Subgroups — C₂×C₃×C₄×C₂₇×C₃₂ #72198313

Order 20736.

1890 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₆×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₂₇×C₃₂	C₂	1	2	yes	maximal
3	C₃×C₄×C₂₇×C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×C₄×C₉×C₃₂	C₃	1	1	yes	maximal, characteristic
5	C₂×C₄×C₂₇×C₃₂	C₃	1	3	yes	maximal, direct product factor
6	C₂×C₃×C₄×C₈×C₂₇	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₁₆×C₂₇	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₁₆×C₂₇	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₁₆×C₂₇	C₄	1	2	yes	—
10	C₃×C₄×C₁₆×C₂₇	C₂²	1	2	yes	—
11	C₂×C₃×C₂₇×C₃₂	C₄	1	8	yes	direct product factor
12	C₂×C₃×C₂₇×C₃₂	C₂²	1	4	yes	—
13	C₂×C₃×C₄×C₉×C₁₆	C₂×C₃	1	1	yes	characteristic
14	C₂×C₄×C₁₆×C₂₇	C₂×C₃	1	3	yes	—
15	C₂²×C₃×C₉×C₃₂	C₂×C₃	1	2	yes	—
16	C₂²×C₂₇×C₃₂	C₂×C₃	1	6	yes	—
17	C₃×C₄×C₉×C₃₂	C₂×C₃	1	4	yes	—
18	C₄×C₂₇×C₃₂	C₂×C₃	1	12	yes	direct product factor
19	C₂×C₃×C₄²×C₂₇	C₈	1	1	yes	characteristic
20	C₂²×C₃×C₈×C₂₇	C₈	1	1	yes	characteristic
21	C₂²×C₃×C₈×C₂₇	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄×C₈×C₂₇	C₈	1	2	yes	—
23	C₃×C₄×C₈×C₂₇	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₁₆×C₂₇	C₈	1	4	yes	—
25	C₂×C₃×C₁₆×C₂₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₁₆×C₂₇	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₁₆×C₂₇	C₂×C₄	1	4	yes	—
28	C₂×C₃×C₁₆×C₂₇	C₂³	1	1	yes	characteristic
29	C₃×C₂₇×C₃₂	C₂×C₄	1	8	yes	direct product factor
30	C₂×C₃²×C₄×C₃₂	C₉	1	1	yes	characteristic
31	C₂×C₄×C₉×C₃₂	C₉	1	2	yes	—
32	C₂×C₄×C₉×C₃₂	C₃²	1	1	yes	characteristic
33	C₂²×C₃×C₉×C₁₆	C₃×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₉×C₁₆	C₂²×C₃	1	1	yes	characteristic
35	C₂×C₃×C₄×C₈×C₉	C₃×C₄	1	1	yes	characteristic
36	C₂×C₃×C₉×C₃₂	C₃×C₄	1	8	yes	—
37	C₂×C₃×C₉×C₃₂	C₂²×C₃	1	4	yes	—
38	C₃×C₄×C₉×C₁₆	C₃×C₄	1	2	yes	—
39	C₃×C₄×C₉×C₁₆	C₂²×C₃	1	2	yes	—
40	C₂²×C₁₆×C₂₇	C₃×C₄	1	3	yes	—
41	C₂²×C₁₆×C₂₇	C₂²×C₃	1	3	yes	—
42	C₂×C₄×C₈×C₂₇	C₃×C₄	1	3	yes	—
43	C₂×C₂₇×C₃₂	C₃×C₄	1	24	yes	direct product factor
44	C₂×C₂₇×C₃₂	C₂²×C₃	1	12	yes	—
45	C₄×C₁₆×C₂₇	C₃×C₄	1	6	yes	—
46	C₄×C₁₆×C₂₇	C₂²×C₃	1	6	yes	—
47	C₂²×C₃×C₄×C₂₇	C₁₆	1	2	yes	—
48	C₂²×C₃×C₄×C₂₇	C₂×C₈	1	1	yes	characteristic
49	C₂×C₃×C₈×C₂₇	C₁₆	1	4	yes	—
50	C₂×C₃×C₈×C₂₇	C₄²	1	2	yes	—
51	C₂×C₃×C₈×C₂₇	C₂×C₈	1	1	yes	characteristic
52	C₂×C₃×C₈×C₂₇	C₂×C₈	1	2	yes	—
53	C₂×C₃×C₈×C₂₇	C₂×C₈	1	2	yes	—
54	C₂×C₃×C₈×C₂₇	C₂²×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₂₇	C₁₆	1	2	yes	—
56	C₃×C₄²×C₂₇	C₂×C₈	1	2	yes	—
57	C₃×C₁₆×C₂₇	C₄²	1	2	yes	—
58	C₃×C₁₆×C₂₇	C₂×C₈	1	4	yes	—
59	C₃×C₁₆×C₂₇	C₂²×C₄	1	2	yes	—
60	C₂²×C₃²×C₃₂	C₂×C₉	1	2	yes	—
61	C₂×C₃²×C₄×C₁₆	C₂×C₉	1	1	yes	characteristic
62	C₃²×C₄×C₃₂	C₂×C₉	1	4	yes	—
63	C₂²×C₉×C₃₂	C₂×C₉	1	4	yes	—
64	C₂²×C₉×C₃₂	C₂×C₃²	1	2	yes	—
65	C₂×C₄×C₉×C₁₆	C₂×C₉	1	2	yes	—
66	C₂×C₄×C₉×C₁₆	C₂×C₃²	1	1	yes	characteristic
67	C₄×C₉×C₃₂	C₂×C₉	1	8	yes	—
68	C₄×C₉×C₃₂	C₂×C₃²	1	4	yes	—
69	C₂²×C₃×C₈×C₉	C₃×C₈	1	1	yes	characteristic
70	C₂²×C₃×C₈×C₉	C₂×C₃×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄²×C₉	C₃×C₈	1	1	yes	characteristic
72	C₂×C₃×C₉×C₁₆	C₃×C₈	1	4	yes	—
73	C₂×C₃×C₉×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
74	C₂×C₃×C₉×C₁₆	C₂×C₃×C₄	1	2	yes	—
75	C₂×C₃×C₉×C₁₆	C₂×C₃×C₄	1	4	yes	—
76	C₂×C₃×C₉×C₁₆	C₂³×C₃	1	1	yes	characteristic
77	C₃×C₄×C₈×C₉	C₃×C₈	1	2	yes	—
78	C₃×C₄×C₈×C₉	C₂×C₃×C₄	1	2	yes	—
79	C₂²×C₈×C₂₇	C₃×C₈	1	3	yes	—
80	C₂²×C₈×C₂₇	C₂×C₃×C₄	1	3	yes	—
81	C₂×C₄²×C₂₇	C₃×C₈	1	3	yes	—
82	C₃×C₉×C₃₂	C₂×C₃×C₄	1	8	yes	—
83	C₂×C₁₆×C₂₇	C₃×C₈	1	12	yes	—
84	C₂×C₁₆×C₂₇	C₂×C₃×C₄	1	3	yes	—
85	C₂×C₁₆×C₂₇	C₂×C₃×C₄	1	6	yes	—
86	C₂×C₁₆×C₂₇	C₂×C₃×C₄	1	12	yes	—
87	C₂×C₁₆×C₂₇	C₂³×C₃	1	3	yes	—
88	C₄×C₈×C₂₇	C₃×C₈	1	6	yes	—
89	C₄×C₈×C₂₇	C₂×C₃×C₄	1	6	yes	—
90	C₂₇×C₃₂	C₂×C₃×C₄	1	24	yes	direct product factor
91	C₂×C₃×C₄×C₃₂	C₂₇	1	3	yes	direct product factor
92	C₂×C₃×C₄×C₃₂	C₃×C₉	1	1	yes	characteristic
93	C₂³×C₃×C₂₇	C₂×C₁₆	1	1	yes	characteristic
94	C₂×C₃×C₄×C₂₇	C₃₂	1	8	yes	direct product factor
95	C₂×C₃×C₄×C₂₇	C₄×C₈	1	2	yes	—
96	C₂×C₃×C₄×C₂₇	C₂×C₁₆	1	1	yes	characteristic
97	C₂×C₃×C₄×C₂₇	C₂×C₁₆	1	2	yes	—
98	C₂×C₃×C₄×C₂₇	C₂×C₁₆	1	4	yes	—
99	C₂×C₃×C₄×C₂₇	C₂²×C₈	1	1	yes	characteristic
100	C₃×C₈×C₂₇	C₄×C₈	1	2	yes	—
101	C₃×C₈×C₂₇	C₂×C₁₆	1	4	yes	—
102	C₃×C₈×C₂₇	C₂×C₄²	1	1	yes	characteristic
103	C₃×C₈×C₂₇	C₂²×C₈	1	1	yes	characteristic
104	C₂²×C₃²×C₁₆	C₄×C₉	1	1	yes	characteristic
105	C₂²×C₃²×C₁₆	C₂²×C₉	1	1	yes	characteristic
106	C₂×C₃²×C₄×C₈	C₄×C₉	1	1	yes	characteristic
107	C₂×C₃²×C₃₂	C₄×C₉	1	8	yes	—
108	C₂×C₃²×C₃₂	C₂²×C₉	1	4	yes	—
109	C₃²×C₄×C₁₆	C₄×C₉	1	2	yes	—
110	C₃²×C₄×C₁₆	C₂²×C₉	1	2	yes	—
111	C₂²×C₉×C₁₆	C₄×C₉	1	2	yes	—
112	C₂²×C₉×C₁₆	C₂²×C₉	1	2	yes	—
113	C₂²×C₉×C₁₆	C₃²×C₄	1	1	yes	characteristic
114	C₂²×C₉×C₁₆	C₂²×C₃²	1	1	yes	characteristic
115	C₂×C₄×C₈×C₉	C₄×C₉	1	2	yes	—
116	C₂×C₄×C₈×C₉	C₃²×C₄	1	1	yes	characteristic
117	C₂×C₉×C₃₂	C₄×C₉	1	16	yes	—
118	C₂×C₉×C₃₂	C₂²×C₉	1	8	yes	—
119	C₂×C₉×C₃₂	C₃²×C₄	1	8	yes	—
120	C₂×C₉×C₃₂	C₂²×C₃²	1	4	yes	—
121	C₄×C₉×C₁₆	C₄×C₉	1	4	yes	—
122	C₄×C₉×C₁₆	C₂²×C₉	1	4	yes	—
123	C₄×C₉×C₁₆	C₃²×C₄	1	2	yes	—
124	C₄×C₉×C₁₆	C₂²×C₃²	1	2	yes	—
125	C₂²×C₃×C₄×C₉	C₃×C₁₆	1	2	yes	—
126	C₂²×C₃×C₄×C₉	C₂×C₃×C₈	1	1	yes	characteristic
127	C₂×C₃×C₈×C₉	C₃×C₁₆	1	4	yes	—
128	C₂×C₃×C₈×C₉	C₃×C₄²	1	2	yes	—
129	C₂×C₃×C₈×C₉	C₂×C₃×C₈	1	1	yes	characteristic
130	C₂×C₃×C₈×C₉	C₂×C₃×C₈	1	2	yes	—
131	C₂×C₃×C₈×C₉	C₂×C₃×C₈	1	2	yes	—
132	C₂×C₃×C₈×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
133	C₃×C₄²×C₉	C₃×C₁₆	1	2	yes	—
134	C₃×C₄²×C₉	C₂×C₃×C₈	1	2	yes	—
135	C₂²×C₄×C₂₇	C₃×C₁₆	1	6	yes	—
136	C₂²×C₄×C₂₇	C₂×C₃×C₈	1	3	yes	—
137	C₃×C₉×C₁₆	C₃×C₄²	1	2	yes	—
138	C₃×C₉×C₁₆	C₂×C₃×C₈	1	4	yes	—
139	C₃×C₉×C₁₆	C₂²×C₃×C₄	1	2	yes	—
140	C₂×C₈×C₂₇	C₃×C₁₆	1	12	yes	—
141	C₂×C₈×C₂₇	C₃×C₄²	1	6	yes	—
142	C₂×C₈×C₂₇	C₂×C₃×C₈	1	3	yes	—
143	C₂×C₈×C₂₇	C₂×C₃×C₈	1	6	yes	—
144	C₂×C₈×C₂₇	C₂×C₃×C₈	1	6	yes	—
145	C₂×C₈×C₂₇	C₂²×C₃×C₄	1	3	yes	—
146	C₄²×C₂₇	C₃×C₁₆	1	6	yes	—
147	C₄²×C₂₇	C₂×C₃×C₈	1	6	yes	—
148	C₁₆×C₂₇	C₃×C₄²	1	6	yes	—
149	C₁₆×C₂₇	C₂×C₃×C₈	1	12	yes	—
150	C₁₆×C₂₇	C₂²×C₃×C₄	1	6	yes	—
151	C₂²×C₃×C₃₂	C₂×C₂₇	1	6	yes	—
152	C₂²×C₃×C₃₂	C₂×C₃×C₉	1	2	yes	—
153	C₂×C₃×C₄×C₁₆	C₂×C₂₇	1	3	yes	—
154	C₂×C₃×C₄×C₁₆	C₂×C₃×C₉	1	1	yes	characteristic
155	C₃×C₄×C₃₂	C₂×C₂₇	1	12	yes	direct product factor
156	C₃×C₄×C₃₂	C₂×C₃×C₉	1	4	yes	—
157	C₂²×C₃×C₂₇	C₄×C₁₆	1	2	yes	—
158	C₂²×C₃×C₂₇	C₂×C₃₂	1	4	yes	—
159	C₂²×C₃×C₂₇	C₂²×C₁₆	1	1	yes	characteristic
160	C₃×C₄×C₂₇	C₄×C₁₆	1	2	yes	—
161	C₃×C₄×C₂₇	C₂×C₃₂	1	8	yes	direct product factor
162	C₃×C₄×C₂₇	C₂×C₄×C₈	1	1	yes	characteristic
163	C₃×C₄×C₂₇	C₂²×C₁₆	1	1	yes	characteristic
164	C₂²×C₃²×C₈	C₈×C₉	1	1	yes	characteristic
165	C₂²×C₃²×C₈	C₂×C₄×C₉	1	1	yes	characteristic
166	C₂×C₃²×C₄²	C₈×C₉	1	1	yes	characteristic
167	C₂×C₃²×C₁₆	C₈×C₉	1	4	yes	—
168	C₂×C₃²×C₁₆	C₂×C₄×C₉	1	1	yes	characteristic
169	C₂×C₃²×C₁₆	C₂×C₄×C₉	1	2	yes	—
170	C₂×C₃²×C₁₆	C₂×C₄×C₉	1	4	yes	—
171	C₂×C₃²×C₁₆	C₂³×C₉	1	1	yes	characteristic
172	C₃²×C₄×C₈	C₈×C₉	1	2	yes	—
173	C₃²×C₄×C₈	C₂×C₄×C₉	1	2	yes	—
174	C₂²×C₈×C₉	C₈×C₉	1	2	yes	—
175	C₂²×C₈×C₉	C₂×C₄×C₉	1	2	yes	—
176	C₂²×C₈×C₉	C₃²×C₈	1	1	yes	characteristic
177	C₂²×C₈×C₉	C₂×C₃²×C₄	1	1	yes	characteristic
178	C₂×C₄²×C₉	C₈×C₉	1	2	yes	—
179	C₂×C₄²×C₉	C₃²×C₈	1	1	yes	characteristic
180	C₃²×C₃₂	C₂×C₄×C₉	1	8	yes	—
181	C₂×C₉×C₁₆	C₈×C₉	1	8	yes	—
182	C₂×C₉×C₁₆	C₂×C₄×C₉	1	2	yes	—
183	C₂×C₉×C₁₆	C₂×C₄×C₉	1	4	yes	—
184	C₂×C₉×C₁₆	C₂×C₄×C₉	1	8	yes	—
185	C₂×C₉×C₁₆	C₃²×C₈	1	4	yes	—
186	C₂×C₉×C₁₆	C₂³×C₉	1	2	yes	—
187	C₂×C₉×C₁₆	C₂×C₃²×C₄	1	1	yes	characteristic
188	C₂×C₉×C₁₆	C₂×C₃²×C₄	1	2	yes	—
189	C₂×C₉×C₁₆	C₂×C₃²×C₄	1	4	yes	—
190	C₂×C₉×C₁₆	C₂³×C₃²	1	1	yes	characteristic
191	C₄×C₈×C₉	C₈×C₉	1	4	yes	—
192	C₄×C₈×C₉	C₂×C₄×C₉	1	4	yes	—
193	C₄×C₈×C₉	C₃²×C₈	1	2	yes	—
194	C₄×C₈×C₉	C₂×C₃²×C₄	1	2	yes	—
195	C₉×C₃₂	C₂×C₄×C₉	1	16	yes	—
196	C₉×C₃₂	C₂×C₃²×C₄	1	8	yes	—
197	C₂×C₄×C₃₂	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
198	C₂³×C₃×C₉	C₂×C₃×C₁₆	1	1	yes	characteristic
199	C₂×C₃×C₄×C₉	C₃×C₃₂	1	8	yes	—
200	C₂×C₃×C₄×C₉	C₃×C₄×C₈	1	2	yes	—
201	C₂×C₃×C₄×C₉	C₂×C₃×C₁₆	1	1	yes	characteristic
202	C₂×C₃×C₄×C₉	C₂×C₃×C₁₆	1	2	yes	—
203	C₂×C₃×C₄×C₉	C₂×C₃×C₁₆	1	4	yes	—
204	C₂×C₃×C₄×C₉	C₂²×C₃×C₈	1	1	yes	characteristic
205	C₂³×C₂₇	C₂×C₃×C₁₆	1	3	yes	—
206	C₃×C₈×C₉	C₃×C₄×C₈	1	2	yes	—
207	C₃×C₈×C₉	C₂×C₃×C₁₆	1	4	yes	—
208	C₃×C₈×C₉	C₂×C₃×C₄²	1	1	yes	characteristic
209	C₃×C₈×C₉	C₂²×C₃×C₈	1	1	yes	characteristic
210	C₂×C₄×C₂₇	C₃×C₃₂	1	24	yes	direct product factor
211	C₂×C₄×C₂₇	C₃×C₄×C₈	1	6	yes	—
212	C₂×C₄×C₂₇	C₂×C₃×C₁₆	1	3	yes	—
213	C₂×C₄×C₂₇	C₂×C₃×C₁₆	1	6	yes	—
214	C₂×C₄×C₂₇	C₂×C₃×C₁₆	1	12	yes	—
215	C₂×C₄×C₂₇	C₂²×C₃×C₈	1	3	yes	—
216	C₈×C₂₇	C₃×C₄×C₈	1	6	yes	—
217	C₈×C₂₇	C₂×C₃×C₁₆	1	12	yes	—
218	C₈×C₂₇	C₂×C₃×C₄²	1	3	yes	—
219	C₈×C₂₇	C₂²×C₃×C₈	1	3	yes	—
220	C₂²×C₃×C₁₆	C₄×C₂₇	1	3	yes	—
221	C₂²×C₃×C₁₆	C₂²×C₂₇	1	3	yes	—
222	C₂²×C₃×C₁₆	C₃×C₄×C₉	1	1	yes	characteristic
223	C₂²×C₃×C₁₆	C₂²×C₃×C₉	1	1	yes	characteristic
224	C₂×C₃×C₄×C₈	C₄×C₂₇	1	3	yes	—
225	C₂×C₃×C₄×C₈	C₃×C₄×C₉	1	1	yes	characteristic
226	C₂×C₃×C₃₂	C₄×C₂₇	1	24	yes	direct product factor
227	C₂×C₃×C₃₂	C₂²×C₂₇	1	12	yes	—
228	C₂×C₃×C₃₂	C₃×C₄×C₉	1	8	yes	—
229	C₂×C₃×C₃₂	C₂²×C₃×C₉	1	4	yes	—
230	C₃×C₄×C₁₆	C₄×C₂₇	1	6	yes	—
231	C₃×C₄×C₁₆	C₂²×C₂₇	1	6	yes	—
232	C₃×C₄×C₁₆	C₃×C₄×C₉	1	2	yes	—
233	C₃×C₄×C₁₆	C₂²×C₃×C₉	1	2	yes	—
234	C₂×C₃×C₂₇	C₄×C₃₂	1	4	yes	direct product factor
235	C₂×C₃×C₂₇	C₂×C₄×C₁₆	1	1	yes	characteristic
236	C₂×C₃×C₂₇	C₂²×C₃₂	1	2	yes	—
237	C₂²×C₃²×C₄	C₉×C₁₆	1	2	yes	—
238	C₂²×C₃²×C₄	C₂×C₈×C₉	1	1	yes	characteristic
239	C₂×C₃²×C₈	C₉×C₁₆	1	4	yes	—
240	C₂×C₃²×C₈	C₄²×C₉	1	2	yes	—
241	C₂×C₃²×C₈	C₂×C₈×C₉	1	1	yes	characteristic
242	C₂×C₃²×C₈	C₂×C₈×C₉	1	2	yes	—
243	C₂×C₃²×C₈	C₂×C₈×C₉	1	2	yes	—
244	C₂×C₃²×C₈	C₂²×C₄×C₉	1	1	yes	characteristic
245	C₃²×C₄²	C₉×C₁₆	1	2	yes	—
246	C₃²×C₄²	C₂×C₈×C₉	1	2	yes	—
247	C₂²×C₄×C₉	C₉×C₁₆	1	4	yes	—
248	C₂²×C₄×C₉	C₂×C₈×C₉	1	2	yes	—
249	C₂²×C₄×C₉	C₃²×C₁₆	1	2	yes	—
250	C₂²×C₄×C₉	C₂×C₃²×C₈	1	1	yes	characteristic
251	C₃²×C₁₆	C₄²×C₉	1	2	yes	—
252	C₃²×C₁₆	C₂×C₈×C₉	1	4	yes	—
253	C₃²×C₁₆	C₂²×C₄×C₉	1	2	yes	—
254	C₂×C₈×C₉	C₉×C₁₆	1	8	yes	—
255	C₂×C₈×C₉	C₄²×C₉	1	4	yes	—
256	C₂×C₈×C₉	C₂×C₈×C₉	1	2	yes	—
257	C₂×C₈×C₉	C₂×C₈×C₉	1	4	yes	—
258	C₂×C₈×C₉	C₂×C₈×C₉	1	4	yes	—
259	C₂×C₈×C₉	C₃²×C₁₆	1	4	yes	—
260	C₂×C₈×C₉	C₂²×C₄×C₉	1	2	yes	—
261	C₂×C₈×C₉	C₃²×C₄²	1	2	yes	—
262	C₂×C₈×C₉	C₂×C₃²×C₈	1	1	yes	characteristic
263	C₂×C₈×C₉	C₂×C₃²×C₈	1	2	yes	—
264	C₂×C₈×C₉	C₂×C₃²×C₈	1	2	yes	—
265	C₂×C₈×C₉	C₂²×C₃²×C₄	1	1	yes	characteristic
266	C₄²×C₉	C₉×C₁₆	1	4	yes	—
267	C₄²×C₉	C₂×C₈×C₉	1	4	yes	—
268	C₄²×C₉	C₃²×C₁₆	1	2	yes	—
269	C₄²×C₉	C₂×C₃²×C₈	1	2	yes	—
270	C₉×C₁₆	C₄²×C₉	1	4	yes	—
271	C₉×C₁₆	C₂×C₈×C₉	1	8	yes	—
272	C₉×C₁₆	C₂²×C₄×C₉	1	4	yes	—
273	C₉×C₁₆	C₃²×C₄²	1	2	yes	—
274	C₉×C₁₆	C₂×C₃²×C₈	1	4	yes	—
275	C₉×C₁₆	C₂²×C₃²×C₄	1	2	yes	—
276	C₂²×C₃₂	C₂×C₃×C₂₇	1	2	yes	—
277	C₂×C₄×C₁₆	C₂×C₃×C₂₇	1	1	yes	characteristic
278	C₄×C₃₂	C₂×C₃×C₂₇	1	4	yes	direct product factor
279	C₂²×C₃×C₉	C₃×C₄×C₁₆	1	2	yes	—
280	C₂²×C₃×C₉	C₂×C₃×C₃₂	1	4	yes	—
281	C₂²×C₃×C₉	C₂²×C₃×C₁₆	1	1	yes	characteristic
282	C₃×C₄×C₉	C₃×C₄×C₁₆	1	2	yes	—
283	C₃×C₄×C₉	C₂×C₃×C₃₂	1	8	yes	—
284	C₃×C₄×C₉	C₂×C₃×C₄×C₈	1	1	yes	characteristic
285	C₃×C₄×C₉	C₂²×C₃×C₁₆	1	1	yes	characteristic
286	C₂²×C₂₇	C₃×C₄×C₁₆	1	6	yes	—
287	C₂²×C₂₇	C₂×C₃×C₃₂	1	12	yes	—
288	C₂²×C₂₇	C₂²×C₃×C₁₆	1	3	yes	—
289	C₄×C₂₇	C₃×C₄×C₁₆	1	6	yes	—
290	C₄×C₂₇	C₂×C₃×C₃₂	1	24	yes	direct product factor
291	C₄×C₂₇	C₂×C₃×C₄×C₈	1	3	yes	—
292	C₄×C₂₇	C₂²×C₃×C₁₆	1	3	yes	—
293	C₂²×C₃×C₈	C₈×C₂₇	1	3	yes	—
294	C₂²×C₃×C₈	C₂×C₄×C₂₇	1	3	yes	—
295	C₂²×C₃×C₈	C₃×C₈×C₉	1	1	yes	characteristic
296	C₂²×C₃×C₈	C₂×C₃×C₄×C₉	1	1	yes	characteristic
297	C₂×C₃×C₄²	C₈×C₂₇	1	3	yes	—
298	C₂×C₃×C₄²	C₃×C₈×C₉	1	1	yes	characteristic
299	C₂×C₃×C₁₆	C₈×C₂₇	1	12	yes	—
300	C₂×C₃×C₁₆	C₂×C₄×C₂₇	1	3	yes	—
301	C₂×C₃×C₁₆	C₂×C₄×C₂₇	1	6	yes	—
302	C₂×C₃×C₁₆	C₂×C₄×C₂₇	1	12	yes	—
303	C₂×C₃×C₁₆	C₃×C₈×C₉	1	4	yes	—
304	C₂×C₃×C₁₆	C₂³×C₂₇	1	3	yes	—
305	C₂×C₃×C₁₆	C₂×C₃×C₄×C₉	1	1	yes	characteristic
306	C₂×C₃×C₁₆	C₂×C₃×C₄×C₉	1	2	yes	—
307	C₂×C₃×C₁₆	C₂×C₃×C₄×C₉	1	4	yes	—
308	C₂×C₃×C₁₆	C₂³×C₃×C₉	1	1	yes	characteristic
309	C₃×C₄×C₈	C₈×C₂₇	1	6	yes	—
310	C₃×C₄×C₈	C₂×C₄×C₂₇	1	6	yes	—
311	C₃×C₄×C₈	C₃×C₈×C₉	1	2	yes	—
312	C₃×C₄×C₈	C₂×C₃×C₄×C₉	1	2	yes	—
313	C₃×C₃₂	C₂×C₄×C₂₇	1	24	yes	direct product factor
314	C₃×C₃₂	C₂×C₃×C₄×C₉	1	8	yes	—
315	C₃×C₂₇	C₂×C₄×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
316	C₂³×C₃²	C₂×C₉×C₁₆	1	1	yes	characteristic
317	C₂×C₃²×C₄	C₉×C₃₂	1	8	yes	—
318	C₂×C₃²×C₄	C₄×C₈×C₉	1	2	yes	—
319	C₂×C₃²×C₄	C₂×C₉×C₁₆	1	1	yes	characteristic
320	C₂×C₃²×C₄	C₂×C₉×C₁₆	1	2	yes	—
321	C₂×C₃²×C₄	C₂×C₉×C₁₆	1	4	yes	—
322	C₂×C₃²×C₄	C₂²×C₈×C₉	1	1	yes	characteristic
323	C₂³×C₉	C₂×C₉×C₁₆	1	2	yes	—
324	C₂³×C₉	C₂×C₃²×C₁₆	1	1	yes	characteristic
325	C₃²×C₈	C₄×C₈×C₉	1	2	yes	—
326	C₃²×C₈	C₂×C₉×C₁₆	1	4	yes	—
327	C₃²×C₈	C₂×C₄²×C₉	1	1	yes	characteristic
328	C₃²×C₈	C₂²×C₈×C₉	1	1	yes	characteristic
329	C₂×C₄×C₉	C₉×C₃₂	1	16	yes	—
330	C₂×C₄×C₉	C₄×C₈×C₉	1	4	yes	—
331	C₂×C₄×C₉	C₂×C₉×C₁₆	1	2	yes	—
332	C₂×C₄×C₉	C₂×C₉×C₁₆	1	4	yes	—
333	C₂×C₄×C₉	C₂×C₉×C₁₆	1	8	yes	—
334	C₂×C₄×C₉	C₃²×C₃₂	1	8	yes	—
335	C₂×C₄×C₉	C₂²×C₈×C₉	1	2	yes	—
336	C₂×C₄×C₉	C₃²×C₄×C₈	1	2	yes	—
337	C₂×C₄×C₉	C₂×C₃²×C₁₆	1	1	yes	characteristic
338	C₂×C₄×C₉	C₂×C₃²×C₁₆	1	2	yes	—
339	C₂×C₄×C₉	C₂×C₃²×C₁₆	1	4	yes	—
340	C₂×C₄×C₉	C₂²×C₃²×C₈	1	1	yes	characteristic
341	C₈×C₉	C₄×C₈×C₉	1	4	yes	—
342	C₈×C₉	C₂×C₉×C₁₆	1	8	yes	—
343	C₈×C₉	C₂×C₄²×C₉	1	2	yes	—
344	C₈×C₉	C₂²×C₈×C₉	1	2	yes	—
345	C₈×C₉	C₃²×C₄×C₈	1	2	yes	—
346	C₈×C₉	C₂×C₃²×C₁₆	1	4	yes	—
347	C₈×C₉	C₂×C₃²×C₄²	1	1	yes	characteristic
348	C₈×C₉	C₂²×C₃²×C₈	1	1	yes	characteristic
349	C₂²×C₁₆	C₃×C₄×C₂₇	1	1	yes	characteristic
350	C₂²×C₁₆	C₂²×C₃×C₂₇	1	1	yes	characteristic
351	C₂×C₄×C₈	C₃×C₄×C₂₇	1	1	yes	characteristic
352	C₂×C₃₂	C₃×C₄×C₂₇	1	8	yes	direct product factor
353	C₂×C₃₂	C₂²×C₃×C₂₇	1	4	yes	—
354	C₄×C₁₆	C₃×C₄×C₂₇	1	2	yes	—
355	C₄×C₁₆	C₂²×C₃×C₂₇	1	2	yes	—
356	C₂×C₃×C₉	C₃×C₄×C₃₂	1	4	yes	—
357	C₂×C₃×C₉	C₂×C₃×C₄×C₁₆	1	1	yes	characteristic
358	C₂×C₃×C₉	C₂²×C₃×C₃₂	1	2	yes	—
359	C₂×C₂₇	C₃×C₄×C₃₂	1	12	yes	direct product factor
360	C₂×C₂₇	C₂×C₃×C₄×C₁₆	1	3	yes	—
361	C₂×C₂₇	C₂²×C₃×C₃₂	1	6	yes	—
362	C₂²×C₃×C₄	C₁₆×C₂₇	1	6	yes	—
363	C₂²×C₃×C₄	C₂×C₈×C₂₇	1	3	yes	—
364	C₂²×C₃×C₄	C₃×C₉×C₁₆	1	2	yes	—
365	C₂²×C₃×C₄	C₂×C₃×C₈×C₉	1	1	yes	characteristic
366	C₂×C₃×C₈	C₁₆×C₂₇	1	12	yes	—
367	C₂×C₃×C₈	C₄²×C₂₇	1	6	yes	—
368	C₂×C₃×C₈	C₂×C₈×C₂₇	1	3	yes	—
369	C₂×C₃×C₈	C₂×C₈×C₂₇	1	6	yes	—
370	C₂×C₃×C₈	C₂×C₈×C₂₇	1	6	yes	—
371	C₂×C₃×C₈	C₃×C₉×C₁₆	1	4	yes	—
372	C₂×C₃×C₈	C₂²×C₄×C₂₇	1	3	yes	—
373	C₂×C₃×C₈	C₃×C₄²×C₉	1	2	yes	—
374	C₂×C₃×C₈	C₂×C₃×C₈×C₉	1	1	yes	characteristic
375	C₂×C₃×C₈	C₂×C₃×C₈×C₉	1	2	yes	—
376	C₂×C₃×C₈	C₂×C₃×C₈×C₉	1	2	yes	—
377	C₂×C₃×C₈	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
378	C₃×C₄²	C₁₆×C₂₇	1	6	yes	—
379	C₃×C₄²	C₂×C₈×C₂₇	1	6	yes	—
380	C₃×C₄²	C₃×C₉×C₁₆	1	2	yes	—
381	C₃×C₄²	C₂×C₃×C₈×C₉	1	2	yes	—
382	C₃×C₁₆	C₄²×C₂₇	1	6	yes	—
383	C₃×C₁₆	C₂×C₈×C₂₇	1	12	yes	—
384	C₃×C₁₆	C₂²×C₄×C₂₇	1	6	yes	—
385	C₃×C₁₆	C₃×C₄²×C₉	1	2	yes	—
386	C₃×C₁₆	C₂×C₃×C₈×C₉	1	4	yes	—
387	C₃×C₁₆	C₂²×C₃×C₄×C₉	1	2	yes	—
388	C₂²×C₃²	C₄×C₉×C₁₆	1	2	yes	—
389	C₂²×C₃²	C₂×C₉×C₃₂	1	4	yes	—
390	C₂²×C₃²	C₂²×C₉×C₁₆	1	1	yes	characteristic
391	C₃²×C₄	C₄×C₉×C₁₆	1	2	yes	—
392	C₃²×C₄	C₂×C₉×C₃₂	1	8	yes	—
393	C₃²×C₄	C₂×C₄×C₈×C₉	1	1	yes	characteristic
394	C₃²×C₄	C₂²×C₉×C₁₆	1	1	yes	characteristic
395	C₂²×C₉	C₄×C₉×C₁₆	1	4	yes	—
396	C₂²×C₉	C₂×C₉×C₃₂	1	8	yes	—
397	C₂²×C₉	C₂²×C₉×C₁₆	1	2	yes	—
398	C₂²×C₉	C₃²×C₄×C₁₆	1	2	yes	—
399	C₂²×C₉	C₂×C₃²×C₃₂	1	4	yes	—
400	C₂²×C₉	C₂²×C₃²×C₁₆	1	1	yes	characteristic
401	C₄×C₉	C₄×C₉×C₁₆	1	4	yes	—
402	C₄×C₉	C₂×C₉×C₃₂	1	16	yes	—
403	C₄×C₉	C₂×C₄×C₈×C₉	1	2	yes	—
404	C₄×C₉	C₂²×C₉×C₁₆	1	2	yes	—
405	C₄×C₉	C₃²×C₄×C₁₆	1	2	yes	—
406	C₄×C₉	C₂×C₃²×C₃₂	1	8	yes	—
407	C₄×C₉	C₂×C₃²×C₄×C₈	1	1	yes	characteristic
408	C₄×C₉	C₂²×C₃²×C₁₆	1	1	yes	characteristic
409	C₂²×C₈	C₃×C₈×C₂₇	1	1	yes	characteristic
410	C₂²×C₈	C₂×C₃×C₄×C₂₇	1	1	yes	characteristic
411	C₂×C₄²	C₃×C₈×C₂₇	1	1	yes	characteristic
412	C₂×C₁₆	C₃×C₈×C₂₇	1	4	yes	—
413	C₂×C₁₆	C₂×C₃×C₄×C₂₇	1	1	yes	characteristic
414	C₂×C₁₆	C₂×C₃×C₄×C₂₇	1	2	yes	—
415	C₂×C₁₆	C₂×C₃×C₄×C₂₇	1	4	yes	—
416	C₂×C₁₆	C₂³×C₃×C₂₇	1	1	yes	characteristic
417	C₄×C₈	C₃×C₈×C₂₇	1	2	yes	—
418	C₄×C₈	C₂×C₃×C₄×C₂₇	1	2	yes	—
419	C₃₂	C₂×C₃×C₄×C₂₇	1	8	yes	direct product factor
420	C₃×C₉	C₂×C₃×C₄×C₃₂	1	1	yes	characteristic
421	C₂₇	C₂×C₃×C₄×C₃₂	1	3	yes	direct product factor
422	C₂³×C₃	C₂×C₁₆×C₂₇	1	3	yes	—
423	C₂³×C₃	C₂×C₃×C₉×C₁₆	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂₇×C₃₂	1	24	yes	direct product factor
425	C₂×C₃×C₄	C₄×C₈×C₂₇	1	6	yes	—
426	C₂×C₃×C₄	C₂×C₁₆×C₂₇	1	3	yes	—
427	C₂×C₃×C₄	C₂×C₁₆×C₂₇	1	6	yes	—
428	C₂×C₃×C₄	C₂×C₁₆×C₂₇	1	12	yes	—
429	C₂×C₃×C₄	C₃×C₉×C₃₂	1	8	yes	—
430	C₂×C₃×C₄	C₂²×C₈×C₂₇	1	3	yes	—
431	C₂×C₃×C₄	C₃×C₄×C₈×C₉	1	2	yes	—
432	C₂×C₃×C₄	C₂×C₃×C₉×C₁₆	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂×C₃×C₉×C₁₆	1	2	yes	—
434	C₂×C₃×C₄	C₂×C₃×C₉×C₁₆	1	4	yes	—
435	C₂×C₃×C₄	C₂²×C₃×C₈×C₉	1	1	yes	characteristic
436	C₃×C₈	C₄×C₈×C₂₇	1	6	yes	—
437	C₃×C₈	C₂×C₁₆×C₂₇	1	12	yes	—
438	C₃×C₈	C₂×C₄²×C₂₇	1	3	yes	—
439	C₃×C₈	C₂²×C₈×C₂₇	1	3	yes	—
440	C₃×C₈	C₃×C₄×C₈×C₉	1	2	yes	—
441	C₃×C₈	C₂×C₃×C₉×C₁₆	1	4	yes	—
442	C₃×C₈	C₂×C₃×C₄²×C₉	1	1	yes	characteristic
443	C₃×C₈	C₂²×C₃×C₈×C₉	1	1	yes	characteristic
444	C₂×C₃²	C₄×C₉×C₃₂	1	4	yes	—
445	C₂×C₃²	C₂×C₄×C₉×C₁₆	1	1	yes	characteristic
446	C₂×C₃²	C₂²×C₉×C₃₂	1	2	yes	—
447	C₂×C₉	C₄×C₉×C₃₂	1	8	yes	—
448	C₂×C₉	C₂×C₄×C₉×C₁₆	1	2	yes	—
449	C₂×C₉	C₂²×C₉×C₃₂	1	4	yes	—
450	C₂×C₉	C₃²×C₄×C₃₂	1	4	yes	—
451	C₂×C₉	C₂×C₃²×C₄×C₁₆	1	1	yes	characteristic
452	C₂×C₉	C₂²×C₃²×C₃₂	1	2	yes	—
453	C₂²×C₄	C₃×C₁₆×C₂₇	1	2	yes	—
454	C₂²×C₄	C₂×C₃×C₈×C₂₇	1	1	yes	characteristic
455	C₂×C₈	C₃×C₁₆×C₂₇	1	4	yes	—
456	C₂×C₈	C₃×C₄²×C₂₇	1	2	yes	—
457	C₂×C₈	C₂×C₃×C₈×C₂₇	1	1	yes	characteristic
458	C₂×C₈	C₂×C₃×C₈×C₂₇	1	2	yes	—
459	C₂×C₈	C₂×C₃×C₈×C₂₇	1	2	yes	—
460	C₂×C₈	C₂²×C₃×C₄×C₂₇	1	1	yes	characteristic
461	C₄²	C₃×C₁₆×C₂₇	1	2	yes	—
462	C₄²	C₂×C₃×C₈×C₂₇	1	2	yes	—
463	C₁₆	C₃×C₄²×C₂₇	1	2	yes	—
464	C₁₆	C₂×C₃×C₈×C₂₇	1	4	yes	—
465	C₁₆	C₂²×C₃×C₄×C₂₇	1	2	yes	—
466	C₂²×C₃	C₄×C₁₆×C₂₇	1	6	yes	—
467	C₂²×C₃	C₂×C₂₇×C₃₂	1	12	yes	—
468	C₂²×C₃	C₂²×C₁₆×C₂₇	1	3	yes	—
469	C₂²×C₃	C₃×C₄×C₉×C₁₆	1	2	yes	—
470	C₂²×C₃	C₂×C₃×C₉×C₃₂	1	4	yes	—
471	C₂²×C₃	C₂²×C₃×C₉×C₁₆	1	1	yes	characteristic
472	C₃×C₄	C₄×C₁₆×C₂₇	1	6	yes	—
473	C₃×C₄	C₂×C₂₇×C₃₂	1	24	yes	direct product factor
474	C₃×C₄	C₂×C₄×C₈×C₂₇	1	3	yes	—
475	C₃×C₄	C₂²×C₁₆×C₂₇	1	3	yes	—
476	C₃×C₄	C₃×C₄×C₉×C₁₆	1	2	yes	—
477	C₃×C₄	C₂×C₃×C₉×C₃₂	1	8	yes	—
478	C₃×C₄	C₂×C₃×C₄×C₈×C₉	1	1	yes	characteristic
479	C₃×C₄	C₂²×C₃×C₉×C₁₆	1	1	yes	characteristic
480	C₃²	C₂×C₄×C₉×C₃₂	1	1	yes	characteristic
481	C₉	C₂×C₄×C₉×C₃₂	1	2	yes	—
482	C₉	C₂×C₃²×C₄×C₃₂	1	1	yes	characteristic
483	C₂³	C₂×C₃×C₁₆×C₂₇	1	1	yes	characteristic
484	C₂×C₄	C₃×C₂₇×C₃₂	1	8	yes	direct product factor
485	C₂×C₄	C₂×C₃×C₁₆×C₂₇	1	1	yes	characteristic
486	C₂×C₄	C₂×C₃×C₁₆×C₂₇	1	2	yes	—
487	C₂×C₄	C₂×C₃×C₁₆×C₂₇	1	4	yes	—
488	C₂×C₄	C₃×C₄×C₈×C₂₇	1	2	yes	—
489	C₂×C₄	C₂²×C₃×C₈×C₂₇	1	1	yes	characteristic
490	C₈	C₂×C₃×C₁₆×C₂₇	1	4	yes	—
491	C₈	C₃×C₄×C₈×C₂₇	1	2	yes	—
492	C₈	C₂²×C₃×C₈×C₂₇	1	1	yes	characteristic
493	C₈	C₂×C₃×C₄²×C₂₇	1	1	yes	characteristic
494	C₂×C₃	C₄×C₂₇×C₃₂	1	12	yes	direct product factor
495	C₂×C₃	C₃×C₄×C₉×C₃₂	1	4	yes	—
496	C₂×C₃	C₂²×C₂₇×C₃₂	1	6	yes	—
497	C₂×C₃	C₂²×C₃×C₉×C₃₂	1	2	yes	—
498	C₂×C₃	C₂×C₄×C₁₆×C₂₇	1	3	yes	—
499	C₂×C₃	C₂×C₃×C₄×C₉×C₁₆	1	1	yes	characteristic
500	C₂²	C₂×C₃×C₂₇×C₃₂	1	4	yes	—
501	C₂²	C₃×C₄×C₁₆×C₂₇	1	2	yes	—
502	C₂²	C₂²×C₃×C₁₆×C₂₇	1	1	yes	characteristic
503	C₄	C₂×C₃×C₂₇×C₃₂	1	8	yes	direct product factor
504	C₄	C₃×C₄×C₁₆×C₂₇	1	2	yes	—
505	C₄	C₂²×C₃×C₁₆×C₂₇	1	1	yes	characteristic
506	C₄	C₂×C₃×C₄×C₈×C₂₇	1	1	yes	characteristic
507	C₃	C₂×C₄×C₂₇×C₃₂	1	3	yes	direct product factor
508	C₃	C₂×C₃×C₄×C₉×C₃₂	1	1	yes	characteristic
509	C₂	C₃×C₄×C₂₇×C₃₂	1	4	yes	direct product factor
510	C₂	C₂²×C₃×C₂₇×C₃₂	1	2	yes	—
511	C₂	C₂×C₃×C₄×C₁₆×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉×C₁₆	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂×C₉×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₂₇×C₃₂	C₂	direct (N × H)
5. C₂×C₄×C₂₇×C₃₂	C₃	direct (N × H)
11. C₂×C₃×C₂₇×C₃₂	C₄	direct (N × H)
18. C₄×C₂₇×C₃₂	C₂×C₃	direct (N × H)
29. C₃×C₂₇×C₃₂	C₂×C₄	direct (N × H)
43. C₂×C₂₇×C₃₂	C₃×C₄	direct (N × H)
90. C₂₇×C₃₂	C₂×C₃×C₄	direct (N × H)
91. C₂×C₃×C₄×C₃₂	C₂₇	direct (N × H)
94. C₂×C₃×C₄×C₂₇	C₃₂	direct (N × H)
155. C₃×C₄×C₃₂	C₂×C₂₇	direct (N × H)
161. C₃×C₄×C₂₇	C₂×C₃₂	direct (N × H)
197. C₂×C₄×C₃₂	C₃×C₂₇	direct (N × H)
210. C₂×C₄×C₂₇	C₃×C₃₂	direct (N × H)
226. C₂×C₃×C₃₂	C₄×C₂₇	direct (N × H)
234. C₂×C₃×C₂₇	C₄×C₃₂	direct (N × H)
278. C₄×C₃₂	C₂×C₃×C₂₇	direct (N × H)
290. C₄×C₂₇	C₂×C₃×C₃₂	direct (N × H)
313. C₃×C₃₂	C₂×C₄×C₂₇	direct (N × H)
315. C₃×C₂₇	C₂×C₄×C₃₂	direct (N × H)
352. C₂×C₃₂	C₃×C₄×C₂₇	direct (N × H)
359. C₂×C₂₇	C₃×C₄×C₃₂	direct (N × H)
419. C₃₂	C₂×C₃×C₄×C₂₇	direct (N × H)
421. C₂₇	C₂×C₃×C₄×C₃₂	direct (N × H)
424. C₂×C₃×C₄	C₂₇×C₃₂	direct (N × H)
473. C₃×C₄	C₂×C₂₇×C₃₂	direct (N × H)
484. C₂×C₄	C₃×C₂₇×C₃₂	direct (N × H)
494. C₂×C₃	C₄×C₂₇×C₃₂	direct (N × H)
503. C₄	C₂×C₃×C₂₇×C₃₂	direct (N × H)
507. C₃	C₂×C₄×C₂₇×C₃₂	direct (N × H)
509. C₂	C₃×C₄×C₂₇×C₃₂	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×C₄×C₁₆×C₂₇	2
C₂²×C₃×C₂₇×C₃₂	2
C₃×C₄×C₂₇×C₃₂	2
C₂×C₃×C₄×C₉×C₃₂	3
C₂×C₄×C₂₇×C₃₂	3

Subgroups — C2×C3×C4×C27×C32 #72198313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₂₇×C₃₂ #72198313