Subgroups — C₄₃×#17852 #24937869

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1580	C₂	1	2	yes	maximal, complemented
5	C₄₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₈×SD₁₆×C₄₃	C₂	1	2	yes	maximal, complemented
7	C₈×D₈×C₄₃	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₃	C₄	1	1	yes	characteristic
13	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
16	C₄₃×#442	C₄	1	2	yes	—
17	C₄₃×#440	C₄	1	2	yes	—
18	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
19	C₄×D₈×C₄₃	C₂²	1	2	yes	—
20	C₈×D₄×C₄₃	—	2	1	no	—
21	C₈×D₄×C₄₃	—	2	1	no	—
22	C₈×D₄×C₄₃	—	2	2	no	—
23	C₈×D₄×C₄₃	C₂²	1	2	yes	—
24	C₈×D₄×C₄₃	C₂²	1	2	yes	—
25	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
26	C₄₃×#431	—	2	1	no	—
27	C₄₃×#431	C₂²	1	1	yes	characteristic
28	C₄₃×#431	C₂²	1	1	yes	characteristic
29	C₄₃×#428	C₄	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#418	C₄	1	1	yes	characteristic
33	C₄₃×#417	C₄	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
35	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#335	C₂²	1	2	yes	complemented
38	C₄₃×#334	C₂²	1	2	yes	complemented
39	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
42	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
43	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₄₃×#322	C₂²	1	2	yes	complemented
46	C₈²×C₄₃	C₂²	1	2	yes	complemented
47	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	—	2	1	no	—
50	AGL(1,ℤ/8)×C₄₃	C₈	1	8	yes	complemented
51	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	C₂²×C₈×C₄₃	—	2	2	no	—
58	C₂²×C₈×C₄₃	—	2	2	no	—
59	C₂²×C₈×C₄₃	—	2	2	no	—
60	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₄₃	—	2	1	no	—
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	1	no	—
65	C₄×D₄×C₄₃	—	2	1	no	—
66	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₄₃	C₂³	1	2	yes	—
69	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
70	#117×C₄₃	—	2	1	no	—
71	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	#107×C₄₃	C₂×C₄	1	2	yes	—
77	#106×C₄₃	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₄₃	—	2	2	no	—
79	C₄⋊C₈×C₄₃	—	2	1	no	—
80	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
83	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
85	#103×C₄₃	C₂×C₄	1	2	yes	—
86	#102×C₄₃	C₂×C₄	1	2	yes	—
87	#102×C₄₃	C₂×C₄	1	2	yes	—
88	#102×C₄₃	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₄₃	—	2	1	no	—
90	C₂²⋊C₈×C₄₃	—	2	2	no	—
91	C₂²⋊C₈×C₄₃	—	2	2	no	—
92	C₂²⋊C₈×C₄₃	—	2	2	no	—
93	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
94	#97×C₄₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₄₃	—	2	2	no	—
96	C₄×C₈×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	—	2	1	no	—
98	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	#41×C₄₃	—	2	2	no	—
104	#41×C₄₃	C₂×C₈	1	4	yes	complemented
105	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	C₂×C₈	1	4	yes	complemented
110	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	8	1	no	—
119	C₂²×C₄×C₄₃	—	8	1	no	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	SD₁₆×C₄₃	C₂×C₈	1	8	yes	complemented
124	D₈×C₄₃	C₂×C₈	1	8	yes	complemented
125	M₁₆×C₄₃	—	2	2	no	—
126	M₁₆×C₄₃	C₂×C₈	1	4	yes	complemented
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	4	2	no	—
133	C₂×C₈×C₄₃	—	8	2	no	—
134	C₂×C₈×C₄₃	—	8	2	no	—
135	C₂×C₈×C₄₃	—	8	2	no	—
136	C₂×C₈×C₄₃	—	8	1	no	—
137	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₃	—	2	2	no	—
148	C₂²⋊C₄×C₄₃	—	2	1	no	—
149	C₂²⋊C₄×C₄₃	—	2	2	no	—
150	C₂²⋊C₄×C₄₃	—	2	1	no	—
151	C₂²⋊C₄×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	—	2	1	no	—
153	C₄²×C₄₃	—	2	1	no	—
154	C₄²×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₃	#41	1	1	yes	characteristic
158	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	4	no	—
162	C₂³×C₄₃	—	8	1	no	—
163	C₂³×C₄₃	—	8	1	no	—
164	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₄₃	—	2	1	no	—
166	Q₈×C₄₃	C₂²×C₈	1	2	yes	—
167	D₄×C₄₃	—	2	4	no	—
168	D₄×C₄₃	—	2	2	no	—
169	D₄×C₄₃	—	2	1	no	—
170	D₄×C₄₃	—	2	4	no	—
171	D₄×C₄₃	C₂²×C₈	1	2	yes	—
172	D₄×C₄₃	C₂²×C₈	1	4	yes	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	8	1	no	—
186	C₂×C₄×C₄₃	—	8	2	no	—
187	C₂×C₄×C₄₃	—	8	1	no	—
188	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
192	C₂×C₄×C₄₃	#131	1	2	yes	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	2	2	no	—
198	C₈×C₄₃	—	2	2	no	—
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	4	1	no	—
201	C₈×C₄₃	—	4	1	no	—
202	C₈×C₄₃	—	4	2	no	—
203	C₈×C₄₃	—	4	1	no	—
204	C₈×C₄₃	C₂²×C₈	1	4	yes	—
205	#17852	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	4	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	—	4	1	no	—
212	C₂²×C₄₃	—	4	2	no	—
213	C₂²×C₄₃	—	4	1	no	—
214	C₂²×C₄₃	—	8	4	no	—
215	C₂²×C₄₃	C₈×D₄	1	2	yes	—
216	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	4	1	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	4	1	no	—
224	C₄×C₄₃	C₈×D₄	1	2	yes	—
225	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
226	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
227	C₄×C₄₃	#576	1	1	yes	characteristic
228	C₄×C₄₃	#577	1	1	yes	characteristic
229	#2988	C₂×C₄₃	1	1	yes	characteristic, complemented
230	#2972	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₄×AGL(1,ℤ/8)	C₂×C₄₃	1	1	yes	characteristic
232	#1580	C₂×C₄₃	1	2	yes	complemented
233	SD₁₆⋊C₈	C₂×C₄₃	1	2	yes	complemented
234	C₈×SD₁₆	C₂×C₄₃	1	2	yes	complemented
235	C₈×D₈	C₂×C₄₃	1	2	yes	complemented
236	#1565	C₂×C₄₃	1	1	yes	characteristic, complemented
237	#1476	C₂×C₄₃	1	1	yes	characteristic, complemented
238	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
239	C₈×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
240	C₂×C₄₃	—	2	2	no	—
241	C₂×C₄₃	—	4	2	no	—
242	C₂×C₄₃	—	4	4	no	—
243	C₂×C₄₃	C₂×C₈×D₄	1	1	yes	characteristic
244	C₂×C₄₃	#2946	1	1	yes	characteristic
245	C₂×C₄₃	#2956	1	1	yes	characteristic
246	C₂×AGL(1,ℤ/8)	C₄×C₄₃	1	1	yes	characteristic
247	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
249	C₈×Q₈	C₂²×C₄₃	1	2	yes	complemented
250	#442	C₄×C₄₃	1	2	yes	—
251	#440	C₄×C₄₃	1	2	yes	—
252	C₄×SD₁₆	C₂²×C₄₃	1	2	yes	—
253	C₄×D₈	C₂²×C₄₃	1	2	yes	—
254	C₈×D₄	—	2	1	no	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	—	2	2	no	—
257	C₈×D₄	C₂²×C₄₃	1	2	yes	—
258	C₈×D₄	C₂²×C₄₃	1	2	yes	—
259	C₈×D₄	C₂²×C₄₃	1	2	yes	complemented
260	#431	—	2	1	no	—
261	#431	C₂²×C₄₃	1	1	yes	characteristic
262	#431	C₂²×C₄₃	1	1	yes	characteristic
263	#428	C₄×C₄₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	—	2	1	no	—
265	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
266	#418	C₄×C₄₃	1	1	yes	characteristic
267	#417	C₄×C₄₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	—	2	2	no	—
269	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
271	#335	C₂²×C₄₃	1	2	yes	complemented
272	#334	C₂²×C₄₃	1	2	yes	complemented
273	Q₈⋊C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
274	Q₈⋊C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
275	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
276	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
277	D₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
278	D₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
279	#322	C₂²×C₄₃	1	2	yes	complemented
280	C₈²	C₂²×C₄₃	1	2	yes	complemented
281	C₄₃	#17852	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×#41	C₂×C₄×C₄₃	1	1	yes	characteristic
283	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	C₈×C₄₃	1	8	yes	complemented
286	C₂×SD₁₆	C₂×C₄×C₄₃	1	2	yes	—
287	C₂×D₈	C₂×C₄×C₄₃	1	2	yes	—
288	C₂×M₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
289	C₂×M₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
302	C₄×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
303	C₄×D₄	C₂³×C₄₃	1	2	yes	—
304	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₂×C₄×C₄₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
311	#107	C₂×C₄×C₄₃	1	2	yes	—
312	#106	C₂×C₄×C₄₃	1	2	yes	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	D₄×C₄₃	1	1	yes	characteristic
316	C₄⋊C₈	D₄×C₄₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
318	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
320	#103	C₂×C₄×C₄₃	1	2	yes	—
321	#102	C₂×C₄×C₄₃	1	2	yes	—
322	#102	C₂×C₄×C₄₃	1	2	yes	—
323	#102	C₂×C₄×C₄₃	1	2	yes	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	D₄×C₄₃	1	2	yes	—
329	#97	C₂×C₄×C₄₃	1	2	yes	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₄₃	1	2	yes	—
336	C₄×C₈	C₂³×C₄₃	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	2	2	no	—
339	#41	C₂×C₈×C₄₃	1	4	yes	complemented
340	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂×C₈×C₄₃	1	4	yes	complemented
345	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
346	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
358	SD₁₆	C₂×C₈×C₄₃	1	8	yes	complemented
359	D₈	C₂×C₈×C₄₃	1	8	yes	complemented
360	M₁₆	—	2	2	no	—
361	M₁₆	C₂×C₈×C₄₃	1	4	yes	complemented
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	8	2	no	—
369	C₂×C₈	—	8	2	no	—
370	C₂×C₈	—	8	2	no	—
371	C₂×C₈	—	8	1	no	—
372	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
373	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
392	C₄²	#41×C₄₃	1	1	yes	characteristic
393	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂²×C₈×C₄₃	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	4	no	—
406	D₄	C₂²×C₈×C₄₃	1	2	yes	—
407	D₄	C₂²×C₈×C₄₃	1	4	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
424	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₈×C₄₃	1	2	yes	—
427	C₂×C₄	#131×C₄₃	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	C₂²×C₈×C₄₃	1	4	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₈×D₄×C₄₃	1	2	yes	—
450	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	C₈×D₄×C₄₃	1	2	yes	—
459	C₄	C₂³×C₈×C₄₃	1	1	yes	characteristic
460	C₄	C₂×#131×C₄₃	1	1	yes	characteristic
461	C₄	C₄₃×#576	1	1	yes	characteristic
462	C₄	C₄₃×#577	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	4	no	—
465	C₂	—	4	2	no	—
466	C₂	C₂×C₈×D₄×C₄₃	1	1	yes	characteristic
467	C₂	C₄₃×#2946	1	1	yes	characteristic
468	C₂	C₄₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂²×D₄
commutator	C₄	C₂³×C₈×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₄₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₄₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#2988	C₂	semidirect
2. C₄₃×#2972	C₂	semidirect
4. C₄₃×#1580	C₂	semidirect
5. C₄₃×SD₁₆⋊C₈	C₂	semidirect
6. C₈×SD₁₆×C₄₃	C₂	semidirect
7. C₈×D₈×C₄₃	C₂	semidirect
8. C₄₃×#1565	C₂	semidirect
9. C₄₃×#1476	C₂	semidirect
10. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
11. C₈×M₁₆×C₄₃	C₂	semidirect
15. C₈×Q₈×C₄₃	C₂²	semidirect
25. C₈×D₄×C₄₃	C₂²	semidirect
37. C₄₃×#335	C₂²	semidirect
38. C₄₃×#334	C₂²	semidirect
39. C₄₃×Q₈⋊C₈	C₂²	semidirect
40. C₄₃×Q₈⋊C₈	C₂²	semidirect
43. C₄₃×D₄⋊C₈	C₂²	semidirect
44. C₄₃×D₄⋊C₈	C₂²	semidirect
45. C₄₃×#322	C₂²	semidirect
46. C₈²×C₄₃	C₂²	semidirect
50. AGL(1,ℤ/8)×C₄₃	C₈	semidirect
104. #41×C₄₃	C₂×C₈	semidirect
109. C₂×D₄×C₄₃	C₂×C₈	semidirect
123. SD₁₆×C₄₃	C₂×C₈	semidirect
124. D₈×C₄₃	C₂×C₈	semidirect
126. M₁₆×C₄₃	C₂×C₈	semidirect
205. #17852	C₄₃	direct (N × H)
229. #2988	C₂×C₄₃	semidirect
230. #2972	C₂×C₄₃	semidirect
232. #1580	C₂×C₄₃	semidirect
233. SD₁₆⋊C₈	C₂×C₄₃	semidirect
234. C₈×SD₁₆	C₂×C₄₃	semidirect
235. C₈×D₈	C₂×C₄₃	semidirect
236. #1565	C₂×C₄₃	semidirect
237. #1476	C₂×C₄₃	semidirect
238. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
239. C₈×M₁₆	C₂×C₄₃	semidirect
249. C₈×Q₈	C₂²×C₄₃	semidirect
259. C₈×D₄	C₂²×C₄₃	semidirect
271. #335	C₂²×C₄₃	semidirect
272. #334	C₂²×C₄₃	semidirect
273. Q₈⋊C₈	C₂²×C₄₃	semidirect
274. Q₈⋊C₈	C₂²×C₄₃	semidirect
277. D₄⋊C₈	C₂²×C₄₃	semidirect
278. D₄⋊C₈	C₂²×C₄₃	semidirect
279. #322	C₂²×C₄₃	semidirect
280. C₈²	C₂²×C₄₃	semidirect
281. C₄₃	#17852	direct (N × H)
285. AGL(1,ℤ/8)	C₈×C₄₃	semidirect
339. #41	C₂×C₈×C₄₃	semidirect
344. C₂×D₄	C₂×C₈×C₄₃	semidirect
358. SD₁₆	C₂×C₈×C₄₃	semidirect
359. D₈	C₂×C₈×C₄₃	semidirect
361. M₁₆	C₂×C₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#2988	2
C₄₃×#2972	2
C₄×AGL(1,ℤ/8)×C₄₃	2
C₄₃×#1580	2
C₄₃×SD₁₆⋊C₈	2
C₈×SD₁₆×C₄₃	2
C₈×D₈×C₄₃	2
C₄₃×#1565	2
C₄₃×#1476	2
C₂×C₄₃×D₄⋊C₈	2
C₈×M₁₆×C₄₃	2
#17852	43

Subgroups — C43×#17852 #24937869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17852 #24937869