Subgroups — C₄₃×#29641 #24949658

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#483	C₂	1	2	yes	maximal
3	C₄₃×#2855	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2058	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2024	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1823	C₂	1	2	yes	maximal
7	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₄₃	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₄₃	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	4	yes	—
12	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#483	—	2	8	no	—
17	C₂×#106×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	C₂²	1	2	yes	—
21	C₄₃×#389	C₂²	1	2	yes	—
22	C₄₃×#387	—	2	2	no	—
23	C₄₃×#385	—	2	1	no	—
24	C₄₃×#381	—	2	1	no	—
25	C₄₃×#380	C₂²	1	1	yes	characteristic
26	C₄₃×#340	C₂²	1	8	yes	—
27	C₄₃×#336	C₂²	1	4	yes	—
28	C₂²×Q₈×C₄₃	—	2	8	no	—
29	C₂²×Q₈×C₄₃	—	2	4	no	—
30	C₂²×Q₈×C₄₃	—	4	4	no	—
31	C₂²×Q₈×C₄₃	—	4	4	no	—
32	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	—	2	2	no	—
34	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
38	C₄⋊Q₈×C₄₃	—	2	16	no	—
39	C₄⋊Q₈×C₄₃	—	2	16	no	—
40	C₂²⋊Q₈×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
51	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₄²×C₄₃	—	2	4	no	—
54	C₂×C₄²×C₄₃	D₄	1	2	yes	—
55	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
56	#106×C₄₃	—	2	8	no	—
57	#103×C₄₃	—	2	8	no	—
58	C₂²⋊C₈×C₄₃	—	2	4	no	—
59	#95×C₄₃	—	2	1	no	—
60	#95×C₄₃	—	2	2	no	—
61	#95×C₄₃	—	2	2	no	—
62	#95×C₄₃	—	2	2	no	—
63	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₂×Q₈×C₄₃	—	2	16	no	—
65	C₂×Q₈×C₄₃	—	2	2	no	—
66	C₂×Q₈×C₄₃	—	2	4	no	—
67	C₂×Q₈×C₄₃	—	4	8	no	—
68	C₂×Q₈×C₄₃	—	4	32	no	—
69	C₂×Q₈×C₄₃	—	4	8	no	—
70	C₂²×C₄×C₄₃	—	2	4	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	8	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	1	no	—
80	C₂²×C₄×C₄₃	—	4	4	no	—
81	C₂²×C₄×C₄₃	—	4	4	no	—
82	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
83	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₄₃	—	2	4	no	—
89	C₂×C₈×C₄₃	—	2	8	no	—
90	C₄⋊C₄×C₄₃	—	2	16	no	—
91	C₄⋊C₄×C₄₃	—	2	8	no	—
92	C₄⋊C₄×C₄₃	—	2	4	no	—
93	C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₄⋊C₄×C₄₃	—	2	4	no	—
95	C₄⋊C₄×C₄₃	—	4	2	no	—
96	C₄⋊C₄×C₄₃	—	4	4	no	—
97	C₄⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
98	C₂²⋊C₄×C₄₃	—	4	2	no	—
99	C₂²⋊C₄×C₄₃	—	4	2	no	—
100	C₄²×C₄₃	—	2	4	no	—
101	C₄²×C₄₃	—	2	4	no	—
102	C₂³×C₄₃	—	2	2	no	—
103	C₂³×C₄₃	—	2	2	no	—
104	C₂³×C₄₃	#120	1	2	yes	—
105	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
106	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
107	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
108	Q₈×C₄₃	—	4	32	no	—
109	Q₈×C₄₃	—	4	4	no	—
110	C₂×C₄×C₄₃	—	2	8	no	—
111	C₂×C₄×C₄₃	—	2	2	no	—
112	C₂×C₄×C₄₃	—	2	2	no	—
113	C₂×C₄×C₄₃	—	2	2	no	—
114	C₂×C₄×C₄₃	—	2	2	no	—
115	C₂×C₄×C₄₃	—	2	2	no	—
116	C₂×C₄×C₄₃	—	2	8	no	—
117	C₂×C₄×C₄₃	—	2	8	no	—
118	C₂×C₄×C₄₃	—	2	8	no	—
119	C₂×C₄×C₄₃	—	4	4	no	—
120	C₂×C₄×C₄₃	—	4	4	no	—
121	C₂×C₄×C₄₃	—	4	16	no	—
122	C₂×C₄×C₄₃	—	4	1	no	—
123	C₂×C₄×C₄₃	—	4	1	no	—
124	C₂×C₄×C₄₃	—	4	2	no	—
125	C₂×C₄×C₄₃	—	4	2	no	—
126	C₂×C₄×C₄₃	—	4	2	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	—	4	2	no	—
129	C₂×C₄×C₄₃	#120	1	2	yes	—
130	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
131	C₂×C₄×C₄₃	#137	1	4	yes	—
132	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
133	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
134	C₈×C₄₃	—	4	4	no	—
135	#29641	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂²×C₄₃	—	2	2	no	—
137	C₂²×C₄₃	—	2	4	no	—
138	C₂²×C₄₃	—	2	4	no	—
139	C₂²×C₄₃	—	2	2	no	—
140	C₂²×C₄₃	#450	1	4	yes	—
141	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
142	C₂²×C₄₃	#536	1	2	yes	—
143	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
144	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂²×C₄₃	C₂×#137	1	2	yes	—
146	C₄×C₄₃	—	2	2	no	—
147	C₄×C₄₃	—	2	4	no	—
148	C₄×C₄₃	—	2	4	no	—
149	C₄×C₄₃	—	4	8	no	—
150	C₄×C₄₃	—	8	1	no	—
151	C₄×C₄₃	—	8	2	no	—
152	C₄×C₄₃	—	8	1	no	—
153	C₄×C₄₃	#536	1	4	yes	—
154	C₂²×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic
155	C₂×#483	C₂×C₄₃	1	2	yes	—
156	#2855	C₂×C₄₃	1	1	yes	characteristic
157	#2058	C₂×C₄₃	1	4	yes	complemented
158	#2024	C₂×C₄₃	1	4	yes	complemented
159	#1823	C₂×C₄₃	1	2	yes	—
160	#1817	C₂×C₄₃	1	1	yes	characteristic
161	C₂×C₄₃	—	2	4	no	—
162	C₂×C₄₃	#2614	1	1	yes	characteristic
163	C₂×C₄₃	C₂×#450	1	1	yes	characteristic
164	C₂×C₄₃	#3004	1	1	yes	characteristic
165	C₂×C₄₃	#3229	1	2	yes	—
166	C₂×C₄₃	#3238	1	2	yes	—
167	C₂³×Q₈	—	2	1	no	—
168	C₂×C₄⋊Q₈	—	2	8	no	—
169	C₂×C₄⋊Q₈	—	2	2	no	—
170	C₂×C₄⋊Q₈	C₂²×C₄₃	1	4	yes	—
171	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
172	C₂²×C₄⋊C₄	—	2	1	no	—
173	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
174	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
175	#483	—	2	8	no	—
176	C₂×#106	C₂²×C₄₃	1	4	yes	—
177	C₂×#103	C₂²×C₄₃	1	4	yes	—
178	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
179	#391	C₂²×C₄₃	1	2	yes	—
180	#389	C₂²×C₄₃	1	2	yes	—
181	#387	—	2	2	no	—
182	#385	—	2	1	no	—
183	#381	—	2	1	no	—
184	#380	C₂²×C₄₃	1	1	yes	characteristic
185	#340	C₂²×C₄₃	1	8	yes	—
186	#336	C₂²×C₄₃	1	4	yes	—
187	C₄₃	#29641	1	1	yes	characteristic, direct product factor, Sylow
188	C₂²×Q₈	—	2	8	no	—
189	C₂²×Q₈	—	2	4	no	—
190	C₂²×Q₈	—	4	4	no	—
191	C₂²×Q₈	—	4	4	no	—
192	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
193	C₂³×C₄	—	2	2	no	—
194	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
195	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
198	C₄⋊Q₈	—	2	16	no	—
199	C₄⋊Q₈	—	2	16	no	—
200	C₂²⋊Q₈	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	8	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
208	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
211	C₂×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₄²	—	2	4	no	—
214	C₂×C₄²	D₄×C₄₃	1	2	yes	—
215	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
216	#106	—	2	8	no	—
217	#103	—	2	8	no	—
218	C₂²⋊C₈	—	2	4	no	—
219	#95	—	2	1	no	—
220	#95	—	2	2	no	—
221	#95	—	2	2	no	—
222	#95	—	2	2	no	—
223	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
224	C₂×Q₈	—	2	16	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	4	no	—
227	C₂×Q₈	—	4	8	no	—
228	C₂×Q₈	—	4	32	no	—
229	C₂×Q₈	—	4	8	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	1	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
243	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
245	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
246	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
247	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	8	no	—
250	C₄⋊C₄	—	2	16	no	—
251	C₄⋊C₄	—	2	8	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	4	no	—
257	C₄⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
258	C₂²⋊C₄	—	4	2	no	—
259	C₂²⋊C₄	—	4	2	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	4	no	—
262	C₂³	—	2	2	no	—
263	C₂³	—	2	2	no	—
264	C₂³	#120×C₄₃	1	2	yes	—
265	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
266	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
267	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
268	Q₈	—	4	32	no	—
269	Q₈	—	4	4	no	—
270	C₂×C₄	—	2	8	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	16	no	—
282	C₂×C₄	—	4	1	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	#120×C₄₃	1	2	yes	—
290	C₂×C₄	C₂×SD₁₆×C₄₃	1	4	yes	—
291	C₂×C₄	#137×C₄₃	1	4	yes	—
292	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
293	C₂×C₄	2₋¹⁺⁴×C₄₃	1	4	yes	—
294	C₈	—	4	4	no	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	4	no	—
298	C₂²	—	2	2	no	—
299	C₂²	C₄₃×#450	1	4	yes	—
300	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
301	C₂²	C₄₃×#536	1	2	yes	—
302	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
303	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
304	C₂²	C₂×#137×C₄₃	1	2	yes	—
305	C₄	—	2	2	no	—
306	C₄	—	2	4	no	—
307	C₄	—	2	4	no	—
308	C₄	—	4	8	no	—
309	C₄	—	8	1	no	—
310	C₄	—	8	2	no	—
311	C₄	—	8	1	no	—
312	C₄	C₄₃×#536	1	4	yes	—
313	C₂	—	2	4	no	—
314	C₂	C₄₃×#2614	1	1	yes	characteristic
315	C₂	C₂×C₄₃×#450	1	1	yes	characteristic
316	C₂	C₄₃×#3004	1	1	yes	characteristic
317	C₂	C₄₃×#3229	1	2	yes	—
318	C₂	C₄₃×#3238	1	2	yes	—

	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×#2058	C₂	semidirect
5. C₄₃×#2024	C₂	semidirect
135. #29641	C₄₃	direct (N × H)
157. #2058	C₂×C₄₃	semidirect
158. #2024	C₂×C₄₃	semidirect
187. C₄₃	#29641	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₃	2
C₂×C₄₃×#483	2
C₄₃×#2855	2
C₄₃×#2058	2
C₄₃×#2024	2
C₄₃×#1823	2
C₄₃×#1817	2
#29641	43

Subgroups — C43×#29641 #24949658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29641 #24949658