Subgroups — C₄₃×#28500 #24948517

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#472	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#471	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2019	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2018	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₃	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#131×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#532	C₂²	1	1	yes	characteristic
22	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#497	—	2	1	no	—
25	C₄₃×#496	—	2	1	no	—
26	C₄₃×#496	—	2	2	no	—
27	C₄₃×#496	—	2	4	no	—
28	C₄₃×#495	—	2	2	no	—
29	C₄₃×#493	—	2	1	no	—
30	C₄₃×#492	—	2	1	no	—
31	C₄₃×#472	—	2	8	no	—
32	C₄₃×#471	—	2	8	no	—
33	C₄₃×#435	—	2	4	no	—
34	C₂×#108×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#423	C₂²	1	1	yes	characteristic
36	C₂×#101×C₄₃	C₂²	1	2	yes	—
37	C₂×#100×C₄₃	C₂²	1	2	yes	—
38	C₂×#100×C₄₃	C₂²	1	2	yes	—
39	C₂×#100×C₄₃	C₂²	1	2	yes	—
40	C₄₃×#408	C₂²	1	2	yes	—
41	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#341	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	C₂³	1	2	yes	—
46	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
51	#137×C₄₃	—	2	4	no	—
52	#137×C₄₃	—	4	2	no	—
53	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
54	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
55	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
56	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
57	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
58	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
59	C₂×Q₁₆×C₄₃	—	2	2	no	—
60	C₂×SD₁₆×C₄₃	—	2	2	no	—
61	C₂×SD₁₆×C₄₃	—	2	2	no	—
62	C₂×SD₁₆×C₄₃	—	2	2	no	—
63	C₂×SD₁₆×C₄₃	—	2	2	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	2	2	no	—
66	C₂×SD₁₆×C₄₃	—	2	2	no	—
67	C₂×SD₁₆×C₄₃	—	4	2	no	—
68	C₂×D₈×C₄₃	—	2	2	no	—
69	C₂×D₈×C₄₃	—	2	2	no	—
70	C₂×D₈×C₄₃	—	2	2	no	—
71	C₂×D₈×C₄₃	—	2	4	no	—
72	C₂×D₈×C₄₃	—	2	2	no	—
73	C₂×D₈×C₄₃	—	2	2	no	—
74	C₂×D₈×C₄₃	—	4	2	no	—
75	#131×C₄₃	—	2	4	no	—
76	#131×C₄₃	—	2	4	no	—
77	C₂×M₁₆×C₄₃	—	2	2	no	—
78	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
79	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
80	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
85	#127×C₄₃	—	2	1	no	—
86	#127×C₄₃	—	2	1	no	—
87	#127×C₄₃	—	2	2	no	—
88	#127×C₄₃	D₄	1	1	yes	characteristic
89	#124×C₄₃	—	2	1	no	—
90	#124×C₄₃	—	2	1	no	—
91	#124×C₄₃	—	2	2	no	—
92	#124×C₄₃	D₄	1	2	yes	—
93	#121×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#108×C₄₃	D₄	1	8	yes	complemented
98	C₄⋊C₈×C₄₃	—	2	2	no	—
99	#101×C₄₃	—	2	4	no	—
100	#100×C₄₃	—	2	4	no	—
101	#100×C₄₃	—	2	4	no	—
102	#100×C₄₃	—	2	4	no	—
103	C₂²⋊C₈×C₄₃	—	2	4	no	—
104	#97×C₄₃	—	2	1	no	—
105	#97×C₄₃	—	2	1	no	—
106	#97×C₄₃	D₄	1	4	yes	—
107	C₄×C₈×C₄₃	—	2	1	no	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₂⁴×C₄₃	—	2	1	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	#41×C₄₃	—	2	2	no	—
113	#41×C₄₃	—	2	2	no	—
114	#41×C₄₃	—	2	2	no	—
115	#41×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₄₃	—	2	2	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	1	no	—
127	C₂×D₄×C₄₃	—	2	1	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	2	1	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	2	no	—
134	C₂×D₄×C₄₃	—	2	2	no	—
135	C₂×D₄×C₄₃	—	4	2	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	—	8	4	no	—
138	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	#41	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₄₃	—	4	4	no	—
144	SD₁₆×C₄₃	—	4	4	no	—
145	SD₁₆×C₄₃	—	4	4	no	—
146	SD₁₆×C₄₃	—	4	4	no	—
147	SD₁₆×C₄₃	—	4	4	no	—
148	SD₁₆×C₄₃	—	4	4	no	—
149	SD₁₆×C₄₃	—	4	4	no	—
150	D₈×C₄₃	—	4	4	no	—
151	D₈×C₄₃	—	4	4	no	—
152	D₈×C₄₃	—	4	4	no	—
153	D₈×C₄₃	—	4	4	no	—
154	D₈×C₄₃	—	4	4	no	—
155	M₁₆×C₄₃	—	2	2	no	—
156	M₁₆×C₄₃	—	2	2	no	—
157	M₁₆×C₄₃	—	2	2	no	—
158	M₁₆×C₄₃	—	2	2	no	—
159	M₁₆×C₄₃	—	4	4	no	—
160	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
161	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	4	4	no	—
167	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₂²⋊C₄×C₄₃	—	2	4	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₂²⋊C₄×C₄₃	—	4	2	no	—
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	2	yes	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	4	1	no	—
179	C₂³×C₄₃	—	4	1	no	—
180	C₂³×C₄₃	—	4	1	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	8	2	no	—
185	C₂³×C₄₃	—	8	2	no	—
186	C₂³×C₄₃	—	8	2	no	—
187	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
188	Q₈×C₄₃	—	2	2	no	—
189	Q₈×C₄₃	—	2	2	no	—
190	Q₈×C₄₃	—	4	1	no	—
191	Q₈×C₄₃	—	4	1	no	—
192	Q₈×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	2	2	no	—
194	D₄×C₄₃	—	2	2	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	1	no	—
198	D₄×C₄₃	—	4	1	no	—
199	D₄×C₄₃	—	4	1	no	—
200	D₄×C₄₃	—	4	1	no	—
201	D₄×C₄₃	—	4	1	no	—
202	D₄×C₄₃	—	4	1	no	—
203	D₄×C₄₃	—	4	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	8	2	no	—
207	D₄×C₄₃	—	8	4	no	—
208	D₄×C₄₃	—	8	4	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	#121	1	2	yes	—
216	C₂×C₄×C₄₃	#121	1	2	yes	—
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₄₃	—	2	2	no	—
222	C₈×C₄₃	—	2	4	no	—
223	C₈×C₄₃	—	2	4	no	—
224	C₈×C₄₃	—	4	2	no	—
225	C₈×C₄₃	#127	1	4	yes	—
226	#28500	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	—	4	4	no	—
230	C₂²×C₄₃	—	8	1	no	—
231	C₂²×C₄₃	—	8	1	no	—
232	C₂²×C₄₃	—	8	1	no	—
233	C₂²×C₄₃	—	8	2	no	—
234	C₂²×C₄₃	—	8	2	no	—
235	C₂²×C₄₃	—	8	2	no	—
236	C₂²×C₄₃	—	16	2	no	—
237	C₂²×C₄₃	—	16	2	no	—
238	C₂²×C₄₃	—	16	2	no	—
239	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
240	C₂²×C₄₃	#550	1	2	yes	—
241	C₄×C₄₃	—	2	2	no	—
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	4	2	no	—
244	C₄×C₄₃	—	8	1	no	—
245	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
246	C₄×C₄₃	#535	1	1	yes	characteristic
247	C₄×C₄₃	D₄²	1	2	yes	—
248	#3153	C₂×C₄₃	1	1	yes	characteristic, complemented
249	#3151	C₂×C₄₃	1	1	yes	characteristic, complemented
250	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
251	C₂×#472	C₂×C₄₃	1	2	yes	complemented
252	C₂×#471	C₂×C₄₃	1	2	yes	complemented
253	#2932	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#2019	C₂×C₄₃	1	2	yes	complemented
255	#2018	C₂×C₄₃	1	2	yes	complemented
256	#1967	C₂×C₄₃	1	1	yes	characteristic, complemented
257	#1965	C₂×C₄₃	1	1	yes	characteristic, complemented
258	#1778	C₂×C₄₃	1	1	yes	characteristic, complemented
259	C₂×C₄₃	—	2	2	no	—
260	C₂×C₄₃	—	8	2	no	—
261	C₂×C₄₃	—	16	1	no	—
262	C₂×C₄₃	—	16	1	no	—
263	C₂×C₄₃	—	16	1	no	—
264	C₂×C₄₃	#2541	1	1	yes	characteristic
265	C₂×C₄₃	#3068	1	2	yes	—
266	C₂×#137	C₂²×C₄₃	1	2	yes	—
267	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
268	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
270	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
271	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
272	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
273	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
274	C₂×#131	C₂²×C₄₃	1	2	yes	—
275	#532	C₂²×C₄₃	1	1	yes	characteristic
276	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
277	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
278	#497	—	2	1	no	—
279	#496	—	2	1	no	—
280	#496	—	2	2	no	—
281	#496	—	2	4	no	—
282	#495	—	2	2	no	—
283	#493	—	2	1	no	—
284	#492	—	2	1	no	—
285	#472	—	2	8	no	—
286	#471	—	2	8	no	—
287	#435	—	2	4	no	—
288	C₂×#108	C₂²×C₄₃	1	2	yes	—
289	#423	C₂²×C₄₃	1	1	yes	characteristic
290	C₂×#101	C₂²×C₄₃	1	2	yes	—
291	C₂×#100	C₂²×C₄₃	1	2	yes	—
292	C₂×#100	C₂²×C₄₃	1	2	yes	—
293	C₂×#100	C₂²×C₄₃	1	2	yes	—
294	#408	C₂²×C₄₃	1	2	yes	—
295	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
296	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
298	#341	C₂²×C₄₃	1	2	yes	—
299	C₄₃	#28500	1	1	yes	characteristic, direct product factor, Sylow
300	C₂×#41	C₂³×C₄₃	1	2	yes	—
301	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
306	#137	—	2	4	no	—
307	#137	—	4	2	no	—
308	AGL(1,ℤ/8)	—	2	4	no	—
309	AGL(1,ℤ/8)	—	2	4	no	—
310	AGL(1,ℤ/8)	—	2	4	no	—
311	AGL(1,ℤ/8)	—	4	2	no	—
312	AGL(1,ℤ/8)	—	4	2	no	—
313	AGL(1,ℤ/8)	—	4	2	no	—
314	C₂×Q₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	4	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂×D₈	—	4	2	no	—
330	#131	—	2	4	no	—
331	#131	—	2	4	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
334	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
335	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
339	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
340	#127	—	2	1	no	—
341	#127	—	2	1	no	—
342	#127	—	2	2	no	—
343	#127	D₄×C₄₃	1	1	yes	characteristic
344	#124	—	2	1	no	—
345	#124	—	2	2	no	—
346	#124	—	2	1	no	—
347	#124	D₄×C₄₃	1	2	yes	—
348	#121	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
352	#108	D₄×C₄₃	1	8	yes	complemented
353	C₄⋊C₈	—	2	2	no	—
354	#101	—	2	4	no	—
355	#100	—	2	4	no	—
356	#100	—	2	4	no	—
357	#100	—	2	4	no	—
358	C₂²⋊C₈	—	2	4	no	—
359	#97	—	2	1	no	—
360	#97	—	2	1	no	—
361	#97	D₄×C₄₃	1	4	yes	—
362	C₄×C₈	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	1	no	—
366	C₂⁴	—	2	1	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	8	4	no	—
393	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	#41×C₄₃	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
398	Q₁₆	—	4	4	no	—
399	SD₁₆	—	4	4	no	—
400	SD₁₆	—	4	4	no	—
401	SD₁₆	—	4	4	no	—
402	SD₁₆	—	4	4	no	—
403	SD₁₆	—	4	4	no	—
404	SD₁₆	—	4	4	no	—
405	D₈	—	4	4	no	—
406	D₈	—	4	4	no	—
407	D₈	—	4	4	no	—
408	D₈	—	4	4	no	—
409	D₈	—	4	4	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	4	4	no	—
415	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
416	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	4	4	no	—
422	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
423	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
424	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
425	C₄⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₄₃	1	2	yes	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	8	2	no	—
440	C₂³	—	8	2	no	—
441	C₂³	—	8	2	no	—
442	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	4	no	—
463	D₄	—	8	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	#121×C₄₃	1	2	yes	—
471	C₂×C₄	#121×C₄₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₈	—	2	4	no	—
479	C₈	—	4	2	no	—
480	C₈	#127×C₄₃	1	4	yes	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	16	2	no	—
491	C₂²	—	16	2	no	—
492	C₂²	—	16	2	no	—
493	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
494	C₂²	C₄₃×#550	1	2	yes	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	C₂×#127×C₄₃	1	1	yes	characteristic
500	C₄	C₄₃×#535	1	1	yes	characteristic
501	C₄	D₄²×C₄₃	1	2	yes	—
502	C₂	—	2	2	no	—
503	C₂	—	8	2	no	—
504	C₂	—	16	1	no	—
505	C₂	—	16	1	no	—
506	C₂	—	16	1	no	—
507	C₂	C₄₃×#2541	1	1	yes	characteristic
508	C₂	C₄₃×#3068	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3153	C₂	semidirect
2. C₄₃×#3151	C₂	semidirect
3. C₂×C₄₃×#496	C₂	semidirect
4. C₂×C₄₃×#472	C₂	semidirect
5. C₂×C₄₃×#471	C₂	semidirect
6. C₄₃×#2932	C₂	semidirect
7. C₄₃×#2019	C₂	semidirect
8. C₄₃×#2018	C₂	semidirect
9. C₄₃×#1967	C₂	semidirect
10. C₄₃×#1965	C₂	semidirect
11. C₄₃×#1778	C₂	semidirect
97. #108×C₄₃	D₄	semidirect
226. #28500	C₄₃	direct (N × H)
248. #3153	C₂×C₄₃	semidirect
249. #3151	C₂×C₄₃	semidirect
250. C₂×#496	C₂×C₄₃	semidirect
251. C₂×#472	C₂×C₄₃	semidirect
252. C₂×#471	C₂×C₄₃	semidirect
253. #2932	C₂×C₄₃	semidirect
254. #2019	C₂×C₄₃	semidirect
255. #2018	C₂×C₄₃	semidirect
256. #1967	C₂×C₄₃	semidirect
257. #1965	C₂×C₄₃	semidirect
258. #1778	C₂×C₄₃	semidirect
299. C₄₃	#28500	direct (N × H)
352. #108	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3153	2
C₄₃×#3151	2
C₂×C₄₃×#496	2
C₂×C₄₃×#472	2
C₂×C₄₃×#471	2
C₄₃×#2932	2
C₄₃×#2019	2
C₄₃×#2018	2
C₄₃×#1967	2
C₄₃×#1965	2
C₄₃×#1778	2
#28500	43

Subgroups — C43×#28500 #24948517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28500 #24948517