Subgroups — C₄₃×#10947 #24930964

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#419	C₂	1	2	yes	maximal
2	C₄₃×#2873	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2310	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1740	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
8	C₂×#117×C₄₃	C₂²	1	2	yes	—
9	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#419	—	2	4	no	—
12	C₄₃×#419	C₄	1	8	yes	complemented
13	C₂×#103×C₄₃	—	2	4	no	—
14	C₄₃×#405	—	2	4	no	—
15	C₄×M₁₆×C₄₃	—	2	2	no	—
16	C₄₃×#391	—	2	2	no	—
17	C₄₃×#391	C₄	1	4	yes	complemented
18	C₄₃×#381	—	2	2	no	—
19	C₄₃×#342	—	2	2	no	—
20	C₄₃×H(3,ℤ/4)	—	2	4	no	—
21	C₂²×Q₈×C₄₃	—	2	1	no	—
22	C₂²×Q₈×C₄₃	—	2	2	no	—
23	C₂²×Q₈×C₄₃	—	2	2	no	—
24	C₂²×Q₈×C₄₃	—	2	2	no	—
25	C₂²×Q₈×C₄₃	—	2	2	no	—
26	C₂²×Q₈×C₄₃	—	2	2	no	—
27	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
29	C₂³×C₄×C₄₃	—	2	1	no	—
30	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂×M₁₆×C₄₃	—	2	2	no	—
32	C₂×M₁₆×C₄₃	—	2	2	no	—
33	C₂×M₁₆×C₄₃	—	2	2	no	—
34	C₂×M₁₆×C₄₃	—	2	2	no	—
35	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
36	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
37	C₂²×C₈×C₄₃	D₄	1	4	yes	—
38	#117×C₄₃	—	2	2	no	—
39	#117×C₄₃	—	2	2	no	—
40	#117×C₄₃	—	2	2	no	—
41	#117×C₄₃	—	2	2	no	—
42	#117×C₄₃	—	2	2	no	—
43	#117×C₄₃	—	2	2	no	—
44	#117×C₄₃	—	2	2	no	—
45	#117×C₄₃	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
52	C₂×C₄²×C₄₃	—	2	2	no	—
53	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₃	D₄	1	2	yes	—
55	#103×C₄₃	—	2	16	no	—
56	#97×C₄₃	—	2	4	no	—
57	C₄×C₈×C₄₃	—	2	4	no	—
58	#95×C₄₃	—	2	8	no	—
59	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂×Q₈×C₄₃	—	2	2	no	—
61	C₂×Q₈×C₄₃	—	2	4	no	—
62	C₂×Q₈×C₄₃	—	2	4	no	—
63	C₂×Q₈×C₄₃	—	2	4	no	—
64	C₂×Q₈×C₄₃	—	2	4	no	—
65	C₂×Q₈×C₄₃	—	2	4	no	—
66	C₂×Q₈×C₄₃	—	2	4	no	—
67	C₂×Q₈×C₄₃	—	2	4	no	—
68	C₂×Q₈×C₄₃	—	4	1	no	—
69	C₂×Q₈×C₄₃	—	4	2	no	—
70	C₂×Q₈×C₄₃	—	4	2	no	—
71	C₂×Q₈×C₄₃	—	4	1	no	—
72	C₂×Q₈×C₄₃	—	4	2	no	—
73	C₂×Q₈×C₄₃	—	4	2	no	—
74	C₂×Q₈×C₄₃	—	4	2	no	—
75	C₂×Q₈×C₄₃	C₄²	1	4	yes	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	4	2	no	—
80	C₂²×C₄×C₄₃	—	4	2	no	—
81	C₂²×C₄×C₄₃	—	4	1	no	—
82	C₂²×C₄×C₄₃	—	4	1	no	—
83	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂²×C₄	1	2	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	#41	1	2	yes	—
90	C₂²×C₄×C₄₃	#41	1	2	yes	—
91	C₂²×C₄×C₄₃	#41	1	2	yes	—
92	M₁₆×C₄₃	—	2	4	no	—
93	M₁₆×C₄₃	—	2	4	no	—
94	M₁₆×C₄₃	—	2	4	no	—
95	M₁₆×C₄₃	—	2	4	no	—
96	C₂×C₈×C₄₃	—	2	4	no	—
97	C₂×C₈×C₄₃	—	2	4	no	—
98	C₂×C₈×C₄₃	C₂²⋊C₄	1	8	yes	—
99	C₄⋊C₄×C₄₃	—	2	4	no	—
100	C₄⋊C₄×C₄₃	—	2	4	no	—
101	C₄⋊C₄×C₄₃	—	4	2	no	—
102	C₄⋊C₄×C₄₃	—	4	2	no	—
103	C₂²⋊C₄×C₄₃	—	2	4	no	—
104	C₂²⋊C₄×C₄₃	—	2	4	no	—
105	C₂²⋊C₄×C₄₃	—	4	1	no	—
106	C₂²⋊C₄×C₄₃	—	4	1	no	—
107	C₂²⋊C₄×C₄₃	—	4	2	no	—
108	C₄²×C₄₃	—	2	2	no	—
109	C₄²×C₄₃	—	2	2	no	—
110	C₄²×C₄₃	—	2	4	no	—
111	C₄²×C₄₃	—	2	4	no	—
112	C₄²×C₄₃	—	4	2	no	—
113	C₂³×C₄₃	—	4	2	no	—
114	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₃	C₄×D₄	1	2	yes	—
116	C₂³×C₄₃	#121	1	2	yes	—
117	C₂³×C₄₃	#124	1	1	yes	characteristic
118	C₂³×C₄₃	#127	1	1	yes	characteristic
119	Q₈×C₄₃	—	2	8	no	—
120	Q₈×C₄₃	—	4	4	no	—
121	Q₈×C₄₃	—	4	4	no	—
122	Q₈×C₄₃	—	4	4	no	—
123	C₂×C₄×C₄₃	—	2	4	no	—
124	C₂×C₄×C₄₃	—	2	4	no	—
125	C₂×C₄×C₄₃	—	4	2	no	—
126	C₂×C₄×C₄₃	—	4	4	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	—	4	4	no	—
131	C₂×C₄×C₄₃	—	4	2	no	—
132	C₂×C₄×C₄₃	—	4	4	no	—
133	C₂×C₄×C₄₃	—	8	4	no	—
134	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₄₃	#117	1	2	yes	—
137	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#121	1	2	yes	—
145	C₂×C₄×C₄₃	#121	1	2	yes	—
146	C₂×C₄×C₄₃	#123	1	2	yes	—
147	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#124	1	2	yes	—
149	C₂×C₄×C₄₃	#126	1	2	yes	—
150	C₈×C₄₃	—	2	8	no	—
151	#10947	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	1	no	—
156	C₂²×C₄₃	—	4	1	no	—
157	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄₃	#386	1	1	yes	characteristic
159	C₂²×C₄₃	#388	1	2	yes	—
160	C₂²×C₄₃	#390	1	1	yes	characteristic
161	C₂²×C₄₃	#390	1	2	yes	—
162	C₄×C₄₃	—	4	4	no	—
163	C₄×C₄₃	—	4	4	no	—
164	C₄×C₄₃	—	8	2	no	—
165	C₄×C₄₃	—	8	4	no	—
166	C₄×C₄₃	C₄×C₂²⋊C₄	1	2	yes	—
167	C₄×C₄₃	#386	1	2	yes	—
168	C₄×C₄₃	#388	1	2	yes	—
169	C₄×C₄₃	#388	1	2	yes	—
170	C₂×#419	C₂×C₄₃	1	2	yes	—
171	#2873	C₂×C₄₃	1	1	yes	characteristic
172	#2310	C₂×C₄₃	1	1	yes	characteristic
173	#1740	C₂×C₄₃	1	1	yes	characteristic
174	C₂×H(3,ℤ/4)	C₂×C₄₃	1	2	yes	—
175	C₂×C₄₃	—	2	1	no	—
176	C₂×C₄₃	—	2	2	no	—
177	C₂×C₄₃	—	2	1	no	—
178	C₂×C₄₃	—	2	2	no	—
179	C₂×C₄₃	#1437	1	1	yes	characteristic
180	C₂×C₄₃	#1909	1	2	yes	—
181	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
182	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
183	C₂×#117	C₂²×C₄₃	1	2	yes	—
184	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
185	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
186	#419	—	2	4	no	—
187	#419	C₄×C₄₃	1	8	yes	complemented
188	C₂×#103	—	2	4	no	—
189	#405	—	2	4	no	—
190	C₄×M₁₆	—	2	2	no	—
191	#391	—	2	2	no	—
192	#391	C₄×C₄₃	1	4	yes	complemented
193	#381	—	2	2	no	—
194	#342	—	2	2	no	—
195	H(3,ℤ/4)	—	2	4	no	—
196	C₄₃	#10947	1	1	yes	characteristic, direct product factor, Sylow
197	C₂²×Q₈	—	2	1	no	—
198	C₂²×Q₈	—	2	2	no	—
199	C₂²×Q₈	—	2	2	no	—
200	C₂²×Q₈	—	2	2	no	—
201	C₂²×Q₈	—	2	2	no	—
202	C₂²×Q₈	—	2	2	no	—
203	C₂²×Q₈	C₂×C₄×C₄₃	1	2	yes	—
204	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
205	C₂³×C₄	—	2	1	no	—
206	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	—
212	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
213	C₂²×C₈	D₄×C₄₃	1	4	yes	—
214	#117	—	2	2	no	—
215	#117	—	2	2	no	—
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	#117	—	2	2	no	—
219	#117	—	2	2	no	—
220	#117	—	2	2	no	—
221	#117	C₂×C₄×C₄₃	1	4	yes	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	1	no	—
227	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
230	C₂×C₄²	D₄×C₄₃	1	2	yes	—
231	#103	—	2	16	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	#95	—	2	8	no	—
235	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	2	4	no	—
242	C₂×Q₈	—	2	4	no	—
243	C₂×Q₈	—	2	4	no	—
244	C₂×Q₈	—	4	1	no	—
245	C₂×Q₈	—	4	2	no	—
246	C₂×Q₈	—	4	2	no	—
247	C₂×Q₈	—	4	1	no	—
248	C₂×Q₈	—	4	2	no	—
249	C₂×Q₈	—	4	2	no	—
250	C₂×Q₈	—	4	2	no	—
251	C₂×Q₈	C₄²×C₄₃	1	4	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
265	C₂²×C₄	#41×C₄₃	1	2	yes	—
266	C₂²×C₄	#41×C₄₃	1	2	yes	—
267	C₂²×C₄	#41×C₄₃	1	2	yes	—
268	M₁₆	—	2	4	no	—
269	M₁₆	—	2	4	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂²⋊C₄×C₄₃	1	8	yes	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₂²⋊C₄	—	2	4	no	—
280	C₂²⋊C₄	—	2	4	no	—
281	C₂²⋊C₄	—	4	1	no	—
282	C₂²⋊C₄	—	4	1	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	4	2	no	—
289	C₂³	—	4	2	no	—
290	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
291	C₂³	C₄×D₄×C₄₃	1	2	yes	—
292	C₂³	#121×C₄₃	1	2	yes	—
293	C₂³	#124×C₄₃	1	1	yes	characteristic
294	C₂³	#127×C₄₃	1	1	yes	characteristic
295	Q₈	—	2	8	no	—
296	Q₈	—	4	4	no	—
297	Q₈	—	4	4	no	—
298	Q₈	—	4	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	8	4	no	—
310	C₂×C₄	C₂×C₄²×C₄₃	1	1	yes	characteristic
311	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
312	C₂×C₄	#117×C₄₃	1	2	yes	—
313	C₂×C₄	#117×C₄₃	1	1	yes	characteristic
314	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
315	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
316	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
317	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
318	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
319	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
320	C₂×C₄	#121×C₄₃	1	2	yes	—
321	C₂×C₄	#121×C₄₃	1	2	yes	—
322	C₂×C₄	#123×C₄₃	1	2	yes	—
323	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
324	C₂×C₄	#124×C₄₃	1	2	yes	—
325	C₂×C₄	#126×C₄₃	1	2	yes	—
326	C₈	—	2	8	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	4	2	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	1	no	—
332	C₂²	C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
333	C₂²	C₄₃×#386	1	1	yes	characteristic
334	C₂²	C₄₃×#388	1	2	yes	—
335	C₂²	C₄₃×#390	1	2	yes	—
336	C₂²	C₄₃×#390	1	1	yes	characteristic
337	C₄	—	4	4	no	—
338	C₄	—	4	4	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	4	no	—
341	C₄	C₄×C₂²⋊C₄×C₄₃	1	2	yes	—
342	C₄	C₄₃×#386	1	2	yes	—
343	C₄	C₄₃×#388	1	2	yes	—
344	C₄	C₄₃×#388	1	2	yes	—
345	C₂	—	2	1	no	—
346	C₂	—	2	2	no	—
347	C₂	—	2	1	no	—
348	C₂	—	2	2	no	—
349	C₂	C₄₃×#1437	1	1	yes	characteristic
350	C₂	C₄₃×#1909	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	#386
commutator	C₂×C₄	C₂×C₄²×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₄₃×#419	C₄	semidirect
17. C₄₃×#391	C₄	semidirect
151. #10947	C₄₃	direct (N × H)
187. #419	C₄×C₄₃	semidirect
192. #391	C₄×C₄₃	semidirect
196. C₄₃	#10947	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×#419	2
C₄₃×#2873	2
C₄₃×#2310	2
C₄₃×#1740	2
C₂×C₄₃×H(3,ℤ/4)	2
#10947	43

Subgroups — C43×#10947 #24930964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10947 #24930964