Subgroups — C₄₃×#28385 #24948402

Order 11008.

902 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	C₂×C₄₃×#475	C₂	1	2	yes	maximal
2	C₂×C₄₃×#462	C₂	1	2	yes	maximal
3	C₄₃×#2862	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2096	C₂	1	2	yes	maximal
6	C₄₃×#2016	C₂	1	2	yes	maximal
7	C₄₃×#1971	C₂	1	4	yes	maximal
8	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#475	—	2	8	no	—
15	C₄₃×#462	—	2	8	no	—
16	C₂×#106×C₄₃	C₂²	1	4	yes	—
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#103×C₄₃	C₂²	1	4	yes	—
19	C₂×#103×C₄₃	C₂²	1	4	yes	—
20	C₂×#97×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#391	—	2	2	no	—
22	C₄₃×#391	C₂²	1	2	yes	—
23	C₄₃×#391	C₂²	1	2	yes	—
24	C₄₃×#391	C₂²	1	2	yes	—
25	C₄₃×#389	—	2	2	no	—
26	C₄₃×#384	C₂²	1	1	yes	characteristic
27	C₄₃×#382	—	2	2	no	—
28	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
29	C₄³×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₄₃	—	2	1	no	—
32	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
33	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
34	C₂×Q₁₆×C₄₃	—	2	8	no	—
35	C₂×Q₁₆×C₄₃	—	2	8	no	—
36	C₂×Q₁₆×C₄₃	—	4	4	no	—
37	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
38	C₄⋊Q₈×C₄₃	—	2	4	no	—
39	C₄⋊Q₈×C₄₃	—	2	4	no	—
40	C₄⋊Q₈×C₄₃	—	2	4	no	—
41	C₄×Q₈×C₄₃	—	2	4	no	—
42	C₄×Q₈×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₄₃	—	2	2	no	—
52	C₂×C₄²×C₄₃	D₄	1	2	yes	—
53	C₂×C₄²×C₄₃	D₄	1	2	yes	—
54	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
57	#106×C₄₃	—	2	8	no	—
58	C₄⋊C₈×C₄₃	D₄	1	8	yes	—
59	#103×C₄₃	—	2	8	no	—
60	#103×C₄₃	—	2	8	no	—
61	#97×C₄₃	—	4	2	no	—
62	#95×C₄₃	—	2	4	no	—
63	#95×C₄₃	—	2	4	no	—
64	#95×C₄₃	—	2	4	no	—
65	C₂×Q₈×C₄₃	—	2	2	no	—
66	C₂×Q₈×C₄₃	—	2	2	no	—
67	C₂×Q₈×C₄₃	—	2	2	no	—
68	C₂×Q₈×C₄₃	—	2	4	no	—
69	C₂×Q₈×C₄₃	—	2	4	no	—
70	C₂×Q₈×C₄₃	—	2	2	no	—
71	C₂×Q₈×C₄₃	—	2	2	no	—
72	C₂×Q₈×C₄₃	—	2	2	no	—
73	C₂×Q₈×C₄₃	—	2	2	no	—
74	C₂×Q₈×C₄₃	—	4	2	no	—
75	C₂×Q₈×C₄₃	—	4	4	no	—
76	C₂×Q₈×C₄₃	#41	1	4	yes	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
86	Q₁₆×C₄₃	—	4	16	no	—
87	C₂×C₈×C₄₃	—	2	4	no	—
88	C₂×C₈×C₄₃	—	2	4	no	—
89	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
90	C₄⋊C₄×C₄₃	—	2	8	no	—
91	C₄⋊C₄×C₄₃	—	2	2	no	—
92	C₄⋊C₄×C₄₃	—	2	4	no	—
93	C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₄⋊C₄×C₄₃	—	4	4	no	—
95	C₄⋊C₄×C₄₃	—	4	2	no	—
96	C₄⋊C₄×C₄₃	—	4	2	no	—
97	C₄⋊C₄×C₄₃	—	4	2	no	—
98	C₄⋊C₄×C₄₃	—	4	4	no	—
99	C₄²×C₄₃	—	2	4	no	—
100	C₄²×C₄₃	—	2	4	no	—
101	C₄²×C₄₃	—	2	2	no	—
102	C₄²×C₄₃	—	2	1	no	—
103	C₄²×C₄₃	—	2	1	no	—
104	C₄²×C₄₃	—	4	4	no	—
105	C₄²×C₄₃	C₂×D₄	1	4	yes	—
106	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
107	Q₈×C₄₃	—	2	4	no	—
108	Q₈×C₄₃	—	2	4	no	—
109	Q₈×C₄₃	—	4	2	no	—
110	Q₈×C₄₃	—	4	2	no	—
111	Q₈×C₄₃	—	4	4	no	—
112	Q₈×C₄₃	—	4	4	no	—
113	Q₈×C₄₃	—	8	4	no	—
114	C₂×C₄×C₄₃	—	2	2	no	—
115	C₂×C₄×C₄₃	—	2	2	no	—
116	C₂×C₄×C₄₃	—	2	2	no	—
117	C₂×C₄×C₄₃	—	2	4	no	—
118	C₂×C₄×C₄₃	—	2	2	no	—
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	4	2	no	—
122	C₂×C₄×C₄₃	—	4	2	no	—
123	C₂×C₄×C₄₃	—	4	2	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	4	no	—
129	C₂×C₄×C₄₃	—	4	4	no	—
130	C₂×C₄×C₄₃	#127	1	2	yes	—
131	C₂×C₄×C₄₃	#127	1	2	yes	—
132	C₂×C₄×C₄₃	#137	1	4	yes	—
133	C₂×C₄×C₄₃	#137	1	4	yes	—
134	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
135	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
136	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
137	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
138	C₈×C₄₃	—	2	8	no	—
139	#28385	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂²×C₄₃	#525	1	1	yes	characteristic
141	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
142	C₂²×C₄₃	#537	1	1	yes	characteristic
143	C₂²×C₄₃	C₂×#137	1	2	yes	—
144	C₂²×C₄₃	C₂×#137	1	2	yes	—
145	C₄×C₄₃	—	2	4	no	—
146	C₄×C₄₃	—	2	2	no	—
147	C₄×C₄₃	—	4	2	no	—
148	C₄×C₄₃	—	4	4	no	—
149	C₄×C₄₃	—	8	2	no	—
150	C₄×C₄₃	—	8	2	no	—
151	C₄×C₄₃	—	8	2	no	—
152	C₄×C₄₃	#497	1	4	yes	—
153	C₄×C₄₃	#546	1	2	yes	—
154	C₄×C₄₃	#548	1	2	yes	—
155	C₂×#475	C₂×C₄₃	1	2	yes	—
156	C₂×#462	C₂×C₄₃	1	2	yes	—
157	#2862	C₂×C₄₃	1	1	yes	characteristic
158	C₄×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic
159	#2096	C₂×C₄₃	1	2	yes	—
160	#2016	C₂×C₄₃	1	2	yes	—
161	#1971	C₂×C₄₃	1	4	yes	—
162	#1767	C₂×C₄₃	1	1	yes	characteristic
163	C₂×C₄₃	#2540	1	1	yes	characteristic
164	C₂×C₄₃	#3113	1	2	yes	—
165	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
166	C₂×C₄₃	#3152	1	1	yes	characteristic
167	C₂×C₄₃	#3255	1	2	yes	—
168	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
169	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
171	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
172	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
173	#475	—	2	8	no	—
174	#462	—	2	8	no	—
175	C₂×#106	C₂²×C₄₃	1	4	yes	—
176	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
177	C₂×#103	C₂²×C₄₃	1	4	yes	—
178	C₂×#103	C₂²×C₄₃	1	4	yes	—
179	C₂×#97	C₂²×C₄₃	1	2	yes	—
180	#391	—	2	2	no	—
181	#391	C₂²×C₄₃	1	2	yes	—
182	#391	C₂²×C₄₃	1	2	yes	—
183	#391	C₂²×C₄₃	1	2	yes	—
184	#389	—	2	2	no	—
185	#384	C₂²×C₄₃	1	1	yes	characteristic
186	#382	—	2	2	no	—
187	C₄×C₄⋊C₄	—	2	2	no	—
188	C₄³	C₂²×C₄₃	1	1	yes	characteristic
189	#336	C₂²×C₄₃	1	2	yes	—
190	C₄₃	#28385	1	1	yes	characteristic, direct product factor, Sylow
191	C₂²×Q₈	—	2	1	no	—
192	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
193	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
194	C₂×Q₁₆	—	2	8	no	—
195	C₂×Q₁₆	—	2	8	no	—
196	C₂×Q₁₆	—	4	4	no	—
197	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
198	C₄⋊Q₈	—	2	4	no	—
199	C₄⋊Q₈	—	2	4	no	—
200	C₄⋊Q₈	—	2	4	no	—
201	C₄×Q₈	—	2	4	no	—
202	C₄×Q₈	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
211	C₂×C₄²	—	2	2	no	—
212	C₂×C₄²	D₄×C₄₃	1	2	yes	—
213	C₂×C₄²	D₄×C₄₃	1	2	yes	—
214	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
217	#106	—	2	8	no	—
218	C₄⋊C₈	D₄×C₄₃	1	8	yes	—
219	#103	—	2	8	no	—
220	#103	—	2	8	no	—
221	#97	—	4	2	no	—
222	#95	—	2	4	no	—
223	#95	—	2	4	no	—
224	#95	—	2	4	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	2	no	—
227	C₂×Q₈	—	2	2	no	—
228	C₂×Q₈	—	2	4	no	—
229	C₂×Q₈	—	2	4	no	—
230	C₂×Q₈	—	2	2	no	—
231	C₂×Q₈	—	2	2	no	—
232	C₂×Q₈	—	2	2	no	—
233	C₂×Q₈	—	2	2	no	—
234	C₂×Q₈	—	4	2	no	—
235	C₂×Q₈	—	4	4	no	—
236	C₂×Q₈	#41×C₄₃	1	4	yes	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
242	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
244	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
245	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
246	Q₁₆	—	4	16	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	—
250	C₄⋊C₄	—	2	8	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	4	4	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₄⋊C₄	—	4	4	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	2	1	no	—
263	C₄²	—	2	1	no	—
264	C₄²	—	4	4	no	—
265	C₄²	C₂×D₄×C₄₃	1	4	yes	—
266	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
267	Q₈	—	2	4	no	—
268	Q₈	—	2	4	no	—
269	Q₈	—	4	2	no	—
270	Q₈	—	4	2	no	—
271	Q₈	—	4	4	no	—
272	Q₈	—	4	4	no	—
273	Q₈	—	8	4	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	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	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	#127×C₄₃	1	2	yes	—
291	C₂×C₄	#127×C₄₃	1	2	yes	—
292	C₂×C₄	#137×C₄₃	1	4	yes	—
293	C₂×C₄	#137×C₄₃	1	4	yes	—
294	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
295	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
296	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
297	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
298	C₈	—	2	8	no	—
299	C₂²	C₄₃×#525	1	1	yes	characteristic
300	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
301	C₂²	C₄₃×#537	1	1	yes	characteristic
302	C₂²	C₂×#137×C₄₃	1	2	yes	—
303	C₂²	C₂×#137×C₄₃	1	2	yes	—
304	C₄	—	2	4	no	—
305	C₄	—	2	2	no	—
306	C₄	—	4	2	no	—
307	C₄	—	4	4	no	—
308	C₄	—	8	2	no	—
309	C₄	—	8	2	no	—
310	C₄	—	8	2	no	—
311	C₄	C₄₃×#497	1	4	yes	—
312	C₄	C₄₃×#546	1	2	yes	—
313	C₄	C₄₃×#548	1	2	yes	—
314	C₂	C₄₃×#2540	1	1	yes	characteristic
315	C₂	C₄₃×#3113	1	2	yes	—
316	C₂	C₂×C₄₃×#497	1	1	yes	characteristic
317	C₂	C₄₃×#3152	1	1	yes	characteristic
318	C₂	C₄₃×#3255	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
139. #28385	C₄₃	direct (N × H)
190. C₄₃	#28385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#475	2
C₂×C₄₃×#462	2
C₄₃×#2862	2
C₄×C₄⋊Q₈×C₄₃	2
C₄₃×#2096	2
C₄₃×#2016	2
C₄₃×#1971	2
C₄₃×#1767	2
#28385	43

Subgroups — C43×#28385 #24948402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28385 #24948402