Subgroups — C₄₃×#29623 #24949640

Order 11008.

1516 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2012	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#124×C₄₃	—	2	4	no	—
15	C₂×#124×C₄₃	—	2	4	no	—
16	C₂×#124×C₄₃	—	2	2	no	—
17	C₂×#124×C₄₃	C₂²	1	4	yes	—
18	C₂×#123×C₄₃	—	2	1	no	—
19	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#448	—	2	4	no	—
24	C₄₃×#447	—	2	4	no	—
25	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
26	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
27	C₂×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	4	yes	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#390	C₂²	1	2	yes	complemented
32	C₄₃×#389	C₂²	1	2	yes	complemented
33	C₄₃×#388	—	2	2	no	—
34	C₄₃×#386	—	2	1	no	—
35	C₄₃×#380	C₂²	1	1	yes	characteristic
36	C₄₃×#336	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₃	—	2	1	no	—
38	C₂²×Q₈×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	—	2	1	no	—
40	C₂²×Q₈×C₄₃	—	4	4	no	—
41	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
42	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	4	4	no	—
47	C₂²×D₄×C₄₃	D₄	1	4	yes	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₄₃	—	2	4	no	—
55	C₂×SD₁₆×C₄₃	—	4	4	no	—
56	C₂×D₈×C₄₃	—	2	4	no	—
57	C₂×D₈×C₄₃	—	4	4	no	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
60	#124×C₄₃	—	2	16	no	—
61	#124×C₄₃	—	2	8	no	—
62	#124×C₄₃	—	2	8	no	—
63	#123×C₄₃	—	4	4	no	—
64	#121×C₄₃	—	2	2	no	—
65	#121×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	D₄	1	2	yes	—
80	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
81	#103×C₄₃	—	2	4	no	—
82	#103×C₄₃	—	4	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	4	4	no	—
85	C₂²⋊C₈×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	2	no	—
89	C₂⁴×C₄₃	—	2	4	no	—
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	—	4	4	no	—
93	C₂⁴×C₄₃	—	4	4	no	—
94	C₂⁴×C₄₃	—	4	2	no	—
95	C₂⁴×C₄₃	—	4	2	no	—
96	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₄₃	—	2	4	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	4	8	no	—
102	C₂×Q₈×C₄₃	—	4	4	no	—
103	C₂×Q₈×C₄₃	—	4	8	no	—
104	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	2	4	no	—
112	C₂×D₄×C₄₃	—	4	8	no	—
113	C₂×D₄×C₄₃	—	4	8	no	—
114	C₂×D₄×C₄₃	—	4	4	no	—
115	C₂×D₄×C₄₃	—	4	2	no	—
116	C₂×D₄×C₄₃	—	4	2	no	—
117	C₂×D₄×C₄₃	—	4	2	no	—
118	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	4	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	1	no	—
128	C₂²×C₄×C₄₃	—	4	2	no	—
129	C₂²×C₄×C₄₃	—	4	4	no	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₄₃	—	4	8	no	—
137	D₈×C₄₃	—	4	8	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	4	no	—
141	C₂×C₈×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	2	4	no	—
145	C₄⋊C₄×C₄₃	—	4	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	16	no	—
147	C₂²⋊C₄×C₄₃	—	2	16	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	4	4	no	—
150	C₂²⋊C₄×C₄₃	—	4	2	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₄²×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	4	no	—
158	C₂³×C₄₃	—	4	8	no	—
159	C₂³×C₄₃	—	4	8	no	—
160	C₂³×C₄₃	—	4	4	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	4	no	—
164	C₂³×C₄₃	—	4	8	no	—
165	C₂³×C₄₃	—	4	1	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	8	8	no	—
171	C₂³×C₄₃	—	8	8	no	—
172	C₂³×C₄₃	#120	1	2	yes	—
173	C₂³×C₄₃	#135	1	2	yes	—
174	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
175	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₃	—	2	4	no	—
177	Q₈×C₄₃	—	2	4	no	—
178	Q₈×C₄₃	—	4	8	no	—
179	Q₈×C₄₃	—	4	4	no	—
180	D₄×C₄₃	—	2	4	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	—	4	8	no	—
183	D₄×C₄₃	—	4	4	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	4	2	no	—
186	D₄×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	4	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	4	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	4	8	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	4	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	#120	1	2	yes	—
208	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
211	C₈×C₄₃	—	4	2	no	—
212	C₈×C₄₃	—	4	2	no	—
213	#29623	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	2	4	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	—	4	4	no	—
220	C₂²×C₄₃	—	4	4	no	—
221	C₂²×C₄₃	—	8	16	no	—
222	C₂²×C₄₃	—	8	4	no	—
223	C₂²×C₄₃	—	8	4	no	—
224	C₂²×C₄₃	—	8	1	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	2	no	—
227	C₂²×C₄₃	—	8	1	no	—
228	C₂²×C₄₃	—	8	1	no	—
229	C₂²×C₄₃	#449	1	4	yes	—
230	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
231	C₂²×C₄₃	#535	1	2	yes	—
232	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
233	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₄₃	#575	1	2	yes	—
235	C₄×C₄₃	—	2	2	no	—
236	C₄×C₄₃	—	4	4	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	—	8	2	no	—
240	C₄×C₄₃	—	8	1	no	—
241	C₄×C₄₃	#534	1	2	yes	—
242	C₄×C₄₃	#534	1	2	yes	—
243	C₂²×#124	C₂×C₄₃	1	1	yes	characteristic, complemented
244	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
245	C₂×#447	C₂×C₄₃	1	1	yes	characteristic
246	#2854	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#2042	C₂×C₄₃	1	4	yes	complemented
248	#2012	C₂×C₄₃	1	4	yes	complemented
249	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#1786	C₂×C₄₃	1	1	yes	characteristic, complemented
252	C₂×C₄₃	—	2	4	no	—
253	C₂×C₄₃	—	8	4	no	—
254	C₂×C₄₃	—	16	1	no	—
255	C₂×C₄₃	#2613	1	1	yes	characteristic
256	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
257	C₂×C₄₃	#3005	1	1	yes	characteristic
258	C₂×C₄₃	#3211	1	2	yes	—
259	C₂×C₄₃	#3213	1	2	yes	—
260	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
261	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
262	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
263	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
264	C₂×#124	—	2	4	no	—
265	C₂×#124	—	2	4	no	—
266	C₂×#124	—	2	2	no	—
267	C₂×#124	C₂²×C₄₃	1	4	yes	—
268	C₂×#123	—	2	1	no	—
269	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	—	2	1	no	—
271	C₂²×C₂²⋊C₄	—	2	1	no	—
272	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
273	#448	—	2	4	no	—
274	#447	—	2	4	no	—
275	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
276	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
277	C₂×#102	C₂²×C₄₃	1	2	yes	—
278	C₂×#102	C₂²×C₄₃	1	4	yes	—
279	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
281	#390	C₂²×C₄₃	1	2	yes	complemented
282	#389	C₂²×C₄₃	1	2	yes	complemented
283	#388	—	2	2	no	—
284	#386	—	2	1	no	—
285	#380	C₂²×C₄₃	1	1	yes	characteristic
286	#336	C₂²×C₄₃	1	4	yes	complemented
287	C₄₃	#29623	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁵	—	2	1	no	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	—	4	4	no	—
292	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
293	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	4	4	no	—
298	C₂²×D₄	D₄×C₄₃	1	4	yes	—
299	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
300	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
305	C₂×SD₁₆	—	2	4	no	—
306	C₂×SD₁₆	—	4	4	no	—
307	C₂×D₈	—	2	4	no	—
308	C₂×D₈	—	4	4	no	—
309	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
311	#124	—	2	16	no	—
312	#124	—	2	8	no	—
313	#124	—	2	8	no	—
314	#123	—	4	4	no	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	8	no	—
321	C₂×C₂²⋊C₄	—	2	8	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	D₄×C₄₃	1	2	yes	—
331	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
332	#103	—	2	4	no	—
333	#103	—	4	4	no	—
334	#102	—	2	4	no	—
335	#102	—	4	4	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	2	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	4	4	no	—
344	C₂⁴	—	4	4	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	4	8	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	—	4	8	no	—
355	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	4	8	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
387	SD₁₆	—	4	8	no	—
388	D₈	—	4	8	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	2	16	no	—
398	C₂²⋊C₄	—	2	16	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	4	8	no	—
410	C₂³	—	4	8	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	4	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	8	8	no	—
422	C₂³	—	8	8	no	—
423	C₂³	#120×C₄₃	1	2	yes	—
424	C₂³	#135×C₄₃	1	2	yes	—
425	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
426	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
427	Q₈	—	2	4	no	—
428	Q₈	—	2	4	no	—
429	Q₈	—	4	8	no	—
430	Q₈	—	4	4	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	4	8	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	#120×C₄₃	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
461	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	16	no	—
472	C₂²	—	8	4	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₄₃×#449	1	4	yes	—
480	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
481	C₂²	C₄₃×#535	1	2	yes	—
482	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
483	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
484	C₂²	C₄₃×#575	1	2	yes	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	C₄₃×#534	1	2	yes	—
492	C₄	C₄₃×#534	1	2	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	8	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₄₃×#2613	1	1	yes	characteristic
497	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
498	C₂	C₄₃×#3005	1	1	yes	characteristic
499	C₂	C₄₃×#3211	1	2	yes	—
500	C₂	C₄₃×#3213	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#447	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
1. C₂²×#124×C₄₃	C₂	semidirect
2. C₂×C₄₃×#448	C₂	semidirect
4. C₄₃×#2854	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2012	C₂	semidirect
7. C₄₃×#1817	C₂	semidirect
8. C₄₃×#1787	C₂	semidirect
9. C₄₃×#1786	C₂	semidirect
12. C₂²×SD₁₆×C₄₃	C₂²	semidirect
25. C₂×#103×C₄₃	C₂²	semidirect
26. C₂×#103×C₄₃	C₂²	semidirect
31. C₄₃×#390	C₂²	semidirect
32. C₄₃×#389	C₂²	semidirect
36. C₄₃×#336	C₂²	semidirect
213. #29623	C₄₃	direct (N × H)
243. C₂²×#124	C₂×C₄₃	semidirect
244. C₂×#448	C₂×C₄₃	semidirect
246. #2854	C₂×C₄₃	semidirect
247. #2042	C₂×C₄₃	semidirect
248. #2012	C₂×C₄₃	semidirect
249. #1817	C₂×C₄₃	semidirect
250. #1787	C₂×C₄₃	semidirect
251. #1786	C₂×C₄₃	semidirect
262. C₂²×SD₁₆	C₂²×C₄₃	semidirect
275. C₂×#103	C₂²×C₄₃	semidirect
276. C₂×#103	C₂²×C₄₃	semidirect
281. #390	C₂²×C₄₃	semidirect
282. #389	C₂²×C₄₃	semidirect
286. #336	C₂²×C₄₃	semidirect
287. C₄₃	#29623	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₃	2
C₂×C₄₃×#448	2
C₂×C₄₃×#447	2
C₄₃×#2854	2
C₄₃×#2042	2
C₄₃×#2012	2
C₄₃×#1817	2
C₄₃×#1787	2
C₄₃×#1786	2
#29623	43

Subgroups — C43×#29623 #24949640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29623 #24949640