Subgroups — C₄₃×#29834 #24949851

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2641	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1843	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
13	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#478	—	2	4	no	—
17	C₄₃×#459	—	2	4	no	—
18	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#394	—	2	1	no	—
30	C₄₃×#394	—	2	1	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#390	C₂²	1	2	yes	—
33	C₄₃×#390	C₂²	1	2	yes	—
34	C₄₃×#390	C₂²	1	2	yes	—
35	C₄₃×#389	C₂²	1	2	yes	—
36	C₄₃×#388	—	2	2	no	—
37	C₄₃×#381	—	2	1	no	—
38	C₄₃×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#376	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂×D₈×C₄₃	—	2	4	no	—
49	C₂×D₈×C₄₃	—	4	2	no	—
50	C₂×D₈×C₄₃	—	4	2	no	—
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	#127×C₄₃	—	2	2	no	—
55	#127×C₄₃	—	2	2	no	—
56	#125×C₄₃	—	2	2	no	—
57	#125×C₄₃	—	2	2	no	—
58	C₄×D₄×C₄₃	—	2	2	no	—
59	C₄×D₄×C₄₃	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
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×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#107×C₄₃	—	2	2	no	—
78	#106×C₄₃	—	2	2	no	—
79	C₄⋊C₈×C₄₃	—	2	2	no	—
80	C₄⋊C₈×C₄₃	—	2	2	no	—
81	C₄⋊C₈×C₄₃	—	4	2	no	—
82	C₄⋊C₈×C₄₃	—	4	2	no	—
83	#102×C₄₃	—	2	2	no	—
84	#102×C₄₃	—	2	2	no	—
85	#102×C₄₃	—	2	4	no	—
86	#102×C₄₃	—	4	2	no	—
87	#102×C₄₃	—	4	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	D₄	1	1	yes	characteristic
91	#95×C₄₃	D₄	1	1	yes	characteristic
92	#95×C₄₃	D₄	1	2	yes	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	1	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	—	2	2	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	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	—	8	1	no	—
107	C₂×D₄×C₄₃	—	8	2	no	—
108	C₂×D₄×C₄₃	—	8	1	no	—
109	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	1	no	—
115	C₂²×C₄×C₄₃	—	8	2	no	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
121	D₈×C₄₃	—	4	8	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	4	2	no	—
137	C₄⋊C₄×C₄₃	—	4	2	no	—
138	C₄⋊C₄×C₄₃	—	8	2	no	—
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	4	no	—
141	C₂²⋊C₄×C₄₃	—	8	2	no	—
142	C₂²⋊C₄×C₄₃	—	8	2	no	—
143	C₂²⋊C₄×C₄₃	—	8	2	no	—
144	C₂²⋊C₄×C₄₃	—	8	2	no	—
145	C₂²⋊C₄×C₄₃	—	8	2	no	—
146	C₂²⋊C₄×C₄₃	—	8	2	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	8	1	no	—
150	C₄²×C₄₃	C₂×D₄	1	2	yes	—
151	C₄²×C₄₃	#41	1	2	yes	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	4	1	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	1	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	D₄×C₄₃	—	2	2	no	—
166	D₄×C₄₃	—	2	2	no	—
167	D₄×C₄₃	—	4	2	no	—
168	D₄×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	8	4	no	—
173	D₄×C₄₃	—	8	4	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	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	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	8	4	no	—
194	C₂×C₄×C₄₃	#121	1	2	yes	—
195	C₂×C₄×C₄₃	#121	1	2	yes	—
196	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₄₃	—	4	1	no	—
201	C₈×C₄₃	—	4	1	no	—
202	C₈×C₄₃	—	4	2	no	—
203	#29834	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	8	2	no	—
208	C₂²×C₄₃	—	8	2	no	—
209	C₂²×C₄₃	—	8	2	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	—	8	2	no	—
215	C₂²×C₄₃	—	8	2	no	—
216	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₃	#537	1	2	yes	—
218	C₂²×C₄₃	#576	1	2	yes	—
219	C₂²×C₄₃	#576	1	1	yes	characteristic
220	C₂²×C₄₃	#577	1	1	yes	characteristic
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	8	2	no	—
227	C₄×C₄₃	—	8	1	no	—
228	C₄×C₄₃	—	8	1	no	—
229	C₄×C₄₃	#535	1	1	yes	characteristic
230	C₄×C₄₃	#536	1	1	yes	characteristic
231	C₄×C₄₃	#542	1	2	yes	—
232	C₂×#478	C₂×C₄₃	1	1	yes	characteristic, complemented
233	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
234	#2641	C₂×C₄₃	1	1	yes	characteristic, complemented
235	#2319	C₂×C₄₃	1	1	yes	characteristic, complemented
236	#2067	C₂×C₄₃	1	2	yes	complemented
237	#2065	C₂×C₄₃	1	2	yes	complemented
238	#2054	C₂×C₄₃	1	2	yes	complemented
239	#2054	C₂×C₄₃	1	2	yes	complemented
240	#1989	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#1843	C₂×C₄₃	1	1	yes	characteristic, complemented
243	C₂×C₄₃	—	8	2	no	—
244	C₂×C₄₃	—	16	2	no	—
245	C₂×C₄₃	#2620	1	1	yes	characteristic
246	C₂×C₄₃	#3041	1	1	yes	characteristic
247	C₂×C₄₃	#3045	1	1	yes	characteristic
248	C₂×C₄₃	#3257	1	2	yes	—
249	C₂×C₄₃	#3259	1	2	yes	—
250	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
251	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
254	#478	—	2	4	no	—
255	#459	—	2	4	no	—
256	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
257	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
261	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
262	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
263	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
264	C₂×#102	C₂²×C₄₃	1	2	yes	—
265	C₂×#102	C₂²×C₄₃	1	2	yes	—
266	C₂×#102	C₂²×C₄₃	1	2	yes	—
267	#394	—	2	1	no	—
268	#394	—	2	1	no	—
269	#394	—	2	2	no	—
270	#390	C₂²×C₄₃	1	2	yes	—
271	#390	C₂²×C₄₃	1	2	yes	—
272	#390	C₂²×C₄₃	1	2	yes	—
273	#389	C₂²×C₄₃	1	2	yes	—
274	#388	—	2	2	no	—
275	#381	—	2	1	no	—
276	#380	—	2	1	no	—
277	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
278	#376	C₂²×C₄₃	1	1	yes	characteristic
279	#340	C₂²×C₄₃	1	2	yes	—
280	#340	C₂²×C₄₃	1	2	yes	—
281	C₄₃	#29834	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
285	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×D₈	—	2	4	no	—
288	C₂×D₈	—	4	2	no	—
289	C₂×D₈	—	4	2	no	—
290	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
293	#127	—	2	2	no	—
294	#127	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	D₄×C₄₃	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
316	#107	—	2	2	no	—
317	#106	—	2	2	no	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₄⋊C₈	—	4	2	no	—
321	C₄⋊C₈	—	4	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	4	no	—
325	#102	—	4	2	no	—
326	#102	—	4	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₄₃	1	1	yes	characteristic
330	#95	D₄×C₄₃	1	1	yes	characteristic
331	#95	D₄×C₄₃	1	2	yes	—
332	C₂⁴	—	2	1	no	—
333	C₂⁴	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	8	1	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	1	no	—
348	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
360	D₈	—	4	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₂²⋊C₄	—	8	2	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	8	1	no	—
389	C₄²	C₂×D₄×C₄₃	1	2	yes	—
390	C₄²	#41×C₄₃	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	#121×C₄₃	1	2	yes	—
434	C₂×C₄	#121×C₄₃	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
438	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
439	C₈	—	4	2	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
455	C₂²	C₄₃×#537	1	2	yes	—
456	C₂²	C₄₃×#576	1	2	yes	—
457	C₂²	C₄₃×#576	1	1	yes	characteristic
458	C₂²	C₄₃×#577	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	C₄₃×#535	1	1	yes	characteristic
468	C₄	C₄₃×#536	1	1	yes	characteristic
469	C₄	C₄₃×#542	1	2	yes	—
470	C₂	—	8	2	no	—
471	C₂	—	16	2	no	—
472	C₂	C₄₃×#2620	1	1	yes	characteristic
473	C₂	C₄₃×#3041	1	1	yes	characteristic
474	C₂	C₄₃×#3045	1	1	yes	characteristic
475	C₂	C₄₃×#3257	1	2	yes	—
476	C₂	C₄₃×#3259	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#478	C₂	semidirect
3. C₄₃×#2641	C₂	semidirect
4. C₄₃×#2319	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2065	C₂	semidirect
7. C₄₃×#2054	C₂	semidirect
8. C₄₃×#2054	C₂	semidirect
9. C₄₃×#1989	C₂	semidirect
10. C₄₃×#1982	C₂	semidirect
11. C₄₃×#1843	C₂	semidirect
203. #29834	C₄₃	direct (N × H)
232. C₂×#478	C₂×C₄₃	semidirect
234. #2641	C₂×C₄₃	semidirect
235. #2319	C₂×C₄₃	semidirect
236. #2067	C₂×C₄₃	semidirect
237. #2065	C₂×C₄₃	semidirect
238. #2054	C₂×C₄₃	semidirect
239. #2054	C₂×C₄₃	semidirect
240. #1989	C₂×C₄₃	semidirect
241. #1982	C₂×C₄₃	semidirect
242. #1843	C₂×C₄₃	semidirect
281. C₄₃	#29834	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#478	2
C₂×C₄₃×#459	2
C₄₃×#2641	2
C₄₃×#2319	2
C₄₃×#2067	2
C₄₃×#2065	2
C₄₃×#2054	2
C₄₃×#1989	2
C₄₃×#1982	2
C₄₃×#1843	2
#29834	43

Subgroups — C43×#29834 #24949851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29834 #24949851