Subgroups — C₄₃×#29197 #24949214

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2065	C₂	1	2	yes	maximal
5	C₄₃×#1959	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1959	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1865	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1862	C₂	1	2	yes	maximal
9	C₄₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₄₃	—	2	1	no	—
13	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#107×C₄₃	C₂²	1	2	yes	—
17	C₂×#106×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂×#103×C₄₃	C₂²	1	2	yes	—
20	C₂×#103×C₄₃	C₂²	1	2	yes	—
21	C₂×#102×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#391	C₂²	1	1	yes	characteristic
26	C₄₃×#390	C₂²	1	1	yes	characteristic
27	C₄₃×#389	—	2	1	no	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	C₂²	1	2	yes	—
30	C₄₃×#389	C₂²	1	2	yes	—
31	C₄₃×#388	—	2	1	no	—
32	C₄₃×#388	—	2	1	no	—
33	C₄₃×#384	C₂²	1	1	yes	characteristic
34	C₄₃×#384	C₂²	1	1	yes	characteristic
35	C₄₃×#382	—	2	1	no	—
36	C₄₃×#382	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄³×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
48	#125×C₄₃	—	4	4	no	—
49	#124×C₄₃	—	2	2	no	—
50	#124×C₄₃	Q₈	1	4	yes	—
51	C₄×Q₈×C₄₃	—	4	2	no	—
52	C₄×D₄×C₄₃	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄²×C₄₃	—	2	1	no	—
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#107×C₄₃	—	4	2	no	—
78	#106×C₄₃	—	4	2	no	—
79	C₄⋊C₈×C₄₃	—	2	4	no	—
80	#103×C₄₃	—	2	4	no	—
81	#103×C₄₃	—	4	2	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	4	2	no	—
84	#97×C₄₃	—	2	2	no	—
85	#97×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	1	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	—	2	1	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	#41	1	4	yes	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	4	2	no	—
130	C₄⋊C₄×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	—	4	4	no	—
134	C₄⋊C₄×C₄₃	—	4	4	no	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₂²⋊C₄×C₄₃	—	2	4	no	—
137	C₂²⋊C₄×C₄₃	—	4	2	no	—
138	C₂²⋊C₄×C₄₃	—	4	2	no	—
139	C₂²⋊C₄×C₄₃	—	4	2	no	—
140	C₄²×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	2	2	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	—	4	1	no	—
145	C₄²×C₄₃	—	4	1	no	—
146	C₄²×C₄₃	—	4	2	no	—
147	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
148	C₄²×C₄₃	#41	1	2	yes	—
149	C₂³×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	—	4	1	no	—
154	C₂³×C₄₃	—	4	1	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₄₃	—	2	4	no	—
158	Q₈×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	2	4	no	—
160	D₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	1	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	1	no	—
190	C₂×C₄×C₄₃	—	8	4	no	—
191	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₄₃	#137	1	2	yes	—
195	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₄₃	—	2	4	no	—
200	C₈×C₄₃	—	4	2	no	—
201	#29197	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	8	1	no	—
206	C₂²×C₄₃	—	8	1	no	—
207	C₂²×C₄₃	—	8	1	no	—
208	C₂²×C₄₃	—	8	1	no	—
209	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₂²×C₄₃	#532	1	1	yes	characteristic
211	C₂²×C₄₃	#535	1	1	yes	characteristic
212	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
214	C₂²×C₄₃	#575	1	1	yes	characteristic
215	C₂²×C₄₃	#575	1	1	yes	characteristic
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	4	1	no	—
222	C₄×C₄₃	—	4	1	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	—	8	2	no	—
225	C₄×C₄₃	—	8	1	no	—
226	C₄×C₄₃	—	8	1	no	—
227	C₄×C₄₃	#553	1	2	yes	—
228	C₄×C₄₃	#554	1	2	yes	—
229	#2859	C₂×C₄₃	1	1	yes	characteristic, complemented
230	C₄×#124	C₂×C₄₃	1	1	yes	characteristic
231	#2068	C₂×C₄₃	1	2	yes	complemented
232	#2065	C₂×C₄₃	1	2	yes	—
233	#1959	C₂×C₄₃	1	1	yes	characteristic
234	#1959	C₂×C₄₃	1	1	yes	characteristic
235	#1865	C₂×C₄₃	1	2	yes	complemented
236	#1862	C₂×C₄₃	1	2	yes	—
237	#1847	C₂×C₄₃	1	1	yes	characteristic, complemented
238	#1836	C₂×C₄₃	1	1	yes	characteristic, complemented
239	#1767	C₂×C₄₃	1	1	yes	characteristic, complemented
240	C₂×C₄₃	—	8	2	no	—
241	C₂×C₄₃	#2566	1	1	yes	characteristic
242	C₂×C₄₃	#3079	1	1	yes	characteristic
243	C₂×C₄₃	#3080	1	1	yes	characteristic
244	C₂×C₄₃	#3171	1	1	yes	characteristic
245	C₂×C₄₃	#3181	1	1	yes	characteristic
246	C₂×C₄₃	#3213	1	1	yes	characteristic
247	C₂×C₄₃	#3216	1	1	yes	characteristic
248	C₂×#125	—	2	1	no	—
249	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#107	C₂²×C₄₃	1	2	yes	—
253	C₂×#106	C₂²×C₄₃	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
255	C₂×#103	C₂²×C₄₃	1	2	yes	—
256	C₂×#103	C₂²×C₄₃	1	2	yes	—
257	C₂×#102	C₂²×C₄₃	1	2	yes	—
258	C₂×#102	C₂²×C₄₃	1	2	yes	—
259	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
261	#391	C₂²×C₄₃	1	1	yes	characteristic
262	#390	C₂²×C₄₃	1	1	yes	characteristic
263	#389	—	2	1	no	—
264	#389	—	2	1	no	—
265	#389	C₂²×C₄₃	1	2	yes	—
266	#389	C₂²×C₄₃	1	2	yes	—
267	#388	—	2	1	no	—
268	#388	—	2	1	no	—
269	#384	C₂²×C₄₃	1	1	yes	characteristic
270	#384	C₂²×C₄₃	1	1	yes	characteristic
271	#382	—	2	1	no	—
272	#382	C₂²×C₄₃	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	—	2	1	no	—
274	C₄×C₂²⋊C₄	—	2	1	no	—
275	C₄³	C₂²×C₄₃	1	1	yes	characteristic
276	#340	C₂²×C₄₃	1	2	yes	—
277	#340	C₂²×C₄₃	1	2	yes	—
278	#336	C₂²×C₄₃	1	2	yes	—
279	C₄₃	#29197	1	1	yes	characteristic, direct product factor, Sylow
280	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
281	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
284	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
285	#125	—	4	4	no	—
286	#124	—	2	2	no	—
287	#124	Q₈×C₄₃	1	4	yes	—
288	C₄×Q₈	—	4	2	no	—
289	C₄×D₄	—	4	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
309	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
310	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
314	#107	—	4	2	no	—
315	#106	—	4	2	no	—
316	C₄⋊C₈	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	—	4	2	no	—
319	#102	—	2	4	no	—
320	#102	—	4	2	no	—
321	#97	—	2	2	no	—
322	#97	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	#41×C₄₃	1	4	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂×Q₈×C₄₃	1	2	yes	—
385	C₄²	#41×C₄₃	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
394	Q₈	—	2	4	no	—
395	Q₈	—	4	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
429	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
430	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
431	C₂×C₄	#137×C₄₃	1	2	yes	—
432	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
435	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
436	C₈	—	2	4	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
446	C₂²	C₄₃×#532	1	1	yes	characteristic
447	C₂²	C₄₃×#535	1	1	yes	characteristic
448	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
449	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
450	C₂²	C₄₃×#575	1	1	yes	characteristic
451	C₂²	C₄₃×#575	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	C₄₃×#553	1	2	yes	—
464	C₄	C₄₃×#554	1	2	yes	—
465	C₂	—	8	2	no	—
466	C₂	C₄₃×#2566	1	1	yes	characteristic
467	C₂	C₄₃×#3079	1	1	yes	characteristic
468	C₂	C₄₃×#3080	1	1	yes	characteristic
469	C₂	C₄₃×#3171	1	1	yes	characteristic
470	C₂	C₄₃×#3181	1	1	yes	characteristic
471	C₂	C₄₃×#3213	1	1	yes	characteristic
472	C₂	C₄₃×#3216	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₃×#2859	C₂	semidirect
3. C₄₃×#2068	C₂	semidirect
7. C₄₃×#1865	C₂	semidirect
9. C₄₃×#1847	C₂	semidirect
10. C₄₃×#1836	C₂	semidirect
11. C₄₃×#1767	C₂	semidirect
201. #29197	C₄₃	direct (N × H)
229. #2859	C₂×C₄₃	semidirect
231. #2068	C₂×C₄₃	semidirect
235. #1865	C₂×C₄₃	semidirect
237. #1847	C₂×C₄₃	semidirect
238. #1836	C₂×C₄₃	semidirect
239. #1767	C₂×C₄₃	semidirect
279. C₄₃	#29197	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2859	2
C₄×#124×C₄₃	2
C₄₃×#2068	2
C₄₃×#2065	2
C₄₃×#1959	2
C₄₃×#1865	2
C₄₃×#1862	2
C₄₃×#1847	2
C₄₃×#1836	2
C₄₃×#1767	2
#29197	43

Subgroups — C43×#29197 #24949214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29197 #24949214