Subgroups — C₉×#5607 #13152826

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	C₂	1	2	yes	maximal, complemented
5	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#937	C₂	1	2	yes	maximal, complemented
7	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#882	C₂	1	2	yes	maximal, complemented
12	C₃×#5607	C₃	1	1	yes	maximal, characteristic
13	C₉×#535	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₉×#67	C₂²	1	1	yes	characteristic
19	C₂×C₉×#67	C₂²	1	2	yes	—
20	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₉×#67	C₂²	1	2	yes	complemented
22	C₂×C₉×#67	C₂²	1	2	yes	complemented
23	D₃×D₄×C₉	—	2	4	no	—
24	C₉×#235	—	2	4	no	—
25	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₉×#217	C₂²	1	2	yes	complemented
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
39	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
41	C₃²×#121	C₂×C₃	1	1	yes	characteristic
42	C₃×#940	C₂×C₃	1	2	yes	—
43	C₃×#938	C₂×C₃	1	1	yes	characteristic
44	C₃×#937	C₂×C₃	1	2	yes	—
45	C₃×#930	C₂×C₃	1	1	yes	characteristic
46	C₃×#895	C₂×C₃	1	1	yes	characteristic
47	C₃×#892	C₂×C₃	1	1	yes	characteristic
48	C₃×#885	C₂×C₃	1	2	yes	—
49	C₃×#882	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#127	—	3	2	no	—
53	C₉×#124	—	3	2	no	—
54	C₉×#121	—	2	1	no	—
55	C₉×#121	—	3	1	no	—
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	1	no	—
58	C₉×#121	D₃	1	1	yes	characteristic, complemented
59	C₉×#120	—	3	2	no	—
60	C₉×#120	—	3	2	no	—
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	2	yes	—
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	4	2	no	—
66	C₂²×D₃×C₉	—	4	2	no	—
67	C₂²×D₃×C₉	C₂³	1	2	yes	—
68	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
69	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
70	C₃×D₄×C₉	—	2	2	no	—
71	C₃×D₄×C₉	—	4	2	no	—
72	C₂×C₃×C₄×C₉	—	2	2	no	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
75	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₉×#67	—	2	2	no	—
77	C₉×#67	—	2	2	no	—
78	C₉×#67	—	2	4	no	—
79	C₉×#67	—	4	2	no	—
80	C₉×#67	—	4	2	no	—
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₉×Dic₃	C₂³	1	2	yes	—
83	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
84	C₉×D₁₂	—	2	2	no	—
85	C₉×D₁₂	—	2	2	no	—
86	C₉×D₁₂	—	4	2	no	—
87	C₄×D₃×C₉	—	2	2	no	—
88	C₄×D₃×C₉	D₄	1	4	yes	complemented
89	C₉×Dic₆	—	2	2	no	—
90	C₃×#535	—	3	1	no	—
91	#5607	C₉	1	1	yes	characteristic, direct product factor
92	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
93	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
95	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
97	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
100	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
101	C₃×D₃×D₄	—	2	4	no	—
102	C₃×#235	—	2	4	no	—
103	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
106	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
109	C₂⁴×C₉	—	3	2	no	—
110	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×#217	C₂²×C₃	1	2	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
116	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
117	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
118	C₉×#41	—	6	4	no	—
119	C₂×Q₈×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	2	1	no	—
121	C₂×D₄×C₉	—	2	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	C₂×D₄×C₉	—	3	2	no	—
127	C₂×D₄×C₉	—	3	1	no	—
128	C₂×D₄×C₉	—	3	1	no	—
129	C₂×D₄×C₉	—	3	2	no	—
130	C₂×D₄×C₉	—	6	4	no	—
131	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
132	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
133	C₂²×C₄×C₉	—	2	1	no	—
134	C₂²×C₄×C₉	—	3	1	no	—
135	C₂²×C₄×C₉	—	3	1	no	—
136	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
137	C₉×C₄⋊C₄	—	2	1	no	—
138	C₉×C₄⋊C₄	—	3	1	no	—
139	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
140	C₉×C₂²⋊C₄	—	2	2	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	—	3	2	no	—
144	C₉×C₂²⋊C₄	—	3	2	no	—
145	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
146	C₄²×C₉	—	3	2	no	—
147	C₂²×C₃×C₉	—	2	1	no	—
148	C₂²×C₃×C₉	—	2	2	no	—
149	C₂²×C₃×C₉	—	2	1	no	—
150	C₂²×C₃×C₉	—	2	1	no	—
151	C₂²×C₃×C₉	—	2	2	no	—
152	C₂²×C₃×C₉	—	2	2	no	—
153	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
154	C₂×D₃×C₉	—	2	1	no	—
155	C₂×D₃×C₉	—	2	1	no	—
156	C₂×D₃×C₉	—	2	1	no	—
157	C₂×D₃×C₉	—	2	2	no	—
158	C₂×D₃×C₉	—	2	1	no	—
159	C₂×D₃×C₉	—	2	2	no	—
160	C₂×D₃×C₉	—	2	1	no	—
161	C₂×D₃×C₉	—	2	2	no	—
162	C₂×D₃×C₉	—	4	8	no	—
163	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
164	C₃×C₄×C₉	—	2	1	no	—
165	C₃×C₄×C₉	—	2	2	no	—
166	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
167	C₉×Dic₃	—	2	1	no	—
168	C₉×Dic₃	—	2	2	no	—
169	C₉×Dic₃	C₂×D₄	1	2	yes	—
170	C₂×C₃×#41	—	3	1	no	—
171	C₂²×C₃×D₄	—	3	1	no	—
172	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
174	C₃×#127	—	3	2	no	—
175	C₃×#124	—	3	2	no	—
176	C₃×#121	—	2	1	no	—
177	C₃×#121	—	3	1	no	—
178	C₃×#121	—	3	1	no	—
179	C₃×#121	—	3	1	no	—
180	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
181	C₃×#121	C₃×D₃	1	1	yes	characteristic
182	C₃×#120	—	3	2	no	—
183	C₃×#120	—	3	2	no	—
184	C₃×#117	—	3	1	no	—
185	#940	C₂×C₉	1	2	yes	complemented
186	#938	C₂×C₉	1	1	yes	characteristic, complemented
187	#937	C₂×C₉	1	2	yes	complemented
188	#930	C₂×C₉	1	1	yes	characteristic, complemented
189	#895	C₂×C₉	1	1	yes	characteristic, complemented
190	#892	C₂×C₉	1	1	yes	characteristic, complemented
191	#885	C₂×C₉	1	2	yes	complemented
192	#882	C₂×C₉	1	2	yes	complemented
193	C₂³×C₃²	C₂³×C₃	1	2	yes	—
194	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×D₃	—	2	4	no	—
196	C₂²×C₃×D₃	—	4	2	no	—
197	C₂²×C₃×D₃	—	4	2	no	—
198	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
199	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
201	C₃²×D₄	—	2	2	no	—
202	C₃²×D₄	—	4	2	no	—
203	C₂×C₃²×C₄	—	2	2	no	—
204	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
205	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₃×#67	—	2	2	no	—
208	C₃×#67	—	2	2	no	—
209	C₃×#67	—	2	4	no	—
210	C₃×#67	—	4	2	no	—
211	C₃×#67	—	4	2	no	—
212	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
213	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
215	C₃×D₁₂	—	2	2	no	—
216	C₃×D₁₂	—	2	2	no	—
217	C₃×D₁₂	—	4	2	no	—
218	C₃×C₄×D₃	—	2	2	no	—
219	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
220	C₃×Dic₆	—	2	2	no	—
221	C₂³×C₉	—	2	1	no	—
222	C₂³×C₉	—	2	2	no	—
223	C₂³×C₉	—	3	1	no	—
224	C₂³×C₉	—	3	2	no	—
225	C₂³×C₉	—	3	1	no	—
226	C₂³×C₉	—	6	4	no	—
227	C₂³×C₉	—	12	2	no	—
228	C₂³×C₉	—	12	2	no	—
229	C₂³×C₉	C₂²×D₃	1	2	yes	—
230	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
231	Q₈×C₉	—	6	2	no	—
232	D₄×C₉	—	2	2	no	—
233	D₄×C₉	—	4	2	no	—
234	D₄×C₉	—	4	2	no	—
235	D₄×C₉	—	4	4	no	—
236	D₄×C₉	—	6	2	no	—
237	D₄×C₉	—	6	4	no	—
238	D₄×C₉	—	6	2	no	—
239	D₄×C₉	—	6	2	no	—
240	D₄×C₉	—	6	2	no	—
241	D₄×C₉	—	12	2	no	—
242	D₄×C₉	—	12	2	no	—
243	D₄×C₉	—	12	2	no	—
244	C₂×C₄×C₉	—	2	2	no	—
245	C₂×C₄×C₉	—	2	1	no	—
246	C₂×C₄×C₉	—	2	1	no	—
247	C₂×C₄×C₉	—	2	2	no	—
248	C₂×C₄×C₉	—	3	1	no	—
249	C₂×C₄×C₉	—	3	4	no	—
250	C₂×C₄×C₉	—	3	2	no	—
251	C₂×C₄×C₉	—	3	1	no	—
252	C₂×C₄×C₉	—	4	2	no	—
253	C₂×C₄×C₉	—	6	2	no	—
254	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
255	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
257	#535	—	3	1	no	Sylow
258	C₂×C₃×C₉	—	4	1	no	—
259	C₂×C₃×C₉	—	4	2	no	—
260	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
263	D₃×C₉	—	2	2	no	—
264	D₃×C₉	—	4	1	no	—
265	D₃×C₉	—	4	2	no	—
266	C₂⁴×C₃	—	3	2	no	—
267	C₂³×D₃	C₂²×C₉	1	2	yes	—
268	C₃×#41	—	6	4	no	—
269	C₂×C₃×Q₈	—	3	1	no	—
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	—	3	1	no	—
273	C₂×C₃×D₄	—	3	2	no	—
274	C₂×C₃×D₄	—	3	1	no	—
275	C₂×C₃×D₄	—	3	2	no	—
276	C₂×C₃×D₄	—	3	2	no	—
277	C₂×C₃×D₄	—	3	1	no	—
278	C₂×C₃×D₄	—	3	1	no	—
279	C₂×C₃×D₄	—	3	2	no	—
280	C₂×C₃×D₄	—	6	4	no	—
281	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
283	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
284	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	3	1	no	—
287	C₂²×C₃×C₄	—	3	1	no	—
288	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
289	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
290	C₂×#67	C₂²×C₉	1	2	yes	—
291	C₂×#67	C₂²×C₉	1	1	yes	characteristic
292	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
293	C₂×#67	C₂²×C₉	1	2	yes	complemented
294	C₂×#67	C₂²×C₉	1	2	yes	complemented
295	D₃×D₄	—	2	4	no	—
296	#235	—	2	4	no	—
297	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
298	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
299	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
300	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
301	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
302	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
303	C₃×C₄⋊C₄	—	2	1	no	—
304	C₃×C₄⋊C₄	—	3	1	no	—
305	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
306	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
307	C₃×C₂²⋊C₄	—	2	2	no	—
308	C₃×C₂²⋊C₄	—	3	2	no	—
309	C₃×C₂²⋊C₄	—	3	2	no	—
310	C₃×C₂²⋊C₄	—	3	2	no	—
311	C₃×C₂²⋊C₄	—	3	2	no	—
312	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
313	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
314	C₃×C₄²	—	3	2	no	—
315	#217	C₂²×C₉	1	2	yes	complemented
316	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
317	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
318	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
319	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
320	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
321	C₂²×C₃²	—	2	1	no	—
322	C₂²×C₃²	—	2	1	no	—
323	C₂²×C₃²	—	2	2	no	—
324	C₂²×C₃²	—	2	1	no	—
325	C₂²×C₃²	—	2	2	no	—
326	C₂²×C₃²	—	2	2	no	—
327	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
328	C₂×C₃×D₃	—	2	1	no	—
329	C₂×C₃×D₃	—	2	1	no	—
330	C₂×C₃×D₃	—	2	1	no	—
331	C₂×C₃×D₃	—	2	2	no	—
332	C₂×C₃×D₃	—	2	1	no	—
333	C₂×C₃×D₃	—	2	2	no	—
334	C₂×C₃×D₃	—	2	1	no	—
335	C₂×C₃×D₃	—	2	2	no	—
336	C₂×C₃×D₃	—	4	8	no	—
337	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
338	C₃²×C₄	—	2	1	no	—
339	C₃²×C₄	—	2	2	no	—
340	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
341	C₃×Dic₃	—	2	1	no	—
342	C₃×Dic₃	—	2	2	no	—
343	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
344	C₂²×C₉	—	2	2	no	—
345	C₂²×C₉	—	2	1	no	—
346	C₂²×C₉	—	2	2	no	—
347	C₂²×C₉	—	2	1	no	—
348	C₂²×C₉	—	2	2	no	—
349	C₂²×C₉	—	2	1	no	—
350	C₂²×C₉	—	2	2	no	—
351	C₂²×C₉	—	2	1	no	—
352	C₂²×C₉	—	3	2	no	—
353	C₂²×C₉	—	4	1	no	—
354	C₂²×C₉	—	4	1	no	—
355	C₂²×C₉	—	4	2	no	—
356	C₂²×C₉	—	4	2	no	—
357	C₂²×C₉	—	4	2	no	—
358	C₂²×C₉	—	6	1	no	—
359	C₂²×C₉	—	6	1	no	—
360	C₂²×C₉	—	6	1	no	—
361	C₂²×C₉	—	6	2	no	—
362	C₂²×C₉	—	6	1	no	—
363	C₂²×C₉	—	6	2	no	—
364	C₂²×C₉	—	6	1	no	—
365	C₂²×C₉	—	6	2	no	—
366	C₂²×C₉	—	12	8	no	—
367	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
368	C₄×C₉	—	2	1	no	—
369	C₄×C₉	—	2	2	no	—
370	C₄×C₉	—	2	2	no	—
371	C₄×C₉	—	3	2	no	—
372	C₄×C₉	—	4	1	no	—
373	C₄×C₉	—	4	2	no	—
374	C₄×C₉	—	6	1	no	—
375	C₄×C₉	—	6	2	no	—
376	C₄×C₉	D₃×D₄	1	2	yes	—
377	C₂×#41	—	3	1	no	—
378	C₂²×D₄	—	3	1	no	—
379	#127	—	3	2	no	—
380	#124	—	3	2	no	—
381	#121	—	3	1	no	—
382	#121	—	3	1	no	—
383	#121	—	3	1	no	—
384	#121	D₃×C₉	1	1	yes	characteristic, complemented
385	#120	—	3	2	no	—
386	#120	—	3	2	no	—
387	#117	—	3	1	no	—
388	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	3	1	no	—
392	C₂³×C₃	—	3	2	no	—
393	C₂³×C₃	—	3	1	no	—
394	C₂³×C₃	—	6	4	no	—
395	C₂³×C₃	—	12	2	no	—
396	C₂³×C₃	—	12	2	no	—
397	C₂³×C₃	C₂³×C₉	1	2	yes	—
398	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
399	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
400	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
401	C₂²×D₃	—	2	4	no	—
402	C₂²×D₃	—	4	2	no	—
403	C₂²×D₃	—	4	2	no	—
404	C₂²×D₃	C₂³×C₉	1	2	yes	—
405	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
406	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
407	C₃×Q₈	—	6	2	no	—
408	C₃×D₄	—	2	2	no	—
409	C₃×D₄	—	2	2	no	—
410	C₃×D₄	—	4	2	no	—
411	C₃×D₄	—	4	2	no	—
412	C₃×D₄	—	4	2	no	—
413	C₃×D₄	—	4	4	no	—
414	C₃×D₄	—	6	2	no	—
415	C₃×D₄	—	6	4	no	—
416	C₃×D₄	—	6	2	no	—
417	C₃×D₄	—	6	2	no	—
418	C₃×D₄	—	6	2	no	—
419	C₃×D₄	—	12	2	no	—
420	C₃×D₄	—	12	2	no	—
421	C₃×D₄	—	12	2	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	3	1	no	—
428	C₂×C₃×C₄	—	3	4	no	—
429	C₂×C₃×C₄	—	3	2	no	—
430	C₂×C₃×C₄	—	3	1	no	—
431	C₂×C₃×C₄	—	4	2	no	—
432	C₂×C₃×C₄	—	6	2	no	—
433	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
434	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
437	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
439	#67	—	2	2	no	—
440	#67	—	2	2	no	—
441	#67	—	2	4	no	—
442	#67	—	4	2	no	—
443	#67	—	4	2	no	—
444	C₂×Dic₃	C₂³×C₉	1	2	yes	—
445	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
446	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
447	D₁₂	—	2	2	no	—
448	D₁₂	—	2	2	no	—
449	D₁₂	—	4	2	no	—
450	C₄×D₃	—	2	2	no	—
451	C₄×D₃	D₄×C₉	1	4	yes	complemented
452	Dic₆	—	2	2	no	—
453	C₂×C₃²	—	4	1	no	—
454	C₂×C₃²	—	4	2	no	—
455	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
456	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
458	C₃×D₃	—	2	2	no	—
459	C₃×D₃	—	4	1	no	—
460	C₃×D₃	—	4	2	no	—
461	C₂×C₉	—	2	1	no	—
462	C₂×C₉	—	2	1	no	—
463	C₂×C₉	—	2	1	no	—
464	C₂×C₉	—	4	2	no	—
465	C₂×C₉	—	4	1	no	—
466	C₂×C₉	—	4	2	no	—
467	C₂×C₉	—	6	2	no	—
468	C₂×C₉	—	8	2	no	—
469	C₂×C₉	—	12	1	no	—
470	C₂×C₉	—	12	2	no	—
471	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
472	C₂×C₉	#1004	1	1	yes	characteristic
473	C₂×C₉	#1009	1	1	yes	characteristic
474	C₂⁴	—	3	2	no	—
475	#41	—	6	4	no	—
476	C₂×Q₈	—	3	1	no	—
477	C₂×D₄	—	3	1	no	—
478	C₂×D₄	—	3	2	no	—
479	C₂×D₄	—	3	1	no	—
480	C₂×D₄	—	3	2	no	—
481	C₂×D₄	—	3	2	no	—
482	C₂×D₄	—	3	1	no	—
483	C₂×D₄	—	3	1	no	—
484	C₂×D₄	—	3	2	no	—
485	C₂×D₄	—	6	4	no	—
486	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
487	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
488	C₂²×C₄	—	3	1	no	—
489	C₂²×C₄	—	3	1	no	—
490	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
491	C₄⋊C₄	—	3	1	no	—
492	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
498	C₄²	—	3	2	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	1	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	3	2	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	2	no	—
517	C₂²×C₃	—	4	2	no	—
518	C₂²×C₃	—	4	2	no	—
519	C₂²×C₃	—	6	1	no	—
520	C₂²×C₃	—	6	1	no	—
521	C₂²×C₃	—	6	1	no	—
522	C₂²×C₃	—	6	2	no	—
523	C₂²×C₃	—	6	1	no	—
524	C₂²×C₃	—	6	2	no	—
525	C₂²×C₃	—	6	1	no	—
526	C₂²×C₃	—	6	2	no	—
527	C₂²×C₃	—	12	8	no	—
528	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
529	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	4	8	no	—
539	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	3	2	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	2	no	—
548	C₃×C₄	—	6	1	no	—
549	C₃×C₄	—	6	2	no	—
550	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
551	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	2	no	—
554	Dic₃	C₂×D₄×C₉	1	2	yes	—
555	C₃²	C₃×#535	1	1	yes	characteristic
556	C₉	—	2	1	no	—
557	C₉	#5607	1	1	yes	characteristic, direct product factor
558	C₂³	—	3	1	no	—
559	C₂³	—	3	2	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	6	4	no	—
562	C₂³	—	12	2	no	—
563	C₂³	—	12	2	no	—
564	C₂³	C₂²×D₃×C₉	1	2	yes	—
565	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
566	Q₈	—	6	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	6	2	no	—
570	D₄	—	6	4	no	—
571	D₄	—	6	2	no	—
572	D₄	—	6	2	no	—
573	D₄	—	6	2	no	—
574	D₄	—	12	2	no	—
575	D₄	—	12	2	no	—
576	D₄	—	12	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	4	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	6	2	no	—
583	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
584	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
586	C₂×C₃	—	2	1	no	—
587	C₂×C₃	—	2	1	no	—
588	C₂×C₃	—	2	1	no	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	4	2	no	—
591	C₂×C₃	—	4	1	no	—
592	C₂×C₃	—	4	2	no	—
593	C₂×C₃	—	4	1	no	—
594	C₂×C₃	—	6	2	no	—
595	C₂×C₃	—	8	2	no	—
596	C₂×C₃	—	12	2	no	—
597	C₂×C₃	—	12	1	no	—
598	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
599	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
602	C₂×C₃	C₃×#1004	1	1	yes	characteristic
603	C₂×C₃	C₃×#1009	1	1	yes	characteristic
604	D₃	—	2	2	no	—
605	D₃	—	4	2	no	—
606	D₃	—	4	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	3	2	no	—
614	C₂²	—	6	1	no	—
615	C₂²	—	6	1	no	—
616	C₂²	—	6	1	no	—
617	C₂²	—	6	2	no	—
618	C₂²	—	6	1	no	—
619	C₂²	—	6	2	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	2	no	—
622	C₂²	—	12	8	no	—
623	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	3	2	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	2	no	—
629	C₄	D₃×D₄×C₉	1	2	yes	—
630	C₃	—	2	1	no	—
631	C₃	C₉×#535	1	1	yes	characteristic, complemented
632	C₃	C₃×#5607	1	1	yes	characteristic
633	C₂	—	4	2	no	—
634	C₂	—	4	1	no	—
635	C₂	—	6	2	no	—
636	C₂	—	12	2	no	—
637	C₂	—	12	1	no	—
638	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
639	C₂	C₉×#1004	1	1	yes	characteristic
640	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×#5607	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#535
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. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×#121	C₂	semidirect
4. C₉×#940	C₂	semidirect
5. C₉×#938	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₉×#930	C₂	semidirect
8. C₉×#895	C₂	semidirect
9. C₉×#892	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#882	C₂	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
21. C₂×C₉×#67	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
27. C₂×C₉×D₁₂	C₂²	semidirect
29. C₂×C₄×D₃×C₉	C₂²	semidirect
30. C₂×C₉×Dic₆	C₂²	semidirect
31. C₃×C₉×C₄⋊C₄	C₂²	semidirect
32. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
33. C₉×#217	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×C₄⋊Dic₃	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
58. C₉×#121	D₃	semidirect
88. C₄×D₃×C₉	D₄	semidirect
91. #5607	C₉	direct (N × H)
132. C₂×D₄×C₉	C₂×D₃	semidirect
136. C₂²×C₄×C₉	C₂×D₃	semidirect
139. C₉×C₄⋊C₄	C₂×D₃	semidirect
145. C₉×C₂²⋊C₄	C₂×D₃	semidirect
172. C₂×D₃×D₄	C₂×C₉	semidirect
173. C₂×#235	C₂×C₉	semidirect
180. C₃×#121	C₂×C₉	semidirect
185. #940	C₂×C₉	semidirect
186. #938	C₂×C₉	semidirect
187. #937	C₂×C₉	semidirect
188. #930	C₂×C₉	semidirect
189. #895	C₂×C₉	semidirect
190. #892	C₂×C₉	semidirect
191. #885	C₂×C₉	semidirect
192. #882	C₂×C₉	semidirect
282. C₂×C₃×D₄	C₂²×C₉	semidirect
288. C₂²×C₃×C₄	C₂²×C₉	semidirect
292. C₂×#67	C₂²×C₉	semidirect
293. C₂×#67	C₂²×C₉	semidirect
294. C₂×#67	C₂²×C₉	semidirect
299. C₂×D₁₂	C₂²×C₉	semidirect
301. C₂×C₄×D₃	C₂²×C₉	semidirect
302. C₂×Dic₆	C₂²×C₉	semidirect
305. C₃×C₄⋊C₄	C₂²×C₉	semidirect
312. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
315. #217	C₂²×C₉	semidirect
317. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
318. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
319. C₄⋊Dic₃	C₂²×C₉	semidirect
320. C₄×Dic₃	C₂²×C₉	semidirect
384. #121	D₃×C₉	semidirect
388. C₃×C₉	#535	semidirect
451. C₄×D₃	D₄×C₉	semidirect
487. C₂×D₄	C₂×D₃×C₉	semidirect
490. C₂²×C₄	C₂×D₃×C₉	semidirect
492. C₄⋊C₄	C₂×D₃×C₉	semidirect
497. C₂²⋊C₄	C₂×D₃×C₉	semidirect
557. C₉	#5607	direct (N × H)
631. C₃	C₉×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂×C₉×#235	2
C₃×C₉×#121	2
C₉×#940	2
C₉×#938	2
C₉×#937	2
C₉×#930	2
C₉×#895	2
C₉×#892	2
C₉×#885	2
C₉×#882	2
C₃×#5607	3
C₉×#535	3

Subgroups — C9×#5607 #13152826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5607 #13152826