Subgroups — C₄₃×#29675 #24949692

Order 11008.

1202 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#463	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1999	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1802	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#540	—	2	8	no	—
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₃	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	—	2	2	no	—
21	C₂×#121×C₄₃	C₂²	1	2	yes	—
22	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
24	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#463	—	2	8	no	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
32	C₄₃×#396	—	2	2	no	—
33	C₄₃×#394	—	2	2	no	—
34	C₄₃×#391	C₂²	1	1	yes	characteristic
35	C₄₃×#390	C₂²	1	1	yes	characteristic
36	C₄₃×#384	C₂²	1	1	yes	characteristic
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#336	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	—	2	2	no	—
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₃	—	2	4	no	—
50	C₂×SD₁₆×C₄₃	—	4	2	no	—
51	C₂×SD₁₆×C₄₃	—	4	2	no	—
52	C₂×D₈×C₄₃	—	2	4	no	—
53	C₂×D₈×C₄₃	—	4	2	no	—
54	C₂×D₈×C₄₃	—	4	2	no	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	#127×C₄₃	—	2	4	no	—
58	#125×C₄₃	—	2	4	no	—
59	#124×C₄₃	—	2	4	no	—
60	#123×C₄₃	—	2	16	no	—
61	C₂²⋊Q₈×C₄₃	—	4	2	no	—
62	#121×C₄₃	—	2	16	no	—
63	#121×C₄₃	—	2	4	no	—
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	—	4	2	no	—
66	C₄×D₄×C₄₃	—	2	4	no	—
67	C₄×D₄×C₄₃	D₄	1	8	yes	complemented
68	#117×C₄₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₄₃	—	2	4	no	—
86	#103×C₄₃	—	2	4	no	—
87	#102×C₄₃	—	2	4	no	—
88	#102×C₄₃	—	4	2	no	—
89	#102×C₄₃	—	4	2	no	—
90	C₂²⋊C₈×C₄₃	—	4	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	8	no	—
100	C₂×D₄×C₄₃	—	2	8	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	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	8	2	no	—
112	C₂×D₄×C₄₃	—	8	2	no	—
113	C₂×D₄×C₄₃	—	8	2	no	—
114	C₂×D₄×C₄₃	—	8	2	no	—
115	C₂×D₄×C₄₃	—	8	2	no	—
116	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	8	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	8	2	no	—
127	C₂²×C₄×C₄₃	—	8	2	no	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	SD₁₆×C₄₃	—	4	8	no	—
133	D₈×C₄₃	—	4	8	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	8	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	8	2	no	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
148	C₂²⋊C₄×C₄₃	—	2	8	no	—
149	C₂²⋊C₄×C₄₃	—	2	8	no	—
150	C₂²⋊C₄×C₄₃	—	2	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	4	no	—
154	C₂²⋊C₄×C₄₃	—	8	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	C₂×D₄	1	4	yes	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	4	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	—	4	1	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₄₃	—	4	2	no	—
176	Q₈×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	2	4	no	—
178	D₄×C₄₃	—	2	4	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	4	2	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	8	8	no	—
184	D₄×C₄₃	—	8	8	no	—
185	D₄×C₄₃	—	8	4	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	1	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	8	8	no	—
207	C₂×C₄×C₄₃	#120	1	4	yes	—
208	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
211	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₄₃	—	4	2	no	—
213	C₈×C₄₃	—	4	2	no	—
214	#29675	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₃	—	4	1	no	—
216	C₂²×C₄₃	—	4	4	no	—
217	C₂²×C₄₃	—	4	1	no	—
218	C₂²×C₄₃	—	4	1	no	—
219	C₂²×C₄₃	—	4	2	no	—
220	C₂²×C₄₃	—	4	2	no	—
221	C₂²×C₄₃	—	4	4	no	—
222	C₂²×C₄₃	—	4	4	no	—
223	C₂²×C₄₃	—	8	2	no	—
224	C₂²×C₄₃	—	8	2	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	—	8	1	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	—	8	2	no	—
232	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
233	C₂²×C₄₃	#535	1	1	yes	characteristic
234	C₂²×C₄₃	#537	1	1	yes	characteristic
235	C₂²×C₄₃	#576	1	2	yes	—
236	C₂²×C₄₃	#577	1	2	yes	—
237	C₄×C₄₃	—	2	4	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	4	2	no	—
240	C₄×C₄₃	—	4	4	no	—
241	C₄×C₄₃	—	8	1	no	—
242	C₄×C₄₃	—	8	1	no	—
243	C₄×C₄₃	—	8	1	no	—
244	C₄×C₄₃	#535	1	2	yes	—
245	C₄×C₄₃	#537	1	2	yes	—
246	C₂×#540	C₂×C₄₃	1	1	yes	characteristic, complemented
247	C₂×#463	C₂×C₄₃	1	2	yes	complemented
248	#2620	C₂×C₄₃	1	1	yes	characteristic, complemented
249	#2026	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#2025	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
252	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2000	C₂×C₄₃	1	2	yes	complemented
254	#1999	C₂×C₄₃	1	2	yes	complemented
255	#1802	C₂×C₄₃	1	2	yes	complemented
256	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
257	C₂×C₄₃	—	8	1	no	—
258	C₂×C₄₃	—	8	4	no	—
259	C₂×C₄₃	—	16	1	no	—
260	C₂×C₄₃	#2615	1	1	yes	characteristic
261	C₂×C₄₃	#3012	1	2	yes	—
262	C₂×C₄₃	#3220	1	1	yes	characteristic
263	C₂×C₄₃	#3221	1	1	yes	characteristic
264	C₂×C₄₃	#3257	1	2	yes	—
265	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
266	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
267	#540	—	2	8	no	—
268	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
271	C₂×#123	—	2	2	no	—
272	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×#121	—	2	2	no	—
274	C₂×#121	C₂²×C₄₃	1	2	yes	—
275	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
277	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
278	#463	—	2	8	no	—
279	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
280	C₂×#103	C₂²×C₄₃	1	2	yes	—
281	C₂×#102	C₂²×C₄₃	1	2	yes	—
282	C₂×#102	C₂²×C₄₃	1	2	yes	—
283	C₂×#102	C₂²×C₄₃	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
285	#396	—	2	2	no	—
286	#394	—	2	2	no	—
287	#391	C₂²×C₄₃	1	1	yes	characteristic
288	#390	C₂²×C₄₃	1	1	yes	characteristic
289	#384	C₂²×C₄₃	1	1	yes	characteristic
290	#340	C₂²×C₄₃	1	2	yes	—
291	#340	C₂²×C₄₃	1	2	yes	—
292	#336	C₂²×C₄₃	1	1	yes	characteristic
293	#336	C₂²×C₄₃	1	1	yes	characteristic
294	C₄₃	#29675	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
300	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×SD₁₆	—	4	2	no	—
305	C₂×SD₁₆	—	4	2	no	—
306	C₂×D₈	—	2	4	no	—
307	C₂×D₈	—	4	2	no	—
308	C₂×D₈	—	4	2	no	—
309	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
311	#127	—	2	4	no	—
312	#125	—	2	4	no	—
313	#124	—	2	4	no	—
314	#123	—	2	16	no	—
315	C₂²⋊Q₈	—	4	2	no	—
316	#121	—	2	16	no	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	#121	—	4	2	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	D₄×C₄₃	1	8	yes	complemented
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
337	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
339	C₄⋊C₈	—	2	4	no	—
340	#103	—	2	4	no	—
341	#102	—	2	4	no	—
342	#102	—	4	2	no	—
343	#102	—	4	2	no	—
344	C₂²⋊C₈	—	4	2	no	—
345	#95	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	—	8	2	no	—
370	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	8	2	no	—
381	C₂²×C₄	—	8	2	no	—
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	C₂⁴×C₄₃	1	1	yes	characteristic
386	SD₁₆	—	4	8	no	—
387	D₈	—	4	8	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	8	2	no	—
401	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	C₂×D₄×C₄₃	1	4	yes	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	8	no	—
438	D₄	—	8	8	no	—
439	D₄	—	8	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	#120×C₄₃	1	4	yes	—
462	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
463	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
465	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
486	C₂²	C₄₃×#535	1	1	yes	characteristic
487	C₂²	C₄₃×#537	1	1	yes	characteristic
488	C₂²	C₄₃×#576	1	2	yes	—
489	C₂²	C₄₃×#577	1	2	yes	—
490	C₄	—	2	4	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	8	1	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	C₄₃×#535	1	2	yes	—
498	C₄	C₄₃×#537	1	2	yes	—
499	C₂	—	8	1	no	—
500	C₂	—	8	4	no	—
501	C₂	—	16	1	no	—
502	C₂	C₄₃×#2615	1	1	yes	characteristic
503	C₂	C₄₃×#3012	1	2	yes	—
504	C₂	C₄₃×#3220	1	1	yes	characteristic
505	C₂	C₄₃×#3221	1	1	yes	characteristic
506	C₂	C₄₃×#3257	1	2	yes	—

	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 ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#540	C₂	semidirect
2. C₂×C₄₃×#463	C₂	semidirect
3. C₄₃×#2620	C₂	semidirect
4. C₄₃×#2026	C₂	semidirect
5. C₄₃×#2025	C₂	semidirect
6. C₄₃×#2014	C₂	semidirect
7. C₄₃×#2011	C₂	semidirect
8. C₄₃×#2000	C₂	semidirect
9. C₄₃×#1999	C₂	semidirect
10. C₄₃×#1802	C₂	semidirect
11. C₄₃×#1798	C₂	semidirect
67. C₄×D₄×C₄₃	D₄	semidirect
214. #29675	C₄₃	direct (N × H)
246. C₂×#540	C₂×C₄₃	semidirect
247. C₂×#463	C₂×C₄₃	semidirect
248. #2620	C₂×C₄₃	semidirect
249. #2026	C₂×C₄₃	semidirect
250. #2025	C₂×C₄₃	semidirect
251. #2014	C₂×C₄₃	semidirect
252. #2011	C₂×C₄₃	semidirect
253. #2000	C₂×C₄₃	semidirect
254. #1999	C₂×C₄₃	semidirect
255. #1802	C₂×C₄₃	semidirect
256. #1798	C₂×C₄₃	semidirect
294. C₄₃	#29675	direct (N × H)
321. C₄×D₄	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×#540	2
C₂×C₄₃×#463	2
C₄₃×#2620	2
C₄₃×#2026	2
C₄₃×#2025	2
C₄₃×#2014	2
C₄₃×#2011	2
C₄₃×#2000	2
C₄₃×#1999	2
C₄₃×#1802	2
C₄₃×#1798	2
#29675	43

Subgroups — C43×#29675 #24949692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29675 #24949692