Subgroups — C₄₃×#29921 #24949938

Order 11008.

912 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×#2856	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2094	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2034	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1982	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1948	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×#121×C₄₃	—	2	1	no	—
11	C₂×#121×C₄₃	—	2	1	no	—
12	C₂×#121×C₄₃	C₂²	1	2	yes	—
13	C₂×#117×C₄₃	—	2	1	no	—
14	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#106×C₄₃	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#102×C₄₃	C₂²	1	4	yes	—
18	C₂×#102×C₄₃	C₂²	1	4	yes	—
19	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#390	—	2	1	no	—
21	C₄₃×#390	—	2	1	no	—
22	C₄₃×#390	C₂²	1	2	yes	—
23	C₄₃×#384	C₂²	1	1	yes	characteristic
24	C₄₃×#384	C₂²	1	1	yes	characteristic
25	C₄₃×#384	C₂²	1	1	yes	characteristic
26	C₄₃×#382	—	2	1	no	—
27	C₄₃×#380	—	2	1	no	—
28	C₄₃×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#340	C₂²	1	4	yes	—
32	C₄₃×#336	C₂²	1	2	yes	—
33	C₂²×D₄×C₄₃	—	2	2	no	—
34	C₂²×D₄×C₄₃	—	2	1	no	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
41	#127×C₄₃	—	2	4	no	—
42	#121×C₄₃	—	4	4	no	—
43	#121×C₄₃	—	4	4	no	—
44	#121×C₄₃	—	4	4	no	—
45	#117×C₄₃	—	4	4	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄²×C₄₃	—	2	4	no	—
60	C₂×C₄²×C₄₃	—	2	2	no	—
61	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
65	#106×C₄₃	—	4	4	no	—
66	C₄⋊C₈×C₄₃	—	2	4	no	—
67	#102×C₄₃	—	4	4	no	—
68	#102×C₄₃	—	4	4	no	—
69	C₂²⋊C₈×C₄₃	—	4	2	no	—
70	#95×C₄₃	—	2	2	no	—
71	#95×C₄₃	—	2	2	no	—
72	C₂⁴×C₄₃	—	2	2	no	—
73	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂×D₄×C₄₃	—	2	4	no	—
75	C₂×D₄×C₄₃	—	2	2	no	—
76	C₂×D₄×C₄₃	—	2	4	no	—
77	C₂×D₄×C₄₃	—	2	2	no	—
78	C₂×D₄×C₄₃	—	4	4	no	—
79	C₂×D₄×C₄₃	—	4	4	no	—
80	C₂×D₄×C₄₃	—	4	2	no	—
81	C₂×D₄×C₄₃	—	4	2	no	—
82	C₂×D₄×C₄₃	—	4	2	no	—
83	C₂×D₄×C₄₃	—	4	2	no	—
84	C₂×D₄×C₄₃	—	4	2	no	—
85	C₂×D₄×C₄₃	—	4	2	no	—
86	C₂×D₄×C₄₃	—	4	4	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	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	4	1	no	—
99	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
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	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₄₃	—	2	4	no	—
107	C₂×C₈×C₄₃	—	2	4	no	—
108	C₂×C₈×C₄₃	—	2	4	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	4	2	no	—
115	C₄⋊C₄×C₄₃	—	4	2	no	—
116	C₄⋊C₄×C₄₃	—	4	2	no	—
117	C₄⋊C₄×C₄₃	—	4	2	no	—
118	C₄⋊C₄×C₄₃	—	4	2	no	—
119	C₄⋊C₄×C₄₃	—	4	2	no	—
120	C₂²⋊C₄×C₄₃	—	4	4	no	—
121	C₂²⋊C₄×C₄₃	—	4	4	no	—
122	C₂²⋊C₄×C₄₃	—	4	4	no	—
123	C₂²⋊C₄×C₄₃	—	4	4	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	4	4	no	—
128	C₄²×C₄₃	#41	1	4	yes	—
129	C₂³×C₄₃	—	2	1	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	—	2	1	no	—
135	C₂³×C₄₃	—	4	2	no	—
136	C₂³×C₄₃	—	4	2	no	—
137	C₂³×C₄₃	—	4	2	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₄₃	—	4	4	no	—
145	D₄×C₄₃	—	4	4	no	—
146	D₄×C₄₃	—	8	4	no	—
147	D₄×C₄₃	—	8	8	no	—
148	D₄×C₄₃	—	8	4	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	8	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	#123	1	2	yes	—
172	C₂×C₄×C₄₃	#123	1	2	yes	—
173	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
178	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
180	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₄₃	—	4	4	no	—
182	#29921	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	—	4	1	no	—
187	C₂²×C₄₃	—	4	1	no	—
188	C₂²×C₄₃	—	4	1	no	—
189	C₂²×C₄₃	—	4	1	no	—
190	C₂²×C₄₃	—	8	2	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	—	8	2	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	—	8	2	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
198	C₂²×C₄₃	#535	1	1	yes	characteristic
199	C₂²×C₄₃	#537	1	1	yes	characteristic
200	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₄₃	#575	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	—	4	1	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	#481	1	4	yes	—
212	C₄×C₄₃	#540	1	2	yes	—
213	C₄×C₄₃	#542	1	2	yes	—
214	#2856	C₂×C₄₃	1	1	yes	characteristic
215	#2285	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#2094	C₂×C₄₃	1	2	yes	complemented
217	#2071	C₂×C₄₃	1	2	yes	complemented
218	#2034	C₂×C₄₃	1	4	yes	complemented
219	#1982	C₂×C₄₃	1	2	yes	complemented
220	#1948	C₂×C₄₃	1	2	yes	complemented
221	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
222	C₂×C₄₃	—	4	2	no	—
223	C₂×C₄₃	—	16	2	no	—
224	C₂×C₄₃	#2624	1	1	yes	characteristic
225	C₂×C₄₃	C₂×#481	1	1	yes	characteristic
226	C₂×C₄₃	#3094	1	1	yes	characteristic
227	C₂×C₄₃	#3208	1	1	yes	characteristic
228	C₂×C₄₃	#3214	1	1	yes	characteristic
229	C₂×C₄₃	#3246	1	1	yes	characteristic
230	C₂×C₄₃	#3253	1	1	yes	characteristic
231	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×#121	—	2	1	no	—
233	C₂×#121	—	2	1	no	—
234	C₂×#121	C₂²×C₄₃	1	2	yes	—
235	C₂×#117	—	2	1	no	—
236	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₄₃	1	4	yes	—
238	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
239	C₂×#102	C₂²×C₄₃	1	4	yes	—
240	C₂×#102	C₂²×C₄₃	1	4	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
242	#390	—	2	1	no	—
243	#390	—	2	1	no	—
244	#390	C₂²×C₄₃	1	2	yes	—
245	#384	C₂²×C₄₃	1	1	yes	characteristic
246	#384	C₂²×C₄₃	1	1	yes	characteristic
247	#384	C₂²×C₄₃	1	1	yes	characteristic
248	#382	—	2	1	no	—
249	#380	—	2	1	no	—
250	#380	C₂²×C₄₃	1	2	yes	—
251	C₄×C₄⋊C₄	—	2	1	no	—
252	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
253	#340	C₂²×C₄₃	1	4	yes	—
254	#336	C₂²×C₄₃	1	2	yes	—
255	C₄₃	#29921	1	1	yes	characteristic, direct product factor, Sylow
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
260	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
264	#127	—	2	4	no	—
265	#121	—	4	4	no	—
266	#121	—	4	4	no	—
267	#121	—	4	4	no	—
268	#117	—	4	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
288	#106	—	4	4	no	—
289	C₄⋊C₈	—	2	4	no	—
290	#102	—	4	4	no	—
291	#102	—	4	4	no	—
292	C₂²⋊C₈	—	4	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
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	C₂×D₄×C₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	4	no	—
351	C₄²	#41×C₄₃	1	4	yes	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
366	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	8	4	no	—
370	D₄	—	8	8	no	—
371	D₄	—	8	4	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	8	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	#123×C₄₃	1	2	yes	—
395	C₂×C₄	#123×C₄₃	1	2	yes	—
396	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
397	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
398	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
399	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
401	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
402	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
403	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
404	C₈	—	4	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
420	C₂²	C₄₃×#535	1	1	yes	characteristic
421	C₂²	C₄₃×#537	1	1	yes	characteristic
422	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
423	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
424	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
425	C₂²	C₄₃×#575	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₄₃×#481	1	4	yes	—
434	C₄	C₄₃×#540	1	2	yes	—
435	C₄	C₄₃×#542	1	2	yes	—
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₄₃×#2624	1	1	yes	characteristic
439	C₂	C₂×C₄₃×#481	1	1	yes	characteristic
440	C₂	C₄₃×#3094	1	1	yes	characteristic
441	C₂	C₄₃×#3208	1	1	yes	characteristic
442	C₂	C₄₃×#3214	1	1	yes	characteristic
443	C₂	C₄₃×#3246	1	1	yes	characteristic
444	C₂	C₄₃×#3253	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2856	C₂
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. C₄₃×#2285	C₂	semidirect
3. C₄₃×#2094	C₂	semidirect
4. C₄₃×#2071	C₂	semidirect
5. C₄₃×#2034	C₂	semidirect
6. C₄₃×#1982	C₂	semidirect
7. C₄₃×#1948	C₂	semidirect
8. C₄₃×#1797	C₂	semidirect
182. #29921	C₄₃	direct (N × H)
215. #2285	C₂×C₄₃	semidirect
216. #2094	C₂×C₄₃	semidirect
217. #2071	C₂×C₄₃	semidirect
218. #2034	C₂×C₄₃	semidirect
219. #1982	C₂×C₄₃	semidirect
220. #1948	C₂×C₄₃	semidirect
221. #1797	C₂×C₄₃	semidirect
255. C₄₃	#29921	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×#2856	2
C₄₃×#2285	2
C₄₃×#2094	2
C₄₃×#2071	2
C₄₃×#2034	2
C₄₃×#1982	2
C₄₃×#1948	2
C₄₃×#1797	2
#29921	43

Subgroups — C43×#29921 #24949938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29921 #24949938