Subgroups — D₄₃×#2264 #25254733

Order 11008.

462 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136915	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136914	C₂	1	2	yes	maximal, complemented
5	#19136913	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136912	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136911	C₂	1	2	yes	maximal, complemented
8	Q₆₄×D₄₃	C₂	1	2	yes	maximal, complemented
9	SD₆₄×D₄₃	C₂	1	2	yes	maximal, complemented
10	M₆₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2264	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₄₃	—	2	1	no	—
13	C₂×Q₁₆×D₄₃	—	2	1	no	—
14	#14583332	C₂²	1	1	yes	characteristic
15	#14583331	C₂²	1	1	yes	characteristic
16	#14583330	—	2	1	no	—
17	#14583329	—	2	1	no	—
18	#14583328	C₂²	1	1	yes	characteristic
19	C₂×Dic₃₄₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13063271	—	2	1	no	—
21	Q₃₂×D₄₃	—	2	1	no	—
22	Q₃₂×D₄₃	—	2	1	no	—
23	Q₃₂×D₄₃	C₂²	1	2	yes	—
24	Q₃₂×D₄₃	C₂²	1	1	yes	characteristic
25	Q₃₂×D₄₃	C₂²	1	2	yes	complemented
26	SD₃₂×D₄₃	—	2	1	no	—
27	D₁₆×D₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₄₃	C₂²	1	1	yes	characteristic
29	Dic₆₈₈	C₂²	1	2	yes	complemented
30	#14582739	C₂²	1	2	yes	complemented
31	#14582739	C₂²	1	2	yes	complemented
32	#14582738	C₂²	1	2	yes	complemented
33	#14582737	C₂²	1	2	yes	complemented
34	#14582736	C₂²	1	2	yes	complemented
35	#14582733	C₂²	1	1	yes	characteristic, complemented
36	#14582732	C₂²	1	2	yes	complemented
37	C₃₂×D₄₃	C₂²	1	2	yes	—
38	C₄₃×#508	C₂²	1	1	yes	characteristic
39	C₂×Q₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×Q₆₄	C₂²	1	2	yes	complemented
41	C₄₃×SD₆₄	C₂²	1	2	yes	complemented
42	C₄₃×M₆₄	C₂²	1	1	yes	characteristic, complemented
43	#41×D₄₃	—	4	1	no	—
44	C₂×Q₈×D₄₃	—	4	1	no	—
45	#13063348	—	2	1	no	—
46	#13063347	—	2	1	no	—
47	#13063346	—	4	1	no	—
48	#13063345	—	4	1	no	—
49	#13063344	—	2	1	no	—
50	C₂×Dic₁₇₂	—	2	1	no	—
51	C₂×#10621885	—	4	1	no	—
52	Q₁₆×D₄₃	—	2	1	no	—
53	Q₁₆×D₄₃	—	2	2	no	—
54	Q₁₆×D₄₃	—	2	2	no	—
55	Q₁₆×D₄₃	—	4	1	no	—
56	Q₁₆×D₄₃	—	4	1	no	—
57	SD₁₆×D₄₃	—	4	1	no	—
58	D₈×D₄₃	—	2	1	no	—
59	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
60	Dic₃₄₄	—	2	1	no	—
61	Dic₃₄₄	C₂³	1	2	yes	—
62	Dic₃₄₄	C₂³	1	1	yes	characteristic
63	#13063271	—	2	2	no	—
64	#13063271	—	2	2	no	—
65	#13063271	—	2	1	no	—
66	#13063270	—	2	1	no	—
67	#13063269	—	2	1	no	—
68	#13063268	—	2	1	no	—
69	D₆₈₈	C₂³	1	1	yes	characteristic
70	#13063266	—	2	1	no	—
71	C₂×C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
72	C₁₆×D₄₃	D₄	1	1	yes	characteristic
73	C₁₆×D₄₃	D₄	1	1	yes	characteristic
74	C₁₆×D₄₃	C₂³	1	1	yes	characteristic
75	C₁₆×D₄₃	C₂³	1	1	yes	characteristic
76	C₄₃⋊C₃₂	C₂³	1	2	yes	—
77	#135×C₄₃	—	2	1	no	—
78	C₂×Q₁₆×C₄₃	—	2	1	no	—
79	Q₃₂×C₄₃	—	2	1	no	—
80	Q₃₂×C₄₃	C₂³	1	2	yes	—
81	Q₃₂×C₄₃	C₂³	1	1	yes	characteristic
82	SD₃₂×C₄₃	—	2	1	no	—
83	D₁₆×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
85	C₃₂×C₄₃	C₂³	1	2	yes	—
86	#41×C₄₃	—	4	1	no	—
87	C₂×Q₈×C₄₃	—	4	1	no	—
88	#10621902	—	4	1	no	—
89	Q₈×D₄₃	—	4	1	no	—
90	Q₈×D₄₃	—	4	2	no	—
91	Q₈×D₄₃	—	4	2	no	—
92	Q₈×D₄₃	—	8	1	no	—
93	Q₈×D₄₃	—	8	1	no	—
94	#10621900	—	4	1	no	—
95	#10621900	—	8	1	no	—
96	D₄×D₄₃	—	4	1	no	—
97	D₄×D₄₃	—	8	1	no	—
98	#10621898	—	4	1	no	—
99	#10621898	—	8	1	no	—
100	C₂×C₄×D₄₃	—	8	1	no	—
101	C₂×C₄×D₄₃	—	8	1	no	—
102	C₂×C₄×D₄₃	D₈	1	1	yes	characteristic
103	C₂×Dic₈₆	—	4	1	no	—
104	C₂×Dic₈₆	—	8	1	no	—
105	Q₁₆×C₄₃	—	2	1	no	—
106	Q₁₆×C₄₃	—	2	2	no	—
107	Q₁₆×C₄₃	—	4	1	no	—
108	SD₁₆×C₄₃	—	4	1	no	—
109	D₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	#10621885	—	4	2	no	—
112	#10621885	—	4	2	no	—
113	#10621885	—	4	1	no	—
114	#10621884	—	4	1	no	—
115	#10621883	—	4	1	no	—
116	#10621882	—	4	1	no	—
117	C₂×C₄₃⋊C₈	D₈	1	1	yes	characteristic
118	Dic₁₇₂	—	2	1	no	—
119	Dic₁₇₂	—	2	2	no	—
120	Dic₁₇₂	—	4	1	no	—
121	D₃₄₄	—	2	1	no	—
122	#10621873	—	4	1	no	—
123	C₈×D₄₃	D₈	1	1	yes	characteristic
124	C₈×D₄₃	D₈	1	1	yes	characteristic
125	C₈×D₄₃	C₂×D₄	1	1	yes	characteristic
126	C₈×D₄₃	C₂×D₄	1	1	yes	characteristic
127	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₄₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
130	C₄₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₄₃	—	8	1	no	—
132	C₂²×D₄₃	D₁₆	1	1	yes	characteristic
133	Q₈×C₄₃	—	4	1	no	—
134	Q₈×C₄₃	—	4	2	no	—
135	Q₈×C₄₃	—	8	1	no	—
136	D₄×C₄₃	—	4	1	no	—
137	D₄×C₄₃	—	8	1	no	—
138	C₂×C₄×C₄₃	—	8	1	no	—
139	C₂×C₄×C₄₃	—	8	1	no	—
140	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
141	C₂²⋊D₄₃	—	8	1	no	—
142	C₂²⋊D₄₃	—	8	1	no	—
143	C₂²⋊D₄₃	—	8	1	no	—
144	C₂×Dic₄₃	—	8	1	no	—
145	C₂×Dic₄₃	—	8	1	no	—
146	C₂×Dic₄₃	D₁₆	1	1	yes	characteristic
147	D₁₇₂	—	4	1	no	—
148	D₁₇₂	—	8	1	no	—
149	C₄×D₄₃	—	8	1	no	—
150	C₄×D₄₃	—	8	2	no	—
151	C₄×D₄₃	—	8	2	no	—
152	C₄×D₄₃	—	8	1	no	—
153	C₄×D₄₃	—	8	1	no	—
154	C₄×D₄₃	D₁₆	1	1	yes	characteristic
155	C₄×D₄₃	D₁₆	1	1	yes	characteristic
156	C₄×D₄₃	C₂×D₈	1	1	yes	characteristic
157	C₄×D₄₃	C₂×D₈	1	1	yes	characteristic
158	Dic₈₆	—	4	1	no	—
159	Dic₈₆	—	4	2	no	—
160	Dic₈₆	—	8	1	no	—
161	Dic₈₆	—	8	2	no	—
162	Dic₈₆	—	8	2	no	—
163	Dic₈₆	—	8	1	no	—
164	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
165	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₄₃⋊C₈	C₂×D₈	1	1	yes	characteristic
167	C₄₃⋊C₈	C₂×D₈	1	1	yes	characteristic
168	C₂×#2264	—	43	1	no	maximal, Sylow
169	C₂²×C₄₃	—	8	1	no	—
170	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
171	C₂×D₄₃	—	2	2	no	—
172	C₂×D₄₃	—	8	1	no	—
173	C₂×D₄₃	—	16	2	no	—
174	C₂×D₄₃	C₂×D₁₆	1	1	yes	characteristic
175	C₂×D₄₃	C₂×D₁₆	1	1	yes	characteristic
176	C₄×C₄₃	—	8	2	no	—
177	C₄×C₄₃	—	8	1	no	—
178	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
179	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
180	Dic₄₃	—	8	2	no	—
181	Dic₄₃	—	8	1	no	—
182	Dic₄₃	C₂×D₁₆	1	1	yes	characteristic
183	Dic₄₃	C₂×D₁₆	1	1	yes	characteristic
184	C₂×#508	—	43	1	no	—
185	C₂²×Q₃₂	—	43	1	no	—
186	#2264	—	43	1	no	—
187	#2264	—	43	1	no	—
188	#2264	—	43	2	no	—
189	#2264	—	43	2	no	—
190	#2264	—	43	1	no	—
191	#2264	D₄₃	1	1	yes	characteristic, direct product factor
192	C₂×Q₆₄	—	43	2	no	—
193	C₂×SD₆₄	—	43	2	no	—
194	C₂×M₆₄	—	43	1	no	—
195	C₂×C₄₃	—	2	1	no	—
196	C₂×C₄₃	—	16	1	no	—
197	C₂×C₄₃	C₂²×D₁₆	1	1	yes	characteristic
198	D₄₃	—	2	1	no	—
199	D₄₃	—	16	1	no	—
200	D₄₃	#2264	1	2	yes	direct product factor
201	C₂×#135	—	86	1	no	—
202	C₂²×Q₁₆	—	86	1	no	—
203	#508	—	43	1	no	—
204	#508	—	43	1	no	—
205	#508	—	43	1	no	—
206	#508	—	86	1	no	—
207	#508	—	86	1	no	—
208	#508	C₂×D₄₃	1	1	yes	characteristic
209	C₂×Q₃₂	—	43	2	no	—
210	C₂×Q₃₂	—	43	1	no	—
211	C₂×Q₃₂	—	43	2	no	—
212	C₂×Q₃₂	—	43	1	no	—
213	C₂×Q₃₂	—	86	1	no	—
214	C₂×Q₃₂	—	86	1	no	—
215	C₂×Q₃₂	—	86	1	no	—
216	C₂×Q₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
217	C₂×SD₃₂	—	86	1	no	—
218	C₂×D₁₆	—	43	1	no	—
219	C₂²×C₁₆	—	43	1	no	—
220	Q₆₄	—	43	2	no	—
221	Q₆₄	—	43	2	no	—
222	Q₆₄	—	43	2	no	—
223	Q₆₄	C₂×D₄₃	1	2	yes	complemented
224	SD₆₄	—	43	2	no	—
225	SD₆₄	—	43	2	no	—
226	SD₆₄	—	43	2	no	—
227	SD₆₄	C₂×D₄₃	1	2	yes	complemented
228	M₆₄	—	43	1	no	—
229	M₆₄	—	43	2	no	—
230	M₆₄	C₂×D₄₃	1	1	yes	characteristic, complemented
231	C₂×C₃₂	—	43	2	no	—
232	C₄₃	C₂×#2264	1	1	yes	characteristic, complemented, Sylow
233	C₂×#41	—	172	1	no	—
234	C₂²×Q₈	—	172	1	no	—
235	#135	—	2	1	no	—
236	#135	—	86	1	no	—
237	#135	—	86	1	no	—
238	#135	—	86	1	no	—
239	#135	—	172	1	no	—
240	#135	—	172	1	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	86	2	no	—
243	C₂×Q₁₆	—	86	2	no	—
244	C₂×Q₁₆	—	86	1	no	—
245	C₂×Q₁₆	—	86	1	no	—
246	C₂×Q₁₆	—	172	1	no	—
247	C₂×Q₁₆	—	172	1	no	—
248	C₂×Q₁₆	—	172	1	no	—
249	C₂×SD₁₆	—	172	1	no	—
250	C₂×D₈	—	86	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	Q₃₂	—	2	1	no	—
253	Q₃₂	—	43	2	no	—
254	Q₃₂	—	43	1	no	—
255	Q₃₂	—	86	2	no	—
256	Q₃₂	—	86	2	no	—
257	Q₃₂	—	86	1	no	—
258	Q₃₂	—	86	1	no	—
259	Q₃₂	C₂²×D₄₃	1	2	yes	—
260	Q₃₂	C₂²×D₄₃	1	1	yes	characteristic
261	SD₃₂	—	2	1	no	—
262	SD₃₂	—	86	1	no	—
263	SD₃₂	—	86	1	no	—
264	SD₃₂	—	86	1	no	—
265	D₁₆	—	43	1	no	—
266	D₁₆	—	86	1	no	—
267	D₁₆	C₂²×D₄₃	1	1	yes	characteristic
268	C₂×C₁₆	—	43	1	no	—
269	C₂×C₁₆	—	43	1	no	—
270	C₂×C₁₆	—	43	1	no	—
271	C₂×C₁₆	—	43	1	no	—
272	C₂×C₁₆	—	43	1	no	—
273	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
274	C₃₂	—	43	2	no	—
275	C₃₂	C₂²×D₄₃	1	2	yes	—
276	#41	—	4	1	no	—
277	#41	—	344	1	no	—
278	#41	—	344	1	no	—
279	#41	—	172	1	no	—
280	#41	—	172	1	no	—
281	#41	—	172	1	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	344	1	no	—
284	C₂×Q₈	—	344	1	no	—
285	C₂×Q₈	—	344	1	no	—
286	C₂×Q₈	—	172	1	no	—
287	C₂×Q₈	—	172	2	no	—
288	C₂×Q₈	—	172	2	no	—
289	C₂×Q₈	—	172	1	no	—
290	C₂×D₄	—	344	1	no	—
291	C₂×D₄	—	172	1	no	—
292	C₂²×C₄	—	43	1	no	—
293	C₂²×C₄	—	344	1	no	—
294	C₂²×C₄	—	344	1	no	—
295	Q₁₆	—	2	1	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	4	1	no	—
298	Q₁₆	—	86	1	no	—
299	Q₁₆	—	86	2	no	—
300	Q₁₆	—	172	2	no	—
301	Q₁₆	—	172	2	no	—
302	Q₁₆	—	172	1	no	—
303	Q₁₆	—	172	1	no	—
304	SD₁₆	—	4	1	no	—
305	SD₁₆	—	172	1	no	—
306	SD₁₆	—	172	1	no	—
307	SD₁₆	—	172	1	no	—
308	D₈	—	2	1	no	—
309	D₈	—	86	1	no	—
310	D₈	—	172	1	no	—
311	C₂×C₈	—	43	1	no	—
312	C₂×C₈	—	43	1	no	—
313	C₂×C₈	—	43	1	no	—
314	C₂×C₈	—	43	1	no	—
315	C₂×C₈	—	43	1	no	—
316	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
317	C₁₆	—	43	1	no	—
318	C₁₆	—	43	1	no	—
319	C₁₆	D₄×D₄₃	1	1	yes	characteristic
320	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
321	C₂³	—	43	1	no	—
322	C₂³	—	344	1	no	—
323	Q₈	—	4	1	no	—
324	Q₈	—	4	2	no	—
325	Q₈	—	8	1	no	—
326	Q₈	—	344	2	no	—
327	Q₈	—	344	2	no	—
328	Q₈	—	344	1	no	—
329	Q₈	—	344	1	no	—
330	Q₈	—	172	1	no	—
331	Q₈	—	172	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	8	1	no	—
334	D₄	—	344	1	no	—
335	D₄	—	344	1	no	—
336	D₄	—	344	1	no	—
337	D₄	—	344	1	no	—
338	D₄	—	172	1	no	—
339	C₂×C₄	—	8	1	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	—	43	1	no	—
342	C₂×C₄	—	43	1	no	—
343	C₂×C₄	—	43	1	no	—
344	C₂×C₄	—	43	1	no	—
345	C₂×C₄	—	43	1	no	—
346	C₂×C₄	—	344	1	no	—
347	C₂×C₄	—	344	1	no	—
348	C₂×C₄	—	344	2	no	—
349	C₂×C₄	—	344	2	no	—
350	C₂×C₄	—	344	1	no	—
351	C₂×C₄	—	344	1	no	—
352	C₂×C₄	—	344	1	no	—
353	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
354	C₈	—	43	1	no	—
355	C₈	—	43	1	no	—
356	C₈	D₈×D₄₃	1	1	yes	characteristic
357	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
358	C₂²	—	8	1	no	—
359	C₂²	—	43	1	no	—
360	C₂²	—	43	1	no	—
361	C₂²	—	86	2	no	—
362	C₂²	—	344	1	no	—
363	C₂²	—	688	2	no	—
364	C₂²	D₁₆×D₄₃	1	1	yes	characteristic
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	43	1	no	—
368	C₄	—	43	1	no	—
369	C₄	—	344	1	no	—
370	C₄	—	344	2	no	—
371	C₄	D₁₆×D₄₃	1	1	yes	characteristic
372	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
373	C₂	—	2	1	no	—
374	C₂	—	16	1	no	—
375	C₂	—	43	2	no	—
376	C₂	—	86	1	no	—
377	C₂	—	688	1	no	—
378	C₂	C₂×D₁₆×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₆×D₄₃
commutator, cosocle	C₁₆×C₄₃	C₂⁴
Frattini	C₁₆	C₂³×D₄₃
Fitting	C₄₃×#2264	C₂
socle	C₂×C₄₃	C₂²×D₁₆
prime radical	#508×D₄₃	C₂
hypercenter	#2264	D₄₃
hypocenter	C₄₃	C₂×#2264
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #2264

Complements

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

N	H ≅ G/N	type
2. C₂×Q₃₂×D₄₃	C₂	semidirect
3. #19136915	C₂	semidirect
4. #19136914	C₂	semidirect
5. #19136913	C₂	semidirect
6. #19136912	C₂	semidirect
7. #19136911	C₂	semidirect
8. Q₆₄×D₄₃	C₂	semidirect
9. SD₆₄×D₄₃	C₂	semidirect
10. M₆₄×D₄₃	C₂	semidirect
11. C₄₃×#2264	C₂	semidirect
19. C₂×Dic₃₄₄	C₂²	semidirect
25. Q₃₂×D₄₃	C₂²	semidirect
29. Dic₆₈₈	C₂²	semidirect
30. #14582739	C₂²	semidirect
31. #14582739	C₂²	semidirect
32. #14582738	C₂²	semidirect
33. #14582737	C₂²	semidirect
34. #14582736	C₂²	semidirect
35. #14582733	C₂²	semidirect
36. #14582732	C₂²	semidirect
39. C₂×Q₃₂×C₄₃	C₂²	semidirect
40. C₄₃×Q₆₄	C₂²	semidirect
41. C₄₃×SD₆₄	C₂²	semidirect
42. C₄₃×M₆₄	C₂²	semidirect
191. #2264	D₄₃	direct (N × H)
200. D₄₃	#2264	direct (N × H)
216. C₂×Q₃₂	C₂×D₄₃	semidirect
223. Q₆₄	C₂×D₄₃	semidirect
227. SD₆₄	C₂×D₄₃	semidirect
230. M₆₄	C₂×D₄₃	semidirect
232. C₄₃	C₂×#2264	semidirect

Maximal subgroups

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

subgroup	index
#508×D₄₃	2
C₂×Q₃₂×D₄₃	2
#19136915	2
#19136914	2
#19136913	2
#19136912	2
#19136911	2
Q₆₄×D₄₃	2
SD₆₄×D₄₃	2
M₆₄×D₄₃	2
C₄₃×#2264	2
C₂×#2264	43

Subgroups — D43×#2264 #25254733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#2264 #25254733