Subgroups — C₂×C₄₃×#1478 #24937451

Order 11008.

1714 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1478	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₃×D₄⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₄₃	—	2	1	no	—
8	C₂×C₄×D₄×C₄₃	—	2	1	no	—
9	C₂×C₄×D₄×C₄₃	—	2	2	no	—
10	C₂×C₄×D₄×C₄₃	—	2	2	no	—
11	C₂×C₄×D₄×C₄₃	—	2	1	no	—
12	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
13	C₂×C₄×D₄×C₄₃	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#431	—	2	2	no	—
20	C₄₃×#431	—	2	2	no	—
21	C₄₃×#431	C₂²	1	4	yes	complemented
22	C₄₃×#431	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
27	C₂×C₄×C₈×C₄₃	—	2	1	no	—
28	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
29	C₄₃×D₄⋊C₈	C₂²	1	16	yes	complemented
30	C₂⁵×C₄₃	—	2	1	no	—
31	C₂²×D₄×C₄₃	—	2	2	no	—
32	C₂²×D₄×C₄₃	—	2	1	no	—
33	C₂²×D₄×C₄₃	—	2	4	no	—
34	C₂²×D₄×C₄₃	C₈	1	8	yes	complemented
35	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₄₃	—	2	1	no	—
38	C₂³×C₄×C₄₃	—	2	2	no	—
39	C₂³×C₄×C₄₃	—	2	4	no	—
40	C₂³×C₄×C₄₃	—	2	4	no	—
41	C₂³×C₄×C₄₃	—	2	2	no	—
42	C₂³×C₄×C₄₃	—	4	8	no	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₄₃	—	2	2	no	—
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₄×D₄×C₄₃	—	2	4	no	—
49	C₄×D₄×C₄₃	—	2	4	no	—
50	C₄×D₄×C₄₃	—	2	4	no	—
51	C₄×D₄×C₄₃	—	2	4	no	—
52	C₄×D₄×C₄₃	—	2	2	no	—
53	C₄×D₄×C₄₃	—	2	2	no	—
54	C₄×D₄×C₄₃	—	2	4	no	—
55	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₄×D₄×C₄₃	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	D₄	1	2	yes	—
70	C₂×C₄²×C₄₃	D₄	1	2	yes	—
71	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	—	2	4	no	—
75	C₄⋊C₈×C₄₃	—	2	2	no	—
76	C₄⋊C₈×C₄₃	C₂³	1	4	yes	complemented
77	C₂²⋊C₈×C₄₃	—	2	4	no	—
78	C₂²⋊C₈×C₄₃	—	2	4	no	—
79	C₄×C₈×C₄₃	—	2	4	no	—
80	C₄×C₈×C₄₃	—	2	2	no	—
81	C₄×C₈×C₄₃	C₂³	1	4	yes	complemented
82	C₂⁴×C₄₃	—	2	8	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	—	2	4	no	—
85	C₂⁴×C₄₃	—	4	4	no	—
86	C₂⁴×C₄₃	—	4	4	no	—
87	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×D₄×C₄₃	—	2	8	no	—
89	C₂×D₄×C₄₃	—	2	16	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	8	no	—
94	C₂×D₄×C₄₃	C₂×C₈	1	8	yes	—
95	C₂×D₄×C₄₃	C₂×C₈	1	16	yes	complemented
96	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	8	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	—	4	4	no	—
105	C₂²×C₄×C₄₃	—	4	16	no	—
106	C₂²×C₄×C₄₃	—	4	16	no	—
107	C₂²×C₄×C₄₃	—	4	8	no	—
108	C₂²×C₄×C₄₃	—	4	8	no	—
109	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	—
116	C₂²×C₄×C₄₃	M₁₆	1	4	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	—	2	4	no	—
125	C₂×C₈×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	—	4	4	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
130	C₂²⋊C₄×C₄₃	—	2	8	no	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	—	2	4	no	—
133	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	2	yes	—
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	C₂×D₄	1	2	yes	—
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	4	no	—
146	C₂³×C₄₃	—	2	8	no	—
147	C₂³×C₄₃	—	2	16	no	—
148	C₂³×C₄₃	—	4	8	no	—
149	C₂³×C₄₃	—	4	8	no	—
150	C₂³×C₄₃	—	4	32	no	—
151	C₂³×C₄₃	—	4	4	no	—
152	C₂³×C₄₃	—	4	4	no	—
153	C₂³×C₄₃	C₂²⋊C₈	1	4	yes	—
154	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	D₄×C₄₃	—	2	4	no	—
157	D₄×C₄₃	—	2	8	no	—
158	D₄×C₄₃	—	2	16	no	—
159	D₄×C₄₃	C₂²×C₈	1	8	yes	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	16	no	—
169	C₂×C₄×C₄₃	—	4	8	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	8	no	—
172	C₂×C₄×C₄₃	—	4	8	no	—
173	C₂×C₄×C₄₃	C₂²⋊C₈	1	8	yes	—
174	C₂×C₄×C₄₃	C₂²⋊C₈	1	4	yes	—
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	—
183	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
184	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
186	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₄₃	—	4	4	no	—
190	C₈×C₄₃	—	4	4	no	—
191	C₂×#1478	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	8	no	—
195	C₂²×C₄₃	—	2	8	no	—
196	C₂²×C₄₃	—	4	32	no	—
197	C₂²×C₄₃	—	4	4	no	—
198	C₂²×C₄₃	—	4	4	no	—
199	C₂²×C₄₃	—	4	16	no	—
200	C₂²×C₄₃	C₂×C₂²⋊C₈	1	4	yes	—
201	C₂²×C₄₃	C₂×C₂²⋊C₈	1	2	yes	—
202	C₂²×C₄₃	#418	1	2	yes	—
203	C₂²×C₄₃	#421	1	2	yes	—
204	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	4	4	no	—
210	C₄×C₄₃	C₂×C₂²⋊C₈	1	2	yes	—
211	C₄×C₄₃	C₂×C₂²⋊C₈	1	4	yes	—
212	C₄×C₄₃	#418	1	2	yes	—
213	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
214	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
215	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
217	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
218	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
219	#1478	C₂×C₄₃	1	8	yes	direct product factor
220	C₂×D₄⋊C₈	C₂×C₄₃	1	4	yes	complemented
221	C₂×C₄₃	—	2	4	no	—
222	C₂×C₄₃	—	4	8	no	—
223	C₂×C₄₃	#1478	1	4	yes	direct product factor
224	C₂×C₄₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
225	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
226	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
227	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic
228	C₂⁴×C₄	—	2	1	no	—
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	—	2	2	no	—
232	C₂×C₄×D₄	—	2	2	no	—
233	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
234	C₂×C₄×D₄	C₄×C₄₃	1	4	yes	—
235	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
236	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
237	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	—	2	1	no	—
239	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
240	#431	—	2	2	no	—
241	#431	—	2	2	no	—
242	#431	C₂²×C₄₃	1	4	yes	complemented
243	#431	C₂²×C₄₃	1	4	yes	complemented
244	C₂×C₄⋊C₈	—	2	1	no	—
245	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
246	C₂×C₂²⋊C₈	—	2	1	no	—
247	C₂×C₂²⋊C₈	—	2	1	no	—
248	C₂×C₄×C₈	—	2	1	no	—
249	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
250	D₄⋊C₈	C₂²×C₄₃	1	16	yes	complemented
251	C₄₃	C₂×#1478	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁵	—	2	1	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	4	no	—
256	C₂²×D₄	C₈×C₄₃	1	8	yes	complemented
257	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
258	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	4	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	2	4	no	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	—	4	8	no	—
265	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
267	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
278	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	—
279	C₄×D₄	C₂³×C₄₃	1	4	yes	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
289	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
290	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₄₃	1	2	yes	—
293	C₂×C₄²	D₄×C₄₃	1	2	yes	—
294	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
296	C₄⋊C₈	—	2	4	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	C₂³×C₄₃	1	4	yes	complemented
299	C₂²⋊C₈	—	2	4	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₄×C₈	—	2	4	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	C₂³×C₄₃	1	4	yes	complemented
304	C₂⁴	—	2	8	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	4	4	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
310	C₂×D₄	—	2	16	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	C₂×C₈×C₄₃	1	8	yes	—
317	C₂×D₄	C₂×C₈×C₄₃	1	16	yes	complemented
318	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	16	no	—
328	C₂²×C₄	—	4	16	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
335	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
336	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₈×C₄₃	1	4	yes	—
338	C₂²×C₄	M₁₆×C₄₃	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	4	4	no	—
348	C₂×C₈	—	4	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
356	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
357	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
358	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
359	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₄₃	1	2	yes	—
361	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₄₃	1	2	yes	—
364	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	32	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	C₂²⋊C₈×C₄₃	1	4	yes	—
376	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
377	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
378	D₄	—	2	4	no	—
379	D₄	—	2	8	no	—
380	D₄	—	2	16	no	—
381	D₄	C₂²×C₈×C₄₃	1	8	yes	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	16	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	C₂²⋊C₈×C₄₃	1	8	yes	—
396	C₂×C₄	C₂²⋊C₈×C₄₃	1	4	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₈×C₄₃	1	2	yes	—
404	C₂×C₄	C₂²×C₈×C₄₃	1	4	yes	—
405	C₂×C₄	C₂×M₁₆×C₄₃	1	4	yes	—
406	C₂×C₄	C₂×M₁₆×C₄₃	1	2	yes	—
407	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
408	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
411	C₈	—	4	4	no	—
412	C₈	—	4	4	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	8	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	32	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	16	no	—
421	C₂²	C₂×C₂²⋊C₈×C₄₃	1	4	yes	—
422	C₂²	C₂×C₂²⋊C₈×C₄₃	1	2	yes	—
423	C₂²	C₄₃×#418	1	2	yes	—
424	C₂²	C₄₃×#421	1	2	yes	—
425	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	4	no	—
431	C₄	C₂×C₂²⋊C₈×C₄₃	1	2	yes	—
432	C₄	C₂×C₂²⋊C₈×C₄₃	1	4	yes	—
433	C₄	C₄₃×#418	1	2	yes	—
434	C₄	C₂³×C₈×C₄₃	1	1	yes	characteristic
435	C₄	C₂²×M₁₆×C₄₃	1	1	yes	characteristic
436	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
437	C₂	—	2	4	no	—
438	C₂	—	4	8	no	—
439	C₂	C₄₃×#1478	1	4	yes	direct product factor
440	C₂	C₂²×C₂²⋊C₈×C₄₃	1	1	yes	characteristic
441	C₂	C₂×C₄₃×#418	1	1	yes	characteristic
442	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₄	C₂³×C₈×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₄₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#431	C₂	semidirect
3. C₂×C₄₃×#431	C₂	semidirect
4. C₄₃×#1478	C₂	direct (N × H)
5. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
21. C₄₃×#431	C₂²	semidirect
22. C₄₃×#431	C₂²	semidirect
24. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
28. C₂×C₄×C₈×C₄₃	C₂²	semidirect
29. C₄₃×D₄⋊C₈	C₂²	semidirect
34. C₂²×D₄×C₄₃	C₈	semidirect
76. C₄⋊C₈×C₄₃	C₂³	semidirect
81. C₄×C₈×C₄₃	C₂³	semidirect
95. C₂×D₄×C₄₃	C₂×C₈	semidirect
191. C₂×#1478	C₄₃	direct (N × H)
217. C₂×#431	C₂×C₄₃	semidirect
218. C₂×#431	C₂×C₄₃	semidirect
219. #1478	C₂×C₄₃	direct (N × H)
220. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
223. C₂×C₄₃	#1478	direct (N × H)
242. #431	C₂²×C₄₃	semidirect
243. #431	C₂²×C₄₃	semidirect
245. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
249. C₂×C₄×C₈	C₂²×C₄₃	semidirect
250. D₄⋊C₈	C₂²×C₄₃	semidirect
251. C₄₃	C₂×#1478	direct (N × H)
256. C₂²×D₄	C₈×C₄₃	semidirect
298. C₄⋊C₈	C₂³×C₄₃	semidirect
303. C₄×C₈	C₂³×C₄₃	semidirect
317. C₂×D₄	C₂×C₈×C₄₃	semidirect
439. C₂	C₄₃×#1478	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#431	2
C₄₃×#1478	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1478	43

Subgroups — C2×C43×#1478 #24937451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1478 #24937451