Subgroups — C₄₃×#29639 #24949656

Order 11008.

1292 conjugacy classes of subgroups.

The subgroup lattice has 344 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, complemented
2	C₂×C₄₃×#481	C₂	1	2	yes	maximal
3	C₄₃×#2854	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2058	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2023	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1824	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
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×#123×C₄₃	—	2	1	no	—
13	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#481	—	2	8	no	—
18	C₂×#106×C₄₃	C₂²	1	4	yes	—
19	C₂×#102×C₄₃	C₂²	1	4	yes	—
20	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#390	C₂²	1	2	yes	—
22	C₄₃×#389	C₂²	1	2	yes	—
23	C₄₃×#388	—	2	2	no	—
24	C₄₃×#386	—	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	8	no	—
31	C₂²×D₄×C₄₃	—	2	1	no	—
32	C₂²×D₄×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	#123×C₄₃	—	4	4	no	—
41	#121×C₄₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	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×C₂²⋊C₄×C₄₃	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄²×C₄₃	—	2	4	no	—
56	C₂×C₄²×C₄₃	D₄	1	2	yes	—
57	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
58	#106×C₄₃	—	2	8	no	—
59	#102×C₄₃	—	2	8	no	—
60	C₂²⋊C₈×C₄₃	—	2	4	no	—
61	#95×C₄₃	—	2	1	no	—
62	#95×C₄₃	—	2	2	no	—
63	C₂⁴×C₄₃	—	2	1	no	—
64	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₃	—	2	16	no	—
66	C₂×Q₈×C₄₃	—	4	32	no	—
67	C₂×Q₈×C₄₃	—	4	8	no	—
68	C₂×Q₈×C₄₃	—	4	8	no	—
69	C₂×D₄×C₄₃	—	2	2	no	—
70	C₂×D₄×C₄₃	—	2	4	no	—
71	C₂×D₄×C₄₃	—	4	2	no	—
72	C₂×D₄×C₄₃	—	4	2	no	—
73	C₂×D₄×C₄₃	—	4	2	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	8	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	4	8	no	—
84	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₄₃	—	2	4	no	—
91	C₂×C₈×C₄₃	—	2	8	no	—
92	C₄⋊C₄×C₄₃	—	2	16	no	—
93	C₄⋊C₄×C₄₃	—	2	8	no	—
94	C₄⋊C₄×C₄₃	—	2	4	no	—
95	C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₄⋊C₄×C₄₃	—	2	4	no	—
97	C₄⋊C₄×C₄₃	—	4	4	no	—
98	C₄⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
99	C₂²⋊C₄×C₄₃	—	4	2	no	—
100	C₂²⋊C₄×C₄₃	—	4	4	no	—
101	C₂²⋊C₄×C₄₃	—	4	4	no	—
102	C₂²⋊C₄×C₄₃	—	4	2	no	—
103	C₄²×C₄₃	—	2	4	no	—
104	C₄²×C₄₃	—	2	4	no	—
105	C₂³×C₄₃	—	2	2	no	—
106	C₂³×C₄₃	—	2	2	no	—
107	C₂³×C₄₃	—	4	1	no	—
108	C₂³×C₄₃	—	4	2	no	—
109	C₂³×C₄₃	—	4	1	no	—
110	C₂³×C₄₃	—	4	2	no	—
111	C₂³×C₄₃	—	4	1	no	—
112	C₂³×C₄₃	#120	1	2	yes	—
113	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
114	C₂³×C₄₃	#137	1	2	yes	—
115	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
116	Q₈×C₄₃	—	4	32	no	—
117	D₄×C₄₃	—	4	4	no	—
118	D₄×C₄₃	—	8	4	no	—
119	C₂×C₄×C₄₃	—	2	8	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	2	2	no	—
122	C₂×C₄×C₄₃	—	2	2	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	8	no	—
126	C₂×C₄×C₄₃	—	2	8	no	—
127	C₂×C₄×C₄₃	—	2	8	no	—
128	C₂×C₄×C₄₃	—	4	16	no	—
129	C₂×C₄×C₄₃	—	4	8	no	—
130	C₂×C₄×C₄₃	—	4	1	no	—
131	C₂×C₄×C₄₃	—	4	2	no	—
132	C₂×C₄×C₄₃	—	4	2	no	—
133	C₂×C₄×C₄₃	—	4	1	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	1	no	—
136	C₂×C₄×C₄₃	#120	1	2	yes	—
137	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
138	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
139	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
141	C₈×C₄₃	—	4	4	no	—
142	#29639	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂²×C₄₃	—	2	2	no	—
144	C₂²×C₄₃	—	2	4	no	—
145	C₂²×C₄₃	—	2	4	no	—
146	C₂²×C₄₃	—	2	2	no	—
147	C₂²×C₄₃	—	8	1	no	—
148	C₂²×C₄₃	—	8	2	no	—
149	C₂²×C₄₃	—	8	2	no	—
150	C₂²×C₄₃	—	8	1	no	—
151	C₂²×C₄₃	—	8	1	no	—
152	C₂²×C₄₃	#448	1	4	yes	—
153	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
154	C₂²×C₄₃	#536	1	2	yes	—
155	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
156	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
157	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
158	C₄×C₄₃	—	2	2	no	—
159	C₄×C₄₃	—	2	4	no	—
160	C₄×C₄₃	—	2	4	no	—
161	C₄×C₄₃	—	4	8	no	—
162	C₄×C₄₃	—	8	2	no	—
163	C₄×C₄₃	—	8	1	no	—
164	C₄×C₄₃	#536	1	4	yes	—
165	C₂²×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
166	C₂×#481	C₂×C₄₃	1	2	yes	—
167	#2854	C₂×C₄₃	1	1	yes	characteristic
168	#2058	C₂×C₄₃	1	4	yes	complemented
169	#2023	C₂×C₄₃	1	4	yes	complemented
170	#1824	C₂×C₄₃	1	2	yes	complemented
171	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
172	C₂×C₄₃	—	2	4	no	—
173	C₂×C₄₃	—	16	1	no	—
174	C₂×C₄₃	#2614	1	1	yes	characteristic
175	C₂×C₄₃	C₂×#448	1	1	yes	characteristic
176	C₂×C₄₃	#3003	1	1	yes	characteristic
177	C₂×C₄₃	#3227	1	2	yes	—
178	C₂×C₄₃	#3239	1	2	yes	—
179	C₂³×Q₈	—	2	1	no	—
180	C₂×C₄⋊Q₈	—	2	8	no	—
181	C₂×C₄⋊Q₈	—	2	2	no	—
182	C₂×C₄⋊Q₈	C₂²×C₄₃	1	4	yes	—
183	C₂×#123	—	2	1	no	—
184	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	—	2	1	no	—
186	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
187	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
188	#481	—	2	8	no	—
189	C₂×#106	C₂²×C₄₃	1	4	yes	—
190	C₂×#102	C₂²×C₄₃	1	4	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
192	#390	C₂²×C₄₃	1	2	yes	—
193	#389	C₂²×C₄₃	1	2	yes	—
194	#388	—	2	2	no	—
195	#386	—	2	1	no	—
196	#380	C₂²×C₄₃	1	1	yes	characteristic
197	#340	C₂²×C₄₃	1	8	yes	—
198	#336	C₂²×C₄₃	1	4	yes	—
199	C₄₃	#29639	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×Q₈	—	2	8	no	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	—	4	8	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
205	C₂³×C₄	—	2	2	no	—
206	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
207	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
210	C₄⋊Q₈	—	2	16	no	—
211	C₄⋊Q₈	—	2	16	no	—
212	#123	—	4	4	no	—
213	#121	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	8	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	4	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
220	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₄²	—	2	4	no	—
228	C₂×C₄²	D₄×C₄₃	1	2	yes	—
229	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
230	#106	—	2	8	no	—
231	#102	—	2	8	no	—
232	C₂²⋊C₈	—	2	4	no	—
233	#95	—	2	1	no	—
234	#95	—	2	2	no	—
235	C₂⁴	—	2	1	no	—
236	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
237	C₂×Q₈	—	2	16	no	—
238	C₂×Q₈	—	4	32	no	—
239	C₂×Q₈	—	4	8	no	—
240	C₂×Q₈	—	4	8	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	4	2	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
257	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
261	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	8	no	—
264	C₄⋊C₄	—	2	16	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₂²⋊C₄	—	4	4	no	—
274	C₂²⋊C₄	—	4	4	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	4	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	4	1	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	1	no	—
282	C₂³	—	4	2	no	—
283	C₂³	—	4	1	no	—
284	C₂³	#120×C₄₃	1	2	yes	—
285	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
286	C₂³	#137×C₄₃	1	2	yes	—
287	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
288	Q₈	—	4	32	no	—
289	D₄	—	4	4	no	—
290	D₄	—	8	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	4	16	no	—
301	C₂×C₄	—	4	8	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	#120×C₄₃	1	2	yes	—
309	C₂×C₄	C₂×SD₁₆×C₄₃	1	4	yes	—
310	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
311	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
312	C₂×C₄	2₋¹⁺⁴×C₄₃	1	4	yes	—
313	C₈	—	4	4	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	8	1	no	—
319	C₂²	—	8	2	no	—
320	C₂²	—	8	2	no	—
321	C₂²	—	8	1	no	—
322	C₂²	—	8	1	no	—
323	C₂²	C₄₃×#448	1	4	yes	—
324	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
325	C₂²	C₄₃×#536	1	2	yes	—
326	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
327	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
328	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
329	C₄	—	2	2	no	—
330	C₄	—	2	4	no	—
331	C₄	—	2	4	no	—
332	C₄	—	4	8	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	1	no	—
335	C₄	C₄₃×#536	1	4	yes	—
336	C₂	—	2	4	no	—
337	C₂	—	16	1	no	—
338	C₂	C₄₃×#2614	1	1	yes	characteristic
339	C₂	C₂×C₄₃×#448	1	1	yes	characteristic
340	C₂	C₄₃×#3003	1	1	yes	characteristic
341	C₂	C₄₃×#3227	1	2	yes	—
342	C₂	C₄₃×#3239	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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
1. C₂²×C₄⋊Q₈×C₄₃	C₂	semidirect
4. C₄₃×#2058	C₂	semidirect
5. C₄₃×#2023	C₂	semidirect
6. C₄₃×#1824	C₂	semidirect
7. C₄₃×#1817	C₂	semidirect
142. #29639	C₄₃	direct (N × H)
165. C₂²×C₄⋊Q₈	C₂×C₄₃	semidirect
168. #2058	C₂×C₄₃	semidirect
169. #2023	C₂×C₄₃	semidirect
170. #1824	C₂×C₄₃	semidirect
171. #1817	C₂×C₄₃	semidirect
199. C₄₃	#29639	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×#481	2
C₄₃×#2854	2
C₄₃×#2058	2
C₄₃×#2023	2
C₄₃×#1824	2
C₄₃×#1817	2
#29639	43

Subgroups — C43×#29639 #24949656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29639 #24949656