Subgroups — D₄₃×#1708 #25084248

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 372 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	1	yes	maximal, characteristic, complemented
2	#492×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#487×D₄₃	C₂	1	2	yes	maximal, complemented
4	#486×D₄₃	C₂	1	2	yes	maximal
5	#19134198	C₂	1	2	yes	maximal, complemented
6	#19134197	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134196	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134195	C₂	1	2	yes	maximal, complemented
9	#19134194	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₄₃	—	2	2	no	—
13	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊Q₈×D₄₃	C₂²	1	2	yes	—
15	#127×D₄₃	C₂²	1	1	yes	characteristic
16	#14583297	C₂²	1	1	yes	characteristic, complemented
17	#14583296	—	2	2	no	—
18	#14583295	C₂²	1	2	yes	complemented
19	#14583273	C₂²	1	1	yes	characteristic
20	#14583272	C₂²	1	1	yes	characteristic
21	#14583271	C₂²	1	1	yes	characteristic
22	#14583270	—	2	2	no	—
23	#14583251	C₂²	1	2	yes	complemented
24	#14583250	C₂²	1	2	yes	complemented
25	#14583249	C₂²	1	2	yes	complemented
26	#14583248	—	2	4	no	—
27	#14583247	C₂²	1	2	yes	—
28	#14583246	C₂²	1	2	yes	—
29	#14583245	C₂²	1	2	yes	—
30	#14583244	—	2	4	no	—
31	#106×D₄₃	—	2	2	no	—
32	#103×D₄₃	—	2	4	no	—
33	#102×D₄₃	—	2	4	no	—
34	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₄₃	C₂²	1	2	yes	—
36	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
38	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#492	C₂²	1	1	yes	characteristic
40	C₄₃×#487	C₂²	1	2	yes	complemented
41	C₄₃×#486	C₂²	1	2	yes	—
42	C₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×Q₈×D₄₃	—	2	2	no	—
44	C₂×Q₈×D₄₃	—	2	1	no	—
45	C₂×D₄×D₄₃	—	2	2	no	—
46	C₂×D₄×D₄₃	—	2	1	no	—
47	C₂×#10621873	—	2	2	no	—
48	C₂×#10621883	—	2	2	no	—
49	C₂×#10621884	—	2	2	no	—
50	SD₁₆×D₄₃	—	4	8	no	—
51	C₂×C₈×D₄₃	D₄	1	4	yes	—
52	C₂×C₈×D₄₃	D₄	1	2	yes	—
53	#13063325	C₂³	1	2	yes	—
54	#13063325	C₂³	1	1	yes	characteristic
55	#13063324	—	2	2	no	—
56	#13063324	—	2	2	no	—
57	#13063324	—	2	2	no	—
58	#13063323	—	2	2	no	—
59	#13063323	—	2	1	no	—
60	#13063322	C₂³	1	1	yes	characteristic
61	#13063321	—	2	2	no	—
62	#13063321	—	2	1	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	2	no	—
68	#13063256	—	2	4	no	—
69	#13063250	—	2	4	no	—
70	#13063249	—	2	4	no	—
71	#13063248	—	2	4	no	—
72	#13063247	—	2	4	no	—
73	#13063246	—	2	4	no	—
74	#13063245	—	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	2	yes	—
78	C₈×Dic₄₃	D₄	1	4	yes	—
79	C₂×SD₁₆×C₄₃	—	2	2	no	—
80	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
82	#127×C₄₃	C₂³	1	1	yes	characteristic
83	#106×C₄₃	—	2	2	no	—
84	#103×C₄₃	—	2	4	no	—
85	#102×C₄₃	—	2	4	no	—
86	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₃	C₂³	1	2	yes	—
88	C₂³×D₄₃	—	4	1	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊D₄₃	—	4	1	no	—
94	C₂×C₂²⋊D₄₃	—	4	2	no	—
95	Q₈×D₄₃	—	4	4	no	—
96	Q₈×D₄₃	—	4	8	no	—
97	D₄×D₄₃	—	4	4	no	—
98	D₄×D₄₃	—	4	8	no	—
99	C₂×D₁₇₂	—	2	2	no	—
100	C₂×D₁₇₂	—	2	1	no	—
101	C₂×C₄×D₄₃	—	4	1	no	—
102	C₂×C₄×D₄₃	—	4	2	no	—
103	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
105	C₂×Dic₈₆	—	2	2	no	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	4	1	no	—
108	C₂×Dic₈₆	—	4	2	no	—
109	SD₁₆×C₄₃	—	4	4	no	—
110	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
116	#10621884	—	4	4	no	—
117	#10621883	—	4	4	no	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	Dic₄₃⋊C₄	—	4	2	no	—
122	Dic₄₃⋊C₄	—	4	2	no	—
123	Dic₄₃⋊C₄	—	4	2	no	—
124	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
125	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
127	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
128	#10621873	—	4	4	no	—
129	C₈×D₄₃	—	2	8	no	—
130	C₈×D₄₃	SD₁₆	1	8	yes	—
131	C₂³×C₄₃	—	4	1	no	—
132	C₂²×D₄₃	—	4	1	no	—
133	C₂²×D₄₃	—	8	2	no	—
134	C₂²×D₄₃	—	8	4	no	—
135	C₂²×D₄₃	#127	1	1	yes	characteristic
136	Q₈×C₄₃	—	4	2	no	—
137	Q₈×C₄₃	—	4	4	no	—
138	D₄×C₄₃	—	4	2	no	—
139	D₄×C₄₃	—	4	4	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
144	C₂²⋊D₄₃	—	8	2	no	—
145	C₂²⋊D₄₃	—	8	4	no	—
146	C₂×Dic₄₃	—	4	1	no	—
147	C₂×Dic₄₃	—	4	2	no	—
148	C₂×Dic₄₃	#127	1	1	yes	characteristic
149	C₂×Dic₄₃	#127	1	2	yes	—
150	D₁₇₂	—	4	2	no	—
151	D₁₇₂	—	4	4	no	—
152	C₄×D₄₃	—	8	2	no	—
153	C₄×D₄₃	—	8	4	no	—
154	C₄×D₄₃	C₂×SD₁₆	1	4	yes	—
155	C₄×D₄₃	#135	1	8	yes	—
156	Dic₈₆	—	4	2	no	—
157	Dic₈₆	—	4	4	no	—
158	Dic₈₆	—	8	2	no	—
159	Dic₈₆	—	8	4	no	—
160	C₈×C₄₃	—	2	4	no	—
161	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
162	C₄₃⋊C₈	—	2	4	no	—
163	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
164	C₂×#1708	—	43	1	no	maximal, Sylow
165	C₂²×C₄₃	—	8	1	no	—
166	C₂²×C₄₃	—	8	2	no	—
167	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
168	C₂×D₄₃	—	8	1	no	—
169	C₂×D₄₃	—	8	2	no	—
170	C₂×D₄₃	—	16	4	no	—
171	C₂×D₄₃	#492	1	2	yes	—
172	C₂×D₄₃	#495	1	4	yes	—
173	C₄×C₄₃	—	8	1	no	—
174	C₄×C₄₃	—	8	2	no	—
175	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
176	C₄×C₄₃	C₂×#135	1	4	yes	—
177	Dic₄₃	—	8	1	no	—
178	Dic₄₃	—	8	2	no	—
179	Dic₄₃	#492	1	2	yes	—
180	Dic₄₃	#495	1	4	yes	—
181	C₂×#498	—	43	1	no	—
182	C₂×#492	—	43	1	no	—
183	C₂×#487	—	43	2	no	—
184	C₂×#486	—	43	2	no	—
185	#1708	—	43	1	no	—
186	#1708	—	43	1	no	—
187	#1708	—	43	2	no	—
188	#1708	—	43	2	no	—
189	#1708	—	43	1	no	—
190	#1708	D₄₃	1	1	yes	characteristic, direct product factor
191	C₂×C₈²	—	43	1	no	—
192	C₂×C₄₃	—	16	1	no	—
193	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
194	C₂×C₄₃	C₂×#495	1	2	yes	—
195	D₄₃	—	16	1	no	—
196	D₄₃	#1708	1	4	yes	direct product factor
197	C₂²×SD₁₆	—	86	2	no	—
198	C₂×C₄⋊Q₈	—	43	2	no	—
199	C₂×C₄⋊Q₈	—	43	1	no	—
200	C₂×#127	—	43	1	no	—
201	#498	—	43	2	no	—
202	#498	—	43	1	no	—
203	#498	—	86	2	no	—
204	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
205	#492	—	43	1	no	—
206	#492	—	43	1	no	—
207	#492	—	43	1	no	—
208	#492	—	86	2	no	—
209	#492	C₂×D₄₃	1	1	yes	characteristic
210	#487	—	43	2	no	—
211	#487	—	43	2	no	—
212	#487	—	43	2	no	—
213	#487	—	86	4	no	—
214	#487	C₂×D₄₃	1	2	yes	complemented
215	#486	—	43	2	no	—
216	#486	—	43	2	no	—
217	#486	—	43	2	no	—
218	#486	—	86	4	no	—
219	#486	C₂×D₄₃	1	2	yes	—
220	C₂×#106	—	86	2	no	—
221	C₂×#103	—	86	4	no	—
222	C₂×#102	—	86	4	no	—
223	C₂×C₄×C₈	—	43	2	no	—
224	C₂×C₄×C₈	—	43	1	no	—
225	C₈²	—	43	1	no	—
226	C₈²	—	43	2	no	—
227	C₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
228	C₄₃	C₂×#1708	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₈	—	86	1	no	—
230	C₂²×Q₈	—	86	2	no	—
231	C₂²×D₄	—	86	1	no	—
232	C₂²×D₄	—	86	2	no	—
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	86	2	no	—
235	C₂×SD₁₆	—	86	2	no	—
236	C₂×SD₁₆	—	86	2	no	—
237	C₂×SD₁₆	—	172	8	no	—
238	C₂²×C₈	—	43	2	no	—
239	C₂²×C₈	—	43	4	no	—
240	C₄⋊Q₈	—	43	2	no	—
241	C₄⋊Q₈	—	43	1	no	—
242	C₄⋊Q₈	—	86	2	no	—
243	C₄⋊Q₈	—	86	2	no	—
244	C₄⋊Q₈	—	86	2	no	—
245	C₄⋊Q₈	—	86	2	no	—
246	C₄⋊Q₈	—	86	1	no	—
247	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
248	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
249	#127	—	43	1	no	—
250	#127	—	86	2	no	—
251	#127	—	86	1	no	—
252	#127	C₂²×D₄₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	86	2	no	—
254	C₂×C₄⋊C₄	—	86	2	no	—
255	C₂×C₄⋊C₄	—	86	2	no	—
256	C₂×C₄²	—	43	1	no	—
257	#106	—	2	2	no	—
258	#106	—	86	4	no	—
259	#106	—	86	2	no	—
260	#103	—	2	4	no	—
261	#103	—	86	4	no	—
262	#103	—	86	4	no	—
263	#103	—	86	4	no	—
264	#102	—	2	4	no	—
265	#102	—	86	4	no	—
266	#102	—	86	4	no	—
267	#102	—	86	4	no	—
268	C₄×C₈	—	43	4	no	—
269	C₄×C₈	—	43	2	no	—
270	C₄×C₈	—	43	2	no	—
271	C₄×C₈	—	43	1	no	—
272	C₄×C₈	C₂²×D₄₃	1	2	yes	—
273	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
274	C₂⁴	—	172	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	86	2	no	—
278	C₂×Q₈	—	86	1	no	—
279	C₂×Q₈	—	172	2	no	—
280	C₂×Q₈	—	172	1	no	—
281	C₂×Q₈	—	172	4	no	—
282	C₂×Q₈	—	172	8	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	86	2	no	—
286	C₂×D₄	—	86	1	no	—
287	C₂×D₄	—	172	4	no	—
288	C₂×D₄	—	172	8	no	—
289	C₂×D₄	—	172	1	no	—
290	C₂×D₄	—	172	2	no	—
291	C₂²×C₄	—	43	1	no	—
292	C₂²×C₄	—	43	2	no	—
293	C₂²×C₄	—	172	2	no	—
294	C₂²×C₄	—	172	1	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	172	4	no	—
297	SD₁₆	—	172	4	no	—
298	SD₁₆	—	172	4	no	—
299	C₂×C₈	—	43	2	no	—
300	C₂×C₈	—	43	8	no	—
301	C₂×C₈	—	43	4	no	—
302	C₂×C₈	—	86	8	no	—
303	C₂×C₈	D₄×D₄₃	1	4	yes	—
304	C₂×C₈	D₄×D₄₃	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	86	2	no	—
309	C₄⋊C₄	—	86	2	no	—
310	C₄⋊C₄	—	86	2	no	—
311	C₄⋊C₄	—	172	2	no	—
312	C₄⋊C₄	—	172	2	no	—
313	C₄⋊C₄	—	172	2	no	—
314	C₄²	—	43	1	no	—
315	C₄²	—	43	2	no	—
316	C₄²	C₂³×D₄₃	1	1	yes	characteristic
317	C₂³	—	4	1	no	—
318	C₂³	—	43	1	no	—
319	C₂³	—	344	2	no	—
320	C₂³	—	344	4	no	—
321	C₂³	—	172	1	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	344	2	no	—
325	Q₈	—	344	4	no	—
326	Q₈	—	172	2	no	—
327	Q₈	—	172	4	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	4	no	—
330	D₄	—	344	2	no	—
331	D₄	—	344	4	no	—
332	D₄	—	172	2	no	—
333	D₄	—	172	4	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	43	1	no	—
337	C₂×C₄	—	43	2	no	—
338	C₂×C₄	—	43	4	no	—
339	C₂×C₄	—	43	8	no	—
340	C₂×C₄	—	344	2	no	—
341	C₂×C₄	—	344	4	no	—
342	C₂×C₄	—	172	1	no	—
343	C₂×C₄	—	172	2	no	—
344	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
345	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
346	C₈	—	2	4	no	—
347	C₈	—	43	4	no	—
348	C₈	—	86	4	no	—
349	C₈	SD₁₆×D₄₃	1	4	yes	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	43	2	no	—
353	C₂²	—	43	4	no	—
354	C₂²	—	344	1	no	—
355	C₂²	—	344	2	no	—
356	C₂²	—	688	4	no	—
357	C₂²	#127×D₄₃	1	1	yes	characteristic
358	C₄	—	8	1	no	—
359	C₄	—	8	2	no	—
360	C₄	—	43	2	no	—
361	C₄	—	43	4	no	—
362	C₄	—	344	1	no	—
363	C₄	—	344	2	no	—
364	C₄	C₂×SD₁₆×D₄₃	1	2	yes	—
365	C₄	#135×D₄₃	1	4	yes	—
366	C₂	—	16	1	no	—
367	C₂	—	43	4	no	—
368	C₂	—	688	1	no	—
369	C₂	#492×D₄₃	1	1	yes	characteristic
370	C₂	#495×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²	#127×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1708	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#127×D₄₃	C₂²
hypercenter	#1708	D₄₃
hypocenter	C₄₃	C₂×#1708
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1708

Complements

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

N	H ≅ G/N	type
1. #498×D₄₃	C₂	semidirect
3. #487×D₄₃	C₂	semidirect
5. #19134198	C₂	semidirect
6. #19134197	C₂	semidirect
7. #19134196	C₂	semidirect
8. #19134195	C₂	semidirect
9. #19134194	C₂	semidirect
10. C₈²×D₄₃	C₂	semidirect
11. C₄₃×#1708	C₂	semidirect
16. #14583297	C₂²	semidirect
18. #14583295	C₂²	semidirect
23. #14583251	C₂²	semidirect
24. #14583250	C₂²	semidirect
25. #14583249	C₂²	semidirect
36. C₈×C₄₃⋊C₈	C₂²	semidirect
37. C₈×C₄₃⋊C₈	C₂²	semidirect
38. C₄₃×#498	C₂²	semidirect
40. C₄₃×#487	C₂²	semidirect
42. C₈²×C₄₃	C₂²	semidirect
190. #1708	D₄₃	direct (N × H)
196. D₄₃	#1708	direct (N × H)
204. #498	C₂×D₄₃	semidirect
214. #487	C₂×D₄₃	semidirect
227. C₈²	C₂×D₄₃	semidirect
228. C₄₃	C₂×#1708	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
#492×D₄₃	2
#487×D₄₃	2
#486×D₄₃	2
#19134198	2
#19134197	2
#19134196	2
#19134195	2
#19134194	2
C₈²×D₄₃	2
C₄₃×#1708	2
C₂×#1708	43

Subgroups — D43×#1708 #25084248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1708 #25084248