Subgroups — C₄₃×#29742 #24949759

Order 11008.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 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, complemented
2	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2847	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2077	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1999	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	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₃	C₂²	1	2	yes	—
15	C₂×#121×C₄₃	C₂²	1	2	yes	—
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₂×#120×C₄₃	—	2	2	no	—
18	C₄₃×#469	—	2	4	no	—
19	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
23	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
24	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
25	C₄₃×#407	—	2	4	no	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₄₃×#386	—	2	2	no	—
29	C₄₃×#386	—	2	2	no	—
30	C₄₃×#386	—	2	2	no	—
31	C₄₃×#380	C₂²	1	2	yes	—
32	C₄₃×#380	C₂²	1	2	yes	—
33	C₄₃×#380	C₂²	1	2	yes	—
34	C₄₃×#340	C₂²	1	2	yes	complemented
35	C₄₃×#340	C₂²	1	2	yes	complemented
36	C₄₃×#340	C₂²	1	2	yes	complemented
37	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	—	2	2	no	—
40	C₂²×D₄×C₄₃	—	2	2	no	—
41	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	—	2	2	no	—
44	C₂³×C₄×C₄₃	—	4	1	no	—
45	C₂³×C₄×C₄₃	—	4	1	no	—
46	C₂³×C₄×C₄₃	—	4	1	no	—
47	C₂³×C₄×C₄₃	—	4	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	2	yes	—
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂×D₈×C₄₃	—	2	2	no	—
53	C₂×D₈×C₄₃	—	4	1	no	—
54	C₂×D₈×C₄₃	—	4	1	no	—
55	C₂×M₁₆×C₄₃	—	2	2	no	—
56	C₂×M₁₆×C₄₃	—	4	1	no	—
57	C₂×M₁₆×C₄₃	—	4	1	no	—
58	C₂×M₁₆×C₄₃	—	4	1	no	—
59	C₂×M₁₆×C₄₃	—	4	1	no	—
60	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
61	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	—	2	4	no	—
66	#121×C₄₃	—	4	2	no	—
67	#121×C₄₃	—	4	2	no	—
68	#121×C₄₃	—	4	2	no	—
69	#121×C₄₃	—	4	2	no	—
70	#120×C₄₃	—	4	8	no	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	#107×C₄₃	—	4	1	no	—
81	#106×C₄₃	—	2	2	no	—
82	#106×C₄₃	—	4	1	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	4	2	no	—
85	#102×C₄₃	—	4	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	4	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	—	2	4	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	4	1	no	—
95	C₂⁴×C₄₃	—	4	1	no	—
96	C₂⁴×C₄₃	—	4	2	no	—
97	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	—	4	4	no	—
107	C₂×D₄×C₄₃	—	4	4	no	—
108	C₂×D₄×C₄₃	—	4	4	no	—
109	C₂×D₄×C₄₃	—	4	4	no	—
110	C₂×D₄×C₄₃	—	4	4	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	4	4	no	—
113	C₂×D₄×C₄₃	—	4	4	no	—
114	C₂²×C₄×C₄₃	—	2	1	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	4	2	no	—
130	C₂²×C₄×C₄₃	—	4	2	no	—
131	C₂²×C₄×C₄₃	—	4	1	no	—
132	C₂²×C₄×C₄₃	—	4	1	no	—
133	C₂²×C₄×C₄₃	—	4	4	no	—
134	C₂²×C₄×C₄₃	—	4	4	no	—
135	C₂²×C₄×C₄₃	—	4	4	no	—
136	C₂²×C₄×C₄₃	—	4	4	no	—
137	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	#41	1	2	yes	—
141	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
142	D₈×C₄₃	—	4	4	no	—
143	M₁₆×C₄₃	—	4	4	no	—
144	M₁₆×C₄₃	—	4	4	no	—
145	C₂×C₈×C₄₃	—	2	1	no	—
146	C₂×C₈×C₄₃	—	2	1	no	—
147	C₂×C₈×C₄₃	—	2	1	no	—
148	C₂×C₈×C₄₃	—	2	1	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	2	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₂²⋊C₄×C₄₃	—	4	4	no	—
161	C₂²⋊C₄×C₄₃	—	4	4	no	—
162	C₂²⋊C₄×C₄₃	—	4	4	no	—
163	C₂²⋊C₄×C₄₃	—	4	4	no	—
164	C₂²⋊C₄×C₄₃	—	4	4	no	—
165	C₂²⋊C₄×C₄₃	—	4	4	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	2	2	no	—
168	C₂³×C₄₃	—	2	2	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	2	2	no	—
174	C₂³×C₄₃	—	2	2	no	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	—	4	4	no	—
177	C₂³×C₄₃	—	4	8	no	—
178	C₂³×C₄₃	—	4	4	no	—
179	C₂³×C₄₃	—	4	8	no	—
180	C₂³×C₄₃	—	4	4	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	2	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	#121	1	2	yes	—
189	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
190	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₄₃	—	4	2	no	—
192	D₄×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	2	no	—
194	D₄×C₄₃	—	4	2	no	—
195	D₄×C₄₃	—	8	8	no	—
196	D₄×C₄₃	—	8	8	no	—
197	D₄×C₄₃	—	8	8	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	4	8	no	—
208	C₂×C₄×C₄₃	—	4	4	no	—
209	C₂×C₄×C₄₃	—	4	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	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	#121	1	2	yes	—
223	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
229	C₈×C₄₃	—	2	2	no	—
230	C₈×C₄₃	—	2	2	no	—
231	C₈×C₄₃	—	4	2	no	—
232	#29742	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	4	no	—
235	C₂²×C₄₃	—	2	4	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	4	16	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	2	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	—	4	2	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	—	8	2	no	—
248	C₂²×C₄₃	—	8	2	no	—
249	C₂²×C₄₃	—	8	2	no	—
250	C₂²×C₄₃	—	8	2	no	—
251	C₂²×C₄₃	—	8	2	no	—
252	C₂²×C₄₃	—	8	2	no	—
253	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
254	C₂²×C₄₃	#534	1	1	yes	characteristic
255	C₂²×C₄₃	#534	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
257	C₂²×C₄₃	#575	1	2	yes	—
258	C₄×C₄₃	—	2	2	no	—
259	C₄×C₄₃	—	4	2	no	—
260	C₄×C₄₃	—	8	2	no	—
261	C₄×C₄₃	—	8	2	no	—
262	C₄×C₄₃	—	8	2	no	—
263	C₄×C₄₃	#534	1	1	yes	characteristic
264	C₄×C₄₃	#535	1	1	yes	characteristic
265	C₄×C₄₃	#538	1	1	yes	characteristic
266	C₄×C₄₃	#538	1	1	yes	characteristic
267	C₂×#469	C₂×C₄₃	1	1	yes	characteristic, complemented
268	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
269	#2847	C₂×C₄₃	1	2	yes	complemented
270	#2077	C₂×C₄₃	1	2	yes	complemented
271	#2034	C₂×C₄₃	1	2	yes	complemented
272	#2033	C₂×C₄₃	1	2	yes	complemented
273	#1999	C₂×C₄₃	1	2	yes	complemented
274	#1895	C₂×C₄₃	1	2	yes	complemented
275	#1809	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂×C₄₃	—	4	2	no	—
277	C₂×C₄₃	—	4	4	no	—
278	C₂×C₄₃	—	16	2	no	—
279	C₂×C₄₃	#2617	1	1	yes	characteristic
280	C₂×C₄₃	#3055	1	2	yes	—
281	C₂×C₄₃	#3192	1	1	yes	characteristic
282	C₂×C₄₃	#3194	1	2	yes	—
283	C₂×C₄₃	#3197	1	1	yes	characteristic
284	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
285	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
286	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
287	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
288	C₂×#121	C₂²×C₄₃	1	2	yes	—
289	C₂×#121	C₂²×C₄₃	1	2	yes	—
290	C₂×#121	C₂²×C₄₃	1	2	yes	—
291	C₂×#120	—	2	2	no	—
292	#469	—	2	4	no	—
293	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic, complemented
294	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
295	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
296	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
297	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
298	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
299	#407	—	2	4	no	—
300	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
302	#386	—	2	2	no	—
303	#386	—	2	2	no	—
304	#386	—	2	2	no	—
305	#380	C₂²×C₄₃	1	2	yes	—
306	#380	C₂²×C₄₃	1	2	yes	—
307	#380	C₂²×C₄₃	1	2	yes	—
308	#340	C₂²×C₄₃	1	2	yes	complemented
309	#340	C₂²×C₄₃	1	2	yes	complemented
310	#340	C₂²×C₄₃	1	2	yes	complemented
311	C₄₃	#29742	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	—	4	1	no	—
320	C₂³×C₄	—	4	1	no	—
321	C₂³×C₄	—	4	1	no	—
322	C₂³×C₄	—	4	1	no	—
323	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
324	C₂³×C₄	D₄×C₄₃	1	2	yes	—
325	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	4	1	no	—
329	C₂×D₈	—	4	1	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	4	1	no	—
332	C₂×M₁₆	—	4	1	no	—
333	C₂×M₁₆	—	4	1	no	—
334	C₂×M₁₆	—	4	1	no	—
335	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
336	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
339	#121	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	4	2	no	—
342	#121	—	4	2	no	—
343	#121	—	4	2	no	—
344	#121	—	4	2	no	—
345	#120	—	4	8	no	—
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	#107	—	4	1	no	—
356	#106	—	2	2	no	—
357	#106	—	4	1	no	—
358	#102	—	2	4	no	—
359	#102	—	4	2	no	—
360	#102	—	4	2	no	—
361	C₂²⋊C₈	—	2	4	no	—
362	C₂²⋊C₈	—	2	4	no	—
363	#95	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	—	2	2	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	4	1	no	—
370	C₂⁴	—	4	1	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
373	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
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	—	4	4	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
415	C₂²×C₄	#41×C₄₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
417	D₈	—	4	4	no	—
418	M₁₆	—	4	4	no	—
419	M₁₆	—	4	4	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	#121×C₄₃	1	2	yes	—
464	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
465	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	8	no	—
471	D₄	—	8	8	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	#121×C₄₃	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
501	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
502	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
503	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
504	C₈	—	2	2	no	—
505	C₈	—	2	2	no	—
506	C₈	—	4	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
528	C₂²	C₄₃×#534	1	1	yes	characteristic
529	C₂²	C₄₃×#534	1	1	yes	characteristic
530	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
531	C₂²	C₄₃×#575	1	2	yes	—
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	8	2	no	—
535	C₄	—	8	2	no	—
536	C₄	—	8	2	no	—
537	C₄	C₄₃×#534	1	1	yes	characteristic
538	C₄	C₄₃×#535	1	1	yes	characteristic
539	C₄	C₄₃×#538	1	1	yes	characteristic
540	C₄	C₄₃×#538	1	1	yes	characteristic
541	C₂	—	4	2	no	—
542	C₂	—	4	4	no	—
543	C₂	—	16	2	no	—
544	C₂	C₄₃×#2617	1	1	yes	characteristic
545	C₂	C₄₃×#3055	1	2	yes	—
546	C₂	C₄₃×#3192	1	1	yes	characteristic
547	C₂	C₄₃×#3194	1	2	yes	—
548	C₂	C₄₃×#3197	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 ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#469	C₂	semidirect
2. C₂×C₄₃×#407	C₂	semidirect
3. C₄₃×#2847	C₂	semidirect
4. C₄₃×#2077	C₂	semidirect
5. C₄₃×#2034	C₂	semidirect
6. C₄₃×#2033	C₂	semidirect
7. C₄₃×#1999	C₂	semidirect
8. C₄₃×#1895	C₂	semidirect
9. C₄₃×#1809	C₂	semidirect
11. C₂²×D₈×C₄₃	C₂²	semidirect
19. C₂×#107×C₄₃	C₂²	semidirect
20. C₂×#106×C₄₃	C₂²	semidirect
21. C₂×#106×C₄₃	C₂²	semidirect
22. C₂×#102×C₄₃	C₂²	semidirect
23. C₂×#102×C₄₃	C₂²	semidirect
24. C₂×#102×C₄₃	C₂²	semidirect
34. C₄₃×#340	C₂²	semidirect
35. C₄₃×#340	C₂²	semidirect
36. C₄₃×#340	C₂²	semidirect
60. C₂×M₁₆×C₄₃	D₄	semidirect
232. #29742	C₄₃	direct (N × H)
267. C₂×#469	C₂×C₄₃	semidirect
268. C₂×#407	C₂×C₄₃	semidirect
269. #2847	C₂×C₄₃	semidirect
270. #2077	C₂×C₄₃	semidirect
271. #2034	C₂×C₄₃	semidirect
272. #2033	C₂×C₄₃	semidirect
273. #1999	C₂×C₄₃	semidirect
274. #1895	C₂×C₄₃	semidirect
275. #1809	C₂×C₄₃	semidirect
285. C₂²×D₈	C₂²×C₄₃	semidirect
293. C₂×#107	C₂²×C₄₃	semidirect
294. C₂×#106	C₂²×C₄₃	semidirect
295. C₂×#106	C₂²×C₄₃	semidirect
296. C₂×#102	C₂²×C₄₃	semidirect
297. C₂×#102	C₂²×C₄₃	semidirect
298. C₂×#102	C₂²×C₄₃	semidirect
308. #340	C₂²×C₄₃	semidirect
309. #340	C₂²×C₄₃	semidirect
310. #340	C₂²×C₄₃	semidirect
311. C₄₃	#29742	direct (N × H)
335. C₂×M₁₆	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×#469	2
C₂×C₄₃×#407	2
C₄₃×#2847	2
C₄₃×#2077	2
C₄₃×#2034	2
C₄₃×#2033	2
C₄₃×#1999	2
C₄₃×#1895	2
C₄₃×#1809	2
#29742	43

Subgroups — C43×#29742 #24949759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29742 #24949759