Subgroups — C₃×C₉×#546 #13154620

Order 1728.

1670 conjugacy classes of subgroups.

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

	subgroup	G/H
center	C₂²×C₃×C₉	C₂⁴
commutator	C₂²	C₂⁴×C₃×C₉
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃²
socle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃²×#546	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂²×C₃×D₄×C₉	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₃×C₉×#123	C₂	semidirect
5. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
6. C₃×C₉×#121	C₂	semidirect
7. C₃×C₉×#121	C₂	semidirect
8. C₃×C₉×#120	C₂	semidirect
9. C₃×C₄×D₄×C₉	C₂	semidirect
10. C₃×C₄×D₄×C₉	C₂	semidirect
11. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
13. C₉×#546	C₃	direct (N × H)
16. C₂×C₃×Q₈×C₉	C₂²	semidirect
22. C₂×C₃×D₄×C₉	C₂²	semidirect
23. C₂×C₃×D₄×C₉	C₂²	semidirect
25. C₂²×C₃×C₄×C₉	C₂²	semidirect
26. C₂²×C₃×C₄×C₉	C₂²	semidirect
27. C₂²×C₃×C₄×C₉	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
30. C₃×C₉×C₄⋊C₄	C₂²	semidirect
33. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
34. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
35. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
36. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
37. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
38. C₃×C₄²×C₉	C₂²	semidirect
50. C₂×C₉×#41	C₂×C₃	semidirect
51. C₂²×D₄×C₉	C₂×C₃	semidirect
52. C₉×#124	C₂×C₃	semidirect
53. C₉×#123	C₂×C₃	semidirect
54. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
55. C₉×#121	C₂×C₃	semidirect
56. C₉×#121	C₂×C₃	semidirect
57. C₉×#120	C₂×C₃	semidirect
58. C₄×D₄×C₉	C₂×C₃	semidirect
59. C₄×D₄×C₉	C₂×C₃	semidirect
60. C₂×C₉×C₂²⋊C₄	C₂×C₃	semidirect
74. C₃×D₄×C₉	D₄	semidirect
86. C₃×#546	C₉	direct (N × H)
115. C₂×Q₈×C₉	C₂²×C₃	semidirect
121. C₂×D₄×C₉	C₂²×C₃	semidirect
122. C₂×D₄×C₉	C₂²×C₃	semidirect
124. C₂²×C₄×C₉	C₂²×C₃	semidirect
125. C₂²×C₄×C₉	C₂²×C₃	semidirect
126. C₂²×C₄×C₉	C₂²×C₃	semidirect
127. C₉×C₄⋊C₄	C₂²×C₃	semidirect
128. C₉×C₄⋊C₄	C₂²×C₃	semidirect
129. C₉×C₄⋊C₄	C₂²×C₃	semidirect
132. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
133. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
134. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
135. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
136. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
137. C₄²×C₉	C₂²×C₃	semidirect
150. C₂²×C₃×C₉	#41	semidirect
159. C₂×C₃×#41	C₂×C₉	semidirect
161. C₂²×C₃×D₄	C₂×C₉	semidirect
163. C₃×#124	C₂×C₉	semidirect
165. C₃×#123	C₂×C₉	semidirect
167. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
169. C₃×#121	C₂×C₉	semidirect
170. C₃×#121	C₂×C₉	semidirect
173. C₃×#120	C₂×C₉	semidirect
175. C₃×C₄×D₄	C₂×C₉	semidirect
176. C₃×C₄×D₄	C₂×C₉	semidirect
179. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
219. D₄×C₉	C₃×D₄	semidirect
231. #546	C₃×C₉	direct (N × H)
243. C₂×C₃×Q₈	C₂²×C₉	semidirect
251. C₂×C₃×D₄	C₂²×C₉	semidirect
252. C₂×C₃×D₄	C₂²×C₉	semidirect
260. C₂²×C₃×C₄	C₂²×C₉	semidirect
261. C₂²×C₃×C₄	C₂²×C₉	semidirect
262. C₂²×C₃×C₄	C₂²×C₉	semidirect
267. C₃×C₄⋊C₄	C₂²×C₉	semidirect
268. C₃×C₄⋊C₄	C₂²×C₉	semidirect
269. C₃×C₄⋊C₄	C₂²×C₉	semidirect
275. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
276. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
277. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
278. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
279. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
287. C₃×C₄²	C₂²×C₉	semidirect
322. C₂²×C₉	C₃×#41	semidirect
331. C₂×#41	C₂×C₃×C₉	semidirect
332. C₂²×D₄	C₂×C₃×C₉	semidirect
333. #124	C₂×C₃×C₉	semidirect
334. #123	C₂×C₃×C₉	semidirect
335. C₂²⋊Q₈	C₂×C₃×C₉	semidirect
336. #121	C₂×C₃×C₉	semidirect
337. #121	C₂×C₃×C₉	semidirect
338. #120	C₂×C₃×C₉	semidirect
339. C₄×D₄	C₂×C₃×C₉	semidirect
340. C₄×D₄	C₂×C₃×C₉	semidirect
341. C₂×C₂²⋊C₄	C₂×C₃×C₉	semidirect
342. C₃×C₉	#546	direct (N × H)
369. C₃×D₄	D₄×C₉	semidirect
409. C₂×Q₈	C₂²×C₃×C₉	semidirect
415. C₂×D₄	C₂²×C₃×C₉	semidirect
416. C₂×D₄	C₂²×C₃×C₉	semidirect
418. C₂²×C₄	C₂²×C₃×C₉	semidirect
419. C₂²×C₄	C₂²×C₃×C₉	semidirect
420. C₂²×C₄	C₂²×C₃×C₉	semidirect
421. C₄⋊C₄	C₂²×C₃×C₉	semidirect
422. C₄⋊C₄	C₂²×C₃×C₉	semidirect
423. C₄⋊C₄	C₂²×C₃×C₉	semidirect
426. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
427. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
428. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
429. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
430. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
431. C₄²	C₂²×C₃×C₉	semidirect
455. C₂²×C₃	C₉×#41	semidirect
475. C₉	C₃×#546	direct (N × H)
489. D₄	C₃×D₄×C₉	semidirect
527. C₂²	C₃×C₉×#41	semidirect
536. C₃	C₉×#546	direct (N × H)

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
C₂²×C₃×D₄×C₉	2
C₃×C₉×#124	2
C₃×C₉×#123	2
C₃×C₉×C₂²⋊Q₈	2
C₃×C₉×#121	2
C₃×C₉×#120	2
C₃×C₄×D₄×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₃²×#546	3
C₉×#546	3

Subgroups — C3×C9×#546 #13154620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#546 #13154620