Subgroups — #25068616

Order 11008.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145150	C₂	1	1	yes	maximal, characteristic
2	#19143696	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133497	C₂	1	2	yes	maximal, complemented
4	#19133436	C₂	1	2	yes	maximal, complemented
5	#19133431	C₂	1	2	yes	maximal, complemented
6	#19133407	C₂	1	2	yes	maximal, complemented
7	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133015	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133012	C₂	1	1	yes	maximal, characteristic
10	#19132885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2979	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583295	C₄	1	1	yes	characteristic
14	#14583271	C₄	1	1	yes	characteristic
15	#14583251	C₄	1	1	yes	characteristic
16	#14583245	C₄	1	1	yes	characteristic
17	#14583126	C₄	1	2	yes	—
18	#14583126	C₄	1	2	yes	—
19	#14583029	C₂²	1	2	yes	—
20	#14583026	—	2	1	no	—
21	C₈×Dic₈₆	C₂²	1	2	yes	—
22	#14583023	—	2	1	no	—
23	C₄×#10621883	C₂²	1	2	yes	—
24	C₄×#10621883	C₂²	1	2	yes	—
25	#14582957	—	2	2	no	—
26	#14582952	C₂²	1	1	yes	characteristic
27	C₄×#10621877	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582651	C₂²	1	1	yes	characteristic
30	#14582651	C₂²	1	1	yes	characteristic
31	#14582649	C₂²	1	1	yes	characteristic
32	#14582649	C₂²	1	1	yes	characteristic
33	#14582629	C₂²	1	2	yes	—
34	#14582629	C₂²	1	2	yes	—
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
37	#14582621	C₂²	1	2	yes	—
38	#14582620	C₂²	1	2	yes	—
39	C₄₃×#532	C₂²	1	1	yes	characteristic
40	C₄₃×#436	—	2	1	no	—
41	C₄₃×#436	C₂²	1	2	yes	—
42	C₈×D₄×C₄₃	—	2	1	no	—
43	C₈×D₄×C₄₃	C₂²	1	2	yes	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄₃×#431	C₂²	1	1	yes	characteristic
46	C₄₃×#408	—	2	2	no	—
47	C₂×#10621883	C₂×C₄	1	2	yes	—
48	C₂×#10621883	C₂×C₄	1	2	yes	—
49	C₂×#10621877	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
52	#13063325	C₂×C₄	1	1	yes	characteristic
53	#13063325	C₂×C₄	1	1	yes	characteristic
54	#13063317	—	2	1	no	—
55	#13063304	—	2	1	no	—
56	#13063304	C₂×C₄	1	2	yes	—
57	C₄×Dic₈₆	—	2	1	no	—
58	C₄×Dic₈₆	C₂³	1	2	yes	—
59	#13063284	—	2	1	no	—
60	#13063256	C₂×C₄	1	2	yes	—
61	#13063256	C₂×C₄	1	2	yes	—
62	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
64	Dic₄₃⋊C₈	—	2	2	no	—
65	Dic₄₃⋊C₈	—	2	2	no	—
66	#13063248	C₂×C₄	1	2	yes	—
67	#13063248	C₂×C₄	1	2	yes	—
68	#13063246	C₂×C₄	1	2	yes	—
69	#13063246	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
71	#13063236	—	2	1	no	—
72	#13063235	—	2	2	no	—
73	C₄×C₄₃⋊C₈	—	2	1	no	—
74	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
77	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₄₃	—	2	2	no	—
80	C₂×#41×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	—	2	2	no	—
83	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
84	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
85	#124×C₄₃	—	2	1	no	—
86	#121×C₄₃	—	2	1	no	—
87	#121×C₄₃	C₂×C₄	1	2	yes	—
88	C₄×D₄×C₄₃	—	2	1	no	—
89	C₄×D₄×C₄₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₄₃	—	2	1	no	—
96	C₂²⋊C₈×C₄₃	—	2	2	no	—
97	C₂²⋊C₈×C₄₃	—	2	2	no	—
98	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
99	C₄×C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	#41×C₄₃	—	8	1	no	—
102	#41×C₄₃	—	8	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂×Dic₈₆	—	2	1	no	—
113	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
114	M₁₆×C₄₃	—	8	2	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	8	2	no	—
118	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₃	—	2	2	no	—
123	C₂²⋊C₄×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	#41	1	1	yes	characteristic
127	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₄₃	—	2	2	no	—
129	#10621883	—	2	4	no	—
130	#10621883	—	4	2	no	—
131	C₄⋊Dic₄₃	—	2	1	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
135	Dic₄₃⋊C₄	—	2	2	no	—
136	Dic₄₃⋊C₄	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	#10621877	—	4	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	2	no	—
143	C₂×C₄₃⋊C₈	—	4	1	no	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
150	Q₈×C₄₃	—	8	1	no	—
151	D₄×C₄₃	—	2	2	no	—
152	D₄×C₄₃	—	2	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	8	1	no	—
155	D₄×C₄₃	—	8	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₃	—	2	2	no	—
171	C₂×Dic₄₃	—	2	2	no	—
172	Dic₈₆	—	2	2	no	—
173	Dic₈₆	—	2	2	no	—
174	Dic₈₆	—	4	2	no	—
175	C₈×C₄₃	—	2	2	no	—
176	C₈×C₄₃	—	2	2	no	—
177	C₈×C₄₃	—	4	1	no	—
178	C₈×C₄₃	—	4	1	no	—
179	C₄₃⋊C₈	—	2	1	no	—
180	C₄₃⋊C₈	—	2	1	no	—
181	C₄₃⋊C₈	—	2	1	no	—
182	C₄₃⋊C₈	—	4	2	no	—
183	C₄₃⋊C₈	—	4	1	no	—
184	C₄₃⋊C₈	—	4	1	no	—
185	C₄₃⋊C₈	#131	1	2	yes	—
186	#18089	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	—	4	2	no	—
191	C₂²×C₄₃	—	4	2	no	—
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	1	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	4	2	no	—
198	C₄×C₄₃	#444	1	2	yes	—
199	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
200	C₄×C₄₃	#568	1	1	yes	characteristic
201	C₄×C₄₃	#577	1	1	yes	characteristic
202	C₄×C₄₃	#577	1	1	yes	characteristic
203	Dic₄₃	—	4	2	no	—
204	Dic₄₃	—	4	2	no	—
205	#3167	—	43	1	no	—
206	#2986	—	43	1	no	—
207	#2979	D₄₃	1	1	yes	characteristic
208	#1592	—	43	2	no	—
209	#1583	—	43	2	no	—
210	#1582	—	43	2	no	—
211	SD₁₆⋊C₈	—	43	2	no	—
212	#1564	—	43	1	no	—
213	#1485	—	43	1	no	—
214	#1484	—	43	1	no	—
215	#1451	—	43	1	no	—
216	C₂×C₄₃	—	4	1	no	—
217	C₂×C₄₃	—	8	2	no	—
218	C₂×C₄₃	#2935	1	1	yes	characteristic
219	C₂×C₄₃	#2949	1	1	yes	characteristic
220	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
221	#533	—	43	1	no	—
222	#532	C₂×D₄₃	1	1	yes	characteristic
223	#498	—	43	1	no	—
224	#492	—	43	1	no	—
225	#487	—	43	1	no	—
226	#486	—	43	1	no	—
227	#465	—	43	2	no	—
228	#465	—	43	2	no	—
229	#446	—	43	2	no	—
230	#446	—	86	1	no	—
231	C₈×Q₈	—	43	2	no	—
232	C₈×Q₈	—	86	1	no	—
233	C₄×SD₁₆	—	43	2	no	—
234	C₄×SD₁₆	—	43	2	no	—
235	#436	—	2	1	no	—
236	#436	C₂×D₄₃	1	2	yes	—
237	C₈×D₄	—	2	1	no	—
238	C₈×D₄	C₂×D₄₃	1	2	yes	—
239	#433	—	86	2	no	—
240	#431	—	43	1	no	—
241	#431	C₂×D₄₃	1	1	yes	characteristic
242	#431	C₂×D₄₃	1	1	yes	characteristic
243	#408	—	2	2	no	—
244	C₄×M₁₆	—	43	1	no	—
245	C₂×C₄×C₈	—	43	1	no	—
246	#335	—	43	1	no	—
247	#335	—	43	1	no	—
248	#334	—	43	1	no	—
249	#334	—	43	1	no	—
250	Q₈⋊C₈	—	43	2	no	—
251	Q₈⋊C₈	—	43	2	no	—
252	D₄⋊C₈	—	43	2	no	—
253	D₄⋊C₈	—	43	2	no	—
254	#322	—	43	2	no	—
255	#322	—	43	2	no	—
256	C₄₃	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	2	1	no	—
258	C₂×SD₁₆	—	43	2	no	—
259	C₂×SD₁₆	—	43	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	86	1	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	43	1	no	—
264	C₂²×C₈	—	43	1	no	—
265	C₄⋊Q₈	—	43	1	no	—
266	C₄⋊Q₈	—	43	1	no	—
267	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
268	#127	C₄×D₄₃	1	1	yes	characteristic
269	#125	—	86	1	no	—
270	#124	—	2	1	no	—
271	C₂²⋊Q₈	—	43	2	no	—
272	C₂²⋊Q₈	—	86	1	no	—
273	#121	—	2	1	no	—
274	#121	C₄×D₄₃	1	2	yes	—
275	C₄×Q₈	—	43	2	no	—
276	C₄×Q₈	—	86	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₂²×D₄₃	1	2	yes	—
279	#117	—	86	1	no	—
280	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
281	#106	—	43	2	no	—
282	#106	—	43	2	no	—
283	C₄⋊C₈	—	43	1	no	—
284	C₄⋊C₈	—	43	1	no	—
285	C₄⋊C₈	—	86	2	no	—
286	C₄⋊C₈	—	86	2	no	—
287	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
288	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
291	#103	—	43	2	no	—
292	#103	—	43	2	no	—
293	#102	—	43	2	no	—
294	#102	—	43	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₂²⋊C₈	—	86	1	no	—
299	C₂²⋊C₈	C₂²⋊D₄₃	1	2	yes	—
300	#97	—	86	2	no	—
301	#97	—	86	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	43	1	no	—
304	C₄×C₈	—	43	1	no	—
305	C₄×C₈	—	43	1	no	—
306	C₄×C₈	—	43	1	no	—
307	C₄×C₈	—	43	2	no	—
308	C₄×C₈	—	86	2	no	—
309	C₄×C₈	—	86	1	no	—
310	C₄×C₈	C₂²×D₄₃	1	2	yes	—
311	#41	—	8	1	no	—
312	#41	—	8	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	43	2	no	—
315	C₂×Q₈	—	86	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
322	C₂²×C₄	#10621898	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
324	SD₁₆	—	86	4	no	—
325	SD₁₆	—	172	2	no	—
326	M₁₆	—	8	2	no	—
327	M₁₆	—	172	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	8	2	no	—
331	C₂×C₈	—	43	1	no	—
332	C₂×C₈	—	43	1	no	—
333	C₂×C₈	—	43	1	no	—
334	C₂×C₈	—	43	1	no	—
335	C₂×C₈	—	86	2	no	—
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	—	172	1	no	—
340	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	86	2	no	—
353	C₄²	—	86	2	no	—
354	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
355	C₄²	#10621898	1	1	yes	characteristic
356	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
357	C₄²	C₂³×D₄₃	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
360	Q₈	—	8	1	no	—
361	Q₈	—	86	2	no	—
362	Q₈	—	86	2	no	—
363	Q₈	—	172	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	86	2	no	—
378	C₂×C₄	—	86	2	no	—
379	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
381	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
384	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	43	2	no	—
390	C₈	—	86	1	no	—
391	C₈	—	86	1	no	—
392	C₈	—	86	1	no	—
393	C₈	—	172	2	no	—
394	C₈	—	172	1	no	—
395	C₈	—	172	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	172	2	no	—
408	C₄	—	172	2	no	—
409	C₄	#14583019	1	2	yes	—
410	C₄	#131×D₄₃	1	1	yes	characteristic
411	C₄	#14583664	1	1	yes	characteristic
412	C₄	#14583710	1	1	yes	characteristic
413	C₄	#14583710	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	#19143337	1	1	yes	characteristic
417	C₂	#19143452	1	1	yes	characteristic
418	C₂	C₂×#14583019	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2979	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₄₃×#532	C₂²
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2979	D₄₃
hypocenter	C₄₃	#18089
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2979

Complements

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

N	H ≅ G/N	type
2. #19143696	C₂	semidirect
3. #19133497	C₂	semidirect
4. #19133436	C₂	semidirect
5. #19133431	C₂	semidirect
6. #19133407	C₂	semidirect
7. #19133341	C₂	semidirect
8. #19133015	C₂	semidirect
10. #19132885	C₂	semidirect
256. C₄₃	#18089	semidirect

Maximal subgroups

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

subgroup	index
#19145150	2
#19143696	2
#19133497	2
#19133436	2
#19133431	2
#19133407	2
#19133341	2
#19133015	2
#19133012	2
#19132885	2
C₄₃×#2979	2
#18089	43