Subgroups — C₄₃×#28539 #24948556

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2563	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2097	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2093	C₂	1	2	yes	maximal
9	C₄₃×#1973	C₂	1	2	yes	maximal
10	C₄₃×#1847	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#500	—	2	4	no	—
18	C₄₃×#477	—	2	4	no	—
19	C₄₃×#476	—	2	4	no	—
20	C₄×SD₁₆×C₄₃	—	2	4	no	—
21	C₂×#107×C₄₃	C₂²	1	2	yes	—
22	C₂×#107×C₄₃	C₂²	1	2	yes	—
23	C₂×#107×C₄₃	C₂²	1	2	yes	—
24	C₂×#106×C₄₃	C₂²	1	2	yes	—
25	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#97×C₄₃	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#395	—	2	2	no	—
34	C₄₃×#393	—	2	2	no	—
35	C₄₃×#391	C₂²	1	2	yes	—
36	C₄₃×#390	C₂²	1	2	yes	—
37	C₄₃×#389	—	2	2	no	—
38	C₄₃×#384	C₂²	1	2	yes	—
39	C₄₃×#382	C₂²	1	2	yes	—
40	C₄₃×#380	—	2	2	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	—	2	1	no	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂×SD₁₆×C₄₃	—	2	2	no	—
49	C₂×SD₁₆×C₄₃	—	2	2	no	—
50	C₂×SD₁₆×C₄₃	Q₈	1	4	yes	complemented
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₃	—	2	2	no	—
55	C₄⋊Q₈×C₄₃	—	2	2	no	—
56	C₄⋊Q₈×C₄₃	—	2	2	no	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄×Q₈×C₄₃	—	2	2	no	—
59	C₄×Q₈×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	#107×C₄₃	—	2	4	no	—
77	#107×C₄₃	—	2	4	no	—
78	#107×C₄₃	—	2	4	no	—
79	#106×C₄₃	—	2	2	no	—
80	#106×C₄₃	—	2	4	no	—
81	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
82	#103×C₄₃	—	2	2	no	—
83	#103×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	2	2	no	—
85	#102×C₄₃	—	2	4	no	—
86	#97×C₄₃	—	2	4	no	—
87	C₄×C₈×C₄₃	D₄	1	4	yes	—
88	#95×C₄₃	—	2	4	no	—
89	#95×C₄₃	—	2	4	no	—
90	#95×C₄₃	D₄	1	2	yes	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	—	2	1	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	4	2	no	—
98	C₂×Q₈×C₄₃	—	4	2	no	—
99	C₂×Q₈×C₄₃	—	8	2	no	—
100	C₂×Q₈×C₄₃	—	8	2	no	—
101	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₄₃	—	2	1	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	4	no	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₄₃	—	2	8	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₄₃	#41	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	4	2	no	—
139	C₄⋊C₄×C₄₃	—	4	2	no	—
140	C₄⋊C₄×C₄₃	—	4	2	no	—
141	C₄⋊C₄×C₄₃	—	8	4	no	—
142	C₂²⋊C₄×C₄₃	—	4	2	no	—
143	C₂²⋊C₄×C₄₃	—	8	4	no	—
144	C₄²×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	—	2	2	no	—
146	C₄²×C₄₃	—	4	2	no	—
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₄²×C₄₃	C₂×D₄	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	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	2	2	no	—
156	Q₈×C₄₃	—	2	2	no	—
157	Q₈×C₄₃	—	4	1	no	—
158	Q₈×C₄₃	—	4	1	no	—
159	Q₈×C₄₃	—	8	4	no	—
160	Q₈×C₄₃	—	8	4	no	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	2	no	—
163	D₄×C₄₃	—	4	1	no	—
164	D₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	4	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	4	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	8	4	no	—
181	C₂×C₄×C₄₃	#127	1	2	yes	—
182	C₂×C₄×C₄₃	#127	1	2	yes	—
183	C₂×C₄×C₄₃	#137	1	4	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₄₃	—	2	2	no	—
191	C₈×C₄₃	—	2	4	no	—
192	C₈×C₄₃	C₂²⋊Q₈	1	4	yes	—
193	#28539	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₃	—	4	4	no	—
195	C₂²×C₄₃	—	4	2	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	—	8	1	no	—
198	C₂²×C₄₃	—	8	1	no	—
199	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
200	C₂²×C₄₃	#547	1	1	yes	characteristic
201	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#137	1	2	yes	—
203	C₂²×C₄₃	#576	1	2	yes	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	4	4	no	—
206	C₄×C₄₃	—	4	2	no	—
207	C₄×C₄₃	—	8	1	no	—
208	C₄×C₄₃	—	8	1	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	#497	1	4	yes	—
212	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₄×C₄₃	#536	1	1	yes	characteristic
214	C₄×C₄₃	#547	1	1	yes	characteristic
215	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
216	C₂×#500	C₂×C₄₃	1	1	yes	characteristic, complemented
217	C₂×#477	C₂×C₄₃	1	1	yes	characteristic, complemented
218	C₂×#476	C₂×C₄₃	1	1	yes	characteristic
219	C₂×C₄×SD₁₆	C₂×C₄₃	1	1	yes	characteristic
220	#2567	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#2563	C₂×C₄₃	1	1	yes	characteristic
222	#2097	C₂×C₄₃	1	2	yes	complemented
223	#2093	C₂×C₄₃	1	2	yes	—
224	#1973	C₂×C₄₃	1	2	yes	—
225	#1847	C₂×C₄₃	1	2	yes	complemented
226	#1770	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×C₄₃	—	8	2	no	—
228	C₂×C₄₃	#2542	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
230	C₂×C₄₃	#3155	1	1	yes	characteristic
231	C₂×C₄₃	#3357	1	2	yes	—
232	C₂×C₄₃	#3385	1	2	yes	—
233	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
238	#500	—	2	4	no	—
239	#477	—	2	4	no	—
240	#476	—	2	4	no	—
241	C₄×SD₁₆	—	2	4	no	—
242	C₂×#107	C₂²×C₄₃	1	2	yes	—
243	C₂×#107	C₂²×C₄₃	1	2	yes	—
244	C₂×#107	C₂²×C₄₃	1	2	yes	—
245	C₂×#106	C₂²×C₄₃	1	2	yes	—
246	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
248	C₂×#103	C₂²×C₄₃	1	2	yes	—
249	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×#102	C₂²×C₄₃	1	2	yes	—
252	C₂×#97	C₂²×C₄₃	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
254	#395	—	2	2	no	—
255	#393	—	2	2	no	—
256	#391	C₂²×C₄₃	1	2	yes	—
257	#390	C₂²×C₄₃	1	2	yes	—
258	#389	—	2	2	no	—
259	#384	C₂²×C₄₃	1	2	yes	—
260	#382	C₂²×C₄₃	1	2	yes	—
261	#380	—	2	2	no	—
262	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
263	#336	C₂²×C₄₃	1	2	yes	—
264	C₄₃	#28539	1	1	yes	characteristic, direct product factor, Sylow
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	Q₈×C₄₃	1	4	yes	complemented
273	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
298	#107	—	2	4	no	—
299	#107	—	2	4	no	—
300	#107	—	2	4	no	—
301	#106	—	2	2	no	—
302	#106	—	2	4	no	—
303	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
304	#103	—	2	2	no	—
305	#103	—	2	4	no	—
306	#102	—	2	2	no	—
307	#102	—	2	4	no	—
308	#97	—	2	4	no	—
309	C₄×C₈	D₄×C₄₃	1	4	yes	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	D₄×C₄₃	1	2	yes	—
313	C₂⁴	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
341	SD₁₆	—	2	8	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
347	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
348	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
349	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
350	C₂×C₈	#41×C₄₃	1	2	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	8	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	8	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×D₄×C₄₃	1	2	yes	—
370	C₄²	C₂×D₄×C₄₃	1	2	yes	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	8	4	no	—
382	Q₈	—	8	4	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	#127×C₄₃	1	2	yes	—
404	C₂×C₄	#127×C₄₃	1	2	yes	—
405	C₂×C₄	#137×C₄₃	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
410	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
411	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	4	no	—
414	C₈	C₂²⋊Q₈×C₄₃	1	4	yes	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
421	C₂²	C₄₃×#547	1	1	yes	characteristic
422	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
423	C₂²	C₂×#137×C₄₃	1	2	yes	—
424	C₂²	C₄₃×#576	1	2	yes	—
425	C₄	—	2	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	C₄₃×#497	1	4	yes	—
433	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
434	C₄	C₄₃×#536	1	1	yes	characteristic
435	C₄	C₄₃×#547	1	1	yes	characteristic
436	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
437	C₂	—	8	2	no	—
438	C₂	C₄₃×#2542	1	1	yes	characteristic
439	C₂	C₂×C₄₃×#497	1	1	yes	characteristic
440	C₂	C₄₃×#3155	1	1	yes	characteristic
441	C₂	C₄₃×#3357	1	2	yes	—
442	C₂	C₄₃×#3385	1	2	yes	—

	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 ◁ C₄×C₄⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#500	C₂	semidirect
2. C₂×C₄₃×#477	C₂	semidirect
5. C₄₃×#2567	C₂	semidirect
7. C₄₃×#2097	C₂	semidirect
10. C₄₃×#1847	C₂	semidirect
11. C₄₃×#1770	C₂	semidirect
50. C₂×SD₁₆×C₄₃	Q₈	semidirect
193. #28539	C₄₃	direct (N × H)
216. C₂×#500	C₂×C₄₃	semidirect
217. C₂×#477	C₂×C₄₃	semidirect
220. #2567	C₂×C₄₃	semidirect
222. #2097	C₂×C₄₃	semidirect
225. #1847	C₂×C₄₃	semidirect
226. #1770	C₂×C₄₃	semidirect
264. C₄₃	#28539	direct (N × H)
272. C₂×SD₁₆	Q₈×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×#500	2
C₂×C₄₃×#477	2
C₂×C₄₃×#476	2
C₂×C₄×SD₁₆×C₄₃	2
C₄₃×#2567	2
C₄₃×#2563	2
C₄₃×#2097	2
C₄₃×#2093	2
C₄₃×#1973	2
C₄₃×#1847	2
C₄₃×#1770	2
#28539	43

Subgroups — C43×#28539 #24948556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28539 #24948556