Subgroups — C₄₃×#29912 #24949929

Order 11008.

796 conjugacy classes of subgroups.

The subgroup lattice has 520 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×#382	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2092	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2085	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2073	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1874	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#1874	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#123×C₄₃	—	2	1	no	—
13	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×#102×C₄₃	C₂²	1	2	yes	—
20	C₂×#102×C₄₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#390	C₂²	1	1	yes	characteristic
24	C₄₃×#390	C₂²	1	1	yes	characteristic
25	C₄₃×#389	C₂²	1	1	yes	characteristic
26	C₄₃×#389	C₂²	1	1	yes	characteristic
27	C₄₃×#388	—	2	1	no	—
28	C₄₃×#388	—	2	1	no	—
29	C₄₃×#386	—	2	1	no	—
30	C₄₃×#382	—	2	1	no	—
31	C₄₃×#382	—	2	1	no	—
32	C₄₃×#382	C₂²	1	2	yes	—
33	C₄₃×#382	C₂²	1	2	yes	—
34	C₄₃×#380	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₃	—	2	1	no	—
36	C₂×#95×C₄₃	—	2	1	no	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	#123×C₄₃	—	4	4	no	—
53	#121×C₄₃	—	2	2	no	—
54	#121×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	—	2	2	no	—
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	4	2	no	—
79	#106×C₄₃	—	4	2	no	—
80	#102×C₄₃	—	4	2	no	—
81	#102×C₄₃	—	4	2	no	—
82	C₂²⋊C₈×C₄₃	—	2	2	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	1	no	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₄₃	—	2	1	no	—
94	C₂×D₄×C₄₃	—	2	1	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	—	4	2	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	4	1	no	—
112	C₂²×C₄×C₄₃	—	4	1	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	—	4	2	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	2	yes	—
125	C₂²×C₄×C₄₃	#41	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	4	2	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	4	2	no	—
144	C₄⋊C₄×C₄₃	—	4	2	no	—
145	C₂²⋊C₄×C₄₃	—	4	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	2	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	2	no	—
149	C₂²⋊C₄×C₄₃	—	4	2	no	—
150	C₂²⋊C₄×C₄₃	—	4	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	—	2	1	no	—
154	C₄²×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	1	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	—	4	1	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	#123	1	2	yes	—
169	C₂³×C₄₃	#135	1	2	yes	—
170	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
171	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₄₃	—	4	2	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	8	4	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	4	4	no	—
192	C₂×C₄×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	1	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	8	4	no	—
209	C₂×C₄×C₄₃	—	8	4	no	—
210	C₂×C₄×C₄₃	#123	1	2	yes	—
211	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
214	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
215	C₈×C₄₃	—	4	2	no	—
216	C₈×C₄₃	—	4	2	no	—
217	#29912	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	2	2	no	—
222	C₂²×C₄₃	—	2	2	no	—
223	C₂²×C₄₃	—	2	2	no	—
224	C₂²×C₄₃	—	8	1	no	—
225	C₂²×C₄₃	—	8	1	no	—
226	C₂²×C₄₃	—	8	1	no	—
227	C₂²×C₄₃	—	8	1	no	—
228	C₂²×C₄₃	—	8	1	no	—
229	C₂²×C₄₃	—	8	1	no	—
230	C₂²×C₄₃	—	8	1	no	—
231	C₂²×C₄₃	#482	1	4	yes	—
232	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
233	C₂²×C₄₃	#535	1	1	yes	characteristic
234	C₂²×C₄₃	#536	1	1	yes	characteristic
235	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
236	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂²×C₄₃	#575	1	1	yes	characteristic
238	C₂²×C₄₃	#575	1	1	yes	characteristic
239	C₄×C₄₃	—	2	2	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	4	1	no	—
242	C₄×C₄₃	—	4	1	no	—
243	C₄×C₄₃	—	4	1	no	—
244	C₄×C₄₃	—	8	1	no	—
245	C₄×C₄₃	—	8	2	no	—
246	C₄×C₄₃	—	8	1	no	—
247	C₄×C₄₃	—	8	2	no	—
248	C₄×C₄₃	—	8	1	no	—
249	C₄×C₄₃	#539	1	2	yes	—
250	C₄×C₄₃	#539	1	2	yes	—
251	#2854	C₂×C₄₃	1	1	yes	characteristic
252	C₂×#382	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2101	C₂×C₄₃	1	2	yes	complemented
254	#2092	C₂×C₄₃	1	2	yes	complemented
255	#2085	C₂×C₄₃	1	2	yes	complemented
256	#2073	C₂×C₄₃	1	2	yes	complemented
257	#1874	C₂×C₄₃	1	1	yes	characteristic
258	#1874	C₂×C₄₃	1	1	yes	characteristic
259	#1853	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#1852	C₂×C₄₃	1	1	yes	characteristic, complemented
261	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
262	C₂×C₄₃	—	2	4	no	—
263	C₂×C₄₃	—	16	1	no	—
264	C₂×C₄₃	#2623	1	1	yes	characteristic
265	C₂×C₄₃	C₂×#482	1	1	yes	characteristic
266	C₂×C₄₃	#3093	1	1	yes	characteristic
267	C₂×C₄₃	#3211	1	1	yes	characteristic
268	C₂×C₄₃	#3213	1	1	yes	characteristic
269	C₂×C₄₃	#3232	1	1	yes	characteristic
270	C₂×C₄₃	#3234	1	1	yes	characteristic
271	C₂×#123	—	2	1	no	—
272	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
275	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
276	C₂×#107	C₂²×C₄₃	1	2	yes	—
277	C₂×#106	C₂²×C₄₃	1	2	yes	—
278	C₂×#102	C₂²×C₄₃	1	2	yes	—
279	C₂×#102	C₂²×C₄₃	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
282	#390	C₂²×C₄₃	1	1	yes	characteristic
283	#390	C₂²×C₄₃	1	1	yes	characteristic
284	#389	C₂²×C₄₃	1	1	yes	characteristic
285	#389	C₂²×C₄₃	1	1	yes	characteristic
286	#388	—	2	1	no	—
287	#388	—	2	1	no	—
288	#386	—	2	1	no	—
289	#382	—	2	1	no	—
290	#382	—	2	1	no	—
291	#382	C₂²×C₄₃	1	2	yes	—
292	#382	C₂²×C₄₃	1	2	yes	—
293	#380	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#95	—	2	1	no	—
295	C₂×#95	—	2	1	no	—
296	#340	C₂²×C₄₃	1	2	yes	—
297	#340	C₂²×C₄₃	1	2	yes	—
298	#340	C₂²×C₄₃	1	2	yes	—
299	#340	C₂²×C₄₃	1	2	yes	—
300	#336	C₂²×C₄₃	1	2	yes	—
301	#336	C₂²×C₄₃	1	2	yes	—
302	C₄₃	#29912	1	1	yes	characteristic, direct product factor, Sylow
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
312	#123	—	4	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	4	2	no	—
320	C₂×C₄⋊C₄	—	4	2	no	—
321	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
335	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
338	#107	—	4	2	no	—
339	#106	—	4	2	no	—
340	#102	—	4	2	no	—
341	#102	—	4	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	C₂⁴	—	2	1	no	—
352	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
384	C₂²×C₄	#41×C₄₃	1	2	yes	—
385	C₂²×C₄	#41×C₄₃	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	#123×C₄₃	1	2	yes	—
429	C₂³	#135×C₄₃	1	2	yes	—
430	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
431	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	8	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	4	no	—
469	C₂×C₄	—	8	4	no	—
470	C₂×C₄	#123×C₄₃	1	2	yes	—
471	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
474	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	C₄₃×#482	1	4	yes	—
491	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
492	C₂²	C₄₃×#535	1	1	yes	characteristic
493	C₂²	C₄₃×#536	1	1	yes	characteristic
494	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
495	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
496	C₂²	C₄₃×#575	1	1	yes	characteristic
497	C₂²	C₄₃×#575	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	2	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	1	no	—
508	C₄	C₄₃×#539	1	2	yes	—
509	C₄	C₄₃×#539	1	2	yes	—
510	C₂	—	2	4	no	—
511	C₂	—	16	1	no	—
512	C₂	C₄₃×#2623	1	1	yes	characteristic
513	C₂	C₂×C₄₃×#482	1	1	yes	characteristic
514	C₂	C₄₃×#3093	1	1	yes	characteristic
515	C₂	C₄₃×#3211	1	1	yes	characteristic
516	C₂	C₄₃×#3213	1	1	yes	characteristic
517	C₂	C₄₃×#3232	1	1	yes	characteristic
518	C₂	C₄₃×#3234	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×#382	C₂	semidirect
3. C₄₃×#2101	C₂	semidirect
4. C₄₃×#2092	C₂	semidirect
5. C₄₃×#2085	C₂	semidirect
6. C₄₃×#2073	C₂	semidirect
9. C₄₃×#1853	C₂	semidirect
10. C₄₃×#1852	C₂	semidirect
11. C₄₃×#1817	C₂	semidirect
217. #29912	C₄₃	direct (N × H)
252. C₂×#382	C₂×C₄₃	semidirect
253. #2101	C₂×C₄₃	semidirect
254. #2092	C₂×C₄₃	semidirect
255. #2085	C₂×C₄₃	semidirect
256. #2073	C₂×C₄₃	semidirect
259. #1853	C₂×C₄₃	semidirect
260. #1852	C₂×C₄₃	semidirect
261. #1817	C₂×C₄₃	semidirect
302. C₄₃	#29912	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×#382	2
C₄₃×#2101	2
C₄₃×#2092	2
C₄₃×#2085	2
C₄₃×#2073	2
C₄₃×#1874	2
C₄₃×#1853	2
C₄₃×#1852	2
C₄₃×#1817	2
#29912	43

Subgroups — C43×#29912 #24949929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29912 #24949929