Subgroups — C₄₃×#29906 #24949923

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2854	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2099	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2093	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2083	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2071	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1874	C₂	1	2	yes	maximal
8	C₄₃×#1852	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#123×C₄₃	—	2	1	no	—
11	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#107×C₄₃	C₂²	1	4	yes	—
17	C₂×#102×C₄₃	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#390	C₂²	1	1	yes	characteristic
20	C₄₃×#390	C₂²	1	1	yes	characteristic
21	C₄₃×#389	C₂²	1	1	yes	characteristic
22	C₄₃×#389	C₂²	1	1	yes	characteristic
23	C₄₃×#388	—	2	1	no	—
24	C₄₃×#388	—	2	1	no	—
25	C₄₃×#386	—	2	1	no	—
26	C₄₃×#384	—	2	1	no	—
27	C₄₃×#384	—	2	1	no	—
28	C₄₃×#384	C₂²	1	2	yes	—
29	C₄₃×#384	C₂²	1	2	yes	—
30	C₄₃×#380	C₂²	1	1	yes	characteristic
31	C₄₃×#340	C₂²	1	4	yes	—
32	C₄₃×#340	C₂²	1	4	yes	—
33	C₄₃×#336	C₂²	1	2	yes	—
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	—	2	2	no	—
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
42	#123×C₄₃	—	4	4	no	—
43	#121×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
53	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄²×C₄₃	—	2	4	no	—
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	#107×C₄₃	—	4	4	no	—
70	#102×C₄₃	—	4	4	no	—
71	C₂²⋊C₈×C₄₃	—	2	4	no	—
72	#95×C₄₃	—	2	1	no	—
73	#95×C₄₃	—	2	1	no	—
74	#95×C₄₃	—	2	1	no	—
75	C₂⁴×C₄₃	—	2	1	no	—
76	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₄₃	—	2	2	no	—
78	C₂×D₄×C₄₃	—	2	2	no	—
79	C₂×D₄×C₄₃	—	2	2	no	—
80	C₂×D₄×C₄₃	—	4	2	no	—
81	C₂×D₄×C₄₃	—	4	2	no	—
82	C₂×D₄×C₄₃	—	4	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	1	no	—
91	C₂²×C₄×C₄₃	—	2	1	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	4	no	—
94	C₂²×C₄×C₄₃	—	4	4	no	—
95	C₂²×C₄×C₄₃	—	4	4	no	—
96	C₂²×C₄×C₄₃	—	4	4	no	—
97	C₂²×C₄×C₄₃	D₈	1	4	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	4	yes	—
104	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₄₃	—	2	4	no	—
106	C₂×C₈×C₄₃	—	2	4	no	—
107	C₂×C₈×C₄₃	—	2	4	no	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	4	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	2	4	no	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₄⋊C₄×C₄₃	—	4	4	no	—
114	C₄⋊C₄×C₄₃	—	4	4	no	—
115	C₄⋊C₄×C₄₃	—	4	4	no	—
116	C₄⋊C₄×C₄₃	—	4	4	no	—
117	C₄⋊C₄×C₄₃	—	4	2	no	—
118	C₄⋊C₄×C₄₃	—	4	2	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₂²⋊C₄×C₄₃	—	4	2	no	—
121	C₂²⋊C₄×C₄₃	—	4	2	no	—
122	C₂²⋊C₄×C₄₃	—	4	2	no	—
123	C₂²⋊C₄×C₄₃	—	4	2	no	—
124	C₂²⋊C₄×C₄₃	—	4	2	no	—
125	C₂²⋊C₄×C₄₃	—	4	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₂³×C₄₃	—	2	1	no	—
131	C₂³×C₄₃	—	2	1	no	—
132	C₂³×C₄₃	—	2	1	no	—
133	C₂³×C₄₃	—	2	1	no	—
134	C₂³×C₄₃	—	4	1	no	—
135	C₂³×C₄₃	—	4	1	no	—
136	C₂³×C₄₃	—	4	1	no	—
137	C₂³×C₄₃	—	4	1	no	—
138	C₂³×C₄₃	—	4	1	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	#123	1	2	yes	—
142	C₂³×C₄₃	C₂×D₈	1	2	yes	—
143	C₂³×C₄₃	#137	1	2	yes	—
144	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
145	D₄×C₄₃	—	4	4	no	—
146	D₄×C₄₃	—	8	4	no	—
147	C₂×C₄×C₄₃	—	2	8	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	8	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	8	8	no	—
173	C₂×C₄×C₄₃	#123	1	2	yes	—
174	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₃	#137	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
179	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
180	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
181	C₈×C₄₃	—	4	4	no	—
182	#29906	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	2	no	—
185	C₂²×C₄₃	—	2	2	no	—
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	8	1	no	—
190	C₂²×C₄₃	—	8	1	no	—
191	C₂²×C₄₃	—	8	1	no	—
192	C₂²×C₄₃	—	8	1	no	—
193	C₂²×C₄₃	—	8	1	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	—	8	1	no	—
196	C₂²×C₄₃	#480	1	4	yes	—
197	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
198	C₂²×C₄₃	#535	1	1	yes	characteristic
199	C₂²×C₄₃	#536	1	1	yes	characteristic
200	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	8	1	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	—	8	4	no	—
212	C₄×C₄₃	—	8	1	no	—
213	C₄×C₄₃	#539	1	4	yes	—
214	#2854	C₂×C₄₃	1	1	yes	characteristic
215	C₂×#384	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#2099	C₂×C₄₃	1	2	yes	complemented
217	#2093	C₂×C₄₃	1	2	yes	complemented
218	#2083	C₂×C₄₃	1	2	yes	complemented
219	#2071	C₂×C₄₃	1	2	yes	complemented
220	#1874	C₂×C₄₃	1	2	yes	—
221	#1852	C₂×C₄₃	1	2	yes	complemented
222	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
223	C₂×C₄₃	—	2	4	no	—
224	C₂×C₄₃	—	16	1	no	—
225	C₂×C₄₃	#2623	1	1	yes	characteristic
226	C₂×C₄₃	C₂×#480	1	1	yes	characteristic
227	C₂×C₄₃	#3092	1	1	yes	characteristic
228	C₂×C₄₃	#3205	1	1	yes	characteristic
229	C₂×C₄₃	#3218	1	1	yes	characteristic
230	C₂×C₄₃	#3226	1	1	yes	characteristic
231	C₂×C₄₃	#3239	1	1	yes	characteristic
232	C₂×#123	—	2	1	no	—
233	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	—	2	1	no	—
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
237	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#107	C₂²×C₄₃	1	4	yes	—
239	C₂×#102	C₂²×C₄₃	1	4	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
241	#390	C₂²×C₄₃	1	1	yes	characteristic
242	#390	C₂²×C₄₃	1	1	yes	characteristic
243	#389	C₂²×C₄₃	1	1	yes	characteristic
244	#389	C₂²×C₄₃	1	1	yes	characteristic
245	#388	—	2	1	no	—
246	#388	—	2	1	no	—
247	#386	—	2	1	no	—
248	#384	—	2	1	no	—
249	#384	—	2	1	no	—
250	#384	C₂²×C₄₃	1	2	yes	—
251	#384	C₂²×C₄₃	1	2	yes	—
252	#380	C₂²×C₄₃	1	1	yes	characteristic
253	#340	C₂²×C₄₃	1	4	yes	—
254	#340	C₂²×C₄₃	1	4	yes	—
255	#336	C₂²×C₄₃	1	2	yes	—
256	#336	C₂²×C₄₃	1	2	yes	—
257	C₄₃	#29906	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
262	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
265	#123	—	4	4	no	—
266	#121	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	4	4	no	—
275	C₂×C₄⋊C₄	—	4	4	no	—
276	C₂×C₄⋊C₄	—	4	4	no	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	#107	—	4	4	no	—
293	#102	—	4	4	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	#95	—	2	1	no	—
296	#95	—	2	1	no	—
297	#95	—	2	1	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	D₈×C₄₃	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂²×C₄	#41×C₄₃	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	#123×C₄₃	1	2	yes	—
365	C₂³	C₂×D₈×C₄₃	1	2	yes	—
366	C₂³	#137×C₄₃	1	2	yes	—
367	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
368	D₄	—	4	4	no	—
369	D₄	—	8	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	8	8	no	—
396	C₂×C₄	#123×C₄₃	1	2	yes	—
397	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
398	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
399	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
400	C₂×C₄	#137×C₄₃	1	2	yes	—
401	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
402	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
403	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
404	C₈	—	4	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	C₄₃×#480	1	4	yes	—
419	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
420	C₂²	C₄₃×#535	1	1	yes	characteristic
421	C₂²	C₄₃×#536	1	1	yes	characteristic
422	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
423	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
424	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
425	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	8	4	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	C₄₃×#539	1	4	yes	—
436	C₂	—	2	4	no	—
437	C₂	—	16	1	no	—
438	C₂	C₄₃×#2623	1	1	yes	characteristic
439	C₂	C₂×C₄₃×#480	1	1	yes	characteristic
440	C₂	C₄₃×#3092	1	1	yes	characteristic
441	C₂	C₄₃×#3205	1	1	yes	characteristic
442	C₂	C₄₃×#3218	1	1	yes	characteristic
443	C₂	C₄₃×#3226	1	1	yes	characteristic
444	C₂	C₄₃×#3239	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#384	C₂	semidirect
3. C₄₃×#2099	C₂	semidirect
4. C₄₃×#2093	C₂	semidirect
5. C₄₃×#2083	C₂	semidirect
6. C₄₃×#2071	C₂	semidirect
8. C₄₃×#1852	C₂	semidirect
9. C₄₃×#1817	C₂	semidirect
182. #29906	C₄₃	direct (N × H)
215. C₂×#384	C₂×C₄₃	semidirect
216. #2099	C₂×C₄₃	semidirect
217. #2093	C₂×C₄₃	semidirect
218. #2083	C₂×C₄₃	semidirect
219. #2071	C₂×C₄₃	semidirect
221. #1852	C₂×C₄₃	semidirect
222. #1817	C₂×C₄₃	semidirect
257. C₄₃	#29906	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2854	2
C₂×C₄₃×#384	2
C₄₃×#2099	2
C₄₃×#2093	2
C₄₃×#2083	2
C₄₃×#2071	2
C₄₃×#1874	2
C₄₃×#1852	2
C₄₃×#1817	2
#29906	43

Subgroups — C43×#29906 #24949923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29906 #24949923