Subgroups — C₄₃×#29715 #24949732

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#451	C₂	1	2	yes	maximal
2	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#391	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2072	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2056	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1872	C₂	1	2	yes	maximal
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#451	—	2	8	no	—
16	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#103×C₄₃	C₂²	1	4	yes	—
18	C₂×#103×C₄₃	C₂²	1	4	yes	—
19	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#391	—	2	1	no	—
21	C₄₃×#391	—	2	1	no	—
22	C₄₃×#391	C₂²	1	2	yes	—
23	C₄₃×#391	C₂²	1	2	yes	—
24	C₄₃×#391	C₂²	1	2	yes	—
25	C₄₃×#389	—	2	1	no	—
26	C₄₃×#389	—	2	1	no	—
27	C₄₃×#384	C₂²	1	1	yes	characteristic
28	C₄₃×#380	—	2	1	no	—
29	C₄₃×#380	—	2	1	no	—
30	C₂×#95×C₄₃	—	2	1	no	—
31	C₂×#95×C₄₃	—	2	1	no	—
32	C₄₃×#340	C₂²	1	4	yes	—
33	C₄₃×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₄₃	—	2	1	no	—
35	C₂²×Q₈×C₄₃	—	2	2	no	—
36	C₂²×Q₈×C₄₃	—	4	2	no	—
37	C₂²×Q₈×C₄₃	—	4	2	no	—
38	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
39	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂³×C₄×C₄₃	—	2	1	no	—
43	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₄₃	—	2	8	no	—
47	C₂×Q₁₆×C₄₃	—	4	4	no	—
48	C₂×Q₁₆×C₄₃	—	4	4	no	—
49	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
50	C₄⋊Q₈×C₄₃	—	4	2	no	—
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄²×C₄₃	—	4	2	no	—
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	—	4	2	no	—
69	#103×C₄₃	—	2	8	no	—
70	#103×C₄₃	—	4	4	no	—
71	C₂²⋊C₈×C₄₃	—	2	4	no	—
72	#95×C₄₃	—	2	2	no	—
73	#95×C₄₃	—	2	2	no	—
74	#95×C₄₃	—	2	2	no	—
75	#95×C₄₃	—	2	2	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₄₃	—	2	4	no	—
80	C₂×Q₈×C₄₃	—	2	2	no	—
81	C₂×Q₈×C₄₃	—	2	2	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	2	4	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×Q₈×C₄₃	—	4	8	no	—
88	C₂×Q₈×C₄₃	—	4	2	no	—
89	C₂×Q₈×C₄₃	—	4	2	no	—
90	C₂×Q₈×C₄₃	—	4	8	no	—
91	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
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	4	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	4	1	no	—
102	C₂²×C₄×C₄₃	—	4	1	no	—
103	C₂²×C₄×C₄₃	—	4	1	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	—	4	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	Q₁₆	1	4	yes	complemented
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₄₃	—	4	16	no	—
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	4	2	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	4	4	no	—
130	C₄⋊C₄×C₄₃	—	4	2	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₄²×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	4	1	no	—
135	C₄²×C₄₃	—	4	1	no	—
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	#121	1	2	yes	—
141	C₂³×C₄₃	C₂×Q₁₆	1	2	yes	—
142	C₂³×C₄₃	#137	1	2	yes	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₃	—	2	8	no	—
145	Q₈×C₄₃	—	4	8	no	—
146	Q₈×C₄₃	—	4	4	no	—
147	Q₈×C₄₃	—	4	4	no	—
148	Q₈×C₄₃	—	4	4	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	8	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	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	—	8	4	no	—
178	C₂×C₄×C₄₃	#121	1	2	yes	—
179	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₄₃	#137	1	2	yes	—
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
185	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₄₃	—	4	4	no	—
187	#29715	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	#462	1	4	yes	—
195	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
196	C₂²×C₄₃	#534	1	1	yes	characteristic
197	C₂²×C₄₃	#535	1	1	yes	characteristic
198	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
201	C₂²×C₄₃	#575	1	1	yes	characteristic
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	—	4	1	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	#534	1	2	yes	—
212	C₄×C₄₃	#538	1	2	yes	—
213	C₂×#451	C₂×C₄₃	1	2	yes	—
214	#2857	C₂×C₄₃	1	1	yes	characteristic
215	C₂×#391	C₂×C₄₃	1	1	yes	characteristic
216	#2072	C₂×C₄₃	1	2	yes	complemented
217	#2056	C₂×C₄₃	1	4	yes	complemented
218	#2016	C₂×C₄₃	1	2	yes	complemented
219	#1872	C₂×C₄₃	1	2	yes	—
220	#1797	C₂×C₄₃	1	1	yes	characteristic
221	C₂×C₄₃	—	2	4	no	—
222	C₂×C₄₃	#2617	1	1	yes	characteristic
223	C₂×C₄₃	C₂×#462	1	1	yes	characteristic
224	C₂×C₄₃	#3037	1	1	yes	characteristic
225	C₂×C₄₃	#3189	1	1	yes	characteristic
226	C₂×C₄₃	#3195	1	1	yes	characteristic
227	C₂×C₄₃	#3209	1	1	yes	characteristic
228	C₂×C₄₃	#3215	1	1	yes	characteristic
229	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
230	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
231	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
235	#451	—	2	8	no	—
236	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
237	C₂×#103	C₂²×C₄₃	1	4	yes	—
238	C₂×#103	C₂²×C₄₃	1	4	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
240	#391	—	2	1	no	—
241	#391	—	2	1	no	—
242	#391	C₂²×C₄₃	1	2	yes	—
243	#391	C₂²×C₄₃	1	2	yes	—
244	#391	C₂²×C₄₃	1	2	yes	—
245	#389	—	2	1	no	—
246	#389	—	2	1	no	—
247	#384	C₂²×C₄₃	1	1	yes	characteristic
248	#380	—	2	1	no	—
249	#380	—	2	1	no	—
250	C₂×#95	—	2	1	no	—
251	C₂×#95	—	2	1	no	—
252	#340	C₂²×C₄₃	1	4	yes	—
253	#336	C₂²×C₄₃	1	2	yes	—
254	C₄₃	#29715	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	4	2	no	—
258	C₂²×Q₈	—	4	2	no	—
259	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
260	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
261	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	8	no	—
268	C₂×Q₁₆	—	4	4	no	—
269	C₂×Q₁₆	—	4	4	no	—
270	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
271	C₄⋊Q₈	—	4	2	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	4	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	4	2	no	—
285	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
289	C₄⋊C₈	—	4	2	no	—
290	#103	—	2	8	no	—
291	#103	—	4	4	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	4	8	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	Q₁₆×C₄₃	1	4	yes	complemented
331	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	#41×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
339	Q₁₆	—	4	16	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	#121×C₄₃	1	2	yes	—
362	C₂³	C₂×Q₁₆×C₄₃	1	2	yes	—
363	C₂³	#137×C₄₃	1	2	yes	—
364	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
365	Q₈	—	2	8	no	—
366	Q₈	—	4	8	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	4	no	—
369	Q₈	—	4	4	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	#121×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
401	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
402	C₂×C₄	#137×C₄₃	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
405	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
406	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
407	C₈	—	4	4	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	C₄₃×#462	1	4	yes	—
415	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
416	C₂²	C₄₃×#534	1	1	yes	characteristic
417	C₂²	C₄₃×#535	1	1	yes	characteristic
418	C₂²	C₂²×Q₁₆×C₄₃	1	1	yes	characteristic
419	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
420	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
421	C₂²	C₄₃×#575	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₄₃×#534	1	2	yes	—
432	C₄	C₄₃×#538	1	2	yes	—
433	C₂	—	2	4	no	—
434	C₂	C₄₃×#2617	1	1	yes	characteristic
435	C₂	C₂×C₄₃×#462	1	1	yes	characteristic
436	C₂	C₄₃×#3037	1	1	yes	characteristic
437	C₂	C₄₃×#3189	1	1	yes	characteristic
438	C₂	C₄₃×#3195	1	1	yes	characteristic
439	C₂	C₄₃×#3209	1	1	yes	characteristic
440	C₂	C₄₃×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#2072	C₂	semidirect
5. C₄₃×#2056	C₂	semidirect
6. C₄₃×#2016	C₂	semidirect
109. C₂²×C₄×C₄₃	Q₁₆	semidirect
187. #29715	C₄₃	direct (N × H)
216. #2072	C₂×C₄₃	semidirect
217. #2056	C₂×C₄₃	semidirect
218. #2016	C₂×C₄₃	semidirect
254. C₄₃	#29715	direct (N × H)
330. C₂²×C₄	Q₁₆×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×#451	2
C₄₃×#2857	2
C₂×C₄₃×#391	2
C₄₃×#2072	2
C₄₃×#2056	2
C₄₃×#2016	2
C₄₃×#1872	2
C₄₃×#1797	2
#29715	43

Subgroups — C43×#29715 #24949732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29715 #24949732