Subgroups — C₄₃×#17065 #24937082

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#387	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1445	C₂	1	2	yes	maximal
4	C₄₃×#1445	C₂	1	2	yes	maximal
5	C₄₃×#1442	C₂	1	2	yes	maximal
6	C₄₃×#1442	C₂	1	2	yes	maximal
7	C₄₃×#1441	C₂	1	2	yes	maximal
8	C₄₃×#1441	C₂	1	2	yes	maximal
9	C₄₃×#1434	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#387	—	2	4	no	—
17	C₄₃×#384	—	2	4	no	—
18	C₂×#95×C₄₃	C₂²	1	2	yes	—
19	C₂×#95×C₄₃	C₂²	1	2	yes	—
20	C₂×#95×C₄₃	C₂²	1	2	yes	—
21	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	4	yes	—
26	C₂×#95×C₄₃	C₂²	1	4	yes	—
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	4	yes	—
29	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
48	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
49	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	—
50	C₂×C₄²×C₄₃	—	2	4	no	—
51	C₂×C₄²×C₄₃	D₄	1	4	yes	—
52	#95×C₄₃	—	2	2	no	—
53	#95×C₄₃	—	2	2	no	—
54	#95×C₄₃	—	2	2	no	—
55	#95×C₄₃	—	2	2	no	—
56	#95×C₄₃	—	2	4	no	—
57	#95×C₄₃	—	2	4	no	—
58	#95×C₄₃	—	2	4	no	—
59	#95×C₄₃	—	4	4	no	—
60	#95×C₄₃	—	4	4	no	—
61	#95×C₄₃	—	4	4	no	—
62	#95×C₄₃	—	4	4	no	—
63	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	—	2	1	no	—
65	C₂²×C₄×C₄₃	—	2	1	no	—
66	C₂²×C₄×C₄₃	—	2	1	no	—
67	C₂²×C₄×C₄₃	—	2	1	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	4	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₄₃	#41	1	2	yes	—
107	C₂²×C₄×C₄₃	#41	1	4	yes	—
108	C₂²×C₄×C₄₃	#41	1	4	yes	—
109	C₄⋊C₄×C₄₃	—	2	8	no	—
110	C₄⋊C₄×C₄₃	—	4	8	no	—
111	C₄⋊C₄×C₄₃	—	4	8	no	—
112	C₄⋊C₄×C₄₃	—	4	4	no	—
113	C₄⋊C₄×C₄₃	—	4	8	no	—
114	C₄²×C₄₃	—	2	8	no	—
115	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
116	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
117	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
118	C₂³×C₄₃	C₂×#41	1	2	yes	—
119	C₂³×C₄₃	C₂×#41	1	2	yes	—
120	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
121	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
122	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
123	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	2	no	—
128	C₂×C₄×C₄₃	—	2	2	no	—
129	C₂×C₄×C₄₃	—	2	2	no	—
130	C₂×C₄×C₄₃	—	2	8	no	—
131	C₂×C₄×C₄₃	—	2	8	no	—
132	C₂×C₄×C₄₃	—	2	4	no	—
133	C₂×C₄×C₄₃	—	2	4	no	—
134	C₂×C₄×C₄₃	—	2	2	no	—
135	C₂×C₄×C₄₃	—	2	2	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	4	1	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	—	4	4	no	—
147	C₂×C₄×C₄₃	—	4	4	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	4	no	—
154	C₂×C₄×C₄₃	—	4	4	no	—
155	C₂×C₄×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
167	C₂×C₄×C₄₃	#123	1	4	yes	—
168	C₂×C₄×C₄₃	#124	1	4	yes	—
169	#17065	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
172	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₃	#535	1	1	yes	characteristic
174	C₂²×C₄₃	#535	1	1	yes	characteristic
175	C₂²×C₄₃	#536	1	1	yes	characteristic
176	C₂²×C₄₃	#536	1	1	yes	characteristic
177	C₂²×C₄₃	#539	1	4	yes	—
178	C₂²×C₄₃	#540	1	4	yes	—
179	C₂²×C₄₃	#542	1	2	yes	—
180	C₂²×C₄₃	#544	1	2	yes	—
181	C₂²×C₄₃	#552	1	4	yes	—
182	C₂²×C₄₃	#553	1	2	yes	—
183	C₂²×C₄₃	#554	1	2	yes	—
184	C₂²×C₄₃	#556	1	2	yes	—
185	C₂²×C₄₃	#557	1	2	yes	—
186	C₂²×C₄₃	#563	1	4	yes	—
187	C₄×C₄₃	—	2	4	no	—
188	C₄×C₄₃	—	2	4	no	—
189	C₄×C₄₃	—	2	4	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	—	4	2	no	—
192	C₄×C₄₃	—	8	1	no	—
193	C₄×C₄₃	—	8	1	no	—
194	C₄×C₄₃	—	8	4	no	—
195	C₄×C₄₃	—	8	4	no	—
196	C₂×#387	C₂×C₄₃	1	1	yes	characteristic
197	C₂×#384	C₂×C₄₃	1	1	yes	characteristic
198	#1445	C₂×C₄₃	1	2	yes	—
199	#1445	C₂×C₄₃	1	2	yes	—
200	#1442	C₂×C₄₃	1	2	yes	—
201	#1442	C₂×C₄₃	1	2	yes	—
202	#1441	C₂×C₄₃	1	2	yes	—
203	#1441	C₂×C₄₃	1	2	yes	—
204	#1434	C₂×C₄₃	1	1	yes	characteristic
205	C₂×C₄₃	#2487	1	1	yes	characteristic
206	C₂×C₄₃	#2503	1	1	yes	characteristic
207	C₂×C₄₃	#2568	1	1	yes	characteristic
208	C₂×C₄₃	#2623	1	1	yes	characteristic
209	C₂×C₄₃	#2628	1	1	yes	characteristic
210	C₂×C₄₃	#2641	1	1	yes	characteristic
211	C₂×C₄₃	#2791	1	4	yes	—
212	C₂×C₄₃	#2793	1	4	yes	—
213	C₂×C₄₃	#2821	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
219	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
220	#387	—	2	4	no	—
221	#384	—	2	4	no	—
222	C₂×#95	C₂²×C₄₃	1	2	yes	—
223	C₂×#95	C₂²×C₄₃	1	2	yes	—
224	C₂×#95	C₂²×C₄₃	1	2	yes	—
225	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
226	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
227	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
228	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×#95	C₂²×C₄₃	1	4	yes	—
230	C₂×#95	C₂²×C₄₃	1	4	yes	—
231	C₂×#95	C₂²×C₄₃	1	4	yes	—
232	C₂×#95	C₂²×C₄₃	1	4	yes	—
233	C₄₃	#17065	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
235	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
238	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	4	4	no	—
253	C₂×C₄⋊C₄	—	4	4	no	—
254	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	D₄×C₄₃	1	4	yes	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	4	no	—
262	#95	—	2	4	no	—
263	#95	—	2	4	no	—
264	#95	—	4	4	no	—
265	#95	—	4	4	no	—
266	#95	—	4	4	no	—
267	#95	—	4	4	no	—
268	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
308	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
309	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
311	C₂²×C₄	#41×C₄₃	1	2	yes	—
312	C₂²×C₄	#41×C₄₃	1	4	yes	—
313	C₂²×C₄	#41×C₄₃	1	4	yes	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	4	8	no	—
316	C₄⋊C₄	—	4	8	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	8	no	—
319	C₄²	—	2	8	no	—
320	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
321	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
322	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
323	C₂³	C₂×#41×C₄₃	1	2	yes	—
324	C₂³	C₂×#41×C₄₃	1	2	yes	—
325	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
326	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
327	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
328	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
372	C₂×C₄	#123×C₄₃	1	4	yes	—
373	C₂×C₄	#124×C₄₃	1	4	yes	—
374	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
375	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
376	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
377	C₂²	C₄₃×#535	1	1	yes	characteristic
378	C₂²	C₄₃×#535	1	1	yes	characteristic
379	C₂²	C₄₃×#536	1	1	yes	characteristic
380	C₂²	C₄₃×#536	1	1	yes	characteristic
381	C₂²	C₄₃×#539	1	4	yes	—
382	C₂²	C₄₃×#540	1	4	yes	—
383	C₂²	C₄₃×#542	1	2	yes	—
384	C₂²	C₄₃×#544	1	2	yes	—
385	C₂²	C₄₃×#552	1	4	yes	—
386	C₂²	C₄₃×#553	1	2	yes	—
387	C₂²	C₄₃×#554	1	2	yes	—
388	C₂²	C₄₃×#556	1	2	yes	—
389	C₂²	C₄₃×#557	1	2	yes	—
390	C₂²	C₄₃×#563	1	4	yes	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	4	no	—
398	C₄	—	8	4	no	—
399	C₄	—	8	1	no	—
400	C₂	C₄₃×#2487	1	1	yes	characteristic
401	C₂	C₄₃×#2503	1	1	yes	characteristic
402	C₂	C₄₃×#2568	1	1	yes	characteristic
403	C₂	C₄₃×#2623	1	1	yes	characteristic
404	C₂	C₄₃×#2628	1	1	yes	characteristic
405	C₂	C₄₃×#2641	1	1	yes	characteristic
406	C₂	C₄₃×#2791	1	4	yes	—
407	C₂	C₄₃×#2793	1	4	yes	—
408	C₂	C₄₃×#2821	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
169. #17065	C₄₃	direct (N × H)
233. C₄₃	#17065	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×#387	2
C₂×C₄₃×#384	2
C₄₃×#1445	2
C₄₃×#1442	2
C₄₃×#1441	2
C₄₃×#1434	2
#17065	43

Subgroups — C43×#17065 #24937082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17065 #24937082