Subgroups — C₉×#5507 #13152419

Order 1728.

968 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#929	C₂	1	2	yes	maximal, complemented
5	C₄×C₉×#67	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×#894	C₂	1	2	yes	maximal, complemented
9	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5507	C₃	1	1	yes	maximal, characteristic
13	C₉×#547	—	3	1	no	maximal
14	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₉×#235	—	2	8	no	—
19	C₂×C₉×D₁₂	C₂²	1	2	yes	—
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
22	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₉×Dic₆	C₂²	1	2	yes	—
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
28	C₉×#217	C₂²	1	1	yes	characteristic
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₃×#235	C₂×C₃	1	2	yes	—
39	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
40	C₃×#930	C₂×C₃	1	1	yes	characteristic
41	C₃×#929	C₂×C₃	1	2	yes	—
42	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
43	C₃×#896	C₂×C₃	1	2	yes	—
44	C₃×#895	C₂×C₃	1	1	yes	characteristic
45	C₃×#894	C₂×C₃	1	2	yes	—
46	C₃×#893	C₂×C₃	1	1	yes	characteristic
47	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×#888	C₂×C₃	1	1	yes	characteristic
49	C₂×C₉×#41	—	3	2	no	—
50	C₉×C₄⋊Q₈	—	3	1	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₉×#121	—	3	1	no	—
55	C₉×#121	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	1	no	—
58	C₂×C₉×C₄⋊C₄	—	2	1	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₂²×D₃×C₉	C₂³	1	2	yes	—
63	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	—	2	4	no	—
65	C₂×C₃×C₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	—	2	4	no	—
71	C₉×#67	D₄	1	4	yes	complemented
72	C₂×C₉×Dic₃	C₂³	1	2	yes	—
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
76	C₉×D₁₂	—	2	4	no	—
77	C₉×D₁₂	—	2	2	no	—
78	C₄×D₃×C₉	—	2	4	no	—
79	C₄×D₃×C₉	—	2	2	no	—
80	C₄×D₃×C₉	—	2	4	no	—
81	C₉×Dic₆	—	2	4	no	—
82	C₃×#547	—	3	1	no	—
83	#5507	C₉	1	1	yes	characteristic, direct product factor
84	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
87	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
88	C₃×#235	—	2	8	no	—
89	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
94	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
95	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×#217	C₂²×C₃	1	1	yes	characteristic
99	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
103	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
105	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
108	C₉×#41	—	6	8	no	—
109	C₂×Q₈×C₉	—	3	2	no	—
110	C₂×D₄×C₉	—	3	1	no	—
111	C₂×D₄×C₉	—	3	2	no	—
112	C₂×D₄×C₉	—	3	1	no	—
113	C₂×D₄×C₉	—	3	2	no	—
114	C₂²×C₄×C₉	—	2	1	no	—
115	C₂²×C₄×C₉	—	2	2	no	—
116	C₂²×C₄×C₉	—	3	1	no	—
117	C₂²×C₄×C₉	—	3	2	no	—
118	C₂²×C₄×C₉	—	3	2	no	—
119	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
121	C₉×C₄⋊C₄	—	2	1	no	—
122	C₉×C₄⋊C₄	—	2	1	no	—
123	C₉×C₄⋊C₄	—	2	2	no	—
124	C₉×C₄⋊C₄	—	3	1	no	—
125	C₉×C₄⋊C₄	—	3	2	no	—
126	C₉×C₄⋊C₄	—	3	1	no	—
127	C₉×C₄⋊C₄	—	3	2	no	—
128	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
131	C₉×C₂²⋊C₄	—	3	1	no	—
132	C₉×C₂²⋊C₄	—	3	1	no	—
133	C₉×C₂²⋊C₄	—	3	2	no	—
134	C₉×C₂²⋊C₄	—	3	2	no	—
135	C₉×C₂²⋊C₄	—	3	2	no	—
136	C₄²×C₉	—	3	1	no	—
137	C₂²×C₃×C₉	—	2	1	no	—
138	C₂²×C₃×C₉	—	2	1	no	—
139	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
140	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
141	C₂×D₃×C₉	—	2	1	no	—
142	C₂×D₃×C₉	—	2	1	no	—
143	C₂×D₃×C₉	—	2	2	no	—
144	C₂×D₃×C₉	—	2	2	no	—
145	C₂×D₃×C₉	—	2	2	no	—
146	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
147	C₃×C₄×C₉	—	2	2	no	—
148	C₃×C₄×C₉	—	2	2	no	—
149	C₃×C₄×C₉	—	2	1	no	—
150	C₃×C₄×C₉	#41	1	2	yes	complemented
151	C₉×Dic₃	—	2	2	no	—
152	C₉×Dic₃	—	2	1	no	—
153	C₉×Dic₃	—	2	1	no	—
154	C₉×Dic₃	C₂×D₄	1	2	yes	—
155	C₂×C₃×#41	—	3	2	no	—
156	C₂×#235	C₂×C₉	1	2	yes	complemented
157	C₃×C₄⋊Q₈	—	3	1	no	—
158	C₃×#123	—	3	2	no	—
159	C₃×#123	—	3	2	no	—
160	C₃×C₂²⋊Q₈	—	3	2	no	—
161	C₃×#121	—	3	1	no	—
162	C₃×#121	—	3	1	no	—
163	C₃×C₄×D₄	—	3	1	no	—
164	C₃×C₄×D₄	—	3	1	no	—
165	C₂×C₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₃×C₄⋊C₄	—	3	1	no	—
167	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
169	#930	C₂×C₉	1	1	yes	characteristic, complemented
170	#929	C₂×C₉	1	2	yes	complemented
171	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
172	#896	C₂×C₉	1	2	yes	complemented
173	#895	C₂×C₉	1	1	yes	characteristic, complemented
174	#894	C₂×C₉	1	2	yes	complemented
175	#893	C₂×C₉	1	1	yes	characteristic, complemented
176	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
177	#888	C₂×C₉	1	1	yes	characteristic, complemented
178	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
180	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃²×C₄	—	2	2	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×#67	—	2	4	no	—
188	C₃×#67	C₃×D₄	1	4	yes	—
189	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
192	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
193	C₃×D₁₂	—	2	4	no	—
194	C₃×D₁₂	—	2	2	no	—
195	C₃×C₄×D₃	—	2	4	no	—
196	C₃×C₄×D₃	—	2	2	no	—
197	C₃×C₄×D₃	—	2	4	no	—
198	C₃×Dic₆	—	2	4	no	—
199	C₂³×C₉	—	2	1	no	—
200	C₂³×C₉	—	3	1	no	—
201	C₂³×C₉	—	3	2	no	—
202	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
203	Q₈×C₉	—	6	4	no	—
204	D₄×C₉	—	3	4	no	—
205	D₄×C₉	—	6	4	no	—
206	D₄×C₉	—	6	4	no	—
207	D₄×C₉	—	6	2	no	—
208	C₂×C₄×C₉	—	2	4	no	—
209	C₂×C₄×C₉	—	2	4	no	—
210	C₂×C₄×C₉	—	2	2	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	2	no	—
214	C₂×C₄×C₉	—	2	2	no	—
215	C₂×C₄×C₉	—	3	1	no	—
216	C₂×C₄×C₉	—	3	1	no	—
217	C₂×C₄×C₉	—	3	1	no	—
218	C₂×C₄×C₉	—	3	2	no	—
219	C₂×C₄×C₉	—	4	4	no	—
220	C₂×C₄×C₉	—	6	4	no	—
221	C₂×C₄×C₉	—	6	4	no	—
222	C₂×C₄×C₉	—	6	2	no	—
223	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
225	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
226	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
227	#547	—	3	1	no	Sylow
228	C₂×C₃×C₉	—	2	2	no	—
229	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
231	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
232	D₃×C₉	—	2	2	no	—
233	D₃×C₉	—	4	2	no	—
234	C₃×#41	—	6	8	no	—
235	C₂×C₃×Q₈	—	3	2	no	—
236	C₂×C₃×D₄	—	3	1	no	—
237	C₂×C₃×D₄	—	3	2	no	—
238	C₂×C₃×D₄	—	3	1	no	—
239	C₂×C₃×D₄	—	3	2	no	—
240	C₂²×C₃×C₄	—	2	1	no	—
241	C₂²×C₃×C₄	—	2	2	no	—
242	C₂²×C₃×C₄	—	3	1	no	—
243	C₂²×C₃×C₄	—	3	2	no	—
244	C₂²×C₃×C₄	—	3	2	no	—
245	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
247	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
249	C₂×#67	C₂²×C₉	1	2	yes	—
250	C₂×#67	C₂²×C₉	1	1	yes	characteristic
251	#235	—	2	8	no	—
252	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
253	C₂×D₁₂	C₂²×C₉	1	2	yes	—
254	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
255	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
257	C₂×Dic₆	C₂²×C₉	1	2	yes	—
258	C₃×C₄⋊C₄	—	2	1	no	—
259	C₃×C₄⋊C₄	—	2	1	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	3	2	no	—
262	C₃×C₄⋊C₄	—	3	1	no	—
263	C₃×C₄⋊C₄	—	3	2	no	—
264	C₃×C₄⋊C₄	—	3	1	no	—
265	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
266	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
267	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
268	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
271	C₃×C₂²⋊C₄	—	3	1	no	—
272	C₃×C₂²⋊C₄	—	3	1	no	—
273	C₃×C₂²⋊C₄	—	3	2	no	—
274	C₃×C₂²⋊C₄	—	3	2	no	—
275	C₃×C₂²⋊C₄	—	3	2	no	—
276	C₃×C₄²	—	3	1	no	—
277	#217	C₂²×C₉	1	1	yes	characteristic
278	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
279	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
280	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
281	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
282	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
283	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
284	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
285	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
286	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
287	C₂²×C₃²	—	2	1	no	—
288	C₂²×C₃²	—	2	1	no	—
289	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
290	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
291	C₂×C₃×D₃	—	2	1	no	—
292	C₂×C₃×D₃	—	2	1	no	—
293	C₂×C₃×D₃	—	2	2	no	—
294	C₂×C₃×D₃	—	2	2	no	—
295	C₂×C₃×D₃	—	2	2	no	—
296	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
297	C₃²×C₄	—	2	1	no	—
298	C₃²×C₄	—	2	2	no	—
299	C₃²×C₄	—	2	2	no	—
300	C₃²×C₄	C₃×#41	1	2	yes	—
301	C₃×Dic₃	—	2	2	no	—
302	C₃×Dic₃	—	2	1	no	—
303	C₃×Dic₃	—	2	1	no	—
304	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
305	C₂²×C₉	—	2	2	no	—
306	C₂²×C₉	—	2	2	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	2	2	no	—
311	C₂²×C₉	—	3	2	no	—
312	C₂²×C₉	—	6	1	no	—
313	C₂²×C₉	—	6	1	no	—
314	C₂²×C₉	—	6	2	no	—
315	C₂²×C₉	—	6	2	no	—
316	C₂²×C₉	—	6	2	no	—
317	C₂²×C₉	D₃×D₄	1	2	yes	—
318	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
319	C₄×C₉	—	2	2	no	—
320	C₄×C₉	—	2	1	no	—
321	C₄×C₉	—	2	2	no	—
322	C₄×C₉	—	2	2	no	—
323	C₄×C₉	—	2	2	no	—
324	C₄×C₉	—	3	2	no	—
325	C₄×C₉	—	4	2	no	—
326	C₄×C₉	—	4	2	no	—
327	C₄×C₉	—	6	1	no	—
328	C₄×C₉	—	6	2	no	—
329	C₄×C₉	—	6	1	no	—
330	C₄×C₉	#235	1	2	yes	complemented
331	C₂×#41	—	3	2	no	—
332	C₄⋊Q₈	—	3	1	no	—
333	#123	—	3	2	no	—
334	#123	—	3	2	no	—
335	C₂²⋊Q₈	—	3	2	no	—
336	#121	—	3	1	no	—
337	#121	—	3	1	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	1	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
342	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	3	1	no	—
345	C₂³×C₃	—	3	2	no	—
346	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
347	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
348	C₂²×D₃	C₂³×C₉	1	2	yes	—
349	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
350	C₃×Q₈	—	6	4	no	—
351	C₃×D₄	—	3	4	no	—
352	C₃×D₄	—	6	4	no	—
353	C₃×D₄	—	6	4	no	—
354	C₃×D₄	—	6	2	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	2	4	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	3	1	no	—
365	C₂×C₃×C₄	—	3	1	no	—
366	C₂×C₃×C₄	—	3	1	no	—
367	C₂×C₃×C₄	—	3	2	no	—
368	C₂×C₃×C₄	—	4	4	no	—
369	C₂×C₃×C₄	—	6	4	no	—
370	C₂×C₃×C₄	—	6	4	no	—
371	C₂×C₃×C₄	—	6	2	no	—
372	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
374	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
375	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
378	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
379	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
380	#67	—	2	4	no	—
381	#67	D₄×C₉	1	4	yes	complemented
382	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
383	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
384	C₂×Dic₃	C₂³×C₉	1	2	yes	—
385	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
386	D₁₂	—	2	4	no	—
387	D₁₂	—	2	2	no	—
388	C₄×D₃	—	2	4	no	—
389	C₄×D₃	—	2	2	no	—
390	C₄×D₃	—	2	4	no	—
391	Dic₆	—	2	4	no	—
392	C₂×C₃²	—	2	2	no	—
393	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
394	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
395	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
396	C₃×D₃	—	2	2	no	—
397	C₃×D₃	—	4	2	no	—
398	C₂×C₉	—	2	4	no	—
399	C₂×C₉	—	2	2	no	—
400	C₂×C₉	—	2	1	no	—
401	C₂×C₉	—	2	1	no	—
402	C₂×C₉	—	2	1	no	—
403	C₂×C₉	—	6	2	no	—
404	C₂×C₉	—	12	2	no	—
405	C₂×C₉	C₂×#235	1	1	yes	characteristic
406	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
407	C₂×C₉	#1007	1	1	yes	characteristic
408	#41	—	6	8	no	—
409	C₂×Q₈	—	3	2	no	—
410	C₂×D₄	—	3	1	no	—
411	C₂×D₄	—	3	2	no	—
412	C₂×D₄	—	3	1	no	—
413	C₂×D₄	—	3	2	no	—
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	—	3	2	no	—
416	C₂²×C₄	—	3	2	no	—
417	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
419	C₄⋊C₄	—	3	1	no	—
420	C₄⋊C₄	—	3	2	no	—
421	C₄⋊C₄	—	3	1	no	—
422	C₄⋊C₄	—	3	2	no	—
423	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
424	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
425	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
426	C₂²⋊C₄	—	3	1	no	—
427	C₂²⋊C₄	—	3	1	no	—
428	C₂²⋊C₄	—	3	2	no	—
429	C₂²⋊C₄	—	3	2	no	—
430	C₂²⋊C₄	—	3	2	no	—
431	C₄²	—	3	1	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	2	1	no	—
435	C₂²×C₃	—	2	1	no	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	3	2	no	—
441	C₂²×C₃	—	6	1	no	—
442	C₂²×C₃	—	6	1	no	—
443	C₂²×C₃	—	6	2	no	—
444	C₂²×C₃	—	6	2	no	—
445	C₂²×C₃	—	6	2	no	—
446	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
447	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
448	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
449	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
450	C₂×D₃	—	2	1	no	—
451	C₂×D₃	—	2	1	no	—
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	2	2	no	—
454	C₂×D₃	—	2	2	no	—
455	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	2	1	no	—
458	C₃×C₄	—	2	2	no	—
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	2	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	2	no	—
464	C₃×C₄	—	3	2	no	—
465	C₃×C₄	—	4	2	no	—
466	C₃×C₄	—	4	2	no	—
467	C₃×C₄	—	6	1	no	—
468	C₃×C₄	—	6	2	no	—
469	C₃×C₄	—	6	1	no	—
470	C₃×C₄	C₉×#41	1	2	yes	complemented
471	C₃×C₄	C₃×#235	1	2	yes	—
472	Dic₃	—	2	2	no	—
473	Dic₃	—	2	1	no	—
474	Dic₃	—	2	1	no	—
475	Dic₃	C₂×D₄×C₉	1	2	yes	—
476	C₃²	C₃×#547	1	1	yes	characteristic
477	C₉	—	2	1	no	—
478	C₉	#5507	1	1	yes	characteristic, direct product factor
479	C₂³	—	3	1	no	—
480	C₂³	—	3	2	no	—
481	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
482	Q₈	—	6	4	no	—
483	D₄	—	3	4	no	—
484	D₄	—	6	4	no	—
485	D₄	—	6	4	no	—
486	D₄	—	6	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	3	1	no	—
490	C₂×C₄	—	3	1	no	—
491	C₂×C₄	—	3	1	no	—
492	C₂×C₄	—	3	2	no	—
493	C₂×C₄	—	6	4	no	—
494	C₂×C₄	—	6	4	no	—
495	C₂×C₄	—	6	2	no	—
496	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
498	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
499	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
500	C₂×C₃	—	2	4	no	—
501	C₂×C₃	—	2	2	no	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	2	1	no	—
505	C₂×C₃	—	2	1	no	—
506	C₂×C₃	—	6	2	no	—
507	C₂×C₃	—	12	2	no	—
508	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
509	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
510	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
512	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
513	C₂×C₃	C₃×#1007	1	1	yes	characteristic
514	D₃	—	2	2	no	—
515	D₃	—	4	2	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	3	2	no	—
519	C₂²	—	6	1	no	—
520	C₂²	—	6	1	no	—
521	C₂²	—	6	2	no	—
522	C₂²	—	6	2	no	—
523	C₂²	—	6	2	no	—
524	C₂²	D₃×D₄×C₉	1	2	yes	—
525	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	3	2	no	—
530	C₄	—	6	1	no	—
531	C₄	—	6	2	no	—
532	C₄	—	6	1	no	—
533	C₄	C₉×#235	1	2	yes	complemented
534	C₃	—	2	1	no	—
535	C₃	C₉×#547	1	1	yes	characteristic, complemented
536	C₃	C₃×#5507	1	1	yes	characteristic
537	C₂	—	2	2	no	—
538	C₂	—	6	2	no	—
539	C₂	—	12	2	no	—
540	C₂	C₂×C₉×#235	1	1	yes	characteristic
541	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
542	C₂	C₉×#1007	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×C₄⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5507	C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₉×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#235	C₂	semidirect
2. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
3. C₉×#930	C₂	semidirect
4. C₉×#929	C₂	semidirect
5. C₄×C₉×#67	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#895	C₂	semidirect
8. C₉×#894	C₂	semidirect
9. C₉×#893	C₂	semidirect
10. D₃×C₉×C₄⋊C₄	C₂	semidirect
11. C₉×#888	C₂	semidirect
60. C₂×C₉×C₄⋊C₄	D₃	semidirect
71. C₉×#67	D₄	semidirect
83. #5507	C₉	direct (N × H)
150. C₃×C₄×C₉	#41	semidirect
156. C₂×#235	C₂×C₉	semidirect
167. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
169. #930	C₂×C₉	semidirect
170. #929	C₂×C₉	semidirect
171. C₄×#67	C₂×C₉	semidirect
172. #896	C₂×C₉	semidirect
173. #895	C₂×C₉	semidirect
174. #894	C₂×C₉	semidirect
175. #893	C₂×C₉	semidirect
176. D₃×C₄⋊C₄	C₂×C₉	semidirect
177. #888	C₂×C₉	semidirect
330. C₄×C₉	#235	semidirect
341. C₂×C₄⋊C₄	D₃×C₉	semidirect
342. C₃×C₉	#547	semidirect
381. #67	D₄×C₉	semidirect
470. C₃×C₄	C₉×#41	semidirect
478. C₉	#5507	direct (N × H)
533. C₄	C₉×#235	semidirect
535. C₃	C₉×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂×C₃×C₉×C₄⋊C₄	2
C₉×#930	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#896	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
D₃×C₉×C₄⋊C₄	2
C₉×#888	2
C₃×#5507	3
C₉×#547	3

Subgroups — C9×#5507 #13152419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5507 #13152419