Subgroups — C₂³×C₃⁴×C₄×C₈ #72198366

Order 20736.

491628 conjugacy classes of subgroups.

The subgroup lattice has 285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⁴×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃⁴×C₈	C₂	1	2	yes	maximal
3	C₂²×C₃⁴×C₄×C₈	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₃³×C₄×C₈	C₃	1	40	yes	maximal, direct product factor
5	C₂⁴×C₃⁴×C₄	C₄	1	2	yes	—
6	C₂⁴×C₃⁴×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₃⁴×C₄²	C₄	1	14	yes	—
8	C₂²×C₃⁴×C₄²	C₂²	1	14	yes	—
9	C₂³×C₃⁴×C₈	C₄	1	32	yes	direct product factor
10	C₂³×C₃⁴×C₈	C₂²	1	28	yes	—
11	C₂×C₃⁴×C₄×C₈	C₂²	1	112	yes	direct product factor
12	C₂³×C₃³×C₄²	C₂×C₃	1	40	yes	—
13	C₂⁴×C₃³×C₈	C₂×C₃	1	80	yes	—
14	C₂²×C₃³×C₄×C₈	C₂×C₃	1	1120	yes	direct product factor
15	C₂⁵×C₃⁴	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₃⁴×C₄	C₈	1	32	yes	direct product factor
17	C₂³×C₃⁴×C₄	C₂×C₄	1	7	yes	—
18	C₂³×C₃⁴×C₄	C₂×C₄	1	16	yes	—
19	C₂³×C₃⁴×C₄	C₂×C₄	1	28	yes	—
20	C₂³×C₃⁴×C₄	C₂³	1	7	yes	—
21	C₂×C₃⁴×C₄²	C₂×C₄	1	84	yes	—
22	C₂×C₃⁴×C₄²	C₂³	1	28	yes	—
23	C₂²×C₃⁴×C₈	C₂×C₄	1	224	yes	direct product factor
24	C₂²×C₃⁴×C₈	C₂³	1	56	yes	—
25	C₃⁴×C₄×C₈	C₂³	1	64	yes	direct product factor
26	C₂³×C₃²×C₄×C₈	C₃²	1	130	yes	direct product factor
27	C₂⁴×C₃³×C₄	C₃×C₄	1	80	yes	—
28	C₂⁴×C₃³×C₄	C₂²×C₃	1	40	yes	—
29	C₂³×C₃³×C₈	C₃×C₄	1	1280	yes	direct product factor
30	C₂³×C₃³×C₈	C₂²×C₃	1	1120	yes	—
31	C₂²×C₃³×C₄²	C₃×C₄	1	560	yes	—
32	C₂²×C₃³×C₄²	C₂²×C₃	1	560	yes	—
33	C₂×C₃³×C₄×C₈	C₂²×C₃	1	4480	yes	direct product factor
34	C₂⁴×C₃⁴	C₄²	1	8	yes	—
35	C₂⁴×C₃⁴	C₂×C₈	1	16	yes	—
36	C₂⁴×C₃⁴	C₂²×C₄	1	7	yes	—
37	C₂²×C₃⁴×C₄	C₄²	1	56	yes	—
38	C₂²×C₃⁴×C₄	C₂×C₈	1	224	yes	direct product factor
39	C₂²×C₃⁴×C₄	C₂²×C₄	1	21	yes	—
40	C₂²×C₃⁴×C₄	C₂²×C₄	1	56	yes	—
41	C₂²×C₃⁴×C₄	C₂²×C₄	1	56	yes	—
42	C₂²×C₃⁴×C₄	C₂⁴	1	7	yes	—
43	C₂×C₃⁴×C₈	C₂²×C₄	1	224	yes	direct product factor
44	C₂×C₃⁴×C₈	C₂⁴	1	16	yes	—
45	C₃⁴×C₄²	C₂²×C₄	1	56	yes	—
46	C₃⁴×C₄²	C₂⁴	1	8	yes	—
47	C₂⁴×C₃²×C₈	C₂×C₃²	1	260	yes	—
48	C₂³×C₃²×C₄²	C₂×C₃²	1	130	yes	—
49	C₂²×C₃²×C₄×C₈	C₂×C₃²	1	3640	yes	direct product factor
50	C₂⁵×C₃³	C₂×C₃×C₄	1	40	yes	—
51	C₂³×C₃³×C₄	C₃×C₈	1	1280	yes	direct product factor
52	C₂³×C₃³×C₄	C₂×C₃×C₄	1	280	yes	—
53	C₂³×C₃³×C₄	C₂×C₃×C₄	1	1120	yes	—
54	C₂³×C₃³×C₄	C₂×C₃×C₄	1	640	yes	—
55	C₂³×C₃³×C₄	C₂³×C₃	1	280	yes	—
56	C₂²×C₃³×C₈	C₂×C₃×C₄	1	8960	yes	direct product factor
57	C₂²×C₃³×C₈	C₂³×C₃	1	2240	yes	—
58	C₂×C₃³×C₄²	C₂×C₃×C₄	1	3360	yes	—
59	C₂×C₃³×C₄²	C₂³×C₃	1	1120	yes	—
60	C₃³×C₄×C₈	C₂³×C₃	1	2560	yes	direct product factor
61	C₂³×C₃×C₄×C₈	C₃³	1	40	yes	direct product factor
62	C₂³×C₃⁴	C₄×C₈	1	64	yes	direct product factor
63	C₂³×C₃⁴	C₂×C₄²	1	28	yes	—
64	C₂³×C₃⁴	C₂²×C₈	1	56	yes	—
65	C₂³×C₃⁴	C₂³×C₄	1	7	yes	—
66	C₂×C₃⁴×C₄	C₂×C₄²	1	84	yes	—
67	C₂×C₃⁴×C₄	C₂²×C₈	1	224	yes	direct product factor
68	C₂×C₃⁴×C₄	C₂³×C₄	1	7	yes	—
69	C₂×C₃⁴×C₄	C₂³×C₄	1	16	yes	—
70	C₂×C₃⁴×C₄	C₂³×C₄	1	28	yes	—
71	C₂×C₃⁴×C₄	C₂⁵	1	1	yes	characteristic
72	C₃⁴×C₈	C₂³×C₄	1	32	yes	direct product factor
73	C₂⁴×C₃²×C₄	C₃²×C₄	1	260	yes	—
74	C₂⁴×C₃²×C₄	C₂²×C₃²	1	130	yes	—
75	C₂³×C₃²×C₈	C₃²×C₄	1	4160	yes	direct product factor
76	C₂³×C₃²×C₈	C₂²×C₃²	1	3640	yes	—
77	C₂²×C₃²×C₄²	C₃²×C₄	1	1820	yes	—
78	C₂²×C₃²×C₄²	C₂²×C₃²	1	1820	yes	—
79	C₂×C₃²×C₄×C₈	C₂²×C₃²	1	14560	yes	direct product factor
80	C₂⁴×C₃³	C₃×C₄²	1	320	yes	—
81	C₂⁴×C₃³	C₂×C₃×C₈	1	640	yes	—
82	C₂⁴×C₃³	C₂²×C₃×C₄	1	280	yes	—
83	C₂²×C₃³×C₄	C₃×C₄²	1	2240	yes	—
84	C₂²×C₃³×C₄	C₂×C₃×C₈	1	8960	yes	direct product factor
85	C₂²×C₃³×C₄	C₂²×C₃×C₄	1	840	yes	—
86	C₂²×C₃³×C₄	C₂²×C₃×C₄	1	2240	yes	—
87	C₂²×C₃³×C₄	C₂²×C₃×C₄	1	2240	yes	—
88	C₂²×C₃³×C₄	C₂⁴×C₃	1	280	yes	—
89	C₂×C₃³×C₈	C₂²×C₃×C₄	1	8960	yes	direct product factor
90	C₂×C₃³×C₈	C₂⁴×C₃	1	640	yes	—
91	C₃³×C₄²	C₂²×C₃×C₄	1	2240	yes	—
92	C₃³×C₄²	C₂⁴×C₃	1	320	yes	—
93	C₂⁴×C₃×C₈	C₂×C₃³	1	80	yes	—
94	C₂³×C₃×C₄²	C₂×C₃³	1	40	yes	—
95	C₂²×C₃×C₄×C₈	C₂×C₃³	1	1120	yes	direct product factor
96	C₂²×C₃⁴	C₂×C₄×C₈	1	112	yes	direct product factor
97	C₂²×C₃⁴	C₂²×C₄²	1	14	yes	—
98	C₂²×C₃⁴	C₂³×C₈	1	28	yes	—
99	C₂²×C₃⁴	C₂⁴×C₄	1	1	yes	characteristic
100	C₃⁴×C₄	C₂²×C₄²	1	14	yes	—
101	C₃⁴×C₄	C₂³×C₈	1	32	yes	direct product factor
102	C₃⁴×C₄	C₂⁴×C₄	1	2	yes	—
103	C₂⁵×C₃²	C₂×C₃²×C₄	1	130	yes	—
104	C₂³×C₃²×C₄	C₃²×C₈	1	4160	yes	direct product factor
105	C₂³×C₃²×C₄	C₂×C₃²×C₄	1	2080	yes	—
106	C₂³×C₃²×C₄	C₂×C₃²×C₄	1	3640	yes	—
107	C₂³×C₃²×C₄	C₂×C₃²×C₄	1	910	yes	—
108	C₂³×C₃²×C₄	C₂³×C₃²	1	910	yes	—
109	C₂²×C₃²×C₈	C₂×C₃²×C₄	1	29120	yes	direct product factor
110	C₂²×C₃²×C₈	C₂³×C₃²	1	7280	yes	—
111	C₂×C₃²×C₄²	C₂×C₃²×C₄	1	10920	yes	—
112	C₂×C₃²×C₄²	C₂³×C₃²	1	3640	yes	—
113	C₃²×C₄×C₈	C₂³×C₃²	1	8320	yes	direct product factor
114	C₂³×C₄×C₈	C₃⁴	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³×C₃³	C₃×C₄×C₈	1	2560	yes	direct product factor
116	C₂³×C₃³	C₂×C₃×C₄²	1	1120	yes	—
117	C₂³×C₃³	C₂²×C₃×C₈	1	2240	yes	—
118	C₂³×C₃³	C₂³×C₃×C₄	1	280	yes	—
119	C₂×C₃³×C₄	C₂×C₃×C₄²	1	3360	yes	—
120	C₂×C₃³×C₄	C₂²×C₃×C₈	1	8960	yes	direct product factor
121	C₂×C₃³×C₄	C₂³×C₃×C₄	1	280	yes	—
122	C₂×C₃³×C₄	C₂³×C₃×C₄	1	1120	yes	—
123	C₂×C₃³×C₄	C₂³×C₃×C₄	1	640	yes	—
124	C₂×C₃³×C₄	C₂⁵×C₃	1	40	yes	—
125	C₃³×C₈	C₂³×C₃×C₄	1	1280	yes	direct product factor
126	C₂⁴×C₃×C₄	C₃³×C₄	1	80	yes	—
127	C₂⁴×C₃×C₄	C₂²×C₃³	1	40	yes	—
128	C₂³×C₃×C₈	C₃³×C₄	1	1280	yes	direct product factor
129	C₂³×C₃×C₈	C₂²×C₃³	1	1120	yes	—
130	C₂²×C₃×C₄²	C₃³×C₄	1	560	yes	—
131	C₂²×C₃×C₄²	C₂²×C₃³	1	560	yes	—
132	C₂×C₃×C₄×C₈	C₂²×C₃³	1	4480	yes	direct product factor
133	C₂×C₃⁴	C₂²×C₄×C₈	1	28	yes	direct product factor
134	C₂×C₃⁴	C₂³×C₄²	1	1	yes	characteristic
135	C₂×C₃⁴	C₂⁴×C₈	1	2	yes	—
136	C₂⁴×C₃²	C₃²×C₄²	1	1040	yes	—
137	C₂⁴×C₃²	C₂×C₃²×C₈	1	2080	yes	—
138	C₂⁴×C₃²	C₂²×C₃²×C₄	1	910	yes	—
139	C₂²×C₃²×C₄	C₃²×C₄²	1	7280	yes	—
140	C₂²×C₃²×C₄	C₂×C₃²×C₈	1	29120	yes	direct product factor
141	C₂²×C₃²×C₄	C₂²×C₃²×C₄	1	7280	yes	—
142	C₂²×C₃²×C₄	C₂²×C₃²×C₄	1	7280	yes	—
143	C₂²×C₃²×C₄	C₂²×C₃²×C₄	1	2730	yes	—
144	C₂²×C₃²×C₄	C₂⁴×C₃²	1	910	yes	—
145	C₂×C₃²×C₈	C₂²×C₃²×C₄	1	29120	yes	direct product factor
146	C₂×C₃²×C₈	C₂⁴×C₃²	1	2080	yes	—
147	C₃²×C₄²	C₂²×C₃²×C₄	1	7280	yes	—
148	C₃²×C₄²	C₂⁴×C₃²	1	1040	yes	—
149	C₂⁴×C₈	C₂×C₃⁴	1	2	yes	—
150	C₂³×C₄²	C₂×C₃⁴	1	1	yes	characteristic
151	C₂²×C₄×C₈	C₂×C₃⁴	1	28	yes	direct product factor
152	C₂²×C₃³	C₂×C₃×C₄×C₈	1	4480	yes	direct product factor
153	C₂²×C₃³	C₂²×C₃×C₄²	1	560	yes	—
154	C₂²×C₃³	C₂³×C₃×C₈	1	1120	yes	—
155	C₂²×C₃³	C₂⁴×C₃×C₄	1	40	yes	—
156	C₃³×C₄	C₂²×C₃×C₄²	1	560	yes	—
157	C₃³×C₄	C₂³×C₃×C₈	1	1280	yes	direct product factor
158	C₃³×C₄	C₂⁴×C₃×C₄	1	80	yes	—
159	C₂⁵×C₃	C₂×C₃³×C₄	1	40	yes	—
160	C₂³×C₃×C₄	C₃³×C₈	1	1280	yes	direct product factor
161	C₂³×C₃×C₄	C₂×C₃³×C₄	1	280	yes	—
162	C₂³×C₃×C₄	C₂×C₃³×C₄	1	1120	yes	—
163	C₂³×C₃×C₄	C₂×C₃³×C₄	1	640	yes	—
164	C₂³×C₃×C₄	C₂³×C₃³	1	280	yes	—
165	C₂²×C₃×C₈	C₂×C₃³×C₄	1	8960	yes	direct product factor
166	C₂²×C₃×C₈	C₂³×C₃³	1	2240	yes	—
167	C₂×C₃×C₄²	C₂×C₃³×C₄	1	3360	yes	—
168	C₂×C₃×C₄²	C₂³×C₃³	1	1120	yes	—
169	C₃×C₄×C₈	C₂³×C₃³	1	2560	yes	direct product factor
170	C₃⁴	C₂³×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×C₃²	C₃²×C₄×C₈	1	8320	yes	direct product factor
172	C₂³×C₃²	C₂×C₃²×C₄²	1	3640	yes	—
173	C₂³×C₃²	C₂²×C₃²×C₈	1	7280	yes	—
174	C₂³×C₃²	C₂³×C₃²×C₄	1	910	yes	—
175	C₂×C₃²×C₄	C₂×C₃²×C₄²	1	10920	yes	—
176	C₂×C₃²×C₄	C₂²×C₃²×C₈	1	29120	yes	direct product factor
177	C₂×C₃²×C₄	C₂³×C₃²×C₄	1	2080	yes	—
178	C₂×C₃²×C₄	C₂³×C₃²×C₄	1	3640	yes	—
179	C₂×C₃²×C₄	C₂³×C₃²×C₄	1	910	yes	—
180	C₂×C₃²×C₄	C₂⁵×C₃²	1	130	yes	—
181	C₃²×C₈	C₂³×C₃²×C₄	1	4160	yes	direct product factor
182	C₂⁴×C₄	C₃⁴×C₄	1	2	yes	—
183	C₂⁴×C₄	C₂²×C₃⁴	1	1	yes	characteristic
184	C₂³×C₈	C₃⁴×C₄	1	32	yes	direct product factor
185	C₂³×C₈	C₂²×C₃⁴	1	28	yes	—
186	C₂²×C₄²	C₃⁴×C₄	1	14	yes	—
187	C₂²×C₄²	C₂²×C₃⁴	1	14	yes	—
188	C₂×C₄×C₈	C₂²×C₃⁴	1	112	yes	direct product factor
189	C₂×C₃³	C₂²×C₃×C₄×C₈	1	1120	yes	direct product factor
190	C₂×C₃³	C₂³×C₃×C₄²	1	40	yes	—
191	C₂×C₃³	C₂⁴×C₃×C₈	1	80	yes	—
192	C₂⁴×C₃	C₃³×C₄²	1	320	yes	—
193	C₂⁴×C₃	C₂×C₃³×C₈	1	640	yes	—
194	C₂⁴×C₃	C₂²×C₃³×C₄	1	280	yes	—
195	C₂²×C₃×C₄	C₃³×C₄²	1	2240	yes	—
196	C₂²×C₃×C₄	C₂×C₃³×C₈	1	8960	yes	direct product factor
197	C₂²×C₃×C₄	C₂²×C₃³×C₄	1	840	yes	—
198	C₂²×C₃×C₄	C₂²×C₃³×C₄	1	2240	yes	—
199	C₂²×C₃×C₄	C₂²×C₃³×C₄	1	2240	yes	—
200	C₂²×C₃×C₄	C₂⁴×C₃³	1	280	yes	—
201	C₂×C₃×C₈	C₂²×C₃³×C₄	1	8960	yes	direct product factor
202	C₂×C₃×C₈	C₂⁴×C₃³	1	640	yes	—
203	C₃×C₄²	C₂²×C₃³×C₄	1	2240	yes	—
204	C₃×C₄²	C₂⁴×C₃³	1	320	yes	—
205	C₂²×C₃²	C₂×C₃²×C₄×C₈	1	14560	yes	direct product factor
206	C₂²×C₃²	C₂²×C₃²×C₄²	1	1820	yes	—
207	C₂²×C₃²	C₂³×C₃²×C₈	1	3640	yes	—
208	C₂²×C₃²	C₂⁴×C₃²×C₄	1	130	yes	—
209	C₃²×C₄	C₂²×C₃²×C₄²	1	1820	yes	—
210	C₃²×C₄	C₂³×C₃²×C₈	1	4160	yes	direct product factor
211	C₃²×C₄	C₂⁴×C₃²×C₄	1	260	yes	—
212	C₂⁵	C₂×C₃⁴×C₄	1	1	yes	characteristic
213	C₂³×C₄	C₃⁴×C₈	1	32	yes	direct product factor
214	C₂³×C₄	C₂×C₃⁴×C₄	1	7	yes	—
215	C₂³×C₄	C₂×C₃⁴×C₄	1	16	yes	—
216	C₂³×C₄	C₂×C₃⁴×C₄	1	28	yes	—
217	C₂³×C₄	C₂³×C₃⁴	1	7	yes	—
218	C₂²×C₈	C₂×C₃⁴×C₄	1	224	yes	direct product factor
219	C₂²×C₈	C₂³×C₃⁴	1	56	yes	—
220	C₂×C₄²	C₂×C₃⁴×C₄	1	84	yes	—
221	C₂×C₄²	C₂³×C₃⁴	1	28	yes	—
222	C₄×C₈	C₂³×C₃⁴	1	64	yes	direct product factor
223	C₃³	C₂³×C₃×C₄×C₈	1	40	yes	direct product factor
224	C₂³×C₃	C₃³×C₄×C₈	1	2560	yes	direct product factor
225	C₂³×C₃	C₂×C₃³×C₄²	1	1120	yes	—
226	C₂³×C₃	C₂²×C₃³×C₈	1	2240	yes	—
227	C₂³×C₃	C₂³×C₃³×C₄	1	280	yes	—
228	C₂×C₃×C₄	C₂×C₃³×C₄²	1	3360	yes	—
229	C₂×C₃×C₄	C₂²×C₃³×C₈	1	8960	yes	direct product factor
230	C₂×C₃×C₄	C₂³×C₃³×C₄	1	280	yes	—
231	C₂×C₃×C₄	C₂³×C₃³×C₄	1	1120	yes	—
232	C₂×C₃×C₄	C₂³×C₃³×C₄	1	640	yes	—
233	C₂×C₃×C₄	C₂⁵×C₃³	1	40	yes	—
234	C₃×C₈	C₂³×C₃³×C₄	1	1280	yes	direct product factor
235	C₂×C₃²	C₂²×C₃²×C₄×C₈	1	3640	yes	direct product factor
236	C₂×C₃²	C₂³×C₃²×C₄²	1	130	yes	—
237	C₂×C₃²	C₂⁴×C₃²×C₈	1	260	yes	—
238	C₂⁴	C₃⁴×C₄²	1	8	yes	—
239	C₂⁴	C₂×C₃⁴×C₈	1	16	yes	—
240	C₂⁴	C₂²×C₃⁴×C₄	1	7	yes	—
241	C₂²×C₄	C₃⁴×C₄²	1	56	yes	—
242	C₂²×C₄	C₂×C₃⁴×C₈	1	224	yes	direct product factor
243	C₂²×C₄	C₂²×C₃⁴×C₄	1	21	yes	—
244	C₂²×C₄	C₂²×C₃⁴×C₄	1	56	yes	—
245	C₂²×C₄	C₂²×C₃⁴×C₄	1	56	yes	—
246	C₂²×C₄	C₂⁴×C₃⁴	1	7	yes	—
247	C₂×C₈	C₂²×C₃⁴×C₄	1	224	yes	direct product factor
248	C₂×C₈	C₂⁴×C₃⁴	1	16	yes	—
249	C₄²	C₂²×C₃⁴×C₄	1	56	yes	—
250	C₄²	C₂⁴×C₃⁴	1	8	yes	—
251	C₂²×C₃	C₂×C₃³×C₄×C₈	1	4480	yes	direct product factor
252	C₂²×C₃	C₂²×C₃³×C₄²	1	560	yes	—
253	C₂²×C₃	C₂³×C₃³×C₈	1	1120	yes	—
254	C₂²×C₃	C₂⁴×C₃³×C₄	1	40	yes	—
255	C₃×C₄	C₂²×C₃³×C₄²	1	560	yes	—
256	C₃×C₄	C₂³×C₃³×C₈	1	1280	yes	direct product factor
257	C₃×C₄	C₂⁴×C₃³×C₄	1	80	yes	—
258	C₃²	C₂³×C₃²×C₄×C₈	1	130	yes	direct product factor
259	C₂³	C₃⁴×C₄×C₈	1	64	yes	direct product factor
260	C₂³	C₂²×C₃⁴×C₈	1	56	yes	—
261	C₂³	C₂×C₃⁴×C₄²	1	28	yes	—
262	C₂³	C₂³×C₃⁴×C₄	1	7	yes	—
263	C₂×C₄	C₂²×C₃⁴×C₈	1	224	yes	direct product factor
264	C₂×C₄	C₂×C₃⁴×C₄²	1	84	yes	—
265	C₂×C₄	C₂³×C₃⁴×C₄	1	7	yes	—
266	C₂×C₄	C₂³×C₃⁴×C₄	1	16	yes	—
267	C₂×C₄	C₂³×C₃⁴×C₄	1	28	yes	—
268	C₂×C₄	C₂⁵×C₃⁴	1	1	yes	characteristic
269	C₈	C₂³×C₃⁴×C₄	1	32	yes	direct product factor
270	C₂×C₃	C₂²×C₃³×C₄×C₈	1	1120	yes	direct product factor
271	C₂×C₃	C₂⁴×C₃³×C₈	1	80	yes	—
272	C₂×C₃	C₂³×C₃³×C₄²	1	40	yes	—
273	C₂²	C₂×C₃⁴×C₄×C₈	1	112	yes	direct product factor
274	C₂²	C₂³×C₃⁴×C₈	1	28	yes	—
275	C₂²	C₂²×C₃⁴×C₄²	1	14	yes	—
276	C₂²	C₂⁴×C₃⁴×C₄	1	1	yes	characteristic
277	C₄	C₂³×C₃⁴×C₈	1	32	yes	direct product factor
278	C₄	C₂²×C₃⁴×C₄²	1	14	yes	—
279	C₄	C₂⁴×C₃⁴×C₄	1	2	yes	—
280	C₃	C₂³×C₃³×C₄×C₈	1	40	yes	direct product factor
281	C₂	C₂²×C₃⁴×C₄×C₈	1	28	yes	direct product factor
282	C₂	C₂⁴×C₃⁴×C₈	1	2	yes	—
283	C₂	C₂³×C₃⁴×C₄²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₃⁴
socle, prime radical	C₂⁵×C₃⁴	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃⁴×C₄×C₈	C₂	direct (N × H)
4. C₂³×C₃³×C₄×C₈	C₃	direct (N × H)
9. C₂³×C₃⁴×C₈	C₄	direct (N × H)
11. C₂×C₃⁴×C₄×C₈	C₂²	direct (N × H)
14. C₂²×C₃³×C₄×C₈	C₂×C₃	direct (N × H)
16. C₂³×C₃⁴×C₄	C₈	direct (N × H)
23. C₂²×C₃⁴×C₈	C₂×C₄	direct (N × H)
25. C₃⁴×C₄×C₈	C₂³	direct (N × H)
26. C₂³×C₃²×C₄×C₈	C₃²	direct (N × H)
29. C₂³×C₃³×C₈	C₃×C₄	direct (N × H)
33. C₂×C₃³×C₄×C₈	C₂²×C₃	direct (N × H)
38. C₂²×C₃⁴×C₄	C₂×C₈	direct (N × H)
43. C₂×C₃⁴×C₈	C₂²×C₄	direct (N × H)
49. C₂²×C₃²×C₄×C₈	C₂×C₃²	direct (N × H)
51. C₂³×C₃³×C₄	C₃×C₈	direct (N × H)
56. C₂²×C₃³×C₈	C₂×C₃×C₄	direct (N × H)
60. C₃³×C₄×C₈	C₂³×C₃	direct (N × H)
61. C₂³×C₃×C₄×C₈	C₃³	direct (N × H)
62. C₂³×C₃⁴	C₄×C₈	direct (N × H)
67. C₂×C₃⁴×C₄	C₂²×C₈	direct (N × H)
72. C₃⁴×C₈	C₂³×C₄	direct (N × H)
75. C₂³×C₃²×C₈	C₃²×C₄	direct (N × H)
79. C₂×C₃²×C₄×C₈	C₂²×C₃²	direct (N × H)
84. C₂²×C₃³×C₄	C₂×C₃×C₈	direct (N × H)
89. C₂×C₃³×C₈	C₂²×C₃×C₄	direct (N × H)
95. C₂²×C₃×C₄×C₈	C₂×C₃³	direct (N × H)
96. C₂²×C₃⁴	C₂×C₄×C₈	direct (N × H)
101. C₃⁴×C₄	C₂³×C₈	direct (N × H)
104. C₂³×C₃²×C₄	C₃²×C₈	direct (N × H)
109. C₂²×C₃²×C₈	C₂×C₃²×C₄	direct (N × H)
113. C₃²×C₄×C₈	C₂³×C₃²	direct (N × H)
114. C₂³×C₄×C₈	C₃⁴	direct (N × H)
115. C₂³×C₃³	C₃×C₄×C₈	direct (N × H)
120. C₂×C₃³×C₄	C₂²×C₃×C₈	direct (N × H)
125. C₃³×C₈	C₂³×C₃×C₄	direct (N × H)
128. C₂³×C₃×C₈	C₃³×C₄	direct (N × H)
132. C₂×C₃×C₄×C₈	C₂²×C₃³	direct (N × H)
133. C₂×C₃⁴	C₂²×C₄×C₈	direct (N × H)
140. C₂²×C₃²×C₄	C₂×C₃²×C₈	direct (N × H)
145. C₂×C₃²×C₈	C₂²×C₃²×C₄	direct (N × H)
151. C₂²×C₄×C₈	C₂×C₃⁴	direct (N × H)
152. C₂²×C₃³	C₂×C₃×C₄×C₈	direct (N × H)
157. C₃³×C₄	C₂³×C₃×C₈	direct (N × H)
160. C₂³×C₃×C₄	C₃³×C₈	direct (N × H)
165. C₂²×C₃×C₈	C₂×C₃³×C₄	direct (N × H)
169. C₃×C₄×C₈	C₂³×C₃³	direct (N × H)
170. C₃⁴	C₂³×C₄×C₈	direct (N × H)
171. C₂³×C₃²	C₃²×C₄×C₈	direct (N × H)
176. C₂×C₃²×C₄	C₂²×C₃²×C₈	direct (N × H)
181. C₃²×C₈	C₂³×C₃²×C₄	direct (N × H)
184. C₂³×C₈	C₃⁴×C₄	direct (N × H)
188. C₂×C₄×C₈	C₂²×C₃⁴	direct (N × H)
189. C₂×C₃³	C₂²×C₃×C₄×C₈	direct (N × H)
196. C₂²×C₃×C₄	C₂×C₃³×C₈	direct (N × H)
201. C₂×C₃×C₈	C₂²×C₃³×C₄	direct (N × H)
205. C₂²×C₃²	C₂×C₃²×C₄×C₈	direct (N × H)
210. C₃²×C₄	C₂³×C₃²×C₈	direct (N × H)
213. C₂³×C₄	C₃⁴×C₈	direct (N × H)
218. C₂²×C₈	C₂×C₃⁴×C₄	direct (N × H)
222. C₄×C₈	C₂³×C₃⁴	direct (N × H)
223. C₃³	C₂³×C₃×C₄×C₈	direct (N × H)
224. C₂³×C₃	C₃³×C₄×C₈	direct (N × H)
229. C₂×C₃×C₄	C₂²×C₃³×C₈	direct (N × H)
234. C₃×C₈	C₂³×C₃³×C₄	direct (N × H)
235. C₂×C₃²	C₂²×C₃²×C₄×C₈	direct (N × H)
242. C₂²×C₄	C₂×C₃⁴×C₈	direct (N × H)
247. C₂×C₈	C₂²×C₃⁴×C₄	direct (N × H)
251. C₂²×C₃	C₂×C₃³×C₄×C₈	direct (N × H)
256. C₃×C₄	C₂³×C₃³×C₈	direct (N × H)
258. C₃²	C₂³×C₃²×C₄×C₈	direct (N × H)
259. C₂³	C₃⁴×C₄×C₈	direct (N × H)
263. C₂×C₄	C₂²×C₃⁴×C₈	direct (N × H)
269. C₈	C₂³×C₃⁴×C₄	direct (N × H)
270. C₂×C₃	C₂²×C₃³×C₄×C₈	direct (N × H)
273. C₂²	C₂×C₃⁴×C₄×C₈	direct (N × H)
277. C₄	C₂³×C₃⁴×C₈	direct (N × H)
280. C₃	C₂³×C₃³×C₄×C₈	direct (N × H)
281. C₂	C₂²×C₃⁴×C₄×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃⁴×C₄²	2
C₂⁴×C₃⁴×C₈	2
C₂²×C₃⁴×C₄×C₈	2
C₂³×C₃³×C₄×C₈	3

Subgroups — C23×C34×C4×C8 #72198366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃⁴×C₄×C₈ #72198366