Subgroups — C₄₃×#28562 #24948579

Order 11008.

976 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	C₂×C₄₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2414	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1936	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1875	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	C₂²	1	2	yes	—
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#466	—	2	4	no	—
20	C₄₃×#435	—	2	4	no	—
21	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
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	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#394	—	2	2	no	—
30	C₄₃×#392	—	2	2	no	—
31	C₄₃×#390	—	2	2	no	—
32	C₄₃×#390	C₂²	1	2	yes	—
33	C₄₃×#389	C₂²	1	2	yes	—
34	C₄₃×#388	—	2	2	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₄₃	—	2	2	no	—
48	C₂×D₈×C₄₃	—	4	2	no	—
49	C₂×M₁₆×C₄₃	—	2	2	no	—
50	C₂×M₁₆×C₄₃	—	4	2	no	—
51	C₂²×C₈×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
53	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
57	#121×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	4	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	4	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	4	no	—
64	#117×C₄₃	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#107×C₄₃	—	2	2	no	—
81	C₄⋊C₈×C₄₃	—	2	2	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	4	2	no	—
85	C₂²⋊C₈×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	#97×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	—	4	4	no	—
102	C₂×D₄×C₄₃	—	4	4	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	8	2	no	—
105	C₂×D₄×C₄₃	—	8	2	no	—
106	C₂×D₄×C₄₃	—	8	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	D₈×C₄₃	—	4	4	no	—
124	M₁₆×C₄₃	—	4	4	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	4	4	no	—
132	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	8	2	no	—
141	C₄⋊C₄×C₄₃	#41	1	4	yes	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	4	no	—
145	C₂²⋊C₄×C₄₃	—	4	4	no	—
146	C₂²⋊C₄×C₄₃	—	4	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	4	no	—
148	C₂²⋊C₄×C₄₃	—	8	2	no	—
149	C₂²⋊C₄×C₄₃	—	8	2	no	—
150	C₄²×C₄₃	—	2	1	no	—
151	C₄²×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	—	4	4	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	—	4	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	#121	1	2	yes	—
170	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	D₄×C₄₃	—	4	4	no	—
172	D₄×C₄₃	—	4	2	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	8	8	no	—
177	D₄×C₄₃	—	8	8	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	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	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	#121	1	2	yes	—
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
204	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₄₃	—	2	2	no	—
207	C₈×C₄₃	—	2	2	no	—
208	C₈×C₄₃	—	4	1	no	—
209	C₈×C₄₃	—	4	1	no	—
210	#28562	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	1	no	—
218	C₂²×C₄₃	—	4	1	no	—
219	C₂²×C₄₃	—	4	1	no	—
220	C₂²×C₄₃	—	4	2	no	—
221	C₂²×C₄₃	—	8	2	no	—
222	C₂²×C₄₃	—	8	2	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	2	no	—
228	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
229	C₂²×C₄₃	#546	1	2	yes	—
230	C₂²×C₄₃	#575	1	2	yes	—
231	C₂²×C₄₃	#576	1	1	yes	characteristic
232	C₂²×C₄₃	#576	1	1	yes	characteristic
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	4	1	no	—
235	C₄×C₄₃	—	4	1	no	—
236	C₄×C₄₃	—	4	1	no	—
237	C₄×C₄₃	—	4	4	no	—
238	C₄×C₄₃	—	8	2	no	—
239	C₄×C₄₃	—	8	2	no	—
240	C₄×C₄₃	#532	1	1	yes	characteristic
241	C₄×C₄₃	#534	1	1	yes	characteristic
242	C₄×C₄₃	#553	1	2	yes	—
243	C₂×#466	C₂×C₄₃	1	1	yes	characteristic, complemented
244	C₂×#435	C₂×C₄₃	1	1	yes	characteristic, complemented
245	#2414	C₂×C₄₃	1	2	yes	complemented
246	#2086	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#2075	C₂×C₄₃	1	1	yes	characteristic, complemented
248	#2054	C₂×C₄₃	1	1	yes	characteristic, complemented
249	#1999	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#1936	C₂×C₄₃	1	2	yes	complemented
251	#1895	C₂×C₄₃	1	2	yes	complemented
252	#1875	C₂×C₄₃	1	2	yes	complemented
253	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
254	C₂×C₄₃	—	4	2	no	—
255	C₂×C₄₃	—	8	1	no	—
256	C₂×C₄₃	—	16	2	no	—
257	C₂×C₄₃	#2543	1	1	yes	characteristic
258	C₂×C₄₃	#3054	1	1	yes	characteristic
259	C₂×C₄₃	#3058	1	1	yes	characteristic
260	C₂×C₄₃	#3309	1	2	yes	—
261	C₂×C₄₃	#3319	1	2	yes	—
262	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
264	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
265	C₂×#121	C₂²×C₄₃	1	2	yes	—
266	C₂×#121	C₂²×C₄₃	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#117	C₂²×C₄₃	1	2	yes	—
269	#466	—	2	4	no	—
270	#435	—	2	4	no	—
271	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×#102	C₂²×C₄₃	1	2	yes	—
274	C₂×#102	C₂²×C₄₃	1	2	yes	—
275	C₂×#102	C₂²×C₄₃	1	2	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
278	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
279	#394	—	2	2	no	—
280	#392	—	2	2	no	—
281	#390	—	2	2	no	—
282	#390	C₂²×C₄₃	1	2	yes	—
283	#389	C₂²×C₄₃	1	2	yes	—
284	#388	—	2	2	no	—
285	#380	C₂²×C₄₃	1	2	yes	—
286	#340	C₂²×C₄₃	1	1	yes	characteristic
287	#340	C₂²×C₄₃	1	2	yes	—
288	#340	C₂²×C₄₃	1	2	yes	—
289	#340	C₂²×C₄₃	1	1	yes	characteristic
290	#340	C₂²×C₄₃	1	2	yes	—
291	C₄₃	#28562	1	1	yes	characteristic, direct product factor, Sylow
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
296	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
298	C₂×D₈	—	2	2	no	—
299	C₂×D₈	—	4	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	4	2	no	—
302	C₂²×C₈	—	4	2	no	—
303	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
304	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
308	#121	—	2	4	no	—
309	#121	—	2	4	no	—
310	#121	—	2	4	no	—
311	#121	—	4	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	#117	—	2	4	no	—
315	#117	—	4	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	4	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	#97	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
343	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂×D₄	—	8	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
372	C₂²×C₄	#41×C₄₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
374	D₈	—	4	4	no	—
375	M₁₆	—	4	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
384	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	8	2	no	—
392	C₄⋊C₄	#41×C₄₃	1	4	yes	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	8	2	no	—
400	C₂²⋊C₄	—	8	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	4	4	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	#121×C₄₃	1	2	yes	—
421	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
422	D₄	—	4	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	8	no	—
428	D₄	—	8	8	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	#121×C₄₃	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
455	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
479	C₂²	C₄₃×#546	1	2	yes	—
480	C₂²	C₄₃×#575	1	2	yes	—
481	C₂²	C₄₃×#576	1	1	yes	characteristic
482	C₂²	C₄₃×#576	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	4	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	2	no	—
490	C₄	C₄₃×#532	1	1	yes	characteristic
491	C₄	C₄₃×#534	1	1	yes	characteristic
492	C₄	C₄₃×#553	1	2	yes	—
493	C₂	—	4	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	16	2	no	—
496	C₂	C₄₃×#2543	1	1	yes	characteristic
497	C₂	C₄₃×#3054	1	1	yes	characteristic
498	C₂	C₄₃×#3058	1	1	yes	characteristic
499	C₂	C₄₃×#3309	1	2	yes	—
500	C₂	C₄₃×#3319	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×C₄×D₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#466	C₂	semidirect
2. C₂×C₄₃×#435	C₂	semidirect
3. C₄₃×#2414	C₂	semidirect
4. C₄₃×#2086	C₂	semidirect
5. C₄₃×#2075	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1999	C₂	semidirect
8. C₄₃×#1936	C₂	semidirect
9. C₄₃×#1895	C₂	semidirect
10. C₄₃×#1875	C₂	semidirect
11. C₄₃×#1735	C₂	semidirect
52. C₂²×C₈×C₄₃	D₄	semidirect
210. #28562	C₄₃	direct (N × H)
243. C₂×#466	C₂×C₄₃	semidirect
244. C₂×#435	C₂×C₄₃	semidirect
245. #2414	C₂×C₄₃	semidirect
246. #2086	C₂×C₄₃	semidirect
247. #2075	C₂×C₄₃	semidirect
248. #2054	C₂×C₄₃	semidirect
249. #1999	C₂×C₄₃	semidirect
250. #1936	C₂×C₄₃	semidirect
251. #1895	C₂×C₄₃	semidirect
252. #1875	C₂×C₄₃	semidirect
253. #1735	C₂×C₄₃	semidirect
291. C₄₃	#28562	direct (N × H)
303. C₂²×C₈	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×#466	2
C₂×C₄₃×#435	2
C₄₃×#2414	2
C₄₃×#2086	2
C₄₃×#2075	2
C₄₃×#2054	2
C₄₃×#1999	2
C₄₃×#1936	2
C₄₃×#1895	2
C₄₃×#1875	2
C₄₃×#1735	2
#28562	43

Subgroups — C43×#28562 #24948579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28562 #24948579