Subgroups — C₄₃×#29741 #24949758

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 546 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	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2615	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2077	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2034	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#465	—	2	4	no	—
21	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#106×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#408	—	2	4	no	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#395	—	2	1	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#394	—	2	1	no	—
33	C₄₃×#393	—	2	1	no	—
34	C₄₃×#392	—	2	2	no	—
35	C₄₃×#392	—	2	1	no	—
36	C₄₃×#380	C₂²	1	1	yes	characteristic
37	C₄₃×#380	C₂²	1	1	yes	characteristic
38	C₄₃×#380	C₂²	1	2	yes	—
39	C₄₃×#380	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	—	4	2	no	—
46	C₂×#41×C₄₃	—	4	2	no	—
47	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	—	2	2	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	D₄	1	2	yes	—
52	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₄₃	—	2	2	no	—
57	C₂×SD₁₆×C₄₃	—	4	2	no	—
58	C₂×M₁₆×C₄₃	—	2	2	no	—
59	C₂×M₁₆×C₄₃	—	4	2	no	—
60	C₂²×C₈×C₄₃	—	4	2	no	—
61	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
62	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
65	C₂²⋊Q₈×C₄₃	—	2	2	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	C₂²⋊Q₈×C₄₃	—	4	2	no	—
68	C₂²⋊Q₈×C₄₃	—	4	2	no	—
69	#121×C₄₃	—	2	2	no	—
70	#121×C₄₃	—	2	2	no	—
71	#121×C₄₃	—	4	2	no	—
72	#121×C₄₃	—	4	2	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
87	#106×C₄₃	—	2	2	no	—
88	#106×C₄₃	—	4	2	no	—
89	#103×C₄₃	—	2	2	no	—
90	#103×C₄₃	—	4	2	no	—
91	#102×C₄₃	—	2	2	no	—
92	#102×C₄₃	—	4	2	no	—
93	C₂²⋊C₈×C₄₃	—	2	4	no	—
94	C₂²⋊C₈×C₄₃	—	2	4	no	—
95	#95×C₄₃	—	2	2	no	—
96	#95×C₄₃	—	2	1	no	—
97	#95×C₄₃	—	2	2	no	—
98	#95×C₄₃	—	2	1	no	—
99	C₂⁴×C₄₃	—	2	1	no	—
100	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
101	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
102	#41×C₄₃	—	4	4	no	—
103	#41×C₄₃	—	4	4	no	—
104	#41×C₄₃	—	4	8	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	4	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	4	2	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	4	4	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	8	2	no	—
123	C₂×D₄×C₄₃	—	8	2	no	—
124	C₂×D₄×C₄₃	—	8	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	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	#41	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₄₃	—	4	4	no	—
144	M₁₆×C₄₃	—	4	4	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	—	2	2	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	4	4	no	—
151	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₄₃	—	2	1	no	—
154	C₄⋊C₄×C₄₃	—	2	1	no	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	1	no	—
157	C₄⋊C₄×C₄₃	—	2	2	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	4	4	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₂²⋊C₄×C₄₃	—	4	4	no	—
164	C₂²⋊C₄×C₄₃	—	4	4	no	—
165	C₂²⋊C₄×C₄₃	—	4	2	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₂²⋊C₄×C₄₃	—	8	1	no	—
168	C₂²⋊C₄×C₄₃	—	8	1	no	—
169	C₂²⋊C₄×C₄₃	—	8	2	no	—
170	C₂²⋊C₄×C₄₃	—	8	2	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	2	1	no	—
173	C₂³×C₄₃	—	2	1	no	—
174	C₂³×C₄₃	—	2	2	no	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	2	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	4	1	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	1	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	4	1	no	—
187	C₂³×C₄₃	#121	1	2	yes	—
188	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₄₃	—	4	4	no	—
190	Q₈×C₄₃	—	4	1	no	—
191	Q₈×C₄₃	—	4	1	no	—
192	Q₈×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	4	no	—
194	D₄×C₄₃	—	4	8	no	—
195	D₄×C₄₃	—	4	1	no	—
196	D₄×C₄₃	—	4	1	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	8	4	no	—
199	D₄×C₄₃	—	8	8	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	4	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	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	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	1	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	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	#121	1	2	yes	—
225	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
228	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
229	C₈×C₄₃	—	2	2	no	—
230	C₈×C₄₃	—	2	2	no	—
231	C₈×C₄₃	—	4	2	no	—
232	#29741	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	4	2	no	—
237	C₂²×C₄₃	—	4	2	no	—
238	C₂²×C₄₃	—	4	2	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	—	4	2	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	2	no	—
245	C₂²×C₄₃	—	8	1	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	—	8	2	no	—
248	C₂²×C₄₃	—	8	1	no	—
249	C₂²×C₄₃	—	8	1	no	—
250	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
251	C₂²×C₄₃	#534	1	2	yes	—
252	C₂²×C₄₃	#577	1	1	yes	characteristic
253	C₂²×C₄₃	#577	1	2	yes	—
254	C₂²×C₄₃	#577	1	1	yes	characteristic
255	C₄×C₄₃	—	2	2	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	8	1	no	—
258	C₄×C₄₃	—	8	2	no	—
259	C₄×C₄₃	—	8	2	no	—
260	C₄×C₄₃	—	8	1	no	—
261	C₄×C₄₃	—	8	1	no	—
262	C₄×C₄₃	#534	1	1	yes	characteristic
263	C₄×C₄₃	#535	1	1	yes	characteristic
264	C₄×C₄₃	#538	1	2	yes	—
265	C₂×#465	C₂×C₄₃	1	1	yes	characteristic, complemented
266	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
267	#2616	C₂×C₄₃	1	1	yes	characteristic, complemented
268	#2615	C₂×C₄₃	1	1	yes	characteristic
269	#2077	C₂×C₄₃	1	2	yes	complemented
270	#2035	C₂×C₄₃	1	2	yes	complemented
271	#2034	C₂×C₄₃	1	2	yes	complemented
272	#2000	C₂×C₄₃	1	2	yes	complemented
273	#1895	C₂×C₄₃	1	1	yes	characteristic, complemented
274	#1894	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#1807	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂×C₄₃	—	4	2	no	—
277	C₂×C₄₃	—	8	2	no	—
278	C₂×C₄₃	—	16	1	no	—
279	C₂×C₄₃	#2617	1	1	yes	characteristic
280	C₂×C₄₃	#3057	1	1	yes	characteristic
281	C₂×C₄₃	#3060	1	1	yes	characteristic
282	C₂×C₄₃	#3200	1	2	yes	—
283	C₂×C₄₃	#3204	1	2	yes	—
284	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
286	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
287	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
290	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
291	C₂×#121	C₂²×C₄₃	1	2	yes	—
292	#465	—	2	4	no	—
293	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#106	C₂²×C₄₃	1	2	yes	—
295	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#103	C₂²×C₄₃	1	2	yes	—
297	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₄₃	1	2	yes	—
299	#408	—	2	4	no	—
300	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
302	#395	—	2	1	no	—
303	#394	—	2	2	no	—
304	#394	—	2	1	no	—
305	#393	—	2	1	no	—
306	#392	—	2	2	no	—
307	#392	—	2	1	no	—
308	#380	C₂²×C₄₃	1	1	yes	characteristic
309	#380	C₂²×C₄₃	1	1	yes	characteristic
310	#380	C₂²×C₄₃	1	2	yes	—
311	#380	C₂²×C₄₃	1	2	yes	—
312	#340	C₂²×C₄₃	1	2	yes	—
313	#340	C₂²×C₄₃	1	2	yes	—
314	#340	C₂²×C₄₃	1	2	yes	—
315	C₄₃	#29741	1	1	yes	characteristic, direct product factor, Sylow
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	4	2	no	—
319	C₂×#41	—	4	2	no	—
320	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	D₄×C₄₃	1	2	yes	—
325	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
328	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	4	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	4	2	no	—
333	C₂²×C₈	—	4	2	no	—
334	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
335	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	4	2	no	—
341	C₂²⋊Q₈	—	4	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	4	2	no	—
345	#121	—	4	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	#106	—	2	2	no	—
361	#106	—	4	2	no	—
362	#103	—	2	2	no	—
363	#103	—	4	2	no	—
364	#102	—	2	2	no	—
365	#102	—	4	2	no	—
366	C₂²⋊C₈	—	2	4	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	#95	—	2	2	no	—
369	#95	—	2	1	no	—
370	#95	—	2	2	no	—
371	#95	—	2	1	no	—
372	C₂⁴	—	2	1	no	—
373	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
374	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	8	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	8	2	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	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	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
414	C₂²×C₄	#41×C₄₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
416	SD₁₆	—	4	4	no	—
417	M₁₆	—	4	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	4	4	no	—
424	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
425	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	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	—	4	4	no	—
435	C₄⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	8	1	no	—
441	C₂²⋊C₄	—	8	2	no	—
442	C₂²⋊C₄	—	8	1	no	—
443	C₂²⋊C₄	—	8	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	#121×C₄₃	1	2	yes	—
461	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
462	Q₈	—	4	4	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	2	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	8	no	—
468	D₄	—	4	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	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	1	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	1	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	2	yes	—
501	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	1	no	—
521	C₂²	—	8	1	no	—
522	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
523	C₂²	C₄₃×#534	1	2	yes	—
524	C₂²	C₄₃×#577	1	1	yes	characteristic
525	C₂²	C₄₃×#577	1	2	yes	—
526	C₂²	C₄₃×#577	1	1	yes	characteristic
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	2	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	C₄₃×#534	1	1	yes	characteristic
535	C₄	C₄₃×#535	1	1	yes	characteristic
536	C₄	C₄₃×#538	1	2	yes	—
537	C₂	—	4	2	no	—
538	C₂	—	8	2	no	—
539	C₂	—	16	1	no	—
540	C₂	C₄₃×#2617	1	1	yes	characteristic
541	C₂	C₄₃×#3057	1	1	yes	characteristic
542	C₂	C₄₃×#3060	1	1	yes	characteristic
543	C₂	C₄₃×#3200	1	2	yes	—
544	C₂	C₄₃×#3204	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2615	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#465	C₂	semidirect
2. C₂×C₄₃×#408	C₂	semidirect
3. C₄₃×#2616	C₂	semidirect
5. C₄₃×#2077	C₂	semidirect
6. C₄₃×#2035	C₂	semidirect
7. C₄₃×#2034	C₂	semidirect
8. C₄₃×#2000	C₂	semidirect
9. C₄₃×#1895	C₂	semidirect
10. C₄₃×#1894	C₂	semidirect
11. C₄₃×#1807	C₂	semidirect
61. C₂²×C₈×C₄₃	D₄	semidirect
232. #29741	C₄₃	direct (N × H)
265. C₂×#465	C₂×C₄₃	semidirect
266. C₂×#408	C₂×C₄₃	semidirect
267. #2616	C₂×C₄₃	semidirect
269. #2077	C₂×C₄₃	semidirect
270. #2035	C₂×C₄₃	semidirect
271. #2034	C₂×C₄₃	semidirect
272. #2000	C₂×C₄₃	semidirect
273. #1895	C₂×C₄₃	semidirect
274. #1894	C₂×C₄₃	semidirect
275. #1807	C₂×C₄₃	semidirect
315. C₄₃	#29741	direct (N × H)
334. 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×#465	2
C₂×C₄₃×#408	2
C₄₃×#2616	2
C₄₃×#2615	2
C₄₃×#2077	2
C₄₃×#2035	2
C₄₃×#2034	2
C₄₃×#2000	2
C₄₃×#1895	2
C₄₃×#1894	2
C₄₃×#1807	2
#29741	43

Subgroups — C43×#29741 #24949758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29741 #24949758