Subgroups — C₉×#5829 #13153702

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	2	yes	maximal, complemented
6	C₉×#937	C₂	1	2	yes	maximal, complemented
7	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#929	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5829	C₃	1	1	yes	maximal, characteristic
13	C₉×#546	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₃×C₉×#41	—	2	4	no	—
16	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	complemented
20	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₉×#67	C₂²	1	2	yes	—
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic
23	C₂×C₉×#67	C₂²	1	2	yes	complemented
24	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
25	D₃×D₄×C₉	—	2	4	no	—
26	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
28	C₉×#217	C₂²	1	1	yes	characteristic, complemented
29	C₉×#217	C₂²	1	2	yes	complemented
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
41	C₃×#947	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#939	C₂×C₃	1	2	yes	—
44	C₃×#937	C₂×C₃	1	2	yes	—
45	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
46	C₃×#930	C₂×C₃	1	1	yes	characteristic
47	C₃×#929	C₂×C₃	1	2	yes	—
48	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
49	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	2	1	no	—
51	C₂×C₉×#41	D₃	1	1	yes	characteristic, complemented
52	C₂²×D₄×C₉	—	3	1	no	—
53	C₉×#124	—	3	1	no	—
54	C₉×#123	—	3	2	no	—
55	C₉×C₂²⋊Q₈	—	3	1	no	—
56	C₉×#121	—	3	2	no	—
57	C₉×#121	—	3	1	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	C₂³×C₃×C₉	C₂³	1	2	yes	—
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	2	4	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	C₃×Q₈×C₉	—	2	2	no	—
70	C₃×D₄×C₉	—	2	4	no	—
71	C₃×D₄×C₉	D₄	1	4	yes	complemented
72	C₂×C₃×C₄×C₉	—	2	4	no	—
73	C₂×C₃×C₄×C₉	—	2	2	no	—
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
76	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₉×#67	—	2	4	no	—
78	C₉×#67	—	2	2	no	—
79	C₉×#67	—	4	2	no	—
80	C₂×C₉×Dic₃	—	4	2	no	—
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₉×Dic₃	C₂³	1	2	yes	—
84	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
85	C₉×D₁₂	—	2	2	no	—
86	C₄×D₃×C₉	—	2	2	no	—
87	C₃×#546	—	3	1	no	—
88	#5829	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
90	C₃²×#41	—	2	4	no	—
91	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
95	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
98	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
99	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
100	C₃×D₃×D₄	—	2	4	no	—
101	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
103	C₂⁴×C₉	—	3	2	no	—
104	C₃×#217	C₂²×C₃	1	1	yes	characteristic
105	C₃×#217	C₂²×C₃	1	2	yes	—
106	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃×(C₂×D₃)⋊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	1	yes	characteristic
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
115	C₉×#41	—	2	8	no	—
116	C₉×#41	—	2	4	no	—
117	C₂×Q₈×C₉	—	2	1	no	—
118	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
119	C₂×D₄×C₉	—	2	1	no	—
120	C₂×D₄×C₉	—	2	2	no	—
121	C₂×D₄×C₉	—	3	1	no	—
122	C₂×D₄×C₉	—	3	2	no	—
123	C₂×D₄×C₉	—	3	2	no	—
124	C₂×D₄×C₉	—	3	1	no	—
125	C₂×D₄×C₉	—	6	4	no	—
126	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
127	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
128	C₂²×C₄×C₉	—	2	2	no	—
129	C₂²×C₄×C₉	—	2	1	no	—
130	C₂²×C₄×C₉	—	3	2	no	—
131	C₂²×C₄×C₉	—	3	1	no	—
132	C₂²×C₄×C₉	C₂×D₃	1	2	yes	complemented
133	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
134	C₉×C₄⋊C₄	—	3	1	no	—
135	C₉×C₄⋊C₄	—	3	1	no	—
136	C₉×C₄⋊C₄	—	3	2	no	—
137	C₉×C₂²⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	—	3	1	no	—
139	C₉×C₂²⋊C₄	—	3	1	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	—	3	2	no	—
144	C₄²×C₉	—	3	1	no	—
145	C₂²×C₃×C₉	—	2	2	no	—
146	C₂²×C₃×C₉	—	2	2	no	—
147	C₂²×C₃×C₉	—	2	1	no	—
148	C₂²×C₃×C₉	—	2	1	no	—
149	C₂²×C₃×C₉	—	2	1	no	—
150	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
151	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	1	no	—
154	C₂×D₃×C₉	—	2	2	no	—
155	C₂×D₃×C₉	—	2	2	no	—
156	C₂×D₃×C₉	—	2	2	no	—
157	C₂×D₃×C₉	—	4	8	no	—
158	C₂×D₃×C₉	#41	1	2	yes	complemented
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	C₉×Dic₃	—	2	2	no	—
166	C₂×C₃×#41	—	2	1	no	—
167	C₂×C₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
169	C₂²×C₃×D₄	—	3	1	no	—
170	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
171	C₃×#124	—	3	1	no	—
172	C₃×#123	—	3	2	no	—
173	C₃×C₂²⋊Q₈	—	3	1	no	—
174	C₃×#121	—	3	2	no	—
175	C₃×#121	—	3	1	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	#946	C₂×C₉	1	1	yes	characteristic, complemented
182	#939	C₂×C₉	1	2	yes	complemented
183	#937	C₂×C₉	1	2	yes	complemented
184	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
185	#930	C₂×C₉	1	1	yes	characteristic, complemented
186	#929	C₂×C₉	1	2	yes	complemented
187	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
188	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
189	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
190	C₂³×C₃²	C₂³×C₃	1	2	yes	—
191	C₂²×C₃×D₃	—	2	4	no	—
192	C₂²×C₃×D₃	—	2	4	no	—
193	C₂²×C₃×D₃	—	4	2	no	—
194	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
195	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
196	C₃²×Q₈	—	2	2	no	—
197	C₃²×D₄	—	2	4	no	—
198	C₃²×D₄	C₃×D₄	1	4	yes	—
199	C₂×C₃²×C₄	—	2	4	no	—
200	C₂×C₃²×C₄	—	2	2	no	—
201	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
203	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₃×#67	—	2	4	no	—
205	C₃×#67	—	2	2	no	—
206	C₃×#67	—	4	2	no	—
207	C₂×C₃×Dic₃	—	4	2	no	—
208	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
212	C₃×D₁₂	—	2	2	no	—
213	C₃×C₄×D₃	—	2	2	no	—
214	C₂³×C₉	—	2	1	no	—
215	C₂³×C₉	—	2	2	no	—
216	C₂³×C₉	—	3	1	no	—
217	C₂³×C₉	—	3	2	no	—
218	C₂³×C₉	—	6	4	no	—
219	C₂³×C₉	—	6	4	no	—
220	C₂³×C₉	—	12	2	no	—
221	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
222	C₂³×C₉	C₂²×D₃	1	2	yes	—
223	Q₈×C₉	—	2	4	no	—
224	Q₈×C₉	—	2	2	no	—
225	D₄×C₉	—	2	8	no	—
226	D₄×C₉	—	2	4	no	—
227	D₄×C₉	—	2	4	no	—
228	D₄×C₉	—	6	2	no	—
229	D₄×C₉	—	6	4	no	—
230	D₄×C₉	—	6	2	no	—
231	D₄×C₉	—	12	2	no	—
232	D₄×C₉	#67	1	4	yes	complemented
233	C₂×C₄×C₉	—	2	8	no	—
234	C₂×C₄×C₉	—	2	4	no	—
235	C₂×C₄×C₉	—	2	4	no	—
236	C₂×C₄×C₉	—	2	2	no	—
237	C₂×C₄×C₉	—	2	1	no	—
238	C₂×C₄×C₉	—	2	2	no	—
239	C₂×C₄×C₉	—	2	1	no	—
240	C₂×C₄×C₉	—	3	1	no	—
241	C₂×C₄×C₉	—	3	1	no	—
242	C₂×C₄×C₉	—	3	2	no	—
243	C₂×C₄×C₉	—	3	1	no	—
244	C₂×C₄×C₉	—	6	2	no	—
245	C₂×C₄×C₉	—	12	2	no	—
246	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
248	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
249	#546	—	3	1	no	Sylow
250	C₂×C₃×C₉	—	2	4	no	—
251	C₂×C₃×C₉	—	4	1	no	—
252	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
255	D₃×C₉	—	2	2	no	—
256	D₃×C₉	—	4	2	no	—
257	C₂⁴×C₃	—	3	2	no	—
258	C₂³×D₃	C₂²×C₉	1	2	yes	—
259	C₃×#41	—	2	8	no	—
260	C₃×#41	—	2	4	no	—
261	C₃×#41	—	2	4	no	—
262	C₂×C₃×Q₈	—	2	1	no	—
263	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
264	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
265	C₂×C₃×D₄	—	2	1	no	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	3	1	no	—
268	C₂×C₃×D₄	—	3	2	no	—
269	C₂×C₃×D₄	—	3	2	no	—
270	C₂×C₃×D₄	—	3	1	no	—
271	C₂×C₃×D₄	—	6	4	no	—
272	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
273	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
274	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	3	2	no	—
279	C₂²×C₃×C₄	—	3	1	no	—
280	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	complemented
281	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
282	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
283	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
284	C₂×#67	C₂²×C₉	1	1	yes	characteristic
285	C₂×#67	C₂²×C₉	1	2	yes	—
286	C₂×#67	C₂²×C₉	1	2	yes	complemented
287	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
288	D₃×D₄	—	2	4	no	—
289	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
291	C₃×C₄⋊C₄	—	3	1	no	—
292	C₃×C₄⋊C₄	—	3	2	no	—
293	C₃×C₄⋊C₄	—	3	1	no	—
294	C₃×C₂²⋊C₄	—	3	2	no	—
295	C₃×C₂²⋊C₄	—	3	1	no	—
296	C₃×C₂²⋊C₄	—	3	1	no	—
297	C₃×C₂²⋊C₄	—	3	2	no	—
298	C₃×C₂²⋊C₄	—	3	2	no	—
299	C₃×C₂²⋊C₄	—	3	2	no	—
300	C₃×C₂²⋊C₄	—	3	2	no	—
301	C₃×C₄²	—	3	1	no	—
302	#217	C₂²×C₉	1	1	yes	characteristic, complemented
303	#217	C₂²×C₉	1	2	yes	complemented
304	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
306	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
307	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
308	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
309	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
310	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
311	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
312	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
313	C₂²×C₃²	—	2	1	no	—
314	C₂²×C₃²	—	2	2	no	—
315	C₂²×C₃²	—	2	2	no	—
316	C₂²×C₃²	—	2	1	no	—
317	C₂²×C₃²	—	2	1	no	—
318	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
319	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
320	C₂×C₃×D₃	—	2	1	no	—
321	C₂×C₃×D₃	—	2	1	no	—
322	C₂×C₃×D₃	—	2	2	no	—
323	C₂×C₃×D₃	—	2	2	no	—
324	C₂×C₃×D₃	—	2	2	no	—
325	C₂×C₃×D₃	—	4	8	no	—
326	C₂×C₃×D₃	C₃×#41	1	2	yes	—
327	C₃²×C₄	—	2	1	no	—
328	C₃²×C₄	—	2	2	no	—
329	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
330	C₃×Dic₃	—	2	1	no	—
331	C₃×Dic₃	—	2	1	no	—
332	C₃×Dic₃	—	2	1	no	—
333	C₃×Dic₃	—	2	2	no	—
334	C₂²×C₉	—	2	2	no	—
335	C₂²×C₉	—	2	2	no	—
336	C₂²×C₉	—	2	2	no	—
337	C₂²×C₉	—	2	1	no	—
338	C₂²×C₉	—	2	1	no	—
339	C₂²×C₉	—	2	1	no	—
340	C₂²×C₉	—	2	1	no	—
341	C₂²×C₉	—	2	4	no	—
342	C₂²×C₉	—	3	2	no	—
343	C₂²×C₉	—	4	2	no	—
344	C₂²×C₉	—	4	2	no	—
345	C₂²×C₉	—	4	1	no	—
346	C₂²×C₉	—	4	1	no	—
347	C₂²×C₉	—	6	1	no	—
348	C₂²×C₉	—	6	1	no	—
349	C₂²×C₉	—	6	2	no	—
350	C₂²×C₉	—	6	2	no	—
351	C₂²×C₉	—	6	2	no	—
352	C₂²×C₉	—	12	8	no	—
353	C₂²×C₉	C₂×#67	1	4	yes	—
354	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
355	C₄×C₉	—	2	2	no	—
356	C₄×C₉	—	2	4	no	—
357	C₄×C₉	—	2	1	no	—
358	C₄×C₉	—	2	2	no	—
359	C₄×C₉	—	2	2	no	—
360	C₄×C₉	—	6	1	no	—
361	C₄×C₉	—	6	1	no	—
362	C₄×C₉	—	6	2	no	—
363	C₄×C₉	—	6	1	no	—
364	C₄×C₉	C₂×#67	1	2	yes	—
365	C₂×#41	D₃×C₉	1	1	yes	characteristic, complemented
366	C₂²×D₄	—	3	1	no	—
367	#124	—	3	1	no	—
368	#123	—	3	2	no	—
369	C₂²⋊Q₈	—	3	1	no	—
370	#121	—	3	2	no	—
371	#121	—	3	1	no	—
372	#120	—	3	2	no	—
373	C₄×D₄	—	3	1	no	—
374	C₄×D₄	—	3	1	no	—
375	C₂×C₂²⋊C₄	—	3	2	no	—
376	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	3	1	no	—
380	C₂³×C₃	—	3	2	no	—
381	C₂³×C₃	—	6	4	no	—
382	C₂³×C₃	—	6	4	no	—
383	C₂³×C₃	—	12	2	no	—
384	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
385	C₂³×C₃	C₂³×C₉	1	2	yes	—
386	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
387	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
388	C₂²×D₃	—	2	4	no	—
389	C₂²×D₃	—	2	4	no	—
390	C₂²×D₃	—	4	2	no	—
391	C₂²×D₃	C₂³×C₉	1	2	yes	—
392	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
393	C₃×Q₈	—	2	4	no	—
394	C₃×Q₈	—	2	2	no	—
395	C₃×Q₈	—	2	2	no	—
396	C₃×D₄	—	2	8	no	—
397	C₃×D₄	—	2	4	no	—
398	C₃×D₄	—	2	4	no	—
399	C₃×D₄	—	2	4	no	—
400	C₃×D₄	—	6	2	no	—
401	C₃×D₄	—	6	4	no	—
402	C₃×D₄	—	6	2	no	—
403	C₃×D₄	—	12	2	no	—
404	C₃×D₄	D₄×C₉	1	4	yes	complemented
405	C₃×D₄	C₃×#67	1	4	yes	—
406	C₂×C₃×C₄	—	2	8	no	—
407	C₂×C₃×C₄	—	2	4	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	3	1	no	—
416	C₂×C₃×C₄	—	3	1	no	—
417	C₂×C₃×C₄	—	3	2	no	—
418	C₂×C₃×C₄	—	3	1	no	—
419	C₂×C₃×C₄	—	6	2	no	—
420	C₂×C₃×C₄	—	12	2	no	—
421	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
423	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
426	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
427	#67	—	2	4	no	—
428	#67	—	2	2	no	—
429	#67	—	4	2	no	—
430	C₂×Dic₃	—	4	2	no	—
431	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
432	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
433	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
434	C₂×Dic₃	C₂³×C₉	1	2	yes	—
435	D₁₂	—	2	2	no	—
436	C₄×D₃	—	2	2	no	—
437	C₂×C₃²	—	2	4	no	—
438	C₂×C₃²	—	4	1	no	—
439	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
440	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
441	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
442	C₃×D₃	—	2	2	no	—
443	C₃×D₃	—	4	2	no	—
444	C₂×C₉	—	2	4	no	—
445	C₂×C₉	—	2	1	no	—
446	C₂×C₉	—	2	1	no	—
447	C₂×C₉	—	2	1	no	—
448	C₂×C₉	—	4	4	no	—
449	C₂×C₉	—	4	2	no	—
450	C₂×C₉	—	4	1	no	—
451	C₂×C₉	—	6	2	no	—
452	C₂×C₉	—	12	2	no	—
453	C₂×C₉	D₃×#41	1	1	yes	characteristic
454	C₂×C₉	#1009	1	1	yes	characteristic
455	C₂×C₉	C₂²×#67	1	1	yes	characteristic
456	C₂⁴	—	3	2	no	—
457	#41	—	2	4	no	—
458	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
459	C₂×D₄	—	3	1	no	—
460	C₂×D₄	—	3	2	no	—
461	C₂×D₄	—	3	2	no	—
462	C₂×D₄	—	3	1	no	—
463	C₂×D₄	—	6	4	no	—
464	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
465	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
466	C₂²×C₄	—	3	2	no	—
467	C₂²×C₄	—	3	1	no	—
468	C₂²×C₄	C₂×D₃×C₉	1	2	yes	complemented
469	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₄²	—	3	1	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	2	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	4	no	—
494	C₂²×C₃	—	3	2	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	4	2	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	6	1	no	—
500	C₂²×C₃	—	6	1	no	—
501	C₂²×C₃	—	6	2	no	—
502	C₂²×C₃	—	6	2	no	—
503	C₂²×C₃	—	6	2	no	—
504	C₂²×C₃	—	12	8	no	—
505	C₂²×C₃	C₂×D₄×C₉	1	4	yes	—
506	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
507	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
508	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
509	C₂×D₃	—	2	1	no	—
510	C₂×D₃	—	2	1	no	—
511	C₂×D₃	—	2	2	no	—
512	C₂×D₃	—	2	2	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	4	8	no	—
515	C₂×D₃	C₉×#41	1	2	yes	complemented
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	4	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	6	1	no	—
524	C₃×C₄	—	6	1	no	—
525	C₃×C₄	—	6	2	no	—
526	C₃×C₄	—	6	1	no	—
527	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
528	C₃×C₄	C₂×C₃×#67	1	2	yes	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	1	no	—
532	Dic₃	—	2	2	no	—
533	C₃²	C₃×#546	1	1	yes	characteristic
534	C₉	—	2	1	no	—
535	C₉	#5829	1	1	yes	characteristic, direct product factor
536	C₂³	—	3	1	no	—
537	C₂³	—	3	2	no	—
538	C₂³	—	6	4	no	—
539	C₂³	—	6	4	no	—
540	C₂³	—	12	2	no	—
541	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
542	C₂³	C₂²×D₃×C₉	1	2	yes	—
543	Q₈	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	6	2	no	—
546	D₄	—	6	4	no	—
547	D₄	—	6	2	no	—
548	D₄	—	12	2	no	—
549	D₄	C₉×#67	1	4	yes	complemented
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	3	1	no	—
553	C₂×C₄	—	3	1	no	—
554	C₂×C₄	—	3	2	no	—
555	C₂×C₄	—	3	1	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	12	2	no	—
558	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
560	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
561	C₂×C₃	—	2	4	no	—
562	C₂×C₃	—	2	4	no	—
563	C₂×C₃	—	2	1	no	—
564	C₂×C₃	—	2	1	no	—
565	C₂×C₃	—	2	1	no	—
566	C₂×C₃	—	4	4	no	—
567	C₂×C₃	—	4	2	no	—
568	C₂×C₃	—	4	1	no	—
569	C₂×C₃	—	4	1	no	—
570	C₂×C₃	—	6	2	no	—
571	C₂×C₃	—	12	2	no	—
572	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
573	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
574	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
576	C₂×C₃	C₃×#1009	1	1	yes	characteristic
577	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
578	D₃	—	2	2	no	—
579	D₃	—	4	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	3	2	no	—
586	C₂²	—	6	1	no	—
587	C₂²	—	6	1	no	—
588	C₂²	—	6	2	no	—
589	C₂²	—	6	2	no	—
590	C₂²	—	6	2	no	—
591	C₂²	—	12	8	no	—
592	C₂²	C₂×C₉×#67	1	4	yes	—
593	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	6	1	no	—
597	C₄	—	6	1	no	—
598	C₄	—	6	2	no	—
599	C₄	—	6	1	no	—
600	C₄	C₂×C₉×#67	1	2	yes	—
601	C₃	—	2	1	no	—
602	C₃	C₉×#546	1	1	yes	characteristic, complemented
603	C₃	C₃×#5829	1	1	yes	characteristic
604	C₂	—	2	4	no	—
605	C₂	—	4	1	no	—
606	C₂	—	6	2	no	—
607	C₂	—	12	2	no	—
608	C₂	D₃×C₉×#41	1	1	yes	characteristic
609	C₂	C₉×#1009	1	1	yes	characteristic
610	C₂	C₂²×C₉×#67	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×#41	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5829	C₃
hypercenter	C₂×C₉×#41	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₉×#947	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. D₄×C₉×Dic₃	C₂	semidirect
8. C₉×#930	C₂	semidirect
9. C₉×#929	C₂	semidirect
10. C₄×C₉×#67	C₂	semidirect
11. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
16. C₂×C₃×Q₈×C₉	C₂²	semidirect
18. C₂×C₃×D₄×C₉	C₂²	semidirect
19. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂²×C₃×C₄×C₉	C₂²	semidirect
23. C₂×C₉×#67	C₂²	semidirect
24. C₂²×C₉×Dic₃	C₂²	semidirect
28. C₉×#217	C₂²	semidirect
29. C₉×#217	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×C₄⋊Dic₃	C₂²	semidirect
36. C₉×Dic₃⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
51. C₂×C₉×#41	D₃	semidirect
71. C₃×D₄×C₉	D₄	semidirect
88. #5829	C₉	direct (N × H)
118. C₂×Q₈×C₉	C₂×D₃	semidirect
127. C₂×D₄×C₉	C₂×D₃	semidirect
132. C₂²×C₄×C₉	C₂×D₃	semidirect
133. C₂²×C₄×C₉	C₂×D₃	semidirect
158. C₂×D₃×C₉	#41	semidirect
167. C₂×C₃×#41	C₂×C₉	semidirect
170. C₂×D₃×D₄	C₂×C₉	semidirect
180. #947	C₂×C₉	semidirect
181. #946	C₂×C₉	semidirect
182. #939	C₂×C₉	semidirect
183. #937	C₂×C₉	semidirect
184. D₄×Dic₃	C₂×C₉	semidirect
185. #930	C₂×C₉	semidirect
186. #929	C₂×C₉	semidirect
187. C₄×#67	C₂×C₉	semidirect
188. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
232. D₄×C₉	#67	semidirect
263. C₂×C₃×Q₈	C₂²×C₉	semidirect
273. C₂×C₃×D₄	C₂²×C₉	semidirect
280. C₂²×C₃×C₄	C₂²×C₉	semidirect
281. C₂²×C₃×C₄	C₂²×C₉	semidirect
286. C₂×#67	C₂²×C₉	semidirect
287. C₂²×Dic₃	C₂²×C₉	semidirect
302. #217	C₂²×C₉	semidirect
303. #217	C₂²×C₉	semidirect
306. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
307. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
308. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
309. C₄⋊Dic₃	C₂²×C₉	semidirect
310. Dic₃⋊C₄	C₂²×C₉	semidirect
311. Dic₃⋊C₄	C₂²×C₉	semidirect
312. C₄×Dic₃	C₂²×C₉	semidirect
365. C₂×#41	D₃×C₉	semidirect
376. C₃×C₉	#546	semidirect
404. C₃×D₄	D₄×C₉	semidirect
458. C₂×Q₈	C₂×D₃×C₉	semidirect
465. C₂×D₄	C₂×D₃×C₉	semidirect
468. C₂²×C₄	C₂×D₃×C₉	semidirect
469. C₂²×C₄	C₂×D₃×C₉	semidirect
515. C₂×D₃	C₉×#41	semidirect
535. C₉	#5829	direct (N × H)
549. D₄	C₉×#67	semidirect
602. 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×C₃×C₉×#41	2
C₂×D₃×D₄×C₉	2
C₉×#947	2
C₉×#946	2
C₉×#939	2
C₉×#937	2
D₄×C₉×Dic₃	2
C₉×#930	2
C₉×#929	2
C₄×C₉×#67	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₃×#5829	3
C₉×#546	3

Subgroups — C9×#5829 #13153702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5829 #13153702