895	C₂×C₉	1	1	yes	characteristic, complemented
183	#895	C₂×C₉	1	2	yes	complemented
184	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
185	#884	C₂×C₉	1	2	yes	complemented
186	#884	C₂×C₉	1	2	yes	complemented
187	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
189	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₃²×Q₈	—	2	2	no	—
192	C₂×C₃²×C₄	—	2	2	no	—
193	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
194	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
195	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
197	C₃×#67	—	2	2	no	—
198	C₃×#67	—	2	2	no	—
199	C₃×#67	—	4	2	no	—
200	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
201	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
203	C₃×D₁₂	—	2	2	no	—
204	C₃×D₁₂	—	2	4	no	—
205	C₃×D₁₂	—	2	2	no	—
206	C₃×D₁₂	—	4	2	no	—
207	C₃×C₄×D₃	—	2	2	no	—
208	C₃×C₄×D₃	—	2	4	no	—
209	C₃×C₄×D₃	—	4	2	no	—
210	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
211	C₃×Dic₆	—	2	2	no	—
212	C₂³×C₉	—	2	1	no	—
213	C₂³×C₉	—	3	1	no	—
214	C₂³×C₉	—	3	1	no	—
215	C₂³×C₉	—	3	2	no	—
216	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
217	Q₈×C₉	—	2	2	no	—
218	Q₈×C₉	—	4	2	no	—
219	Q₈×C₉	—	6	2	no	—
220	D₄×C₉	—	6	2	no	—
221	D₄×C₉	—	6	4	no	—
222	D₄×C₉	—	6	2	no	—
223	D₄×C₉	—	6	2	no	—
224	D₄×C₉	—	6	2	no	—
225	D₄×C₉	—	12	2	no	—
226	D₄×C₉	—	12	2	no	—
227	C₂×C₄×C₉	—	2	2	no	—
228	C₂×C₄×C₉	—	2	1	no	—
229	C₂×C₄×C₉	—	2	2	no	—
230	C₂×C₄×C₉	—	2	2	no	—
231	C₂×C₄×C₉	—	2	1	no	—
232	C₂×C₄×C₉	—	3	1	no	—
233	C₂×C₄×C₉	—	3	4	no	—
234	C₂×C₄×C₉	—	3	2	no	—
235	C₂×C₄×C₉	—	3	1	no	—
236	C₂×C₄×C₉	—	4	2	no	—
237	C₂×C₄×C₉	—	6	4	no	—
238	C₂×C₄×C₉	—	6	2	no	—
239	C₂×C₄×C₉	—	12	2	no	—
240	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
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	#537	—	3	1	no	Sylow
245	C₂×C₃×C₉	—	4	1	no	—
246	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
249	D₃×C₉	—	2	2	no	—
250	D₃×C₉	—	4	2	no	—
251	D₃×C₉	—	4	1	no	—
252	C₃×#41	—	6	4	no	—
253	C₃×#41	—	6	4	no	—
254	C₂×C₃×Q₈	—	2	1	no	—
255	C₂×C₃×Q₈	—	3	1	no	—
256	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
257	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
258	C₂×C₃×D₄	—	3	1	no	—
259	C₂×C₃×D₄	—	3	1	no	—
260	C₂×C₃×D₄	—	3	2	no	—
261	C₂×C₃×D₄	—	3	1	no	—
262	C₂×C₃×D₄	—	3	2	no	—
263	C₂×C₃×D₄	—	3	1	no	—
264	C₂×C₃×D₄	—	3	2	no	—
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	—	3	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	C₂×#67	C₂²×C₉	1	1	yes	characteristic
274	C₂×#67	C₂²×C₉	1	2	yes	—
275	#239	—	2	4	no	—
276	#235	—	2	4	no	—
277	C₂×D₁₂	C₂²×C₉	1	2	yes	—
278	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
279	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
280	C₂×D₁₂	C₂²×C₉	1	2	yes	—
281	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
282	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
284	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
285	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	2	2	no	—
288	C₃×C₄⋊C₄	—	3	2	no	—
289	C₃×C₄⋊C₄	—	3	2	no	—
290	C₃×C₄⋊C₄	—	3	1	no	—
291	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
292	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
293	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
294	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	3	2	no	—
297	C₃×C₂²⋊C₄	—	3	2	no	—
298	C₃×C₂²⋊C₄	—	3	2	no	—
299	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
300	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
301	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
302	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
303	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
304	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
305	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
306	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
307	C₂²×C₃²	—	2	1	no	—
308	C₂²×C₃²	—	2	1	no	—
309	C₂²×C₃²	—	2	1	no	—
310	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
311	C₂×C₃×D₃	—	2	1	no	—
312	C₂×C₃×D₃	—	2	1	no	—
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	—	2	1	no	—
315	C₂×C₃×D₃	—	2	1	no	—
316	C₂×C₃×D₃	—	2	2	no	—
317	C₂×C₃×D₃	—	2	2	no	—
318	C₂×C₃×D₃	—	2	1	no	—
319	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
320	C₃²×C₄	—	2	1	no	—
321	C₃²×C₄	—	2	2	no	—
322	C₃²×C₄	—	2	2	no	—
323	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
324	C₃×Dic₃	—	2	1	no	—
325	C₃×Dic₃	—	2	2	no	—
326	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
327	C₂²×C₉	—	2	2	no	—
328	C₂²×C₉	—	2	1	no	—
329	C₂²×C₉	—	2	1	no	—
330	C₂²×C₉	—	2	1	no	—
331	C₂²×C₉	—	2	1	no	—
332	C₂²×C₉	—	3	2	no	—
333	C₂²×C₉	—	4	1	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	6	1	no	—
336	C₂²×C₉	—	6	1	no	—
337	C₂²×C₉	—	6	2	no	—
338	C₂²×C₉	—	6	1	no	—
339	C₂²×C₉	—	6	1	no	—
340	C₂²×C₉	—	6	2	no	—
341	C₂²×C₉	—	6	1	no	—
342	C₂²×C₉	—	6	2	no	—
343	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
344	C₄×C₉	—	2	1	no	—
345	C₄×C₉	—	2	2	no	—
346	C₄×C₉	—	2	2	no	—
347	C₄×C₉	—	2	2	no	—
348	C₄×C₉	—	3	2	no	—
349	C₄×C₉	—	4	2	no	—
350	C₄×C₉	—	4	1	no	—
351	C₄×C₉	—	4	2	no	—
352	C₄×C₉	—	6	1	no	—
353	C₄×C₉	—	6	2	no	—
354	C₄×C₉	D₃×D₄	1	2	yes	—
355	C₂×#41	—	3	1	no	—
356	C₂×#41	—	3	1	no	—
357	C₂²⋊Q₈	—	3	1	no	—
358	C₂²⋊Q₈	—	3	2	no	—
359	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
360	#121	—	3	1	no	—
361	#121	—	3	1	no	—
362	#121	—	3	2	no	—
363	#121	—	3	2	no	—
364	#121	—	3	2	no	—
365	C₂×C₄⋊C₄	—	3	1	no	—
366	C₃×C₉	#537	1	1	yes	characteristic, complemented, Sylow
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	3	1	no	—
369	C₂³×C₃	—	3	1	no	—
370	C₂³×C₃	—	3	2	no	—
371	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
372	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₂²×D₃	C₂³×C₉	1	2	yes	—
374	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
375	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
376	C₃×Q₈	—	2	2	no	—
377	C₃×Q₈	—	2	2	no	—
378	C₃×Q₈	—	4	2	no	—
379	C₃×Q₈	—	6	2	no	—
380	C₃×D₄	—	6	2	no	—
381	C₃×D₄	—	6	4	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	6	2	no	—
384	C₃×D₄	—	6	2	no	—
385	C₃×D₄	—	12	2	no	—
386	C₃×D₄	—	12	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	3	1	no	—
394	C₂×C₃×C₄	—	3	4	no	—
395	C₂×C₃×C₄	—	3	2	no	—
396	C₂×C₃×C₄	—	3	1	no	—
397	C₂×C₃×C₄	—	4	2	no	—
398	C₂×C₃×C₄	—	6	4	no	—
399	C₂×C₃×C₄	—	6	2	no	—
400	C₂×C₃×C₄	—	12	2	no	—
401	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
402	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
403	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
407	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
408	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
409	#67	—	2	2	no	—
410	#67	—	2	2	no	—
411	#67	—	4	2	no	—
412	C₂×Dic₃	C₂³×C₉	1	2	yes	—
413	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
414	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
415	D₁₂	—	2	2	no	—
416	D₁₂	—	2	4	no	—
417	D₁₂	—	2	2	no	—
418	D₁₂	—	4	2	no	—
419	C₄×D₃	—	2	2	no	—
420	C₄×D₃	—	2	4	no	—
421	C₄×D₃	—	4	2	no	—
422	C₄×D₃	D₄×C₉	1	4	yes	complemented
423	Dic₆	—	2	2	no	—
424	C₂×C₃²	—	4	1	no	—
425	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
426	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
428	C₃×D₃	—	2	2	no	—
429	C₃×D₃	—	4	2	no	—
430	C₃×D₃	—	4	1	no	—
431	C₂×C₉	—	2	1	no	—
432	C₂×C₉	—	2	1	no	—
433	C₂×C₉	—	2	1	no	—
434	C₂×C₉	—	4	2	no	—
435	C₂×C₉	—	4	1	no	—
436	C₂×C₉	—	6	2	no	—
437	C₂×C₉	—	12	2	no	—
438	C₂×C₉	—	12	1	no	—
439	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
440	C₂×C₉	#1007	1	1	yes	characteristic
441	C₂×C₉	#1009	1	1	yes	characteristic
442	#41	—	6	4	no	—
443	#41	—	6	4	no	—
444	C₂×Q₈	—	3	1	no	—
445	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
446	C₂×D₄	—	3	1	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	2	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
463	C₂²⋊C₄	—	3	2	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	2	1	no	—
469	C₂²×C₃	—	2	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	—	3	2	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	6	1	no	—
479	C₂²×C₃	—	6	1	no	—
480	C₂²×C₃	—	6	2	no	—
481	C₂²×C₃	—	6	1	no	—
482	C₂²×C₃	—	6	1	no	—
483	C₂²×C₃	—	6	2	no	—
484	C₂²×C₃	—	6	1	no	—
485	C₂²×C₃	—	6	2	no	—
486	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
487	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
488	C₂×D₃	—	2	1	no	—
489	C₂×D₃	—	2	1	no	—
490	C₂×D₃	—	2	2	no	—
491	C₂×D₃	—	2	1	no	—
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	—	2	2	no	—
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	2	no	—
499	C₃×C₄	—	2	2	no	—
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	3	2	no	—
505	C₃×C₄	—	4	1	no	—
506	C₃×C₄	—	4	2	no	—
507	C₃×C₄	—	4	2	no	—
508	C₃×C₄	—	6	1	no	—
509	C₃×C₄	—	6	2	no	—
510	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
511	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
512	Dic₃	—	2	1	no	—
513	Dic₃	—	2	2	no	—
514	Dic₃	C₂×D₄×C₉	1	2	yes	—
515	C₃²	C₃×#537	1	1	yes	characteristic
516	C₉	—	2	1	no	—
517	C₉	#5629	1	1	yes	characteristic, direct product factor
518	C₂³	—	3	1	no	—
519	C₂³	—	3	1	no	—
520	C₂³	—	3	2	no	—
521	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	6	2	no	—
524	D₄	—	6	2	no	—
525	D₄	—	6	4	no	—
526	D₄	—	6	2	no	—
527	D₄	—	6	2	no	—
528	D₄	—	6	2	no	—
529	D₄	—	12	2	no	—
530	D₄	—	12	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	3	4	no	—
534	C₂×C₄	—	3	2	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	6	4	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	12	2	no	—
539	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
541	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
542	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	4	2	no	—
547	C₂×C₃	—	4	1	no	—
548	C₂×C₃	—	4	1	no	—
549	C₂×C₃	—	6	2	no	—
550	C₂×C₃	—	12	2	no	—
551	C₂×C₃	—	12	1	no	—
552	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
553	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
556	C₂×C₃	C₃×#1007	1	1	yes	characteristic
557	C₂×C₃	C₃×#1009	1	1	yes	characteristic
558	D₃	—	2	2	no	—
559	D₃	—	4	2	no	—
560	D₃	—	4	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	3	2	no	—
565	C₂²	—	6	1	no	—
566	C₂²	—	6	1	no	—
567	C₂²	—	6	2	no	—
568	C₂²	—	6	1	no	—
569	C₂²	—	6	1	no	—
570	C₂²	—	6	2	no	—
571	C₂²	—	6	1	no	—
572	C₂²	—	6	2	no	—
573	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	3	2	no	—
578	C₄	—	6	1	no	—
579	C₄	—	6	2	no	—
580	C₄	D₃×D₄×C₉	1	2	yes	—
581	C₃	—	2	1	no	—
582	C₃	C₉×#537	1	1	yes	characteristic, complemented
583	C₃	C₃×#5629	1	1	yes	characteristic
584	C₂	—	4	1	no	—
585	C₂	—	6	2	no	—
586	C₂	—	12	2	no	—
587	C₂	—	12	1	no	—
588	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
589	C₂	C₉×#1007	1	1	yes	characteristic
590	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×#5629	C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#537
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. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#930	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#895	C₂	semidirect
8. C₉×#895	C₂	semidirect
9. D₃×C₉×C₄⋊C₄	C₂	semidirect
10. C₉×#884	C₂	semidirect
11. C₉×#884	C₂	semidirect
55. C₉×C₂²⋊Q₈	D₃	semidirect
85. C₄×D₃×C₉	D₄	semidirect
88. #5629	C₉	direct (N × H)
166. C₂×#239	C₂×C₉	semidirect
167. C₂×#235	C₂×C₉	semidirect
171. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
179. #946	C₂×C₉	semidirect
180. #930	C₂×C₉	semidirect
181. #896	C₂×C₉	semidirect
182. #895	C₂×C₉	semidirect
183. #895	C₂×C₉	semidirect
184. D₃×C₄⋊C₄	C₂×C₉	semidirect
185. #884	C₂×C₉	semidirect
186. #884	C₂×C₉	semidirect
359. C₂²⋊Q₈	D₃×C₉	semidirect
366. C₃×C₉	#537	semidirect
422. C₄×D₃	D₄×C₉	semidirect
517. C₉	#5629	direct (N × H)
582. C₃	C₉×#537	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
C₂×C₉×#235	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#930	2
C₉×#896	2
C₉×#895	2
D₃×C₉×C₄⋊C₄	2
C₉×#884	2
C₃×#5629	3
C₉×#537	3

Subgroups — C9×#5629 #13152928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5629 #13152928