Subgroups — C₄₃×#29782 #24949799

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2854	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2088	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#123×C₄₃	—	2	2	no	—
14	C₂×#121×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#469	—	2	4	no	—
17	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#423	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#390	C₂²	1	2	yes	—
27	C₄₃×#390	C₂²	1	2	yes	—
28	C₄₃×#389	C₂²	1	2	yes	—
29	C₄₃×#389	C₂²	1	2	yes	—
30	C₄₃×#388	—	2	2	no	—
31	C₄₃×#388	—	2	2	no	—
32	C₄₃×#386	—	2	2	no	—
33	C₄₃×#380	C₂²	1	2	yes	—
34	C₄₃×#340	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	D₄	1	2	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₄₃	—	2	2	no	—
42	C₂×D₈×C₄₃	—	4	1	no	—
43	C₂×D₈×C₄₃	—	4	1	no	—
44	C₂×M₁₆×C₄₃	—	2	2	no	—
45	C₂×M₁₆×C₄₃	—	4	1	no	—
46	C₂×M₁₆×C₄₃	—	4	1	no	—
47	C₂×M₁₆×C₄₃	—	4	1	no	—
48	C₂×M₁₆×C₄₃	—	4	1	no	—
49	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	#123×C₄₃	—	4	8	no	—
54	#121×C₄₃	—	2	4	no	—
55	#121×C₄₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄²×C₄₃	—	2	2	no	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
72	#107×C₄₃	—	4	1	no	—
73	#106×C₄₃	—	2	2	no	—
74	#106×C₄₃	—	4	1	no	—
75	C₄⋊C₈×C₄₃	—	2	4	no	—
76	C₄⋊C₈×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	2	4	no	—
78	#102×C₄₃	—	4	2	no	—
79	#102×C₄₃	—	4	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×D₄×C₄₃	—	2	2	no	—
86	C₂×D₄×C₄₃	—	2	2	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	4	4	no	—
92	C₂×D₄×C₄₃	—	4	4	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	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	—	4	2	no	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₃	#41	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	D₈×C₄₃	—	4	4	no	—
111	M₁₆×C₄₃	—	4	4	no	—
112	M₁₆×C₄₃	—	4	4	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	4	4	no	—
129	C₄⋊C₄×C₄₃	—	4	4	no	—
130	C₂²⋊C₄×C₄₃	—	4	4	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	4	no	—
133	C₂²⋊C₄×C₄₃	—	4	4	no	—
134	C₂²⋊C₄×C₄₃	—	4	4	no	—
135	C₂²⋊C₄×C₄₃	—	4	4	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	#121	1	2	yes	—
152	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	2	no	—
155	D₄×C₄₃	—	4	2	no	—
156	D₄×C₄₃	—	4	2	no	—
157	D₄×C₄₃	—	8	8	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	4	8	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	#121	1	2	yes	—
180	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₄₃	—	2	2	no	—
188	C₈×C₄₃	—	2	2	no	—
189	C₈×C₄₃	—	4	2	no	—
190	#29782	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	4	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	4	1	no	—
195	C₂²×C₄₃	—	4	1	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	—	8	2	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	2	no	—
201	C₂²×C₄₃	—	8	2	no	—
202	C₂²×C₄₃	—	8	2	no	—
203	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₂²×C₄₃	#537	1	1	yes	characteristic
205	C₂²×C₄₃	#537	1	1	yes	characteristic
206	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
207	C₂²×C₄₃	#575	1	2	yes	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	4	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	—	8	2	no	—
212	C₄×C₄₃	—	8	2	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	#534	1	1	yes	characteristic
215	C₄×C₄₃	#536	1	1	yes	characteristic
216	C₄×C₄₃	#539	1	1	yes	characteristic
217	C₄×C₄₃	#539	1	1	yes	characteristic
218	C₂×#469	C₂×C₄₃	1	1	yes	characteristic
219	C₂×#423	C₂×C₄₃	1	1	yes	characteristic, complemented
220	#2854	C₂×C₄₃	1	2	yes	complemented
221	#2088	C₂×C₄₃	1	2	yes	complemented
222	#2067	C₂×C₄₃	1	2	yes	complemented
223	#2065	C₂×C₄₃	1	2	yes	complemented
224	#2054	C₂×C₄₃	1	2	yes	complemented
225	#1895	C₂×C₄₃	1	2	yes	complemented
226	#1809	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×C₄₃	—	4	2	no	—
228	C₂×C₄₃	—	16	2	no	—
229	C₂×C₄₃	#2618	1	1	yes	characteristic
230	C₂×C₄₃	#3055	1	2	yes	—
231	C₂×C₄₃	#3251	1	2	yes	—
232	C₂×C₄₃	#3253	1	1	yes	characteristic
233	C₂×C₄₃	#3256	1	1	yes	characteristic
234	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#123	—	2	2	no	—
238	C₂×#121	C₂²×C₄₃	1	2	yes	—
239	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
240	#469	—	2	4	no	—
241	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
243	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
244	#423	—	2	4	no	—
245	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
247	C₂×#102	C₂²×C₄₃	1	2	yes	—
248	C₂×#102	C₂²×C₄₃	1	2	yes	—
249	C₂×#102	C₂²×C₄₃	1	2	yes	—
250	#390	C₂²×C₄₃	1	2	yes	—
251	#390	C₂²×C₄₃	1	2	yes	—
252	#389	C₂²×C₄₃	1	2	yes	—
253	#389	C₂²×C₄₃	1	2	yes	—
254	#388	—	2	2	no	—
255	#388	—	2	2	no	—
256	#386	—	2	2	no	—
257	#380	C₂²×C₄₃	1	2	yes	—
258	#340	C₂²×C₄₃	1	2	yes	—
259	#340	C₂²×C₄₃	1	2	yes	—
260	#340	C₂²×C₄₃	1	2	yes	—
261	C₄₃	#29782	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
264	C₂³×C₄	D₄×C₄₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
266	C₂×D₈	—	2	2	no	—
267	C₂×D₈	—	4	1	no	—
268	C₂×D₈	—	4	1	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	4	1	no	—
271	C₂×M₁₆	—	4	1	no	—
272	C₂×M₁₆	—	4	1	no	—
273	C₂×M₁₆	—	4	1	no	—
274	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
275	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
278	#123	—	4	8	no	—
279	#121	—	2	4	no	—
280	#121	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
295	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
297	#107	—	4	1	no	—
298	#106	—	2	2	no	—
299	#106	—	4	1	no	—
300	C₄⋊C₈	—	2	4	no	—
301	C₄⋊C₈	—	2	4	no	—
302	#102	—	2	4	no	—
303	#102	—	4	2	no	—
304	#102	—	4	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	C₂⁴	—	2	2	no	—
309	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
333	C₂²×C₄	#41×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
335	D₈	—	4	4	no	—
336	M₁₆	—	4	4	no	—
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	#121×C₄₃	1	2	yes	—
377	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	8	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	#121×C₄₃	1	2	yes	—
405	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
408	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
409	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
410	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
411	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
428	C₂²	C₄₃×#537	1	1	yes	characteristic
429	C₂²	C₄₃×#537	1	1	yes	characteristic
430	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
431	C₂²	C₄₃×#575	1	2	yes	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₄₃×#534	1	1	yes	characteristic
439	C₄	C₄₃×#536	1	1	yes	characteristic
440	C₄	C₄₃×#539	1	1	yes	characteristic
441	C₄	C₄₃×#539	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	16	2	no	—
444	C₂	C₄₃×#2618	1	1	yes	characteristic
445	C₂	C₄₃×#3055	1	2	yes	—
446	C₂	C₄₃×#3251	1	2	yes	—
447	C₂	C₄₃×#3253	1	1	yes	characteristic
448	C₂	C₄₃×#3256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#469	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. C₂×C₄₃×#423	C₂	semidirect
3. C₄₃×#2854	C₂	semidirect
4. C₄₃×#2088	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2065	C₂	semidirect
7. C₄₃×#2054	C₂	semidirect
8. C₄₃×#1895	C₂	semidirect
9. C₄₃×#1809	C₂	semidirect
190. #29782	C₄₃	direct (N × H)
219. C₂×#423	C₂×C₄₃	semidirect
220. #2854	C₂×C₄₃	semidirect
221. #2088	C₂×C₄₃	semidirect
222. #2067	C₂×C₄₃	semidirect
223. #2065	C₂×C₄₃	semidirect
224. #2054	C₂×C₄₃	semidirect
225. #1895	C₂×C₄₃	semidirect
226. #1809	C₂×C₄₃	semidirect
261. C₄₃	#29782	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#469	2
C₂×C₄₃×#423	2
C₄₃×#2854	2
C₄₃×#2088	2
C₄₃×#2067	2
C₄₃×#2065	2
C₄₃×#2054	2
C₄₃×#1895	2
C₄₃×#1809	2
#29782	43

Subgroups — C43×#29782 #24949799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29782 #24949799