Subgroups — C₄₃×#9590 #24929607

Order 11008.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#1980	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1540	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1492	C₂	1	1	yes	maximal, characteristic
5	C₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#532	C₂²	1	1	yes	characteristic
9	C₄₃×#431	C₂²	1	1	yes	characteristic
10	C₂×#108×C₄₃	—	2	1	no	—
11	C₄₃×#423	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#104×C₄₃	—	2	1	no	—
14	C₂×#104×C₄₃	—	2	1	no	—
15	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#341	—	2	1	no	—
19	C₄₃×#332	C₄	1	1	yes	characteristic, complemented
20	C₄₃×#332	C₄	1	1	yes	characteristic, complemented
21	C₄₃×#331	C₄	1	1	yes	characteristic, complemented
22	C₄₃×#331	C₄	1	1	yes	characteristic, complemented
23	C₄₃×D₄⋊C₈	—	2	1	no	—
24	C₄₃×D₄⋊C₈	—	2	1	no	—
25	C₄₃×#322	—	2	1	no	—
26	C₈²×C₄₃	—	2	1	no	—
27	C₂×#41×C₄₃	—	2	1	no	—
28	C₂×M₁₆×C₄₃	—	2	1	no	—
29	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₃	—	2	1	no	—
32	C₂²×C₈×C₄₃	—	2	1	no	—
33	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
34	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
35	#124×C₄₃	—	2	1	no	—
36	#121×C₄₃	—	2	1	no	—
37	#121×C₄₃	—	2	1	no	—
38	C₄×D₄×C₄₃	—	2	1	no	—
39	C₄×D₄×C₄₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₂×C₄²×C₄₃	—	2	1	no	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	#108×C₄₃	—	4	2	no	—
44	C₄⋊C₈×C₄₃	—	2	1	no	—
45	C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₄⋊C₈×C₄₃	—	2	1	no	—
47	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
50	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
51	#104×C₄₃	—	4	2	no	—
52	#104×C₄₃	—	4	2	no	—
53	C₂²⋊C₈×C₄₃	—	2	1	no	—
54	#97×C₄₃	—	2	1	no	—
55	C₄×C₈×C₄₃	—	2	1	no	—
56	C₄×C₈×C₄₃	—	2	1	no	—
57	C₄×C₈×C₄₃	—	2	1	no	—
58	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
59	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
60	#95×C₄₃	—	2	1	no	—
61	#41×C₄₃	—	4	1	no	—
62	#41×C₄₃	—	4	1	no	—
63	#41×C₄₃	—	4	1	no	—
64	#41×C₄₃	—	4	1	no	—
65	C₂×Q₈×C₄₃	—	2	1	no	—
66	C₂×D₄×C₄₃	—	2	1	no	—
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	—	2	1	no	—
69	C₂×D₄×C₄₃	—	4	1	no	—
70	C₂²×C₄×C₄₃	—	4	1	no	—
71	C₂²×C₄×C₄₃	—	4	1	no	—
72	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
75	M₁₆×C₄₃	—	2	1	no	—
76	M₁₆×C₄₃	—	2	1	no	—
77	M₁₆×C₄₃	—	4	1	no	—
78	M₁₆×C₄₃	—	4	1	no	—
79	M₁₆×C₄₃	D₈	1	2	yes	—
80	M₁₆×C₄₃	SD₁₆	1	2	yes	—
81	C₂×C₈×C₄₃	—	2	1	no	—
82	C₂×C₈×C₄₃	—	2	1	no	—
83	C₂×C₈×C₄₃	—	2	1	no	—
84	C₂×C₈×C₄₃	—	2	1	no	—
85	C₂×C₈×C₄₃	—	2	1	no	—
86	C₂×C₈×C₄₃	—	2	1	no	—
87	C₂×C₈×C₄₃	—	2	1	no	—
88	C₂×C₈×C₄₃	—	2	1	no	—
89	C₂×C₈×C₄₃	—	4	2	no	—
90	C₂×C₈×C₄₃	—	4	1	no	—
91	C₂×C₈×C₄₃	—	4	1	no	—
92	C₂×C₈×C₄₃	—	4	1	no	—
93	C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₄⋊C₄×C₄₃	—	4	1	no	—
97	C₂²⋊C₄×C₄₃	—	4	1	no	—
98	C₂²⋊C₄×C₄₃	—	4	1	no	—
99	C₄²×C₄₃	—	4	1	no	—
100	C₄²×C₄₃	—	4	1	no	—
101	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₃	#41	1	1	yes	characteristic
104	C₄²×C₄₃	#41	1	1	yes	characteristic
105	C₂³×C₄₃	—	4	1	no	—
106	C₂³×C₄₃	#124	1	1	yes	characteristic
107	Q₈×C₄₃	—	4	1	no	—
108	Q₈×C₄₃	—	4	1	no	—
109	D₄×C₄₃	—	4	1	no	—
110	D₄×C₄₃	—	4	1	no	—
111	D₄×C₄₃	—	4	1	no	—
112	D₄×C₄₃	—	4	1	no	—
113	D₄×C₄₃	—	8	1	no	—
114	D₄×C₄₃	—	8	1	no	—
115	D₄×C₄₃	—	8	1	no	—
116	C₂×C₄×C₄₃	—	2	1	no	—
117	C₂×C₄×C₄₃	—	2	1	no	—
118	C₂×C₄×C₄₃	—	4	1	no	—
119	C₂×C₄×C₄₃	—	4	2	no	—
120	C₂×C₄×C₄₃	—	4	1	no	—
121	C₂×C₄×C₄₃	—	8	1	no	—
122	C₂×C₄×C₄₃	—	8	1	no	—
123	C₂×C₄×C₄₃	—	8	1	no	—
124	C₂×C₄×C₄₃	—	8	1	no	—
125	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
126	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
127	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
128	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
129	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
130	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
131	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
133	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
134	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
135	C₈×C₄₃	—	2	2	no	—
136	C₈×C₄₃	—	2	2	no	—
137	C₈×C₄₃	—	2	2	no	—
138	C₈×C₄₃	—	4	1	no	—
139	C₈×C₄₃	—	4	1	no	—
140	C₈×C₄₃	—	4	1	no	—
141	C₈×C₄₃	—	4	1	no	—
142	C₈×C₄₃	—	4	1	no	—
143	C₈×C₄₃	—	8	1	no	—
144	#9590	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₄₃	—	2	1	no	—
146	C₂²×C₄₃	—	2	1	no	—
147	C₂²×C₄₃	—	8	1	no	—
148	C₂²×C₄₃	—	8	1	no	—
149	C₂²×C₄₃	—	8	1	no	—
150	C₂²×C₄₃	#388	1	1	yes	characteristic
151	C₂²×C₄₃	#486	1	1	yes	characteristic
152	C₂²×C₄₃	#488	1	1	yes	characteristic
153	C₄×C₄₃	—	2	1	no	—
154	C₄×C₄₃	—	2	1	no	—
155	C₄×C₄₃	—	2	1	no	—
156	C₄×C₄₃	—	8	2	no	—
157	C₄×C₄₃	—	8	1	no	—
158	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
159	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
160	C₄×C₄₃	#443	1	1	yes	characteristic
161	C₄×C₄₃	#444	1	1	yes	characteristic
162	C₄×C₄₃	#465	1	1	yes	characteristic
163	C₄×C₄₃	#466	1	1	yes	characteristic
164	#1980	C₂×C₄₃	1	1	yes	characteristic
165	#1950	C₂×C₄₃	1	1	yes	characteristic, complemented
166	#1540	C₂×C₄₃	1	1	yes	characteristic
167	#1492	C₂×C₄₃	1	1	yes	characteristic
168	C₈×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
169	#1303	C₂×C₄₃	1	1	yes	characteristic, complemented
170	#1279	C₂×C₄₃	1	1	yes	characteristic, complemented
171	C₂×C₄₃	—	2	1	no	—
172	C₂×C₄₃	—	2	1	no	—
173	C₂×C₄₃	—	16	1	no	—
174	C₂×C₄₃	#1929	1	1	yes	characteristic
175	C₂×C₄₃	#1932	1	1	yes	characteristic
176	C₂×C₄₃	#1934	1	1	yes	characteristic
177	#532	C₂²×C₄₃	1	1	yes	characteristic
178	#431	C₂²×C₄₃	1	1	yes	characteristic
179	C₂×#108	—	2	1	no	—
180	#423	C₂²×C₄₃	1	1	yes	characteristic
181	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
182	C₂×#104	—	2	1	no	—
183	C₂×#104	—	2	1	no	—
184	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
187	#341	—	2	1	no	—
188	#332	C₄×C₄₃	1	1	yes	characteristic, complemented
189	#332	C₄×C₄₃	1	1	yes	characteristic, complemented
190	#331	C₄×C₄₃	1	1	yes	characteristic, complemented
191	#331	C₄×C₄₃	1	1	yes	characteristic, complemented
192	D₄⋊C₈	—	2	1	no	—
193	D₄⋊C₈	—	2	1	no	—
194	#322	—	2	1	no	—
195	C₈²	—	2	1	no	—
196	C₄₃	#9590	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×#41	—	2	1	no	—
198	C₂×M₁₆	—	2	1	no	—
199	C₂×M₁₆	D₄×C₄₃	1	1	yes	characteristic
200	C₂×M₁₆	D₄×C₄₃	1	1	yes	characteristic
201	C₂²×C₈	—	2	1	no	—
202	C₂²×C₈	—	2	1	no	—
203	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
204	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
205	#124	—	2	1	no	—
206	#121	—	2	1	no	—
207	#121	—	2	1	no	—
208	C₄×D₄	—	2	1	no	—
209	C₄×D₄	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	1	no	—
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
213	#108	—	4	2	no	—
214	C₄⋊C₈	—	2	1	no	—
215	C₄⋊C₈	—	2	1	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
218	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
219	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
220	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
221	#104	—	4	2	no	—
222	#104	—	4	2	no	—
223	C₂²⋊C₈	—	2	1	no	—
224	#97	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
229	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
230	#95	—	2	1	no	—
231	#41	—	4	1	no	—
232	#41	—	4	1	no	—
233	#41	—	4	1	no	—
234	#41	—	4	1	no	—
235	C₂×Q₈	—	2	1	no	—
236	C₂×D₄	—	2	1	no	—
237	C₂×D₄	—	2	1	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	4	1	no	—
240	C₂²×C₄	—	4	1	no	—
241	C₂²×C₄	—	4	1	no	—
242	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
243	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
244	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
245	M₁₆	—	2	1	no	—
246	M₁₆	—	2	1	no	—
247	M₁₆	—	4	1	no	—
248	M₁₆	—	4	1	no	—
249	M₁₆	D₈×C₄₃	1	2	yes	—
250	M₁₆	SD₁₆×C₄₃	1	2	yes	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	1	no	—
261	C₂×C₈	—	4	1	no	—
262	C₂×C₈	—	4	1	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	4	1	no	—
267	C₂²⋊C₄	—	4	1	no	—
268	C₂²⋊C₄	—	4	1	no	—
269	C₄²	—	4	1	no	—
270	C₄²	—	4	1	no	—
271	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
272	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
273	C₄²	#41×C₄₃	1	1	yes	characteristic
274	C₄²	#41×C₄₃	1	1	yes	characteristic
275	C₂³	—	4	1	no	—
276	C₂³	#124×C₄₃	1	1	yes	characteristic
277	Q₈	—	4	1	no	—
278	Q₈	—	4	1	no	—
279	D₄	—	4	1	no	—
280	D₄	—	4	1	no	—
281	D₄	—	4	1	no	—
282	D₄	—	4	1	no	—
283	D₄	—	8	1	no	—
284	D₄	—	8	1	no	—
285	D₄	—	8	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	8	1	no	—
292	C₂×C₄	—	8	1	no	—
293	C₂×C₄	—	8	1	no	—
294	C₂×C₄	—	8	1	no	—
295	C₂×C₄	#117×C₄₃	1	1	yes	characteristic
296	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
297	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
298	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
299	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
300	C₂×C₄	#126×C₄₃	1	1	yes	characteristic
301	C₂×C₄	C₂×D₈×C₄₃	1	1	yes	characteristic
302	C₂×C₄	C₂×SD₁₆×C₄₃	1	1	yes	characteristic
303	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
304	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
305	C₈	—	2	2	no	—
306	C₈	—	2	2	no	—
307	C₈	—	2	2	no	—
308	C₈	—	4	1	no	—
309	C₈	—	4	1	no	—
310	C₈	—	4	1	no	—
311	C₈	—	4	1	no	—
312	C₈	—	4	1	no	—
313	C₈	—	8	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	1	no	—
316	C₂²	—	8	1	no	—
317	C₂²	—	8	1	no	—
318	C₂²	—	8	1	no	—
319	C₂²	C₄₃×#388	1	1	yes	characteristic
320	C₂²	C₄₃×#486	1	1	yes	characteristic
321	C₂²	C₄₃×#488	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	8	2	no	—
326	C₄	—	8	1	no	—
327	C₄	C₄×D₈×C₄₃	1	1	yes	characteristic
328	C₄	C₄×SD₁₆×C₄₃	1	1	yes	characteristic
329	C₄	C₄₃×#443	1	1	yes	characteristic
330	C₄	C₄₃×#444	1	1	yes	characteristic
331	C₄	C₄₃×#465	1	1	yes	characteristic
332	C₄	C₄₃×#466	1	1	yes	characteristic
333	C₂	—	2	1	no	—
334	C₂	—	2	1	no	—
335	C₂	—	16	1	no	—
336	C₂	C₄₃×#1929	1	1	yes	characteristic
337	C₂	C₄₃×#1932	1	1	yes	characteristic
338	C₂	C₄₃×#1934	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#121
commutator	C₄²	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂²×C₄₃	#388
prime radical	C₄₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#1950	C₂	semidirect
5. C₈×M₁₆×C₄₃	C₂	semidirect
6. C₄₃×#1303	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
19. C₄₃×#332	C₄	semidirect
20. C₄₃×#332	C₄	semidirect
21. C₄₃×#331	C₄	semidirect
22. C₄₃×#331	C₄	semidirect
144. #9590	C₄₃	direct (N × H)
165. #1950	C₂×C₄₃	semidirect
168. C₈×M₁₆	C₂×C₄₃	semidirect
169. #1303	C₂×C₄₃	semidirect
170. #1279	C₂×C₄₃	semidirect
188. #332	C₄×C₄₃	semidirect
189. #332	C₄×C₄₃	semidirect
190. #331	C₄×C₄₃	semidirect
191. #331	C₄×C₄₃	semidirect
196. C₄₃	#9590	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#1980	2
C₄₃×#1950	2
C₄₃×#1540	2
C₄₃×#1492	2
C₈×M₁₆×C₄₃	2
C₄₃×#1303	2
C₄₃×#1279	2
#9590	43

Subgroups — C43×#9590 #24929607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#9590 #24929607