Subgroups — C₄₃×#23943 #24943960

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#451	C₂	1	2	yes	maximal
3	C₄₃×#2310	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2026	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1878	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1873	C₂	1	2	yes	maximal
8	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
11	C₄₃×#541	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#126×C₄₃	—	2	2	no	—
14	C₂×#125×C₄₃	—	2	2	no	—
15	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#451	—	2	8	no	—
21	C₂×#103×C₄₃	C₂²	1	4	yes	—
22	C₂×#103×C₄₃	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#391	—	2	2	no	—
25	C₄₃×#391	C₂²	1	2	yes	—
26	C₄₃×#391	C₂²	1	2	yes	—
27	C₄₃×#381	—	2	2	no	—
28	C₄₃×#340	C₂²	1	4	yes	—
29	C₄₃×#336	C₂²	1	2	yes	—
30	C₄₃×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₄₃	—	2	4	no	—
32	C₂²×Q₈×C₄₃	—	2	1	no	—
33	C₂²×Q₈×C₄₃	—	2	4	no	—
34	C₂²×Q₈×C₄₃	—	4	2	no	—
35	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	—	2	1	no	—
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₄₃	—	2	8	no	—
40	C₂×Q₁₆×C₄₃	—	2	8	no	—
41	C₂×Q₁₆×C₄₃	—	4	4	no	—
42	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
43	C₄⋊Q₈×C₄₃	—	2	4	no	—
44	#126×C₄₃	—	2	16	no	—
45	#125×C₄₃	—	2	16	no	—
46	#125×C₄₃	—	2	4	no	—
47	C₂²⋊Q₈×C₄₃	—	2	4	no	—
48	C₂²⋊Q₈×C₄₃	D₄	1	8	yes	—
49	C₄×Q₈×C₄₃	—	2	4	no	—
50	C₄×Q₈×C₄₃	—	2	4	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
63	C₂×C₄²×C₄₃	—	2	2	no	—
64	C₂×C₄²×C₄₃	—	2	1	no	—
65	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	#103×C₄₃	—	2	8	no	—
68	#103×C₄₃	—	4	4	no	—
69	C₂²⋊C₈×C₄₃	—	2	4	no	—
70	#95×C₄₃	—	2	4	no	—
71	#95×C₄₃	—	2	4	no	—
72	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₄₃	—	2	4	no	—
74	C₂×Q₈×C₄₃	—	2	2	no	—
75	C₂×Q₈×C₄₃	—	2	2	no	—
76	C₂×Q₈×C₄₃	—	2	4	no	—
77	C₂×Q₈×C₄₃	—	2	4	no	—
78	C₂×Q₈×C₄₃	—	2	4	no	—
79	C₂×Q₈×C₄₃	—	2	4	no	—
80	C₂×Q₈×C₄₃	—	4	16	no	—
81	C₂×Q₈×C₄₃	—	4	2	no	—
82	C₂×Q₈×C₄₃	—	4	2	no	—
83	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
84	C₂×Q₈×C₄₃	#41	1	4	yes	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	4	2	no	—
93	C₂²×C₄×C₄₃	—	4	2	no	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₄₃	—	4	16	no	—
100	C₂×C₈×C₄₃	—	2	4	no	—
101	C₂×C₈×C₄₃	—	2	4	no	—
102	C₂×C₈×C₄₃	—	2	4	no	—
103	C₄⋊C₄×C₄₃	—	2	8	no	—
104	C₄⋊C₄×C₄₃	—	2	8	no	—
105	C₄⋊C₄×C₄₃	—	2	8	no	—
106	C₄⋊C₄×C₄₃	—	2	8	no	—
107	C₄⋊C₄×C₄₃	—	2	4	no	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	4	no	—
110	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
111	C₂²⋊C₄×C₄₃	—	2	8	no	—
112	C₂²⋊C₄×C₄₃	—	2	4	no	—
113	C₂²⋊C₄×C₄₃	—	4	2	no	—
114	C₄²×C₄₃	—	2	8	no	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	—	4	2	no	—
118	C₂³×C₄₃	—	2	1	no	—
119	C₂³×C₄₃	—	2	1	no	—
120	C₂³×C₄₃	—	2	4	no	—
121	C₂³×C₄₃	#120	1	2	yes	—
122	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₄₃	—	2	8	no	—
124	Q₈×C₄₃	—	2	8	no	—
125	Q₈×C₄₃	—	4	8	no	—
126	Q₈×C₄₃	—	4	4	no	—
127	Q₈×C₄₃	—	4	4	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	8	no	—
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	2	2	no	—
133	C₂×C₄×C₄₃	—	2	4	no	—
134	C₂×C₄×C₄₃	—	2	4	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	4	8	no	—
139	C₂×C₄×C₄₃	—	4	2	no	—
140	C₂×C₄×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	4	no	—
144	C₂×C₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	#120	1	2	yes	—
147	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
149	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
150	C₈×C₄₃	—	4	4	no	—
151	#23943	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂²×C₄₃	—	2	2	no	—
153	C₂²×C₄₃	—	2	4	no	—
154	C₂²×C₄₃	—	4	2	no	—
155	C₂²×C₄₃	—	4	2	no	—
156	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
157	C₂²×C₄₃	#525	1	1	yes	characteristic
158	C₂²×C₄₃	#535	1	1	yes	characteristic
159	C₂²×C₄₃	#578	1	4	yes	—
160	C₄×C₄₃	—	2	2	no	—
161	C₄×C₄₃	—	4	4	no	—
162	C₄×C₄₃	—	4	4	no	—
163	C₄×C₄₃	—	4	2	no	—
164	C₄×C₄₃	—	4	2	no	—
165	C₄×C₄₃	—	4	4	no	—
166	C₄×C₄₃	—	8	2	no	—
167	C₄×C₄₃	#546	1	4	yes	—
168	C₂×#541	C₂×C₄₃	1	1	yes	characteristic
169	C₂×#451	C₂×C₄₃	1	2	yes	—
170	#2310	C₂×C₄₃	1	1	yes	characteristic
171	#2026	C₂×C₄₃	1	2	yes	complemented
172	#2016	C₂×C₄₃	1	2	yes	complemented
173	#1878	C₂×C₄₃	1	4	yes	complemented
174	#1873	C₂×C₄₃	1	2	yes	—
175	#1818	C₂×C₄₃	1	1	yes	characteristic
176	C₂×C₄₃	—	4	2	no	—
177	C₂×C₄₃	#2404	1	1	yes	characteristic
178	C₂×C₄₃	#3011	1	2	yes	—
179	C₂×C₄₃	#3127	1	2	yes	—
180	C₂×C₄₃	#3223	1	2	yes	—
181	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
182	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
183	#541	—	2	8	no	—
184	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
185	C₂×#126	—	2	2	no	—
186	C₂×#125	—	2	2	no	—
187	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
188	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
189	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
190	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
191	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
192	#451	—	2	8	no	—
193	C₂×#103	C₂²×C₄₃	1	4	yes	—
194	C₂×#103	C₂²×C₄₃	1	4	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
196	#391	—	2	2	no	—
197	#391	C₂²×C₄₃	1	2	yes	—
198	#391	C₂²×C₄₃	1	2	yes	—
199	#381	—	2	2	no	—
200	#340	C₂²×C₄₃	1	4	yes	—
201	#336	C₂²×C₄₃	1	2	yes	—
202	#336	C₂²×C₄₃	1	2	yes	—
203	C₄₃	#23943	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	2	1	no	—
206	C₂²×Q₈	—	2	4	no	—
207	C₂²×Q₈	—	4	2	no	—
208	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
209	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
212	C₂×Q₁₆	—	2	8	no	—
213	C₂×Q₁₆	—	2	8	no	—
214	C₂×Q₁₆	—	4	4	no	—
215	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
216	C₄⋊Q₈	—	2	4	no	—
217	#126	—	2	16	no	—
218	#125	—	2	16	no	—
219	#125	—	2	4	no	—
220	C₂²⋊Q₈	—	2	4	no	—
221	C₂²⋊Q₈	D₄×C₄₃	1	8	yes	—
222	C₄×Q₈	—	2	4	no	—
223	C₄×Q₈	—	2	4	no	—
224	#117	—	2	4	no	—
225	#117	—	4	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
240	#103	—	2	8	no	—
241	#103	—	4	4	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	#95	—	2	4	no	—
244	#95	—	2	4	no	—
245	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	—	4	16	no	—
254	C₂×Q₈	—	4	2	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
257	C₂×Q₈	#41×C₄₃	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
272	Q₁₆	—	4	16	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
284	C₂²⋊C₄	—	2	8	no	—
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₄²	—	2	8	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	4	2	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	4	no	—
294	C₂³	#120×C₄₃	1	2	yes	—
295	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
296	Q₈	—	2	8	no	—
297	Q₈	—	2	8	no	—
298	Q₈	—	4	8	no	—
299	Q₈	—	4	4	no	—
300	Q₈	—	4	4	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	#120×C₄₃	1	2	yes	—
320	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
321	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
322	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
323	C₈	—	4	4	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
329	C₂²	C₄₃×#525	1	1	yes	characteristic
330	C₂²	C₄₃×#535	1	1	yes	characteristic
331	C₂²	C₄₃×#578	1	4	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	4	4	no	—
334	C₄	—	4	4	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	2	no	—
337	C₄	—	4	4	no	—
338	C₄	—	8	2	no	—
339	C₄	C₄₃×#546	1	4	yes	—
340	C₂	—	4	2	no	—
341	C₂	C₄₃×#2404	1	1	yes	characteristic
342	C₂	C₄₃×#3011	1	2	yes	—
343	C₂	C₄₃×#3127	1	2	yes	—
344	C₂	C₄₃×#3223	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 ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#2026	C₂	semidirect
5. C₄₃×#2016	C₂	semidirect
6. C₄₃×#1878	C₂	semidirect
151. #23943	C₄₃	direct (N × H)
171. #2026	C₂×C₄₃	semidirect
172. #2016	C₂×C₄₃	semidirect
173. #1878	C₂×C₄₃	semidirect
203. C₄₃	#23943	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×#541	2
C₂×C₄₃×#451	2
C₄₃×#2310	2
C₄₃×#2026	2
C₄₃×#2016	2
C₄₃×#1878	2
C₄₃×#1873	2
C₄₃×#1818	2
#23943	43

Subgroups — C43×#23943 #24943960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23943 #24943960