Subgroups — D₄₃×#1716 #25084320

Order 11008.

798 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	#498×D₄₃	C₂	1	2	yes	maximal
2	#498×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#494×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#487×D₄₃	C₂	1	2	yes	maximal
5	#19134230	C₂	1	2	yes	maximal, complemented
6	#19134229	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134228	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134227	C₂	1	2	yes	maximal, complemented
9	#19134226	C₂	1	1	yes	maximal, characteristic, complemented
10	#322×D₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1716	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₄₃	—	2	2	no	—
13	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×D₄₃	C₂²	1	2	yes	—
16	#14583297	C₂²	1	1	yes	characteristic
17	#14583297	C₂²	1	2	yes	—
18	#14583296	—	2	4	no	—
19	#14583296	—	2	2	no	—
20	#14583295	C₂²	1	2	yes	—
21	#14583295	C₂²	1	2	yes	—
22	#14583295	C₂²	1	2	yes	—
23	#14583279	C₂²	1	1	yes	characteristic
24	#14583278	C₂²	1	1	yes	characteristic
25	#14583278	C₂²	1	1	yes	characteristic
26	#14583277	—	2	2	no	—
27	#14583251	C₂²	1	2	yes	—
28	#14583250	C₂²	1	2	yes	—
29	#14583249	C₂²	1	2	yes	—
30	#14583248	—	2	4	no	—
31	#106×D₄₃	—	2	4	no	—
32	#106×D₄₃	—	2	2	no	—
33	#103×D₄₃	—	2	4	no	—
34	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₄₃	C₂²	1	2	yes	—
36	#14582621	C₂²	1	2	yes	—
37	#14582620	C₂²	1	1	yes	characteristic
38	C₄₃×#498	C₂²	1	2	yes	—
39	C₄₃×#498	C₂²	1	1	yes	characteristic
40	C₄₃×#494	C₂²	1	1	yes	characteristic
41	C₄₃×#487	C₂²	1	2	yes	—
42	C₄₃×#322	C₂²	1	1	yes	characteristic
43	C₂×Q₈×D₄₃	—	2	2	no	—
44	C₂×Q₈×D₄₃	—	2	1	no	—
45	C₂×Q₈×D₄₃	—	2	1	no	—
46	C₂×Dic₁₇₂	—	2	2	no	—
47	C₂×#10621885	—	2	2	no	—
48	C₂×#10621885	—	2	2	no	—
49	Q₁₆×D₄₃	—	4	8	no	—
50	C₂×C₈×D₄₃	D₄	1	4	yes	—
51	C₂×C₈×D₄₃	D₄	1	2	yes	—
52	#13063325	C₂³	1	2	yes	—
53	#13063325	C₂³	1	1	yes	characteristic
54	#13063325	C₂³	1	1	yes	characteristic
55	#13063324	—	2	2	no	—
56	#13063324	—	2	2	no	—
57	#13063324	—	2	2	no	—
58	#13063324	—	2	2	no	—
59	#13063323	—	2	2	no	—
60	#13063323	—	2	1	no	—
61	#13063323	—	2	1	no	—
62	C₄⋊C₄×D₄₃	—	2	2	no	—
63	C₄⋊C₄×D₄₃	—	2	2	no	—
64	C₄⋊C₄×D₄₃	—	2	2	no	—
65	C₄⋊C₄×D₄₃	—	2	2	no	—
66	C₄²×D₄₃	C₂³	1	1	yes	characteristic
67	#13063257	—	2	4	no	—
68	#13063257	—	2	2	no	—
69	#13063256	—	2	4	no	—
70	#13063256	—	2	4	no	—
71	#13063256	—	2	4	no	—
72	#13063250	—	2	4	no	—
73	#13063249	—	2	4	no	—
74	#13063248	—	2	4	no	—
75	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
76	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₈×Dic₄₃	D₄	1	4	yes	—
78	C₈×Dic₄₃	D₄	1	2	yes	—
79	C₂×Q₁₆×C₄₃	—	2	2	no	—
80	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
83	#106×C₄₃	—	2	4	no	—
84	#106×C₄₃	—	2	2	no	—
85	#103×C₄₃	—	2	4	no	—
86	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₃	C₂³	1	2	yes	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	Q₈×D₄₃	—	4	4	no	—
92	Q₈×D₄₃	—	4	4	no	—
93	Q₈×D₄₃	—	4	8	no	—
94	C₂×C₄×D₄₃	—	4	1	no	—
95	C₂×C₄×D₄₃	—	4	1	no	—
96	C₂×C₄×D₄₃	—	4	2	no	—
97	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
99	C₂×Dic₈₆	—	2	2	no	—
100	C₂×Dic₈₆	—	2	1	no	—
101	C₂×Dic₈₆	—	2	1	no	—
102	C₂×Dic₈₆	—	4	1	no	—
103	C₂×Dic₈₆	—	4	1	no	—
104	C₂×Dic₈₆	—	4	2	no	—
105	Q₁₆×C₄₃	—	4	4	no	—
106	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
107	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
113	#10621885	—	4	4	no	—
114	#10621885	—	4	4	no	—
115	C₄⋊Dic₄₃	—	2	2	no	—
116	C₄⋊Dic₄₃	—	2	2	no	—
117	C₄⋊Dic₄₃	—	2	2	no	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	Dic₄₃⋊C₄	—	4	2	no	—
120	Dic₄₃⋊C₄	—	4	2	no	—
121	Dic₄₃⋊C₄	—	4	2	no	—
122	Dic₄₃⋊C₄	—	4	2	no	—
123	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
124	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
126	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
127	Dic₁₇₂	—	4	4	no	—
128	C₈×D₄₃	—	2	8	no	—
129	C₈×D₄₃	SD₁₆	1	8	yes	—
130	C₂²×D₄₃	#127	1	1	yes	characteristic
131	Q₈×C₄₃	—	4	2	no	—
132	Q₈×C₄₃	—	4	2	no	—
133	Q₈×C₄₃	—	4	4	no	—
134	C₂×C₄×C₄₃	—	4	1	no	—
135	C₂×C₄×C₄₃	—	4	1	no	—
136	C₂×C₄×C₄₃	—	4	2	no	—
137	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
139	C₂×Dic₄₃	—	4	1	no	—
140	C₂×Dic₄₃	—	4	1	no	—
141	C₂×Dic₄₃	—	4	2	no	—
142	C₂×Dic₄₃	#127	1	1	yes	characteristic
143	C₂×Dic₄₃	#127	1	2	yes	—
144	C₄×D₄₃	—	8	2	no	—
145	C₄×D₄₃	—	8	2	no	—
146	C₄×D₄₃	—	8	4	no	—
147	C₄×D₄₃	C₂×SD₁₆	1	4	yes	—
148	C₄×D₄₃	#137	1	8	yes	—
149	Dic₈₆	—	4	2	no	—
150	Dic₈₆	—	4	2	no	—
151	Dic₈₆	—	4	4	no	—
152	Dic₈₆	—	8	2	no	—
153	Dic₈₆	—	8	2	no	—
154	Dic₈₆	—	8	4	no	—
155	C₈×C₄₃	—	2	4	no	—
156	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
157	C₄₃⋊C₈	—	2	4	no	—
158	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
159	C₂×#1716	—	43	1	no	maximal, Sylow
160	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
161	C₂×D₄₃	#492	1	2	yes	—
162	C₂×D₄₃	#497	1	4	yes	—
163	C₄×C₄₃	—	8	1	no	—
164	C₄×C₄₃	—	8	1	no	—
165	C₄×C₄₃	—	8	2	no	—
166	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
167	C₄×C₄₃	C₂×#137	1	4	yes	—
168	Dic₄₃	—	8	1	no	—
169	Dic₄₃	—	8	1	no	—
170	Dic₄₃	—	8	2	no	—
171	Dic₄₃	#492	1	2	yes	—
172	Dic₄₃	#497	1	4	yes	—
173	C₂×#498	—	43	1	no	—
174	C₂×#498	—	43	2	no	—
175	C₂×#494	—	43	1	no	—
176	C₂×#487	—	43	2	no	—
177	#1716	—	43	2	no	—
178	#1716	—	43	1	no	—
179	#1716	—	43	1	no	—
180	#1716	—	43	2	no	—
181	#1716	—	43	1	no	—
182	#1716	D₄₃	1	1	yes	characteristic, direct product factor
183	C₂×#322	—	43	1	no	—
184	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
185	C₂×C₄₃	C₂×#497	1	2	yes	—
186	D₄₃	#1716	1	4	yes	direct product factor
187	C₂²×Q₁₆	—	86	2	no	—
188	C₂×C₄⋊Q₈	—	43	1	no	—
189	C₂×C₄⋊Q₈	—	43	2	no	—
190	C₂×C₄⋊Q₈	—	43	1	no	—
191	#498	—	43	2	no	—
192	#498	—	43	2	no	—
193	#498	—	43	2	no	—
194	#498	—	43	2	no	—
195	#498	—	43	1	no	—
196	#498	—	86	4	no	—
197	#498	—	86	2	no	—
198	#498	C₂×D₄₃	1	2	yes	—
199	#498	C₂×D₄₃	1	1	yes	characteristic
200	#494	—	43	1	no	—
201	#494	—	43	1	no	—
202	#494	—	43	1	no	—
203	#494	—	86	2	no	—
204	#494	C₂×D₄₃	1	1	yes	characteristic
205	#487	—	43	2	no	—
206	#487	—	43	2	no	—
207	#487	—	43	2	no	—
208	#487	—	86	4	no	—
209	#487	C₂×D₄₃	1	2	yes	—
210	C₂×#106	—	86	2	no	—
211	C₂×#106	—	86	4	no	—
212	C₂×#103	—	86	4	no	—
213	C₂×C₄×C₈	—	43	2	no	—
214	C₂×C₄×C₈	—	43	1	no	—
215	#322	—	43	1	no	—
216	#322	—	43	2	no	—
217	#322	C₂×D₄₃	1	1	yes	characteristic
218	C₄₃	C₂×#1716	1	1	yes	characteristic, complemented, Sylow
219	C₂²×Q₈	—	86	1	no	—
220	C₂²×Q₈	—	86	1	no	—
221	C₂²×Q₈	—	86	2	no	—
222	C₂×Q₁₆	—	2	2	no	—
223	C₂×Q₁₆	—	86	2	no	—
224	C₂×Q₁₆	—	86	2	no	—
225	C₂×Q₁₆	—	86	2	no	—
226	C₂×Q₁₆	—	172	8	no	—
227	C₂²×C₈	—	43	2	no	—
228	C₂²×C₈	—	43	4	no	—
229	C₄⋊Q₈	—	43	1	no	—
230	C₄⋊Q₈	—	43	2	no	—
231	C₄⋊Q₈	—	43	1	no	—
232	C₄⋊Q₈	—	86	2	no	—
233	C₄⋊Q₈	—	86	2	no	—
234	C₄⋊Q₈	—	86	2	no	—
235	C₄⋊Q₈	—	86	2	no	—
236	C₄⋊Q₈	—	86	2	no	—
237	C₄⋊Q₈	—	86	1	no	—
238	C₄⋊Q₈	—	86	1	no	—
239	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
240	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
241	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	86	2	no	—
243	C₂×C₄⋊C₄	—	86	2	no	—
244	C₂×C₄⋊C₄	—	86	2	no	—
245	C₂×C₄⋊C₄	—	86	2	no	—
246	C₂×C₄²	—	43	1	no	—
247	#106	—	2	4	no	—
248	#106	—	2	2	no	—
249	#106	—	86	4	no	—
250	#106	—	86	4	no	—
251	#106	—	86	4	no	—
252	#106	—	86	4	no	—
253	#106	—	86	2	no	—
254	#103	—	2	4	no	—
255	#103	—	86	4	no	—
256	#103	—	86	4	no	—
257	#103	—	86	4	no	—
258	C₄×C₈	—	43	4	no	—
259	C₄×C₈	—	43	2	no	—
260	C₄×C₈	—	43	2	no	—
261	C₄×C₈	—	43	1	no	—
262	C₄×C₈	C₂²×D₄₃	1	2	yes	—
263	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	86	2	no	—
268	C₂×Q₈	—	86	1	no	—
269	C₂×Q₈	—	86	1	no	—
270	C₂×Q₈	—	172	2	no	—
271	C₂×Q₈	—	172	1	no	—
272	C₂×Q₈	—	172	1	no	—
273	C₂×Q₈	—	172	4	no	—
274	C₂×Q₈	—	172	4	no	—
275	C₂×Q₈	—	172	8	no	—
276	C₂²×C₄	—	43	2	no	—
277	C₂²×C₄	—	43	1	no	—
278	C₂²×C₄	—	172	1	no	—
279	C₂²×C₄	—	172	1	no	—
280	C₂²×C₄	—	172	2	no	—
281	Q₁₆	—	4	4	no	—
282	Q₁₆	—	172	4	no	—
283	Q₁₆	—	172	4	no	—
284	Q₁₆	—	172	4	no	—
285	C₂×C₈	—	43	2	no	—
286	C₂×C₈	—	43	8	no	—
287	C₂×C₈	—	43	4	no	—
288	C₂×C₈	—	86	8	no	—
289	C₂×C₈	D₄×D₄₃	1	4	yes	—
290	C₂×C₈	D₄×D₄₃	1	2	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	86	2	no	—
296	C₄⋊C₄	—	86	2	no	—
297	C₄⋊C₄	—	86	2	no	—
298	C₄⋊C₄	—	86	2	no	—
299	C₄⋊C₄	—	172	2	no	—
300	C₄⋊C₄	—	172	2	no	—
301	C₄⋊C₄	—	172	2	no	—
302	C₄⋊C₄	—	172	2	no	—
303	C₄²	—	43	1	no	—
304	C₄²	—	43	2	no	—
305	C₄²	C₂³×D₄₃	1	1	yes	characteristic
306	C₂³	—	43	1	no	—
307	Q₈	—	4	2	no	—
308	Q₈	—	4	2	no	—
309	Q₈	—	4	4	no	—
310	Q₈	—	344	2	no	—
311	Q₈	—	344	2	no	—
312	Q₈	—	344	4	no	—
313	Q₈	—	172	2	no	—
314	Q₈	—	172	2	no	—
315	Q₈	—	172	4	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	43	2	no	—
320	C₂×C₄	—	43	1	no	—
321	C₂×C₄	—	43	4	no	—
322	C₂×C₄	—	43	8	no	—
323	C₂×C₄	—	344	2	no	—
324	C₂×C₄	—	344	2	no	—
325	C₂×C₄	—	344	4	no	—
326	C₂×C₄	—	172	1	no	—
327	C₂×C₄	—	172	1	no	—
328	C₂×C₄	—	172	2	no	—
329	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
331	C₈	—	2	4	no	—
332	C₈	—	43	4	no	—
333	C₈	—	86	4	no	—
334	C₈	SD₁₆×D₄₃	1	4	yes	—
335	C₂²	—	43	2	no	—
336	C₂²	—	43	4	no	—
337	C₂²	#127×D₄₃	1	1	yes	characteristic
338	C₄	—	8	1	no	—
339	C₄	—	8	1	no	—
340	C₄	—	8	2	no	—
341	C₄	—	43	2	no	—
342	C₄	—	43	4	no	—
343	C₄	—	344	1	no	—
344	C₄	—	344	1	no	—
345	C₄	—	344	2	no	—
346	C₄	C₂×SD₁₆×D₄₃	1	2	yes	—
347	C₄	#137×D₄₃	1	4	yes	—
348	C₂	—	43	4	no	—
349	C₂	#492×D₄₃	1	1	yes	characteristic
350	C₂	#497×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²	#127×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1716	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	C₂²×D₄₃	#127
hypercenter	#1716	D₄₃
hypocenter	C₄₃	C₂×#1716
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1716

Complements

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

N	H ≅ G/N	type
5. #19134230	C₂	semidirect
6. #19134229	C₂	semidirect
7. #19134228	C₂	semidirect
8. #19134227	C₂	semidirect
9. #19134226	C₂	semidirect
11. C₄₃×#1716	C₂	semidirect
182. #1716	D₄₃	direct (N × H)
186. D₄₃	#1716	direct (N × H)
218. C₄₃	C₂×#1716	semidirect

Maximal subgroups

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

subgroup	index
#498×D₄₃	2
#494×D₄₃	2
#487×D₄₃	2
#19134230	2
#19134229	2
#19134228	2
#19134227	2
#19134226	2
#322×D₄₃	2
C₄₃×#1716	2
C₂×#1716	43

Subgroups — D43×#1716 #25084320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1716 #25084320