Subgroups — C₄₃×#28571 #24948588

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#465	C₂	1	2	yes	maximal
2	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1892	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
16	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₃	—	2	1	no	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#465	—	2	8	no	—
21	C₂×#106×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#391	C₂²	1	2	yes	—
27	C₄₃×#390	C₂²	1	1	yes	characteristic
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	—	2	1	no	—
30	C₄₃×#389	C₂²	1	1	yes	characteristic
31	C₄₃×#388	—	2	1	no	—
32	C₄₃×#386	—	2	1	no	—
33	C₄₃×#384	C₂²	1	1	yes	characteristic
34	C₄₃×#380	—	2	1	no	—
35	C₄₃×#380	—	2	1	no	—
36	C₄₃×#380	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₄₃	—	2	4	no	—
52	C₂×SD₁₆×C₄₃	—	2	4	no	—
53	C₂×SD₁₆×C₄₃	—	4	2	no	—
54	C₂²×C₈×C₄₃	—	2	4	no	—
55	C₂²×C₈×C₄₃	—	2	4	no	—
56	C₂²×C₈×C₄₃	—	4	2	no	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₃	—	4	2	no	—
60	C₂²⋊Q₈×C₄₃	—	2	4	no	—
61	C₂²⋊Q₈×C₄₃	—	2	4	no	—
62	#121×C₄₃	—	2	2	no	—
63	#121×C₄₃	D₄	1	4	yes	—
64	C₄×D₄×C₄₃	—	4	2	no	—
65	C₄×D₄×C₄₃	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	4	2	no	—
84	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	#106×C₄₃	—	2	4	no	—
89	#103×C₄₃	—	2	4	no	—
90	#103×C₄₃	—	2	4	no	—
91	#103×C₄₃	—	4	2	no	—
92	#102×C₄₃	—	2	4	no	—
93	#95×C₄₃	—	2	1	no	—
94	#95×C₄₃	—	2	1	no	—
95	#95×C₄₃	—	2	1	no	—
96	#95×C₄₃	—	2	2	no	—
97	#95×C₄₃	—	2	2	no	—
98	C₂⁴×C₄₃	—	2	1	no	—
99	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	4	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	4	1	no	—
123	C₂²×C₄×C₄₃	—	4	1	no	—
124	C₂²×C₄×C₄₃	—	4	1	no	—
125	C₂²×C₄×C₄₃	—	4	2	no	—
126	C₂²×C₄×C₄₃	—	4	2	no	—
127	C₂²×C₄×C₄₃	—	4	2	no	—
128	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	complemented
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	#41	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
137	SD₁₆×C₄₃	—	4	8	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	4	8	no	—
144	C₂×C₈×C₄₃	#41	1	4	yes	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	2	no	—
150	C₄⋊C₄×C₄₃	—	4	2	no	—
151	C₄⋊C₄×C₄₃	—	4	2	no	—
152	C₄⋊C₄×C₄₃	—	4	2	no	—
153	C₄⋊C₄×C₄₃	—	4	4	no	—
154	C₄⋊C₄×C₄₃	—	4	2	no	—
155	C₄⋊C₄×C₄₃	—	4	2	no	—
156	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₄₃	—	2	4	no	—
158	C₂²⋊C₄×C₄₃	—	4	2	no	—
159	C₂²⋊C₄×C₄₃	—	4	2	no	—
160	C₂²⋊C₄×C₄₃	—	4	2	no	—
161	C₂²⋊C₄×C₄₃	—	4	4	no	—
162	C₂²⋊C₄×C₄₃	—	4	2	no	—
163	C₄²×C₄₃	—	2	2	no	—
164	C₄²×C₄₃	—	2	2	no	—
165	C₄²×C₄₃	—	4	1	no	—
166	C₄²×C₄₃	—	4	1	no	—
167	C₄²×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	2	1	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	—	2	1	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	4	1	no	—
174	C₂³×C₄₃	—	4	1	no	—
175	C₂³×C₄₃	—	4	1	no	—
176	C₂³×C₄₃	—	4	1	no	—
177	C₂³×C₄₃	—	4	1	no	—
178	C₂³×C₄₃	—	4	1	no	—
179	C₂³×C₄₃	#121	1	2	yes	—
180	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
181	C₂³×C₄₃	#137	1	2	yes	—
182	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₄₃	—	4	2	no	—
184	Q₈×C₄₃	—	4	2	no	—
185	Q₈×C₄₃	—	4	2	no	—
186	Q₈×C₄₃	—	4	2	no	—
187	D₄×C₄₃	—	2	4	no	—
188	D₄×C₄₃	—	4	8	no	—
189	D₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	4	no	—
199	C₂×C₄×C₄₃	—	2	4	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	—	4	4	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	1	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	8	4	no	—
221	C₂×C₄×C₄₃	#121	1	2	yes	—
222	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₄₃	#135	1	2	yes	—
225	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
227	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
229	C₈×C₄₃	—	2	4	no	—
230	C₈×C₄₃	—	4	2	no	—
231	#28571	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₄₃	—	2	2	no	—
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	2	2	no	—
238	C₂²×C₄₃	—	4	2	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	—	8	1	no	—
242	C₂²×C₄₃	—	8	1	no	—
243	C₂²×C₄₃	—	8	1	no	—
244	C₂²×C₄₃	—	8	1	no	—
245	C₂²×C₄₃	#461	1	4	yes	—
246	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
247	C₂²×C₄₃	#532	1	1	yes	characteristic
248	C₂²×C₄₃	#534	1	1	yes	characteristic
249	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
250	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
251	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
252	C₂²×C₄₃	#575	1	1	yes	characteristic
253	C₄×C₄₃	—	2	2	no	—
254	C₄×C₄₃	—	2	2	no	—
255	C₄×C₄₃	—	2	2	no	—
256	C₄×C₄₃	—	2	2	no	—
257	C₄×C₄₃	—	4	1	no	—
258	C₄×C₄₃	—	4	2	no	—
259	C₄×C₄₃	—	8	1	no	—
260	C₄×C₄₃	—	8	1	no	—
261	C₄×C₄₃	—	8	2	no	—
262	C₄×C₄₃	—	8	2	no	—
263	C₄×C₄₃	#546	1	2	yes	—
264	C₄×C₄₃	#553	1	2	yes	—
265	C₂×#465	C₂×C₄₃	1	2	yes	—
266	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
267	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
268	#2084	C₂×C₄₃	1	1	yes	characteristic, complemented
269	#2071	C₂×C₄₃	1	1	yes	characteristic, complemented
270	#2043	C₂×C₄₃	1	1	yes	characteristic, complemented
271	#2013	C₂×C₄₃	1	1	yes	characteristic, complemented
272	#1927	C₂×C₄₃	1	2	yes	complemented
273	#1892	C₂×C₄₃	1	2	yes	complemented
274	#1877	C₂×C₄₃	1	2	yes	complemented
275	C₂×#336	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂×C₄₃	—	2	4	no	—
277	C₂×C₄₃	—	8	2	no	—
278	C₂×C₄₃	#2543	1	1	yes	characteristic
279	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
280	C₂×C₄₃	#3035	1	1	yes	characteristic
281	C₂×C₄₃	#3167	1	1	yes	characteristic
282	C₂×C₄₃	#3181	1	1	yes	characteristic
283	C₂×C₄₃	#3187	1	1	yes	characteristic
284	C₂×C₄₃	#3190	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
286	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
289	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
290	C₂×C₄×D₄	—	2	1	no	—
291	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
293	#465	—	2	8	no	—
294	C₂×#106	C₂²×C₄₃	1	2	yes	—
295	C₂×#103	C₂²×C₄₃	1	2	yes	—
296	C₂×#103	C₂²×C₄₃	1	2	yes	—
297	C₂×#103	C₂²×C₄₃	1	2	yes	—
298	C₂×#102	C₂²×C₄₃	1	2	yes	—
299	#391	C₂²×C₄₃	1	2	yes	—
300	#390	C₂²×C₄₃	1	1	yes	characteristic
301	#389	—	2	1	no	—
302	#389	—	2	1	no	—
303	#389	C₂²×C₄₃	1	1	yes	characteristic
304	#388	—	2	1	no	—
305	#386	—	2	1	no	—
306	#384	C₂²×C₄₃	1	1	yes	characteristic
307	#380	—	2	1	no	—
308	#380	—	2	1	no	—
309	#380	C₂²×C₄₃	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
311	C₄×C₂²⋊C₄	—	2	1	no	—
312	#340	C₂²×C₄₃	1	2	yes	—
313	#340	C₂²×C₄₃	1	2	yes	—
314	#336	C₂²×C₄₃	1	1	yes	characteristic
315	#336	C₂²×C₄₃	1	1	yes	characteristic
316	#336	C₂²×C₄₃	1	2	yes	—
317	C₄₃	#28571	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
323	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	4	2	no	—
328	C₂²×C₈	—	2	4	no	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	—	4	2	no	—
331	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
333	C₄⋊Q₈	—	4	2	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	#121	—	2	2	no	—
337	#121	D₄×C₄₃	1	4	yes	—
338	C₄×D₄	—	4	2	no	—
339	C₄×D₄	—	4	4	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	—	4	2	no	—
358	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
362	#106	—	2	4	no	—
363	#103	—	2	4	no	—
364	#103	—	2	4	no	—
365	#103	—	4	2	no	—
366	#102	—	2	4	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	C₂⁴	—	2	1	no	—
373	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	complemented
403	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
409	C₂²×C₄	#41×C₄₃	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
411	SD₁₆	—	4	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	8	no	—
418	C₂×C₈	#41×C₄₃	1	4	yes	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	2	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	4	1	no	—
440	C₄²	—	4	1	no	—
441	C₄²	—	4	2	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	#121×C₄₃	1	2	yes	—
454	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
455	C₂³	#137×C₄₃	1	2	yes	—
456	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	4	8	no	—
463	D₄	—	4	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	8	4	no	—
495	C₂×C₄	#121×C₄₃	1	2	yes	—
496	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
497	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
498	C₂×C₄	#135×C₄₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
501	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
502	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
503	C₈	—	2	4	no	—
504	C₈	—	4	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	C₄₃×#461	1	4	yes	—
519	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
520	C₂²	C₄₃×#532	1	1	yes	characteristic
521	C₂²	C₄₃×#534	1	1	yes	characteristic
522	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
523	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
524	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
525	C₂²	C₄₃×#575	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	2	no	—
535	C₄	—	8	2	no	—
536	C₄	C₄₃×#546	1	2	yes	—
537	C₄	C₄₃×#553	1	2	yes	—
538	C₂	—	2	4	no	—
539	C₂	—	8	2	no	—
540	C₂	C₄₃×#2543	1	1	yes	characteristic
541	C₂	C₂×C₄₃×#461	1	1	yes	characteristic
542	C₂	C₄₃×#3035	1	1	yes	characteristic
543	C₂	C₄₃×#3167	1	1	yes	characteristic
544	C₂	C₄₃×#3181	1	1	yes	characteristic
545	C₂	C₄₃×#3187	1	1	yes	characteristic
546	C₂	C₄₃×#3190	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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×#2857	C₂	semidirect
4. C₄₃×#2084	C₂	semidirect
5. C₄₃×#2071	C₂	semidirect
6. C₄₃×#2043	C₂	semidirect
7. C₄₃×#2013	C₂	semidirect
8. C₄₃×#1927	C₂	semidirect
9. C₄₃×#1892	C₂	semidirect
10. C₄₃×#1877	C₂	semidirect
11. C₂×C₄₃×#336	C₂	semidirect
128. C₂²×C₄×C₄₃	SD₁₆	semidirect
231. #28571	C₄₃	direct (N × H)
266. #2857	C₂×C₄₃	semidirect
268. #2084	C₂×C₄₃	semidirect
269. #2071	C₂×C₄₃	semidirect
270. #2043	C₂×C₄₃	semidirect
271. #2013	C₂×C₄₃	semidirect
272. #1927	C₂×C₄₃	semidirect
273. #1892	C₂×C₄₃	semidirect
274. #1877	C₂×C₄₃	semidirect
275. C₂×#336	C₂×C₄₃	semidirect
317. C₄₃	#28571	direct (N × H)
402. C₂²×C₄	SD₁₆×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×#465	2
C₄₃×#2857	2
C₄×#121×C₄₃	2
C₄₃×#2084	2
C₄₃×#2071	2
C₄₃×#2043	2
C₄₃×#2013	2
C₄₃×#1927	2
C₄₃×#1892	2
C₄₃×#1877	2
C₂×C₄₃×#336	2
#28571	43

Subgroups — C43×#28571 #24948588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28571 #24948588