Subgroups — D₄₃×#1335 #25006378

Order 11008.

414 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#443×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#364×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132569	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132568	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1335	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×D₄₃	C₄	1	1	yes	characteristic
9	#131×D₄₃	—	2	1	no	—
10	M₃₂×D₄₃	—	2	1	no	—
11	#14583017	C₂²	1	1	yes	characteristic
12	#14583016	C₄	1	1	yes	characteristic
13	#14583015	C₄	1	1	yes	characteristic
14	#14583014	—	2	1	no	—
15	#14583013	—	2	1	no	—
16	#108×D₄₃	C₄	1	1	yes	characteristic
17	#104×D₄₃	—	2	1	no	—
18	C₄×C₈×D₄₃	—	2	1	no	—
19	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
20	#14582720	C₂²	1	1	yes	characteristic, complemented
21	#14582719	—	2	1	no	—
22	C₈×C₄₃⋊C₈	—	2	1	no	—
23	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₄₃×#443	C₂²	1	1	yes	characteristic
25	C₄₃×#364	C₂²	1	1	yes	characteristic, complemented
26	C₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
27	#41×D₄₃	—	2	1	no	—
28	#13063348	C₈	1	1	yes	characteristic, complemented
29	#13063347	C₂×C₄	1	1	yes	characteristic
30	#13063346	—	2	1	no	—
31	#13063345	—	2	1	no	—
32	#13063344	C₈	1	1	yes	characteristic, complemented
33	Q₁₆×D₄₃	C₈	1	1	yes	characteristic, complemented
34	SD₁₆×D₄₃	—	2	1	no	—
35	D₈×D₄₃	C₈	1	1	yes	characteristic, complemented
36	#13063333	—	2	1	no	—
37	#13063333	—	4	1	no	—
38	#13063332	—	2	1	no	—
39	#13063331	—	2	1	no	—
40	#13063331	—	4	1	no	—
41	M₁₆×D₄₃	—	2	1	no	—
42	M₁₆×D₄₃	—	4	1	no	—
43	C₂×C₈×D₄₃	—	2	2	no	—
44	C₂×C₈×D₄₃	—	4	1	no	—
45	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
47	C₄²×D₄₃	D₄	1	1	yes	characteristic
48	#13063265	—	2	1	no	—
49	#13063264	—	4	1	no	—
50	C₁₆×D₄₃	—	4	1	no	—
51	#13063261	C₂×C₄	1	1	yes	characteristic
52	#13063260	—	2	1	no	—
53	#13063253	—	2	1	no	—
54	#13063252	—	2	1	no	—
55	#13063251	—	2	1	no	—
56	C₄×C₄₃⋊C₈	—	2	1	no	—
57	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
58	C₈×Dic₄₃	—	2	2	no	—
59	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₈×Dic₄₃	D₄	1	1	yes	characteristic
61	#135×C₄₃	C₂×C₄	1	1	yes	characteristic
62	#131×C₄₃	—	2	1	no	—
63	M₃₂×C₄₃	—	2	1	no	—
64	#108×C₄₃	C₂×C₄	1	1	yes	characteristic
65	#104×C₄₃	—	2	1	no	—
66	C₄×C₈×C₄₃	—	2	1	no	—
67	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	#41×C₄₃	—	2	1	no	—
69	#10621902	—	2	1	no	—
70	Q₈×D₄₃	—	2	1	no	—
71	#10621900	—	2	1	no	—
72	#10621900	—	4	1	no	—
73	D₄×D₄₃	—	2	1	no	—
74	D₄×D₄₃	—	4	1	no	—
75	#10621898	—	2	1	no	—
76	#10621898	—	4	1	no	—
77	C₂×C₄×D₄₃	—	2	1	no	—
78	C₂×C₄×D₄₃	—	4	1	no	—
79	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
80	Q₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic, complemented
81	SD₁₆×C₄₃	—	2	1	no	—
82	D₈×C₄₃	C₂×C₈	1	1	yes	characteristic, complemented
83	M₁₆×C₄₃	—	2	1	no	—
84	M₁₆×C₄₃	—	4	1	no	—
85	C₂×C₈×C₄₃	—	2	2	no	—
86	C₂×C₈×C₄₃	—	4	1	no	—
87	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
90	#10621885	—	2	1	no	—
91	#10621884	—	2	1	no	—
92	#10621883	—	2	1	no	—
93	#10621882	—	2	1	no	—
94	C₄×Dic₄₃	—	2	1	no	—
95	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
96	#10621877	—	2	1	no	—
97	#10621877	—	4	1	no	—
98	C₂×C₄₃⋊C₈	—	2	2	no	—
99	C₂×C₄₃⋊C₈	—	4	1	no	—
100	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
102	Dic₁₇₂	C₂×C₈	1	1	yes	characteristic, complemented
103	D₃₄₄	C₂×C₈	1	1	yes	characteristic, complemented
104	#10621873	—	2	1	no	—
105	#10621872	—	4	1	no	—
106	#10621872	—	4	1	no	—
107	#10621872	—	4	1	no	—
108	C₈×D₄₃	—	2	8	no	—
109	C₈×D₄₃	—	4	1	no	—
110	C₈×D₄₃	—	4	1	no	—
111	C₈×D₄₃	—	4	1	no	—
112	C₈×D₄₃	C₂×C₈	1	1	yes	characteristic
113	C₈×D₄₃	C₂×C₈	1	1	yes	characteristic
114	C₈×D₄₃	M₁₆	1	1	yes	characteristic
115	C₈×D₄₃	M₁₆	1	1	yes	characteristic
116	C₈×D₄₃	D₈	1	1	yes	characteristic
117	C₈×D₄₃	D₈	1	1	yes	characteristic
118	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
119	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
120	C₁₆×C₄₃	—	4	1	no	—
121	C₄₃⋊C₁₆	—	4	1	no	—
122	C₂²×D₄₃	—	4	1	no	—
123	C₂²×D₄₃	#104	1	1	yes	characteristic
124	Q₈×C₄₃	—	2	1	no	—
125	D₄×C₄₃	—	2	1	no	—
126	D₄×C₄₃	—	4	1	no	—
127	C₂×C₄×C₄₃	—	2	1	no	—
128	C₂×C₄×C₄₃	—	4	1	no	—
129	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²⋊D₄₃	—	4	1	no	—
131	C₂²⋊D₄₃	—	4	1	no	—
132	C₂²⋊D₄₃	—	4	1	no	—
133	C₂×Dic₄₃	—	2	1	no	—
134	C₂×Dic₄₃	—	4	1	no	—
135	C₂×Dic₄₃	#104	1	1	yes	characteristic
136	D₁₇₂	—	2	1	no	—
137	D₁₇₂	—	4	1	no	—
138	C₄×D₄₃	—	2	4	no	—
139	C₄×D₄₃	—	4	1	no	—
140	C₄×D₄₃	—	4	1	no	—
141	C₄×D₄₃	—	4	1	no	—
142	C₄×D₄₃	C₂²⋊C₈	1	1	yes	characteristic
143	C₄×D₄₃	C₂²⋊C₈	1	1	yes	characteristic
144	C₄×D₄₃	#102	1	1	yes	characteristic
145	C₄×D₄₃	#102	1	1	yes	characteristic
146	Dic₈₆	—	2	1	no	—
147	Dic₈₆	—	4	1	no	—
148	C₈×C₄₃	—	2	4	no	—
149	C₈×C₄₃	—	4	1	no	—
150	C₈×C₄₃	C₂²×C₈	1	1	yes	characteristic
151	C₈×C₄₃	C₂×M₁₆	1	1	yes	characteristic
152	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
153	C₈×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
154	C₄₃⋊C₈	—	2	4	no	—
155	C₄₃⋊C₈	—	4	1	no	—
156	C₄₃⋊C₈	C₂²⋊C₈	1	1	yes	characteristic
157	C₄₃⋊C₈	C₂²⋊C₈	1	1	yes	characteristic
158	C₄₃⋊C₈	#102	1	1	yes	characteristic
159	C₄₃⋊C₈	#102	1	1	yes	characteristic
160	C₂×#1335	—	43	1	no	maximal, Sylow
161	C₂²×C₄₃	—	4	1	no	—
162	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
163	C₂×D₄₃	—	2	2	no	—
164	C₂×D₄₃	—	4	1	no	—
165	C₂×D₄₃	—	8	2	no	—
166	C₂×D₄₃	D₄⋊C₈	1	1	yes	characteristic
167	C₂×D₄₃	D₄⋊C₈	1	1	yes	characteristic
168	C₄×C₄₃	—	2	2	no	—
169	C₄×C₄₃	—	4	1	no	—
170	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
171	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
172	Dic₄₃	—	2	2	no	—
173	Dic₄₃	—	4	1	no	—
174	Dic₄₃	D₄⋊C₈	1	1	yes	characteristic
175	Dic₄₃	D₄⋊C₈	1	1	yes	characteristic
176	C₂×#443	—	43	1	no	—
177	C₂×#364	—	43	1	no	—
178	C₂×C₈²	—	43	1	no	—
179	#1335	—	43	1	no	—
180	#1335	—	43	1	no	—
181	#1335	—	43	1	no	—
182	#1335	D₄₃	1	1	yes	characteristic, direct product factor
183	C₂×C₄₃	—	2	1	no	—
184	C₂×C₄₃	—	8	1	no	—
185	C₂×C₄₃	C₂×D₄⋊C₈	1	1	yes	characteristic
186	D₄₃	—	2	1	no	—
187	D₄₃	—	8	1	no	—
188	D₄₃	#1335	1	2	yes	direct product factor
189	C₂×#135	—	43	1	no	—
190	C₂×#131	—	86	1	no	—
191	C₂×M₃₂	—	86	1	no	—
192	#443	—	43	1	no	—
193	#443	—	43	1	no	—
194	#443	—	43	1	no	—
195	#443	—	86	1	no	—
196	#443	—	86	1	no	—
197	#443	C₂×D₄₃	1	1	yes	characteristic
198	C₂×#108	—	43	1	no	—
199	C₂×#104	—	86	1	no	—
200	C₂×C₄×C₈	—	43	1	no	—
201	C₂×C₄×C₈	—	86	1	no	—
202	#364	—	43	1	no	—
203	#364	—	86	1	no	—
204	#364	C₂×D₄₃	1	1	yes	characteristic, complemented
205	C₈²	—	43	1	no	—
206	C₈²	—	86	1	no	—
207	C₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
208	C₄₃	C₂×#1335	1	1	yes	characteristic, complemented, Sylow
209	C₂×#41	—	86	1	no	—
210	#135	—	43	1	no	—
211	#135	—	43	1	no	—
212	#135	—	43	1	no	—
213	#135	—	86	1	no	—
214	#135	—	86	1	no	—
215	#135	C₄×D₄₃	1	1	yes	characteristic
216	C₂×Q₁₆	—	43	1	no	—
217	C₂×SD₁₆	—	86	1	no	—
218	C₂×D₈	—	43	1	no	—
219	#131	—	2	1	no	—
220	#131	—	86	1	no	—
221	#131	—	86	1	no	—
222	#131	—	86	1	no	—
223	#131	—	172	1	no	—
224	#131	—	172	1	no	—
225	C₂×M₁₆	—	86	1	no	—
226	C₂×M₁₆	—	172	1	no	—
227	C₂²×C₈	—	43	1	no	—
228	C₂²×C₈	—	43	1	no	—
229	C₂²×C₈	—	86	2	no	—
230	C₂²×C₈	—	172	1	no	—
231	C₂×C₄²	—	43	1	no	—
232	M₃₂	—	2	1	no	—
233	M₃₂	—	86	1	no	—
234	M₃₂	—	172	1	no	—
235	C₂×C₁₆	—	172	1	no	—
236	#108	—	43	1	no	—
237	#108	—	86	1	no	—
238	#108	C₄×D₄₃	1	1	yes	characteristic
239	#104	—	2	1	no	—
240	#104	—	86	1	no	—
241	#104	—	86	1	no	—
242	#104	—	86	1	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	43	1	no	—
245	C₄×C₈	—	43	1	no	—
246	C₄×C₈	—	43	1	no	—
247	C₄×C₈	—	86	2	no	—
248	C₄×C₈	—	86	1	no	—
249	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
250	#41	—	2	1	no	—
251	#41	—	86	1	no	—
252	#41	—	86	1	no	—
253	#41	—	86	1	no	—
254	#41	—	172	1	no	—
255	#41	—	172	1	no	—
256	C₂×Q₈	—	86	1	no	—
257	C₂×D₄	—	86	1	no	—
258	C₂×D₄	—	172	1	no	—
259	C₂²×C₄	—	43	1	no	—
260	C₂²×C₄	—	86	1	no	—
261	C₂²×C₄	—	172	1	no	—
262	Q₁₆	—	43	1	no	—
263	Q₁₆	—	86	1	no	—
264	Q₁₆	C₈×D₄₃	1	1	yes	characteristic, complemented
265	SD₁₆	—	2	1	no	—
266	SD₁₆	—	86	1	no	—
267	SD₁₆	—	86	1	no	—
268	SD₁₆	—	86	1	no	—
269	D₈	—	43	1	no	—
270	D₈	—	86	1	no	—
271	D₈	C₈×D₄₃	1	1	yes	characteristic, complemented
272	M₁₆	—	2	1	no	—
273	M₁₆	—	4	1	no	—
274	M₁₆	—	86	1	no	—
275	M₁₆	—	172	1	no	—
276	M₁₆	—	172	1	no	—
277	M₁₆	—	172	1	no	—
278	M₁₆	—	172	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	43	1	no	—
282	C₂×C₈	—	43	1	no	—
283	C₂×C₈	—	43	1	no	—
284	C₂×C₈	—	43	1	no	—
285	C₂×C₈	—	43	1	no	—
286	C₂×C₈	—	43	1	no	—
287	C₂×C₈	—	43	1	no	—
288	C₂×C₈	—	43	1	no	—
289	C₂×C₈	—	43	1	no	—
290	C₂×C₈	—	43	1	no	—
291	C₂×C₈	—	86	8	no	—
292	C₂×C₈	—	86	2	no	—
293	C₂×C₈	—	172	1	no	—
294	C₂×C₈	—	172	1	no	—
295	C₂×C₈	—	172	1	no	—
296	C₂×C₈	—	172	1	no	—
297	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
298	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
299	C₄²	—	43	1	no	—
300	C₄²	—	86	1	no	—
301	C₄²	D₄×D₄₃	1	1	yes	characteristic
302	C₁₆	—	4	1	no	—
303	C₁₆	—	172	1	no	—
304	C₂³	—	43	1	no	—
305	C₂³	—	172	1	no	—
306	Q₈	—	2	1	no	—
307	Q₈	—	86	1	no	—
308	Q₈	—	172	1	no	—
309	D₄	—	2	1	no	—
310	D₄	—	4	1	no	—
311	D₄	—	86	1	no	—
312	D₄	—	172	1	no	—
313	D₄	—	172	1	no	—
314	D₄	—	172	1	no	—
315	D₄	—	172	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	43	1	no	—
319	C₂×C₄	—	43	1	no	—
320	C₂×C₄	—	43	1	no	—
321	C₂×C₄	—	43	1	no	—
322	C₂×C₄	—	43	1	no	—
323	C₂×C₄	—	86	4	no	—
324	C₂×C₄	—	86	1	no	—
325	C₂×C₄	—	172	1	no	—
326	C₂×C₄	—	172	1	no	—
327	C₂×C₄	—	172	1	no	—
328	C₂×C₄	—	172	1	no	—
329	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
330	C₈	—	2	4	no	—
331	C₈	—	4	1	no	—
332	C₈	—	43	1	no	—
333	C₈	—	43	1	no	—
334	C₈	—	43	1	no	—
335	C₈	—	43	1	no	—
336	C₈	—	86	4	no	—
337	C₈	—	172	1	no	—
338	C₈	C₂×C₈×D₄₃	1	1	yes	characteristic
339	C₈	M₁₆×D₄₃	1	1	yes	characteristic
340	C₈	D₈×D₄₃	1	1	yes	characteristic
341	C₈	SD₁₆×D₄₃	1	1	yes	characteristic
342	C₂²	—	4	1	no	—
343	C₂²	—	43	1	no	—
344	C₂²	—	43	1	no	—
345	C₂²	—	86	2	no	—
346	C₂²	—	344	2	no	—
347	C₂²	—	172	1	no	—
348	C₂²	#104×D₄₃	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	1	no	—
351	C₄	—	43	1	no	—
352	C₄	—	43	1	no	—
353	C₄	—	86	2	no	—
354	C₄	—	172	1	no	—
355	C₄	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
356	C₄	#102×D₄₃	1	1	yes	characteristic
357	C₂	—	2	1	no	—
358	C₂	—	8	1	no	—
359	C₂	—	43	2	no	—
360	C₂	—	86	1	no	—
361	C₂	—	344	1	no	—
362	C₂	D₄⋊C₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1335	C₂
socle	C₂×C₄₃	C₂×D₄⋊C₈
prime radical	#135×D₄₃	C₄
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1335	D₄₃
hypocenter	C₄₃	C₂×#1335
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1335

Complements

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

N	H ≅ G/N	type
2. #364×D₄₃	C₂	semidirect
3. C₈²×D₄₃	C₂	semidirect
4. #19132569	C₂	semidirect
5. #19132568	C₂	semidirect
6. #19132567	C₂	semidirect
7. C₄₃×#1335	C₂	semidirect
20. #14582720	C₂²	semidirect
23. C₈×C₄₃⋊C₈	C₂²	semidirect
25. C₄₃×#364	C₂²	semidirect
26. C₈²×C₄₃	C₂²	semidirect
28. #13063348	C₈	semidirect
32. #13063344	C₈	semidirect
33. Q₁₆×D₄₃	C₈	semidirect
35. D₈×D₄₃	C₈	semidirect
80. Q₁₆×C₄₃	C₂×C₈	semidirect
82. D₈×C₄₃	C₂×C₈	semidirect
102. Dic₁₇₂	C₂×C₈	semidirect
103. D₃₄₄	C₂×C₈	semidirect
182. #1335	D₄₃	direct (N × H)
188. D₄₃	#1335	direct (N × H)
204. #364	C₂×D₄₃	semidirect
207. C₈²	C₂×D₄₃	semidirect
208. C₄₃	C₂×#1335	semidirect
264. Q₁₆	C₈×D₄₃	semidirect
271. D₈	C₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#443×D₄₃	2
#364×D₄₃	2
C₈²×D₄₃	2
#19132569	2
#19132568	2
#19132567	2
C₄₃×#1335	2
C₂×#1335	43

Subgroups — D43×#1335 #25006378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1335 #25006378