Subgroups — C₂×C₃³×C₇×C₈×C₉ #72204288

Order 27216.

8712 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₈×C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⁴×C₇×C₈	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃²×C₇×C₈×C₉	C₃	1	39	yes	maximal, direct product factor
5	C₂²×C₃³×C₇×C₉	C₄	1	1	yes	characteristic
6	C₃³×C₄×C₇×C₉	C₄	1	1	yes	characteristic
7	C₃³×C₄×C₇×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃⁴×C₄×C₇	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃²×C₄×C₇×C₉	C₂×C₃	1	39	yes	—
10	C₃²×C₇×C₈×C₉	C₂×C₃	1	78	yes	direct product factor
11	C₃⁴×C₇×C₈	C₂×C₃	1	2	yes	—
12	C₂×C₃³×C₈×C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃³×C₇×C₉	C₈	1	2	yes	direct product factor
14	C₂×C₃³×C₇×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃³×C₇×C₈	C₉	1	27	yes	direct product factor
16	C₂×C₃³×C₇×C₈	C₃²	1	13	yes	—
17	C₂×C₃×C₇×C₈×C₉	C₃²	1	117	yes	direct product factor
18	C₂²×C₃⁴×C₇	C₃×C₄	1	1	yes	characteristic
19	C₂²×C₃²×C₇×C₉	C₃×C₄	1	39	yes	—
20	C₃⁴×C₄×C₇	C₃×C₄	1	1	yes	characteristic
21	C₃⁴×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
22	C₃²×C₄×C₇×C₉	C₃×C₄	1	39	yes	—
23	C₃²×C₄×C₇×C₉	C₂²×C₃	1	39	yes	—
24	C₂×C₃³×C₄×C₉	C₂×C₇	1	1	yes	characteristic
25	C₃³×C₈×C₉	C₂×C₇	1	2	yes	direct product factor
26	C₃³×C₇×C₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃³×C₄×C₇	C₂×C₉	1	27	yes	—
28	C₂×C₃³×C₄×C₇	C₂×C₃²	1	13	yes	—
29	C₃³×C₇×C₈	C₂×C₉	1	54	yes	direct product factor
30	C₃³×C₇×C₈	C₂×C₃²	1	26	yes	—
31	C₂×C₃×C₄×C₇×C₉	C₂×C₃²	1	117	yes	—
32	C₃×C₇×C₈×C₉	C₂×C₃²	1	234	yes	direct product factor
33	C₂×C₃⁴×C₈	C₃×C₇	1	1	yes	characteristic
34	C₂×C₃²×C₈×C₉	C₃×C₇	1	39	yes	direct product factor
35	C₂×C₃⁴×C₇	C₃×C₈	1	2	yes	—
36	C₂×C₃⁴×C₇	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂×C₃²×C₇×C₉	C₃×C₈	1	78	yes	direct product factor
38	C₂×C₃²×C₇×C₉	C₂×C₃×C₄	1	39	yes	—
39	C₂×C₃²×C₇×C₈	C₃×C₉	1	117	yes	direct product factor
40	C₂×C₃²×C₇×C₈	C₃³	1	13	yes	—
41	C₂×C₇×C₈×C₉	C₃³	1	27	yes	direct product factor
42	C₂²×C₃³×C₉	C₄×C₇	1	1	yes	characteristic
43	C₃³×C₄×C₉	C₄×C₇	1	1	yes	characteristic
44	C₃³×C₄×C₉	C₂²×C₇	1	1	yes	characteristic
45	C₂²×C₃³×C₇	C₄×C₉	1	27	yes	—
46	C₂²×C₃³×C₇	C₃²×C₄	1	13	yes	—
47	C₃³×C₄×C₇	C₄×C₉	1	27	yes	—
48	C₃³×C₄×C₇	C₂²×C₉	1	27	yes	—
49	C₃³×C₄×C₇	C₃²×C₄	1	13	yes	—
50	C₃³×C₄×C₇	C₂²×C₃²	1	13	yes	—
51	C₂²×C₃×C₇×C₉	C₃²×C₄	1	117	yes	—
52	C₃×C₄×C₇×C₉	C₃²×C₄	1	117	yes	—
53	C₃×C₄×C₇×C₉	C₂²×C₃²	1	117	yes	—
54	C₂×C₃⁴×C₄	C₂×C₃×C₇	1	1	yes	characteristic
55	C₃⁴×C₈	C₂×C₃×C₇	1	2	yes	—
56	C₂×C₃²×C₄×C₉	C₂×C₃×C₇	1	39	yes	—
57	C₃²×C₈×C₉	C₂×C₃×C₇	1	78	yes	direct product factor
58	C₃⁴×C₇	C₂×C₃×C₈	1	1	yes	characteristic
59	C₃²×C₇×C₉	C₂×C₃×C₈	1	39	yes	direct product factor
60	C₂×C₃²×C₄×C₇	C₂×C₃×C₉	1	117	yes	—
61	C₂×C₃²×C₄×C₇	C₂×C₃³	1	13	yes	—
62	C₃²×C₇×C₈	C₂×C₃×C₉	1	234	yes	direct product factor
63	C₃²×C₇×C₈	C₂×C₃³	1	26	yes	—
64	C₂×C₄×C₇×C₉	C₂×C₃³	1	27	yes	—
65	C₇×C₈×C₉	C₂×C₃³	1	54	yes	direct product factor
66	C₂×C₃³×C₉	C₇×C₈	1	2	yes	direct product factor
67	C₂×C₃³×C₉	C₂×C₄×C₇	1	1	yes	characteristic
68	C₂×C₃³×C₈	C₇×C₉	1	27	yes	direct product factor
69	C₂×C₃³×C₈	C₃²×C₇	1	13	yes	—
70	C₂×C₃×C₈×C₉	C₃²×C₇	1	117	yes	direct product factor
71	C₂×C₃³×C₇	C₈×C₉	1	54	yes	direct product factor
72	C₂×C₃³×C₇	C₂×C₄×C₉	1	27	yes	—
73	C₂×C₃³×C₇	C₃²×C₈	1	26	yes	—
74	C₂×C₃³×C₇	C₂×C₃²×C₄	1	13	yes	—
75	C₂×C₃×C₇×C₉	C₃²×C₈	1	234	yes	direct product factor
76	C₂×C₃×C₇×C₉	C₂×C₃²×C₄	1	117	yes	—
77	C₂×C₃×C₇×C₈	C₃²×C₉	1	39	yes	direct product factor
78	C₂×C₃×C₇×C₈	C₃⁴	1	1	yes	characteristic
79	C₂²×C₃⁴	C₃×C₄×C₇	1	1	yes	characteristic
80	C₃⁴×C₄	C₃×C₄×C₇	1	1	yes	characteristic
81	C₃⁴×C₄	C₂²×C₃×C₇	1	1	yes	characteristic
82	C₂²×C₃²×C₉	C₃×C₄×C₇	1	39	yes	—
83	C₃²×C₄×C₉	C₃×C₄×C₇	1	39	yes	—
84	C₃²×C₄×C₉	C₂²×C₃×C₇	1	39	yes	—
85	C₂²×C₃²×C₇	C₃×C₄×C₉	1	117	yes	—
86	C₂²×C₃²×C₇	C₃³×C₄	1	13	yes	—
87	C₃²×C₄×C₇	C₃×C₄×C₉	1	117	yes	—
88	C₃²×C₄×C₇	C₂²×C₃×C₉	1	117	yes	—
89	C₃²×C₄×C₇	C₃³×C₄	1	13	yes	—
90	C₃²×C₄×C₇	C₂²×C₃³	1	13	yes	—
91	C₂²×C₇×C₉	C₃³×C₄	1	27	yes	—
92	C₄×C₇×C₉	C₃³×C₄	1	27	yes	—
93	C₄×C₇×C₉	C₂²×C₃³	1	27	yes	—
94	C₃³×C₉	C₂×C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×C₃³×C₄	C₂×C₇×C₉	1	27	yes	—
96	C₂×C₃³×C₄	C₂×C₃²×C₇	1	13	yes	—
97	C₃³×C₈	C₂×C₇×C₉	1	54	yes	direct product factor
98	C₃³×C₈	C₂×C₃²×C₇	1	26	yes	—
99	C₂×C₃×C₄×C₉	C₂×C₃²×C₇	1	117	yes	—
100	C₃×C₈×C₉	C₂×C₃²×C₇	1	234	yes	direct product factor
101	C₃³×C₇	C₂×C₈×C₉	1	27	yes	direct product factor
102	C₃³×C₇	C₂×C₃²×C₈	1	13	yes	—
103	C₃×C₇×C₉	C₂×C₃²×C₈	1	117	yes	direct product factor
104	C₂×C₃×C₄×C₇	C₂×C₃²×C₉	1	39	yes	—
105	C₂×C₃×C₄×C₇	C₂×C₃⁴	1	1	yes	characteristic
106	C₃×C₇×C₈	C₂×C₃²×C₉	1	78	yes	direct product factor
107	C₃×C₇×C₈	C₂×C₃⁴	1	2	yes	—
108	C₂×C₃⁴	C₃×C₇×C₈	1	2	yes	—
109	C₂×C₃⁴	C₂×C₃×C₄×C₇	1	1	yes	characteristic
110	C₂×C₃²×C₉	C₃×C₇×C₈	1	78	yes	direct product factor
111	C₂×C₃²×C₉	C₂×C₃×C₄×C₇	1	39	yes	—
112	C₂×C₃²×C₈	C₃×C₇×C₉	1	117	yes	direct product factor
113	C₂×C₃²×C₈	C₃³×C₇	1	13	yes	—
114	C₂×C₈×C₉	C₃³×C₇	1	27	yes	direct product factor
115	C₂×C₃²×C₇	C₃×C₈×C₉	1	234	yes	direct product factor
116	C₂×C₃²×C₇	C₂×C₃×C₄×C₉	1	117	yes	—
117	C₂×C₃²×C₇	C₃³×C₈	1	26	yes	—
118	C₂×C₃²×C₇	C₂×C₃³×C₄	1	13	yes	—
119	C₂×C₇×C₉	C₃³×C₈	1	54	yes	direct product factor
120	C₂×C₇×C₉	C₂×C₃³×C₄	1	27	yes	—
121	C₂×C₇×C₈	C₃³×C₉	1	1	yes	characteristic, direct product factor, Hall
122	C₂²×C₃³	C₄×C₇×C₉	1	27	yes	—
123	C₂²×C₃³	C₃²×C₄×C₇	1	13	yes	—
124	C₃³×C₄	C₄×C₇×C₉	1	27	yes	—
125	C₃³×C₄	C₂²×C₇×C₉	1	27	yes	—
126	C₃³×C₄	C₃²×C₄×C₇	1	13	yes	—
127	C₃³×C₄	C₂²×C₃²×C₇	1	13	yes	—
128	C₂²×C₃×C₉	C₃²×C₄×C₇	1	117	yes	—
129	C₃×C₄×C₉	C₃²×C₄×C₇	1	117	yes	—
130	C₃×C₄×C₉	C₂²×C₃²×C₇	1	117	yes	—
131	C₂²×C₃×C₇	C₃²×C₄×C₉	1	39	yes	—
132	C₂²×C₃×C₇	C₃⁴×C₄	1	1	yes	characteristic
133	C₃×C₄×C₇	C₃²×C₄×C₉	1	39	yes	—
134	C₃×C₄×C₇	C₂²×C₃²×C₉	1	39	yes	—
135	C₃×C₄×C₇	C₃⁴×C₄	1	1	yes	characteristic
136	C₃×C₄×C₇	C₂²×C₃⁴	1	1	yes	characteristic
137	C₃⁴	C₂×C₃×C₇×C₈	1	1	yes	characteristic
138	C₃²×C₉	C₂×C₃×C₇×C₈	1	39	yes	direct product factor
139	C₂×C₃²×C₄	C₂×C₃×C₇×C₉	1	117	yes	—
140	C₂×C₃²×C₄	C₂×C₃³×C₇	1	13	yes	—
141	C₃²×C₈	C₂×C₃×C₇×C₉	1	234	yes	direct product factor
142	C₃²×C₈	C₂×C₃³×C₇	1	26	yes	—
143	C₂×C₄×C₉	C₂×C₃³×C₇	1	27	yes	—
144	C₈×C₉	C₂×C₃³×C₇	1	54	yes	direct product factor
145	C₃²×C₇	C₂×C₃×C₈×C₉	1	117	yes	direct product factor
146	C₃²×C₇	C₂×C₃³×C₈	1	13	yes	—
147	C₇×C₉	C₂×C₃³×C₈	1	27	yes	direct product factor
148	C₂×C₄×C₇	C₂×C₃³×C₉	1	1	yes	characteristic
149	C₇×C₈	C₂×C₃³×C₉	1	2	yes	direct product factor
150	C₂×C₃³	C₇×C₈×C₉	1	54	yes	direct product factor
151	C₂×C₃³	C₂×C₄×C₇×C₉	1	27	yes	—
152	C₂×C₃³	C₃²×C₇×C₈	1	26	yes	—
153	C₂×C₃³	C₂×C₃²×C₄×C₇	1	13	yes	—
154	C₂×C₃×C₉	C₃²×C₇×C₈	1	234	yes	direct product factor
155	C₂×C₃×C₉	C₂×C₃²×C₄×C₇	1	117	yes	—
156	C₂×C₃×C₈	C₃²×C₇×C₉	1	39	yes	direct product factor
157	C₂×C₃×C₈	C₃⁴×C₇	1	1	yes	characteristic
158	C₂×C₃×C₇	C₃²×C₈×C₉	1	78	yes	direct product factor
159	C₂×C₃×C₇	C₂×C₃²×C₄×C₉	1	39	yes	—
160	C₂×C₃×C₇	C₃⁴×C₈	1	2	yes	—
161	C₂×C₃×C₇	C₂×C₃⁴×C₄	1	1	yes	characteristic
162	C₂²×C₃²	C₃×C₄×C₇×C₉	1	117	yes	—
163	C₂²×C₃²	C₃³×C₄×C₇	1	13	yes	—
164	C₃²×C₄	C₃×C₄×C₇×C₉	1	117	yes	—
165	C₃²×C₄	C₂²×C₃×C₇×C₉	1	117	yes	—
166	C₃²×C₄	C₃³×C₄×C₇	1	13	yes	—
167	C₃²×C₄	C₂²×C₃³×C₇	1	13	yes	—
168	C₂²×C₉	C₃³×C₄×C₇	1	27	yes	—
169	C₄×C₉	C₃³×C₄×C₇	1	27	yes	—
170	C₄×C₉	C₂²×C₃³×C₇	1	27	yes	—
171	C₂²×C₇	C₃³×C₄×C₉	1	1	yes	characteristic
172	C₄×C₇	C₃³×C₄×C₉	1	1	yes	characteristic
173	C₄×C₇	C₂²×C₃³×C₉	1	1	yes	characteristic
174	C₃³	C₂×C₇×C₈×C₉	1	27	yes	direct product factor
175	C₃³	C₂×C₃²×C₇×C₈	1	13	yes	—
176	C₃×C₉	C₂×C₃²×C₇×C₈	1	117	yes	direct product factor
177	C₂×C₃×C₄	C₂×C₃²×C₇×C₉	1	39	yes	—
178	C₂×C₃×C₄	C₂×C₃⁴×C₇	1	1	yes	characteristic
179	C₃×C₈	C₂×C₃²×C₇×C₉	1	78	yes	direct product factor
180	C₃×C₈	C₂×C₃⁴×C₇	1	2	yes	—
181	C₃×C₇	C₂×C₃²×C₈×C₉	1	39	yes	direct product factor
182	C₃×C₇	C₂×C₃⁴×C₈	1	1	yes	characteristic
183	C₂×C₃²	C₃×C₇×C₈×C₉	1	234	yes	direct product factor
184	C₂×C₃²	C₂×C₃×C₄×C₇×C₉	1	117	yes	—
185	C₂×C₃²	C₃³×C₇×C₈	1	26	yes	—
186	C₂×C₃²	C₂×C₃³×C₄×C₇	1	13	yes	—
187	C₂×C₉	C₃³×C₇×C₈	1	54	yes	direct product factor
188	C₂×C₉	C₂×C₃³×C₄×C₇	1	27	yes	—
189	C₂×C₈	C₃³×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×C₇	C₃³×C₈×C₉	1	2	yes	direct product factor
191	C₂×C₇	C₂×C₃³×C₄×C₉	1	1	yes	characteristic
192	C₂²×C₃	C₃²×C₄×C₇×C₉	1	39	yes	—
193	C₂²×C₃	C₃⁴×C₄×C₇	1	1	yes	characteristic
194	C₃×C₄	C₃²×C₄×C₇×C₉	1	39	yes	—
195	C₃×C₄	C₃⁴×C₄×C₇	1	1	yes	characteristic
196	C₃×C₄	C₂²×C₃²×C₇×C₉	1	39	yes	—
197	C₃×C₄	C₂²×C₃⁴×C₇	1	1	yes	characteristic
198	C₃²	C₂×C₃×C₇×C₈×C₉	1	117	yes	direct product factor
199	C₃²	C₂×C₃³×C₇×C₈	1	13	yes	—
200	C₉	C₂×C₃³×C₇×C₈	1	27	yes	direct product factor
201	C₂×C₄	C₂×C₃³×C₇×C₉	1	1	yes	characteristic
202	C₈	C₂×C₃³×C₇×C₉	1	2	yes	direct product factor
203	C₇	C₂×C₃³×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×C₃	C₃⁴×C₇×C₈	1	2	yes	—
205	C₂×C₃	C₃²×C₇×C₈×C₉	1	78	yes	direct product factor
206	C₂×C₃	C₂×C₃²×C₄×C₇×C₉	1	39	yes	—
207	C₂×C₃	C₂×C₃⁴×C₄×C₇	1	1	yes	characteristic
208	C₂²	C₃³×C₄×C₇×C₉	1	1	yes	characteristic
209	C₄	C₃³×C₄×C₇×C₉	1	1	yes	characteristic
210	C₄	C₂²×C₃³×C₇×C₉	1	1	yes	characteristic
211	C₃	C₂×C₃²×C₇×C₈×C₉	1	39	yes	direct product factor
212	C₃	C₂×C₃⁴×C₇×C₈	1	1	yes	characteristic
213	C₂	C₃³×C₇×C₈×C₉	1	2	yes	direct product factor
214	C₂	C₂×C₃³×C₄×C₇×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃⁴×C₇
socle, prime radical	C₂²×C₃⁴×C₇	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₇×C₈×C₉	C₂	direct (N × H)
4. C₂×C₃²×C₇×C₈×C₉	C₃	direct (N × H)
10. C₃²×C₇×C₈×C₉	C₂×C₃	direct (N × H)
12. C₂×C₃³×C₈×C₉	C₇	direct (N × H)
13. C₂×C₃³×C₇×C₉	C₈	direct (N × H)
15. C₂×C₃³×C₇×C₈	C₉	direct (N × H)
17. C₂×C₃×C₇×C₈×C₉	C₃²	direct (N × H)
25. C₃³×C₈×C₉	C₂×C₇	direct (N × H)
26. C₃³×C₇×C₉	C₂×C₈	direct (N × H)
29. C₃³×C₇×C₈	C₂×C₉	direct (N × H)
32. C₃×C₇×C₈×C₉	C₂×C₃²	direct (N × H)
34. C₂×C₃²×C₈×C₉	C₃×C₇	direct (N × H)
37. C₂×C₃²×C₇×C₉	C₃×C₈	direct (N × H)
39. C₂×C₃²×C₇×C₈	C₃×C₉	direct (N × H)
41. C₂×C₇×C₈×C₉	C₃³	direct (N × H)
57. C₃²×C₈×C₉	C₂×C₃×C₇	direct (N × H)
59. C₃²×C₇×C₉	C₂×C₃×C₈	direct (N × H)
62. C₃²×C₇×C₈	C₂×C₃×C₉	direct (N × H)
65. C₇×C₈×C₉	C₂×C₃³	direct (N × H)
66. C₂×C₃³×C₉	C₇×C₈	direct (N × H)
68. C₂×C₃³×C₈	C₇×C₉	direct (N × H)
70. C₂×C₃×C₈×C₉	C₃²×C₇	direct (N × H)
71. C₂×C₃³×C₇	C₈×C₉	direct (N × H)
75. C₂×C₃×C₇×C₉	C₃²×C₈	direct (N × H)
77. C₂×C₃×C₇×C₈	C₃²×C₉	direct (N × H)
94. C₃³×C₉	C₂×C₇×C₈	direct (N × H)
97. C₃³×C₈	C₂×C₇×C₉	direct (N × H)
100. C₃×C₈×C₉	C₂×C₃²×C₇	direct (N × H)
101. C₃³×C₇	C₂×C₈×C₉	direct (N × H)
103. C₃×C₇×C₉	C₂×C₃²×C₈	direct (N × H)
106. C₃×C₇×C₈	C₂×C₃²×C₉	direct (N × H)
110. C₂×C₃²×C₉	C₃×C₇×C₈	direct (N × H)
112. C₂×C₃²×C₈	C₃×C₇×C₉	direct (N × H)
114. C₂×C₈×C₉	C₃³×C₇	direct (N × H)
115. C₂×C₃²×C₇	C₃×C₈×C₉	direct (N × H)
119. C₂×C₇×C₉	C₃³×C₈	direct (N × H)
121. C₂×C₇×C₈	C₃³×C₉	direct (N × H)
138. C₃²×C₉	C₂×C₃×C₇×C₈	direct (N × H)
141. C₃²×C₈	C₂×C₃×C₇×C₉	direct (N × H)
144. C₈×C₉	C₂×C₃³×C₇	direct (N × H)
145. C₃²×C₇	C₂×C₃×C₈×C₉	direct (N × H)
147. C₇×C₉	C₂×C₃³×C₈	direct (N × H)
149. C₇×C₈	C₂×C₃³×C₉	direct (N × H)
150. C₂×C₃³	C₇×C₈×C₉	direct (N × H)
154. C₂×C₃×C₉	C₃²×C₇×C₈	direct (N × H)
156. C₂×C₃×C₈	C₃²×C₇×C₉	direct (N × H)
158. C₂×C₃×C₇	C₃²×C₈×C₉	direct (N × H)
174. C₃³	C₂×C₇×C₈×C₉	direct (N × H)
176. C₃×C₉	C₂×C₃²×C₇×C₈	direct (N × H)
179. C₃×C₈	C₂×C₃²×C₇×C₉	direct (N × H)
181. C₃×C₇	C₂×C₃²×C₈×C₉	direct (N × H)
183. C₂×C₃²	C₃×C₇×C₈×C₉	direct (N × H)
187. C₂×C₉	C₃³×C₇×C₈	direct (N × H)
189. C₂×C₈	C₃³×C₇×C₉	direct (N × H)
190. C₂×C₇	C₃³×C₈×C₉	direct (N × H)
198. C₃²	C₂×C₃×C₇×C₈×C₉	direct (N × H)
200. C₉	C₂×C₃³×C₇×C₈	direct (N × H)
202. C₈	C₂×C₃³×C₇×C₉	direct (N × H)
203. C₇	C₂×C₃³×C₈×C₉	direct (N × H)
205. C₂×C₃	C₃²×C₇×C₈×C₉	direct (N × H)
211. C₃	C₂×C₃²×C₇×C₈×C₉	direct (N × H)
213. C₂	C₃³×C₇×C₈×C₉	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×C₃³×C₄×C₇×C₉	2
C₃³×C₇×C₈×C₉	2
C₂×C₃⁴×C₇×C₈	3
C₂×C₃²×C₇×C₈×C₉	3
C₂×C₃³×C₈×C₉	7

Subgroups — C2×C33×C7×C8×C9 #72204288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₇×C₈×C₉ #72204288