Subgroups — D₄₃×#2159 #25249627

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#427×D₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#107×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19136384	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136383	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136382	C₂	1	2	yes	maximal, complemented
7	#19136381	C₂	1	1	yes	maximal, characteristic, complemented
8	#19136380	C₂	1	2	yes	maximal, complemented
9	#367×D₄₃	C₂	1	2	yes	maximal, complemented
10	#366×D₄₃	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
13	#117×D₄₃	—	2	1	no	—
14	C₂×C₄⋊C₄×D₄₃	—	2	1	no	—
15	C₂×#13063265	C₂²	1	1	yes	characteristic
16	C₂×#13063264	C₂²	1	2	yes	—
17	M₃₂×D₄₃	C₄	1	8	yes	complemented
18	C₂×C₁₆×D₄₃	C₂²	1	2	yes	—
19	#14582937	C₂²	1	1	yes	characteristic
20	#14582936	C₂²	1	1	yes	characteristic
21	#14582936	C₂²	1	1	yes	characteristic
22	#14582935	—	2	1	no	—
23	#14582934	—	2	1	no	—
24	C₂×#13063259	C₂²	1	1	yes	characteristic
25	C₂×#13063258	—	2	1	no	—
26	#107×D₄₃	—	2	1	no	—
27	#107×D₄₃	—	2	1	no	—
28	#107×D₄₃	C₂²	1	2	yes	—
29	#107×D₄₃	C₂²	1	2	yes	—
30	#107×D₄₃	C₂²	1	1	yes	characteristic
31	#107×D₄₃	C₂²	1	1	yes	characteristic
32	#106×D₄₃	—	2	1	no	—
33	#14582727	C₂²	1	2	yes	complemented
34	#14582726	C₂²	1	2	yes	complemented
35	#14582726	C₂²	1	2	yes	complemented
36	#14582725	C₂²	1	2	yes	complemented
37	#14582724	C₂²	1	2	yes	complemented
38	#14582724	C₂²	1	2	yes	complemented
39	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#427	C₂²	1	1	yes	characteristic
41	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#367	C₂²	1	2	yes	complemented
43	C₄₃×#366	C₂²	1	2	yes	complemented
44	C₂²×C₄×D₄₃	—	4	1	no	—
45	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
46	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
47	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
48	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
49	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
50	C₂×C₈×D₄₃	Q₈	1	4	yes	—
51	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
53	#13063284	—	2	1	no	—
54	#13063283	—	2	1	no	—
55	#13063283	—	2	1	no	—
56	#13063282	—	4	1	no	—
57	#13063281	—	4	1	no	—
58	C₂×C₄⋊Dic₄₃	—	2	1	no	—
59	C₂×Dic₄₃⋊C₄	—	4	1	no	—
60	C₄⋊C₄×D₄₃	—	2	2	no	—
61	C₄⋊C₄×D₄₃	—	2	2	no	—
62	C₄⋊C₄×D₄₃	—	2	1	no	—
63	C₄⋊C₄×D₄₃	—	2	1	no	—
64	C₄⋊C₄×D₄₃	—	4	1	no	—
65	C₄⋊C₄×D₄₃	—	4	1	no	—
66	C₂²⋊C₄×D₄₃	—	4	1	no	—
67	C₄²×D₄₃	—	4	1	no	—
68	#13063265	C₂×C₄	1	4	yes	complemented
69	#13063264	C₂×C₄	1	8	yes	complemented
70	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
71	C₁₆×D₄₃	C₂×C₄	1	8	yes	complemented
72	#13063259	—	2	1	no	—
73	#13063259	C₂³	1	2	yes	—
74	#13063259	C₂³	1	1	yes	characteristic
75	#13063259	C₂³	1	1	yes	characteristic
76	#13063258	—	2	2	no	—
77	#13063258	—	2	2	no	—
78	#13063258	—	2	1	no	—
79	#13063258	—	2	1	no	—
80	#13063257	—	2	1	no	—
81	#13063256	—	2	1	no	—
82	#13063256	—	2	1	no	—
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	#117×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	M₃₂×C₄₃	C₂×C₄	1	4	yes	complemented
87	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
88	#107×C₄₃	—	2	1	no	—
89	#107×C₄₃	C₂³	1	1	yes	characteristic
90	#107×C₄₃	C₂³	1	2	yes	—
91	#107×C₄₃	C₂³	1	1	yes	characteristic
92	#106×C₄₃	—	2	1	no	—
93	C₂³×D₄₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	—	4	1	no	—
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₄₃	—	4	1	no	—
97	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
98	C₂×C₄×D₄₃	—	4	1	no	—
99	C₂×C₄×D₄₃	—	4	1	no	—
100	C₂×C₄×D₄₃	—	4	2	no	—
101	C₂×C₄×D₄₃	—	4	2	no	—
102	C₂×C₄×D₄₃	—	8	4	no	—
103	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
104	C₂×C₄×D₄₃	D₈	1	1	yes	characteristic
105	C₂×C₄×D₄₃	D₈	1	1	yes	characteristic
106	C₂×C₄×D₄₃	Q₁₆	1	4	yes	—
107	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₄⋊C₄×C₄₃	—	2	1	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	4	1	no	—
117	C₂²⋊C₄×C₄₃	—	4	1	no	—
118	C₄²×C₄₃	—	4	1	no	—
119	C₂²⋊Dic₄₃	—	4	1	no	—
120	(C₂×D₄₃)⋊C₄	—	4	1	no	—
121	(C₂×D₄₃)⋊C₄	—	4	1	no	—
122	C₄⋊Dic₄₃	—	2	1	no	—
123	C₄⋊Dic₄₃	—	2	1	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	4	1	no	—
126	Dic₄₃⋊C₄	—	4	2	no	—
127	Dic₄₃⋊C₄	—	4	2	no	—
128	Dic₄₃⋊C₄	—	4	1	no	—
129	Dic₄₃⋊C₄	—	4	1	no	—
130	C₄×Dic₄₃	—	4	1	no	—
131	C₄×Dic₄₃	—	4	1	no	—
132	C₄×Dic₄₃	—	4	1	no	—
133	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
134	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
137	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
138	C₈×D₄₃	C₂²×C₄	1	2	yes	—
139	C₈×D₄₃	C₂²×C₄	1	2	yes	—
140	C₈×D₄₃	C₂×Q₈	1	2	yes	—
141	C₈×D₄₃	C₂×Q₈	1	2	yes	—
142	C₁₆×C₄₃	C₂²×C₄	1	4	yes	complemented
143	C₄₃⋊C₁₆	C₂²×C₄	1	4	yes	complemented
144	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
145	C₂²×D₄₃	—	2	2	no	—
146	C₂²×D₄₃	—	2	2	no	—
147	C₂²×D₄₃	#107	1	4	yes	—
148	C₂²×D₄₃	C₂×D₈	1	1	yes	characteristic
149	C₂²×D₄₃	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	8	2	no	—
154	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
157	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	8	2	no	—
162	C₂×Dic₄₃	#107	1	4	yes	—
163	C₂×Dic₄₃	C₂×D₈	1	1	yes	characteristic
164	C₂×Dic₄₃	C₂×D₈	1	1	yes	characteristic
165	C₄×D₄₃	—	8	4	no	—
166	C₄×D₄₃	—	8	2	no	—
167	C₄×D₄₃	—	8	4	no	—
168	C₄×D₄₃	—	8	2	no	—
169	C₄×D₄₃	#107	1	4	yes	—
170	C₄×D₄₃	#107	1	4	yes	—
171	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
172	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₄×D₄₃	C₂×Q₁₆	1	2	yes	—
174	C₄×D₄₃	C₂×Q₁₆	1	2	yes	—
175	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	C₈×C₄₃	C₂²×Q₈	1	1	yes	characteristic
178	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
179	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×#2159	—	43	1	no	maximal, Sylow
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	C₂×#107	1	2	yes	—
184	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
185	C₂×D₄₃	—	2	1	no	—
186	C₂×D₄₃	—	2	1	no	—
187	C₂×D₄₃	—	2	8	no	—
188	C₂×D₄₃	C₂×#107	1	2	yes	—
189	C₂×D₄₃	C₂×#107	1	2	yes	—
190	C₂×D₄₃	#509	1	2	yes	—
191	C₂×D₄₃	#510	1	2	yes	—
192	C₄×C₄₃	—	8	2	no	—
193	C₄×C₄₃	—	8	1	no	—
194	C₄×C₄₃	—	8	1	no	—
195	C₄×C₄₃	C₂×#107	1	2	yes	—
196	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
198	Dic₄₃	—	8	2	no	—
199	Dic₄₃	—	8	1	no	—
200	Dic₄₃	—	8	1	no	—
201	Dic₄₃	C₂×#107	1	2	yes	—
202	Dic₄₃	C₂×#107	1	2	yes	—
203	C₂²×M₃₂	—	43	1	no	—
204	C₂×#427	—	43	1	no	—
205	C₂²×#107	—	43	1	no	—
206	#2159	—	43	1	no	—
207	#2159	—	43	1	no	—
208	#2159	—	43	1	no	—
209	#2159	—	43	2	no	—
210	#2159	—	43	2	no	—
211	#2159	D₄₃	1	1	yes	characteristic, direct product factor
212	C₂×#367	—	43	2	no	—
213	C₂×#366	—	43	2	no	—
214	C₂×C₄₃	—	2	2	no	—
215	C₂×C₄₃	C₂²×#107	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#509	1	1	yes	characteristic
217	C₂×C₄₃	C₂×#510	1	1	yes	characteristic
218	D₄₃	—	2	2	no	—
219	D₄₃	#2159	1	4	yes	direct product factor
220	C₂³×C₈	—	43	1	no	—
221	C₂×#117	—	86	1	no	—
222	C₂²×C₄⋊C₄	—	86	1	no	—
223	C₂×M₃₂	—	43	1	no	—
224	C₂×M₃₂	—	43	8	no	—
225	C₂×M₃₂	—	43	2	no	—
226	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
227	C₂²×C₁₆	—	43	2	no	—
228	#427	—	43	1	no	—
229	#427	—	43	1	no	—
230	#427	—	43	1	no	—
231	#427	—	86	1	no	—
232	#427	—	86	1	no	—
233	#427	C₂×D₄₃	1	1	yes	characteristic
234	C₂×#107	—	43	1	no	—
235	C₂×#107	—	43	2	no	—
236	C₂×#107	—	43	2	no	—
237	C₂×#107	—	43	1	no	—
238	C₂×#107	—	43	1	no	—
239	C₂×#107	—	86	1	no	—
240	C₂×#107	—	86	1	no	—
241	C₂×#107	—	86	1	no	—
242	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
243	C₂×#106	—	86	1	no	—
244	#367	—	43	2	no	—
245	#367	—	43	2	no	—
246	#367	—	43	2	no	—
247	#367	C₂×D₄₃	1	2	yes	complemented
248	#366	—	43	2	no	—
249	#366	—	43	2	no	—
250	#366	—	43	2	no	—
251	#366	C₂×D₄₃	1	2	yes	complemented
252	C₄₃	C₂×#2159	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	43	1	no	—
254	C₂³×C₄	—	172	1	no	—
255	C₂²×C₈	—	43	1	no	—
256	C₂²×C₈	—	43	4	no	—
257	C₂²×C₈	—	43	1	no	—
258	C₂²×C₈	—	43	1	no	—
259	C₂²×C₈	—	43	4	no	—
260	C₂²×C₈	—	43	1	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	#117	—	86	1	no	—
265	#117	—	86	1	no	—
266	#117	—	86	1	no	—
267	#117	—	172	1	no	—
268	#117	—	172	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	86	2	no	—
271	C₂×C₄⋊C₄	—	86	2	no	—
272	C₂×C₄⋊C₄	—	86	1	no	—
273	C₂×C₄⋊C₄	—	86	1	no	—
274	C₂×C₄⋊C₄	—	86	1	no	—
275	C₂×C₄⋊C₄	—	172	1	no	—
276	C₂×C₄⋊C₄	—	172	1	no	—
277	C₂×C₄⋊C₄	—	172	1	no	—
278	C₂×C₂²⋊C₄	—	172	1	no	—
279	C₂×C₄²	—	172	1	no	—
280	M₃₂	—	43	4	no	—
281	M₃₂	—	43	8	no	—
282	M₃₂	C₄×D₄₃	1	4	yes	complemented
283	C₂×C₁₆	—	43	2	no	—
284	C₂×C₁₆	—	43	8	no	—
285	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
286	#107	—	2	1	no	—
287	#107	—	43	1	no	—
288	#107	—	43	2	no	—
289	#107	—	43	1	no	—
290	#107	—	86	2	no	—
291	#107	—	86	2	no	—
292	#107	—	86	1	no	—
293	#107	—	86	1	no	—
294	#107	—	86	1	no	—
295	#107	C₂²×D₄₃	1	1	yes	characteristic
296	#107	C₂²×D₄₃	1	2	yes	—
297	#107	C₂²×D₄₃	1	1	yes	characteristic
298	#106	—	2	1	no	—
299	#106	—	86	1	no	—
300	#106	—	86	1	no	—
301	#106	—	86	1	no	—
302	C₂⁴	—	43	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	43	1	no	—
305	C₂²×C₄	—	43	4	no	—
306	C₂²×C₄	—	43	1	no	—
307	C₂²×C₄	—	43	1	no	—
308	C₂²×C₄	—	43	4	no	—
309	C₂²×C₄	—	43	1	no	—
310	C₂²×C₄	—	43	1	no	—
311	C₂²×C₄	—	344	4	no	—
312	C₂²×C₄	—	172	1	no	—
313	C₂²×C₄	—	172	1	no	—
314	C₂²×C₄	—	172	2	no	—
315	C₂²×C₄	—	172	2	no	—
316	C₂²×C₄	—	172	1	no	—
317	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
318	C₂×C₈	—	43	4	no	—
319	C₂×C₈	—	43	1	no	—
320	C₂×C₈	—	43	1	no	—
321	C₂×C₈	—	43	4	no	—
322	C₂×C₈	—	43	4	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	43	2	no	—
325	C₂×C₈	—	43	2	no	—
326	C₂×C₈	—	43	2	no	—
327	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
328	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
329	C₂×C₈	Q₈×D₄₃	1	2	yes	—
330	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	86	1	no	—
336	C₄⋊C₄	—	86	1	no	—
337	C₄⋊C₄	—	86	2	no	—
338	C₄⋊C₄	—	172	2	no	—
339	C₄⋊C₄	—	172	2	no	—
340	C₄⋊C₄	—	172	1	no	—
341	C₄⋊C₄	—	172	1	no	—
342	C₄⋊C₄	—	172	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	172	1	no	—
345	C₂²⋊C₄	—	172	1	no	—
346	C₂²⋊C₄	—	172	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	172	1	no	—
349	C₄²	—	172	1	no	—
350	C₄²	—	172	1	no	—
351	C₁₆	—	43	4	no	—
352	C₁₆	C₂×C₄×D₄₃	1	4	yes	complemented
353	C₂³	—	43	1	no	—
354	C₂³	—	43	1	no	—
355	C₂³	—	43	4	no	—
356	C₂³	—	86	2	no	—
357	C₂³	—	86	2	no	—
358	C₂³	D₈×D₄₃	1	1	yes	characteristic
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	43	1	no	—
364	C₂×C₄	—	43	1	no	—
365	C₂×C₄	—	43	4	no	—
366	C₂×C₄	—	43	2	no	—
367	C₂×C₄	—	43	2	no	—
368	C₂×C₄	—	43	2	no	—
369	C₂×C₄	—	43	2	no	—
370	C₂×C₄	—	43	4	no	—
371	C₂×C₄	—	43	4	no	—
372	C₂×C₄	—	344	4	no	—
373	C₂×C₄	—	344	2	no	—
374	C₂×C₄	—	344	2	no	—
375	C₂×C₄	—	344	4	no	—
376	C₂×C₄	—	344	2	no	—
377	C₂×C₄	—	172	1	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	—	172	2	no	—
380	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
381	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
382	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
383	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
384	C₈	—	43	2	no	—
385	C₈	—	43	2	no	—
386	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
387	C₈	C₂²×C₄×D₄₃	1	1	yes	characteristic
388	C₈	C₂×Q₈×D₄₃	1	1	yes	characteristic
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	43	2	no	—
392	C₂²	—	43	2	no	—
393	C₂²	—	43	2	no	—
394	C₂²	—	43	2	no	—
395	C₂²	—	86	8	no	—
396	C₂²	—	86	1	no	—
397	C₂²	—	86	1	no	—
398	C₂²	#107×D₄₃	1	2	yes	—
399	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	43	2	no	—
404	C₄	—	43	2	no	—
405	C₄	—	344	2	no	—
406	C₄	—	344	1	no	—
407	C₄	—	344	1	no	—
408	C₄	#107×D₄₃	1	2	yes	—
409	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
410	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	43	4	no	—
413	C₂	—	86	2	no	—
414	C₂	C₂×#107×D₄₃	1	1	yes	characteristic
415	C₂	#509×D₄₃	1	1	yes	characteristic
416	C₂	#510×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₃
commutator	C₈×C₄₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2159	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	C₂³×D₄₃	D₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2159	D₄₃
hypocenter	C₄₃	C₂×#2159
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2159

Complements

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

N	H ≅ G/N	type
4. #19136384	C₂	semidirect
5. #19136383	C₂	semidirect
6. #19136382	C₂	semidirect
7. #19136381	C₂	semidirect
8. #19136380	C₂	semidirect
9. #367×D₄₃	C₂	semidirect
10. #366×D₄₃	C₂	semidirect
11. C₄₃×#2159	C₂	semidirect
17. M₃₂×D₄₃	C₄	semidirect
33. #14582727	C₂²	semidirect
34. #14582726	C₂²	semidirect
35. #14582726	C₂²	semidirect
36. #14582725	C₂²	semidirect
37. #14582724	C₂²	semidirect
38. #14582724	C₂²	semidirect
42. C₄₃×#367	C₂²	semidirect
43. C₄₃×#366	C₂²	semidirect
68. #13063265	C₂×C₄	semidirect
69. #13063264	C₂×C₄	semidirect
71. C₁₆×D₄₃	C₂×C₄	semidirect
86. M₃₂×C₄₃	C₂×C₄	semidirect
142. C₁₆×C₄₃	C₂²×C₄	semidirect
143. C₄₃⋊C₁₆	C₂²×C₄	semidirect
211. #2159	D₄₃	direct (N × H)
219. D₄₃	#2159	direct (N × H)
247. #367	C₂×D₄₃	semidirect
251. #366	C₂×D₄₃	semidirect
252. C₄₃	C₂×#2159	semidirect
282. M₃₂	C₄×D₄₃	semidirect
352. C₁₆	C₂×C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₃	2
#427×D₄₃	2
C₂×#107×D₄₃	2
#19136384	2
#19136383	2
#19136382	2
#19136381	2
#19136380	2
#367×D₄₃	2
#366×D₄₃	2
C₄₃×#2159	2
C₂×#2159	43

Subgroups — D43×#2159 #25249627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#2159 #25249627