Subgroups — C₄₃×#29895 #24949912

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2848	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2076	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2036	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1872	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1852	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1779	C₂	1	1	yes	maximal, characteristic
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
13	C₂×#107×C₄₃	C₂²	1	4	yes	complemented
14	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
15	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
17	C₄₃×#385	—	2	1	no	—
18	C₄₃×#385	—	2	2	no	—
19	C₄₃×#380	—	2	2	no	—
20	C₄₃×#380	C₂²	1	2	yes	—
21	C₄₃×#380	C₂²	1	4	yes	—
22	C₄₃×#380	C₂²	1	1	yes	characteristic
23	C₄₃×#379	—	2	1	no	—
24	C₂×#95×C₄₃	—	2	1	no	—
25	C₄₃×#340	C₂²	1	4	yes	complemented
26	C₄₃×#340	C₂²	1	4	yes	complemented
27	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	—	2	4	no	—
30	C₂³×C₄×C₄₃	—	2	2	no	—
31	C₂³×C₄×C₄₃	—	4	4	no	—
32	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	D₄	1	2	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
37	C₂²⋊Q₈×C₄₃	—	2	4	no	—
38	C₂²⋊Q₈×C₄₃	—	4	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
42	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
43	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
44	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
46	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
52	#107×C₄₃	—	4	4	no	—
53	#103×C₄₃	—	4	4	no	—
54	C₂²⋊C₈×C₄₃	—	2	4	no	—
55	C₂²⋊C₈×C₄₃	—	4	4	no	—
56	#95×C₄₃	—	2	4	no	—
57	#95×C₄₃	—	2	2	no	—
58	#95×C₄₃	—	2	1	no	—
59	C₂⁴×C₄₃	—	2	2	no	—
60	C₂⁴×C₄₃	—	2	2	no	—
61	C₂⁴×C₄₃	—	4	2	no	—
62	C₂⁴×C₄₃	—	4	2	no	—
63	C₂⁴×C₄₃	Q₁₆	1	4	yes	—
64	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
65	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₄₃	—	2	2	no	—
67	C₂×Q₈×C₄₃	—	2	4	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	4	no	—
70	C₂²×C₄×C₄₃	—	2	4	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	1	no	—
78	C₂²×C₄×C₄₃	—	4	2	no	—
79	C₂²×C₄×C₄₃	—	4	2	no	—
80	C₂²×C₄×C₄₃	—	4	2	no	—
81	C₂²×C₄×C₄₃	—	4	4	no	—
82	C₂²×C₄×C₄₃	—	4	4	no	—
83	C₂²×C₄×C₄₃	—	4	16	no	—
84	C₂²×C₄×C₄₃	—	4	4	no	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	#41	1	4	yes	—
88	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
89	C₂×C₈×C₄₃	—	2	4	no	—
90	C₂×C₈×C₄₃	—	2	4	no	—
91	C₂×C₈×C₄₃	—	2	4	no	—
92	C₄⋊C₄×C₄₃	—	2	2	no	—
93	C₄⋊C₄×C₄₃	—	2	4	no	—
94	C₄⋊C₄×C₄₃	—	2	4	no	—
95	C₄⋊C₄×C₄₃	—	2	4	no	—
96	C₄⋊C₄×C₄₃	—	4	4	no	—
97	C₄⋊C₄×C₄₃	—	4	4	no	—
98	C₄⋊C₄×C₄₃	—	4	2	no	—
99	C₂²⋊C₄×C₄₃	—	4	4	no	—
100	C₂²⋊C₄×C₄₃	—	4	8	no	—
101	C₂²⋊C₄×C₄₃	—	4	4	no	—
102	C₂²⋊C₄×C₄₃	—	4	2	no	—
103	C₂²⋊C₄×C₄₃	—	4	2	no	—
104	C₂³×C₄₃	—	2	2	no	—
105	C₂³×C₄₃	—	2	2	no	—
106	C₂³×C₄₃	—	2	2	no	—
107	C₂³×C₄₃	—	2	2	no	—
108	C₂³×C₄₃	—	2	2	no	—
109	C₂³×C₄₃	—	2	2	no	—
110	C₂³×C₄₃	—	2	2	no	—
111	C₂³×C₄₃	—	2	2	no	—
112	C₂³×C₄₃	—	2	8	no	—
113	C₂³×C₄₃	—	4	8	no	—
114	C₂³×C₄₃	—	4	4	no	—
115	C₂³×C₄₃	—	4	4	no	—
116	C₂³×C₄₃	—	4	8	no	—
117	C₂³×C₄₃	#123	1	2	yes	—
118	C₂³×C₄₃	C₂×Q₁₆	1	4	yes	—
119	C₂³×C₄₃	C₂×Q₁₆	1	2	yes	—
120	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
121	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₄₃	—	4	4	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	8	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	2	no	—
128	C₂×C₄×C₄₃	—	4	8	no	—
129	C₂×C₄×C₄₃	—	4	4	no	—
130	C₂×C₄×C₄₃	—	4	8	no	—
131	C₂×C₄×C₄₃	—	4	1	no	—
132	C₂×C₄×C₄₃	—	4	1	no	—
133	C₂×C₄×C₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	4	no	—
136	C₂×C₄×C₄₃	—	4	4	no	—
137	C₂×C₄×C₄₃	—	4	2	no	—
138	C₂×C₄×C₄₃	—	4	2	no	—
139	C₂×C₄×C₄₃	—	4	2	no	—
140	C₂×C₄×C₄₃	—	4	4	no	—
141	C₂×C₄×C₄₃	—	8	8	no	—
142	C₂×C₄×C₄₃	#123	1	2	yes	—
143	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
144	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
145	C₈×C₄₃	—	4	4	no	—
146	#29895	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₃	—	2	2	no	—
148	C₂²×C₄₃	—	2	2	no	—
149	C₂²×C₄₃	—	2	4	no	—
150	C₂²×C₄₃	—	2	4	no	—
151	C₂²×C₄₃	—	2	4	no	—
152	C₂²×C₄₃	—	2	4	no	—
153	C₂²×C₄₃	—	2	4	no	—
154	C₂²×C₄₃	—	4	16	no	—
155	C₂²×C₄₃	—	4	2	no	—
156	C₂²×C₄₃	—	4	2	no	—
157	C₂²×C₄₃	—	4	2	no	—
158	C₂²×C₄₃	—	4	2	no	—
159	C₂²×C₄₃	#484	1	4	yes	—
160	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
161	C₂²×C₄₃	#534	1	2	yes	—
162	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
163	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²×C₄₃	#575	1	2	yes	—
165	C₄×C₄₃	—	2	2	no	—
166	C₄×C₄₃	—	4	2	no	—
167	C₄×C₄₃	—	8	1	no	—
168	C₄×C₄₃	—	8	1	no	—
169	C₄×C₄₃	—	8	2	no	—
170	C₄×C₄₃	—	8	4	no	—
171	C₄×C₄₃	#538	1	4	yes	—
172	#2848	C₂×C₄₃	1	1	yes	characteristic
173	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
174	#2076	C₂×C₄₃	1	4	yes	complemented
175	#2036	C₂×C₄₃	1	4	yes	complemented
176	#1872	C₂×C₄₃	1	2	yes	complemented
177	#1852	C₂×C₄₃	1	2	yes	complemented
178	#1779	C₂×C₄₃	1	1	yes	characteristic
179	C₂×C₄₃	—	2	4	no	—
180	C₂×C₄₃	—	4	4	no	—
181	C₂×C₄₃	#2622	1	1	yes	characteristic
182	C₂×C₄₃	C₂×#484	1	1	yes	characteristic
183	C₂×C₄₃	#3093	1	1	yes	characteristic
184	C₂×C₄₃	#3189	1	2	yes	—
185	C₂×C₄₃	#3194	1	2	yes	—
186	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
187	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
188	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	—	2	1	no	—
191	C₂×#107	C₂²×C₄₃	1	4	yes	complemented
192	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
193	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
195	#385	—	2	1	no	—
196	#385	—	2	2	no	—
197	#380	—	2	2	no	—
198	#380	C₂²×C₄₃	1	2	yes	—
199	#380	C₂²×C₄₃	1	4	yes	—
200	#380	C₂²×C₄₃	1	1	yes	characteristic
201	#379	—	2	1	no	—
202	C₂×#95	—	2	1	no	—
203	#340	C₂²×C₄₃	1	4	yes	complemented
204	#340	C₂²×C₄₃	1	4	yes	complemented
205	C₄₃	#29895	1	1	yes	characteristic, direct product factor, Sylow
206	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
207	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	—	4	4	no	—
211	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₄₃	1	2	yes	—
213	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
214	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
216	C₂²⋊Q₈	—	2	4	no	—
217	C₂²⋊Q₈	—	4	4	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	4	4	no	—
222	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
223	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	4	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	4	4	no	—
231	#107	—	4	4	no	—
232	#103	—	4	4	no	—
233	C₂²⋊C₈	—	2	4	no	—
234	C₂²⋊C₈	—	4	4	no	—
235	#95	—	2	4	no	—
236	#95	—	2	2	no	—
237	#95	—	2	1	no	—
238	C₂⁴	—	2	2	no	—
239	C₂⁴	—	2	2	no	—
240	C₂⁴	—	4	2	no	—
241	C₂⁴	—	4	2	no	—
242	C₂⁴	Q₁₆×C₄₃	1	4	yes	—
243	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
244	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	16	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
266	C₂²×C₄	#41×C₄₃	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₂²⋊C₄	—	4	8	no	—
279	C₂²⋊C₄	—	4	4	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	4	8	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	8	no	—
296	C₂³	#123×C₄₃	1	2	yes	—
297	C₂³	C₂×Q₁₆×C₄₃	1	4	yes	—
298	C₂³	C₂×Q₁₆×C₄₃	1	2	yes	—
299	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
300	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
301	Q₈	—	4	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	8	8	no	—
321	C₂×C₄	#123×C₄₃	1	2	yes	—
322	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
323	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
324	C₈	—	4	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	16	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	C₄₃×#484	1	4	yes	—
338	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
339	C₂²	C₄₃×#534	1	2	yes	—
340	C₂²	C₂²×Q₁₆×C₄₃	1	1	yes	characteristic
341	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
342	C₂²	C₄₃×#575	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	4	2	no	—
345	C₄	—	8	1	no	—
346	C₄	—	8	1	no	—
347	C₄	—	8	4	no	—
348	C₄	—	8	2	no	—
349	C₄	C₄₃×#538	1	4	yes	—
350	C₂	—	2	4	no	—
351	C₂	—	4	4	no	—
352	C₂	C₄₃×#2622	1	1	yes	characteristic
353	C₂	C₂×C₄₃×#484	1	1	yes	characteristic
354	C₂	C₄₃×#3093	1	1	yes	characteristic
355	C₂	C₄₃×#3189	1	2	yes	—
356	C₂	C₄₃×#3194	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁵×C₄₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#2076	C₂	semidirect
4. C₄₃×#2036	C₂	semidirect
5. C₄₃×#1872	C₂	semidirect
6. C₄₃×#1852	C₂	semidirect
13. C₂×#107×C₄₃	C₂²	semidirect
14. C₂×#103×C₄₃	C₂²	semidirect
25. C₄₃×#340	C₂²	semidirect
26. C₄₃×#340	C₂²	semidirect
146. #29895	C₄₃	direct (N × H)
174. #2076	C₂×C₄₃	semidirect
175. #2036	C₂×C₄₃	semidirect
176. #1872	C₂×C₄₃	semidirect
177. #1852	C₂×C₄₃	semidirect
191. C₂×#107	C₂²×C₄₃	semidirect
192. C₂×#103	C₂²×C₄₃	semidirect
203. #340	C₂²×C₄₃	semidirect
204. #340	C₂²×C₄₃	semidirect
205. C₄₃	#29895	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×#2848	2
C₂×C₄₃×#380	2
C₄₃×#2076	2
C₄₃×#2036	2
C₄₃×#1872	2
C₄₃×#1852	2
C₄₃×#1779	2
#29895	43

Subgroups — C43×#29895 #24949912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29895 #24949912