Subgroups — C₄₃×#29667 #24949684

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#463	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1999	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1804	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	—	2	1	no	—
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#532	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	—	2	1	no	—
19	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₄₃	—	2	1	no	—
22	C₂×#121×C₄₃	C₂²	1	2	yes	—
23	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₃	—	2	1	no	—
25	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#463	—	2	8	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₂×#103×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
34	C₄₃×#391	C₂²	1	1	yes	characteristic
35	C₄₃×#390	C₂²	1	1	yes	characteristic
36	C₄₃×#388	—	2	1	no	—
37	C₄₃×#388	—	2	1	no	—
38	C₄₃×#386	—	2	1	no	—
39	C₄₃×#386	—	2	1	no	—
40	C₄₃×#382	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#336	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₃	—	2	8	no	—
46	C₂×#41×C₄₃	—	4	4	no	—
47	C₂×#41×C₄₃	—	4	4	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₃	—	2	2	no	—
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	—	2	1	no	—
54	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₃	—	2	2	no	—
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₄₃	—	2	4	no	—
61	C₂×SD₁₆×C₄₃	—	4	2	no	—
62	C₂×SD₁₆×C₄₃	—	4	2	no	—
63	C₂×D₈×C₄₃	—	2	4	no	—
64	C₂×D₈×C₄₃	—	4	2	no	—
65	C₂×D₈×C₄₃	—	4	2	no	—
66	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₄₃	—	2	4	no	—
69	#127×C₄₃	—	2	4	no	—
70	#124×C₄₃	—	2	8	no	—
71	#124×C₄₃	—	2	4	no	—
72	C₂²⋊Q₈×C₄₃	—	4	2	no	—
73	#121×C₄₃	—	2	8	no	—
74	#121×C₄₃	—	2	4	no	—
75	#121×C₄₃	—	2	4	no	—
76	#121×C₄₃	—	4	2	no	—
77	C₄×D₄×C₄₃	—	2	8	no	—
78	C₄×D₄×C₄₃	—	2	4	no	—
79	C₄×D₄×C₄₃	D₄	1	8	yes	complemented
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	—	2	4	no	—
94	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	—	2	4	no	—
99	#103×C₄₃	—	2	4	no	—
100	#102×C₄₃	—	2	4	no	—
101	#102×C₄₃	—	4	2	no	—
102	#102×C₄₃	—	4	2	no	—
103	C₂²⋊C₈×C₄₃	—	4	2	no	—
104	#95×C₄₃	—	2	1	no	—
105	#95×C₄₃	—	2	1	no	—
106	#95×C₄₃	—	2	1	no	—
107	#95×C₄₃	—	2	1	no	—
108	C₂⁴×C₄₃	—	2	2	no	—
109	C₂⁴×C₄₃	—	2	1	no	—
110	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₃	—	4	32	no	—
112	C₂×Q₈×C₄₃	—	2	4	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂×Q₈×C₄₃	—	4	2	no	—
118	C₂×Q₈×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	2	4	no	—
120	C₂×D₄×C₄₃	—	2	8	no	—
121	C₂×D₄×C₄₃	—	2	4	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	—	4	2	no	—
133	C₂×D₄×C₄₃	—	4	2	no	—
134	C₂×D₄×C₄₃	—	4	2	no	—
135	C₂×D₄×C₄₃	—	4	2	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	4	4	no	—
139	C₂×D₄×C₄₃	—	4	2	no	—
140	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	8	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	4	1	no	—
156	C₂²×C₄×C₄₃	—	4	4	no	—
157	C₂²×C₄×C₄₃	—	4	4	no	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	SD₁₆×C₄₃	—	4	8	no	—
165	D₈×C₄₃	—	4	8	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	—	2	4	no	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	4	2	no	—
177	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
178	C₂²⋊C₄×C₄₃	—	2	8	no	—
179	C₂²⋊C₄×C₄₃	—	2	8	no	—
180	C₂²⋊C₄×C₄₃	—	4	2	no	—
181	C₂²⋊C₄×C₄₃	—	4	2	no	—
182	C₂²⋊C₄×C₄₃	—	4	2	no	—
183	C₂²⋊C₄×C₄₃	—	4	2	no	—
184	C₂²⋊C₄×C₄₃	—	4	2	no	—
185	C₂²⋊C₄×C₄₃	—	4	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₄²×C₄₃	—	2	2	no	—
189	C₄²×C₄₃	C₂×D₄	1	4	yes	—
190	C₂³×C₄₃	—	2	1	no	—
191	C₂³×C₄₃	—	2	1	no	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	—	2	1	no	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	—	2	1	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	1	no	—
204	C₂³×C₄₃	—	4	1	no	—
205	C₂³×C₄₃	—	4	1	no	—
206	C₂³×C₄₃	—	4	1	no	—
207	C₂³×C₄₃	—	4	1	no	—
208	C₂³×C₄₃	—	4	1	no	—
209	C₂³×C₄₃	—	4	1	no	—
210	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
211	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₄₃	—	4	8	no	—
213	Q₈×C₄₃	—	4	2	no	—
214	Q₈×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	2	4	no	—
216	D₄×C₄₃	—	2	4	no	—
217	D₄×C₄₃	—	4	8	no	—
218	D₄×C₄₃	—	4	8	no	—
219	D₄×C₄₃	—	4	16	no	—
220	D₄×C₄₃	—	4	2	no	—
221	D₄×C₄₃	—	4	2	no	—
222	D₄×C₄₃	—	4	2	no	—
223	D₄×C₄₃	—	4	2	no	—
224	D₄×C₄₃	—	8	4	no	—
225	C₂×C₄×C₄₃	—	2	8	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	2	1	no	—
233	C₂×C₄×C₄₃	—	2	1	no	—
234	C₂×C₄×C₄₃	—	2	1	no	—
235	C₂×C₄×C₄₃	—	2	4	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	1	no	—
238	C₂×C₄×C₄₃	—	4	4	no	—
239	C₂×C₄×C₄₃	—	4	16	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	2	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	—	4	1	no	—
253	C₂×C₄×C₄₃	#120	1	2	yes	—
254	C₂×C₄×C₄₃	#120	1	2	yes	—
255	C₂×C₄×C₄₃	#135	1	2	yes	—
256	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
257	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
260	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
261	C₈×C₄₃	—	4	2	no	—
262	C₈×C₄₃	—	4	2	no	—
263	#29667	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₄₃	—	2	2	no	—
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	—	4	1	no	—
268	C₂²×C₄₃	—	4	1	no	—
269	C₂²×C₄₃	—	4	1	no	—
270	C₂²×C₄₃	—	4	1	no	—
271	C₂²×C₄₃	—	4	4	no	—
272	C₂²×C₄₃	—	4	4	no	—
273	C₂²×C₄₃	—	4	4	no	—
274	C₂²×C₄₃	—	8	2	no	—
275	C₂²×C₄₃	—	8	2	no	—
276	C₂²×C₄₃	—	8	2	no	—
277	C₂²×C₄₃	—	8	2	no	—
278	C₂²×C₄₃	—	8	1	no	—
279	C₂²×C₄₃	—	8	1	no	—
280	C₂²×C₄₃	—	8	1	no	—
281	C₂²×C₄₃	—	8	1	no	—
282	C₂²×C₄₃	—	8	1	no	—
283	C₂²×C₄₃	—	8	1	no	—
284	C₂²×C₄₃	—	8	1	no	—
285	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
286	C₂²×C₄₃	#535	1	1	yes	characteristic
287	C₂²×C₄₃	#537	1	1	yes	characteristic
288	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
289	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₂²×C₄₃	#575	1	1	yes	characteristic
292	C₄×C₄₃	—	2	2	no	—
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	2	no	—
295	C₄×C₄₃	—	2	2	no	—
296	C₄×C₄₃	—	4	1	no	—
297	C₄×C₄₃	—	4	4	no	—
298	C₄×C₄₃	—	8	1	no	—
299	C₄×C₄₃	—	8	1	no	—
300	C₄×C₄₃	—	8	1	no	—
301	C₄×C₄₃	#535	1	2	yes	—
302	C₄×C₄₃	#537	1	2	yes	—
303	C₂×#532	C₂×C₄₃	1	1	yes	characteristic, complemented
304	C₂×#463	C₂×C₄₃	1	2	yes	complemented
305	#2850	C₂×C₄₃	1	1	yes	characteristic, complemented
306	#2024	C₂×C₄₃	1	1	yes	characteristic, complemented
307	#2023	C₂×C₄₃	1	1	yes	characteristic, complemented
308	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
309	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
310	#2000	C₂×C₄₃	1	2	yes	complemented
311	#1999	C₂×C₄₃	1	2	yes	complemented
312	#1804	C₂×C₄₃	1	2	yes	complemented
313	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
314	C₂×C₄₃	—	4	2	no	—
315	C₂×C₄₃	—	8	4	no	—
316	C₂×C₄₃	—	16	1	no	—
317	C₂×C₄₃	#2615	1	1	yes	characteristic
318	C₂×C₄₃	#3002	1	1	yes	characteristic
319	C₂×C₄₃	#3003	1	1	yes	characteristic
320	C₂×C₄₃	#3207	1	1	yes	characteristic
321	C₂×C₄₃	#3213	1	1	yes	characteristic
322	C₂×C₄₃	#3247	1	1	yes	characteristic
323	C₂×C₄₃	#3251	1	1	yes	characteristic
324	C₂²×#41	—	2	1	no	—
325	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
326	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
327	#532	—	2	8	no	—
328	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
329	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
330	C₂×#124	—	2	1	no	—
331	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
332	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
333	C₂×#121	—	2	1	no	—
334	C₂×#121	C₂²×C₄₃	1	2	yes	—
335	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
338	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
339	#463	—	2	8	no	—
340	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
341	C₂×#103	C₂²×C₄₃	1	2	yes	—
342	C₂×#102	C₂²×C₄₃	1	2	yes	—
343	C₂×#102	C₂²×C₄₃	1	2	yes	—
344	C₂×#102	C₂²×C₄₃	1	2	yes	—
345	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
346	#391	C₂²×C₄₃	1	1	yes	characteristic
347	#390	C₂²×C₄₃	1	1	yes	characteristic
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
350	#386	—	2	1	no	—
351	#386	—	2	1	no	—
352	#382	C₂²×C₄₃	1	1	yes	characteristic
353	#340	C₂²×C₄₃	1	2	yes	—
354	#340	C₂²×C₄₃	1	2	yes	—
355	#336	C₂²×C₄₃	1	1	yes	characteristic
356	#336	C₂²×C₄₃	1	1	yes	characteristic
357	C₄₃	#29667	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	—	2	8	no	—
359	C₂×#41	—	4	4	no	—
360	C₂×#41	—	4	4	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
369	C₂³×C₄	—	2	2	no	—
370	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
371	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
373	C₂×SD₁₆	—	2	4	no	—
374	C₂×SD₁₆	—	4	2	no	—
375	C₂×SD₁₆	—	4	2	no	—
376	C₂×D₈	—	2	4	no	—
377	C₂×D₈	—	4	2	no	—
378	C₂×D₈	—	4	2	no	—
379	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
380	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
381	C₄⋊Q₈	—	2	4	no	—
382	#127	—	2	4	no	—
383	#124	—	2	8	no	—
384	#124	—	2	4	no	—
385	C₂²⋊Q₈	—	4	2	no	—
386	#121	—	2	8	no	—
387	#121	—	2	4	no	—
388	#121	—	2	4	no	—
389	#121	—	4	2	no	—
390	C₄×D₄	—	2	8	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	D₄×C₄₃	1	8	yes	complemented
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₄²	—	2	4	no	—
407	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
408	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
411	C₄⋊C₈	—	2	4	no	—
412	#103	—	2	4	no	—
413	#102	—	2	4	no	—
414	#102	—	4	2	no	—
415	#102	—	4	2	no	—
416	C₂²⋊C₈	—	4	2	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
424	#41	—	4	32	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	4	2	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
477	SD₁₆	—	4	8	no	—
478	D₈	—	4	8	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	C₂×D₄×C₄₃	1	4	yes	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
524	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
525	Q₈	—	4	8	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	2	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	16	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	4	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	16	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	#120×C₄₃	1	2	yes	—
567	C₂×C₄	#120×C₄₃	1	2	yes	—
568	C₂×C₄	#135×C₄₃	1	2	yes	—
569	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
571	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
572	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
573	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
574	C₈	—	4	2	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	2	no	—
589	C₂²	—	8	2	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
598	C₂²	C₄₃×#535	1	1	yes	characteristic
599	C₂²	C₄₃×#537	1	1	yes	characteristic
600	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
601	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
602	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
603	C₂²	C₄₃×#575	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	4	no	—
610	C₄	—	8	1	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	C₄₃×#535	1	2	yes	—
614	C₄	C₄₃×#537	1	2	yes	—
615	C₂	—	4	2	no	—
616	C₂	—	8	4	no	—
617	C₂	—	16	1	no	—
618	C₂	C₄₃×#2615	1	1	yes	characteristic
619	C₂	C₄₃×#3002	1	1	yes	characteristic
620	C₂	C₄₃×#3003	1	1	yes	characteristic
621	C₂	C₄₃×#3207	1	1	yes	characteristic
622	C₂	C₄₃×#3213	1	1	yes	characteristic
623	C₂	C₄₃×#3247	1	1	yes	characteristic
624	C₂	C₄₃×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
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
1. C₂×C₄₃×#532	C₂	semidirect
2. C₂×C₄₃×#463	C₂	semidirect
3. C₄₃×#2850	C₂	semidirect
4. C₄₃×#2024	C₂	semidirect
5. C₄₃×#2023	C₂	semidirect
6. C₄₃×#2014	C₂	semidirect
7. C₄₃×#2011	C₂	semidirect
8. C₄₃×#2000	C₂	semidirect
9. C₄₃×#1999	C₂	semidirect
10. C₄₃×#1804	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
79. C₄×D₄×C₄₃	D₄	semidirect
263. #29667	C₄₃	direct (N × H)
303. C₂×#532	C₂×C₄₃	semidirect
304. C₂×#463	C₂×C₄₃	semidirect
305. #2850	C₂×C₄₃	semidirect
306. #2024	C₂×C₄₃	semidirect
307. #2023	C₂×C₄₃	semidirect
308. #2014	C₂×C₄₃	semidirect
309. #2011	C₂×C₄₃	semidirect
310. #2000	C₂×C₄₃	semidirect
311. #1999	C₂×C₄₃	semidirect
312. #1804	C₂×C₄₃	semidirect
313. #1797	C₂×C₄₃	semidirect
357. C₄₃	#29667	direct (N × H)
392. C₄×D₄	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#532	2
C₂×C₄₃×#463	2
C₄₃×#2850	2
C₄₃×#2024	2
C₄₃×#2023	2
C₄₃×#2014	2
C₄₃×#2011	2
C₄₃×#2000	2
C₄₃×#1999	2
C₄₃×#1804	2
C₄₃×#1797	2
#29667	43

Subgroups — C43×#29667 #24949684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29667 #24949684