Subgroups — D₄₃×#1747 #25094098

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#405×D₄₃	C₂	1	3	yes	maximal
2	#19134351	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134350	C₂	1	3	yes	maximal, complemented
4	#19134349	C₂	1	3	yes	maximal, complemented
5	#338×D₄₃	C₂	1	1	yes	maximal, characteristic
6	H(3,ℤ/4)×D₄₃	C₂	1	3	yes	maximal
7	C₄₃×#1747	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₃	C₂²	1	3	yes	—
9	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#117×D₄₃	C₂²	1	3	yes	—
11	#14582857	C₂²	1	3	yes	—
12	#14582856	C₄	1	6	yes	complemented
13	#14582855	C₂²	1	3	yes	—
14	#14582854	C₂²	1	3	yes	—
15	#14582853	C₄	1	6	yes	complemented
16	#97×D₄₃	C₄	1	6	yes	complemented
17	C₄×C₈×D₄₃	C₄	1	6	yes	complemented
18	C₄₃⋊#338	C₂²	1	3	yes	—
19	#14582656	C₂²	1	3	yes	—
20	#14582655	C₂²	1	6	yes	—
21	C₄₃×#405	C₂²	1	3	yes	—
22	C₄₃×#338	C₂²	1	1	yes	characteristic
23	C₄₃×H(3,ℤ/4)	C₂²	1	3	yes	—
24	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
25	C₂×#10621877	C₂³	1	3	yes	—
26	C₂×#10621872	C₂×C₄	1	6	yes	—
27	M₁₆×D₄₃	—	2	6	no	—
28	M₁₆×D₄₃	—	2	6	no	—
29	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
30	C₂×C₈×D₄₃	C₂×C₄	1	6	yes	—
31	C₂×C₈×D₄₃	C₂×C₄	1	3	yes	—
32	C₂×C₈×D₄₃	C₂×C₄	1	3	yes	—
33	C₂×C₈×D₄₃	C₂×C₄	1	3	yes	—
34	C₂×C₈×D₄₃	C₂×C₄	1	3	yes	—
35	#13063284	C₂³	1	3	yes	—
36	#13063283	—	2	3	no	—
37	#13063282	C₂×C₄	1	6	yes	—
38	#13063281	—	2	3	no	—
39	C₄⋊C₄×D₄₃	—	2	3	no	—
40	C₂²⋊C₄×D₄₃	—	2	3	no	—
41	C₄²×D₄₃	C₂×C₄	1	6	yes	—
42	#13063236	C₂×C₄	1	6	yes	complemented
43	#13063235	C₂×C₄	1	6	yes	complemented
44	#13063235	C₂×C₄	1	6	yes	complemented
45	C₄×C₄₃⋊C₈	C₂×C₄	1	6	yes	complemented
46	C₈×Dic₄₃	C₂×C₄	1	6	yes	complemented
47	C₈×Dic₄₃	C₂×C₄	1	6	yes	complemented
48	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
49	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	#117×C₄₃	C₂³	1	3	yes	—
51	#97×C₄₃	C₂×C₄	1	6	yes	complemented
52	C₄×C₈×C₄₃	C₂×C₄	1	6	yes	complemented
53	C₂³×D₄₃	#41	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
55	C₂²×Dic₄₃	#41	1	1	yes	characteristic
56	C₂×C₄×D₄₃	—	2	6	no	—
57	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
58	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
59	C₂×C₄×D₄₃	#41	1	3	yes	—
60	C₂×C₄×D₄₃	#41	1	3	yes	—
61	M₁₆×C₄₃	—	2	6	no	—
62	C₂×C₈×C₄₃	C₂²×C₄	1	6	yes	—
63	C₂×C₈×C₄₃	C₂²×C₄	1	3	yes	—
64	C₂×C₈×C₄₃	C₂²×C₄	1	3	yes	—
65	C₄⋊C₄×C₄₃	—	2	3	no	—
66	C₂²⋊C₄×C₄₃	—	2	3	no	—
67	C₄²×C₄₃	C₂²×C₄	1	6	yes	—
68	C₂²⋊Dic₄₃	—	2	3	no	—
69	(C₂×D₄₃)⋊C₄	—	2	6	no	—
70	C₄⋊Dic₄₃	—	2	3	no	—
71	Dic₄₃⋊C₄	—	2	6	no	—
72	C₄×Dic₄₃	—	2	6	no	—
73	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
74	#10621877	—	2	6	no	—
75	C₂×C₄₃⋊C₈	C₂²×C₄	1	6	yes	—
76	C₂×C₄₃⋊C₈	C₂²×C₄	1	3	yes	—
77	C₂×C₄₃⋊C₈	C₂²×C₄	1	3	yes	—
78	#10621872	—	2	12	no	—
79	C₈×D₄₃	—	2	6	no	—
80	C₈×D₄₃	—	2	6	no	—
81	C₈×D₄₃	C₄²	1	3	yes	—
82	C₈×D₄₃	C₄²	1	3	yes	—
83	C₈×D₄₃	C₄²	1	6	yes	—
84	C₈×D₄₃	C₄²	1	1	yes	characteristic
85	C₈×D₄₃	C₄²	1	3	yes	—
86	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
87	C₂²×D₄₃	—	4	2	no	—
88	C₂²×D₄₃	#117	1	3	yes	—
89	C₂²×D₄₃	#117	1	3	yes	—
90	C₂×C₄×C₄₃	—	2	6	no	—
91	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
92	C₂×C₄×C₄₃	C₂×#41	1	3	yes	—
93	C₂×Dic₄₃	—	2	6	no	—
94	C₂×Dic₄₃	#117	1	3	yes	—
95	C₂×Dic₄₃	#117	1	3	yes	—
96	C₄×D₄₃	—	4	12	no	—
97	C₄×D₄₃	C₂×C₄²	1	3	yes	—
98	C₄×D₄₃	C₂×C₄²	1	1	yes	characteristic
99	C₄×D₄₃	#117	1	3	yes	—
100	C₄×D₄₃	#117	1	3	yes	—
101	C₄×D₄₃	#117	1	6	yes	—
102	C₈×C₄₃	—	2	6	no	—
103	C₈×C₄₃	C₂×C₄²	1	3	yes	—
104	C₈×C₄₃	C₂×C₄²	1	1	yes	characteristic
105	C₄₃⋊C₈	—	2	6	no	—
106	C₄₃⋊C₈	C₂×C₄²	1	1	yes	characteristic
107	C₄₃⋊C₈	C₂×C₄²	1	3	yes	—
108	C₂×#1747	—	43	1	no	maximal, Sylow
109	C₂²×C₄₃	—	4	1	no	—
110	C₂²×C₄₃	C₂×#117	1	3	yes	—
111	C₂×D₄₃	—	2	6	no	—
112	C₂×D₄₃	—	4	3	no	—
113	C₂×D₄₃	#376	1	3	yes	—
114	C₂×D₄₃	#376	1	1	yes	characteristic
115	C₄×C₄₃	—	4	6	no	—
116	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
117	C₄×C₄₃	C₂×#117	1	3	yes	—
118	Dic₄₃	—	4	6	no	—
119	Dic₄₃	#376	1	1	yes	characteristic
120	Dic₄₃	#376	1	3	yes	—
121	C₂×#405	—	43	3	no	—
122	#1747	—	43	3	no	—
123	#1747	—	43	1	no	—
124	#1747	—	43	3	no	—
125	#1747	D₄₃	1	1	yes	characteristic, direct product factor
126	C₂×#338	—	43	1	no	—
127	C₂×H(3,ℤ/4)	—	43	3	no	—
128	C₂×C₄₃	—	2	3	no	—
129	C₂×C₄₃	C₂×#376	1	1	yes	characteristic
130	D₄₃	—	2	3	no	—
131	D₄₃	#1747	1	2	yes	direct product factor
132	C₂²×M₁₆	—	43	3	no	—
133	C₂³×C₈	—	43	1	no	—
134	C₂×#117	—	43	3	no	—
135	#405	—	43	3	no	—
136	#405	—	43	3	no	—
137	#405	—	43	3	no	—
138	#405	—	43	6	no	—
139	#405	—	43	6	no	—
140	#405	C₂×D₄₃	1	3	yes	—
141	C₂×#97	—	43	6	no	—
142	C₂×C₄×C₈	—	43	6	no	—
143	#338	—	43	3	no	—
144	#338	C₂×D₄₃	1	1	yes	characteristic
145	H(3,ℤ/4)	—	43	3	no	—
146	H(3,ℤ/4)	—	43	6	no	—
147	H(3,ℤ/4)	C₂×D₄₃	1	3	yes	—
148	C₄₃	C₂×#1747	1	1	yes	characteristic, complemented, Sylow
149	C₂³×C₄	—	43	1	no	—
150	C₂×M₁₆	—	43	3	no	—
151	C₂×M₁₆	—	43	6	no	—
152	C₂×M₁₆	—	86	6	no	—
153	C₂×M₁₆	—	86	6	no	—
154	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
155	C₂²×C₈	—	43	1	no	—
156	C₂²×C₈	—	43	3	no	—
157	C₂²×C₈	—	43	3	no	—
158	C₂²×C₈	—	43	3	no	—
159	C₂²×C₈	—	43	3	no	—
160	C₂²×C₈	—	43	6	no	—
161	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
162	#117	—	43	3	no	—
163	#117	—	43	6	no	—
164	#117	—	86	3	no	—
165	#117	—	86	3	no	—
166	#117	C₂²×D₄₃	1	3	yes	—
167	C₂×C₄⋊C₄	—	86	3	no	—
168	C₂×C₂²⋊C₄	—	86	3	no	—
169	C₂×C₄²	—	43	6	no	—
170	#97	—	43	6	no	—
171	#97	—	43	6	no	—
172	#97	—	43	6	no	—
173	#97	C₄×D₄₃	1	6	yes	complemented
174	C₄×C₈	—	43	6	no	—
175	C₄×C₈	—	43	6	no	—
176	C₄×C₈	—	43	6	no	—
177	C₄×C₈	C₄×D₄₃	1	6	yes	complemented
178	C₂⁴	—	43	1	no	—
179	C₂²×C₄	—	43	1	no	—
180	C₂²×C₄	—	43	3	no	—
181	C₂²×C₄	—	43	3	no	—
182	C₂²×C₄	—	43	3	no	—
183	C₂²×C₄	—	43	3	no	—
184	C₂²×C₄	—	86	6	no	—
185	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
186	M₁₆	—	2	6	no	—
187	M₁₆	—	86	12	no	—
188	M₁₆	—	86	6	no	—
189	C₂×C₈	—	43	3	no	—
190	C₂×C₈	—	43	3	no	—
191	C₂×C₈	—	43	3	no	—
192	C₂×C₈	—	43	3	no	—
193	C₂×C₈	—	43	6	no	—
194	C₂×C₈	—	43	1	no	—
195	C₂×C₈	—	43	3	no	—
196	C₂×C₈	—	43	6	no	—
197	C₂×C₈	—	86	6	no	—
198	C₂×C₈	—	86	6	no	—
199	C₂×C₈	C₂×C₄×D₄₃	1	6	yes	—
200	C₂×C₈	C₂×C₄×D₄₃	1	3	yes	—
201	C₂×C₈	C₂×C₄×D₄₃	1	3	yes	—
202	C₄⋊C₄	—	2	3	no	—
203	C₄⋊C₄	—	86	6	no	—
204	C₄⋊C₄	—	86	3	no	—
205	C₂²⋊C₄	—	2	3	no	—
206	C₂²⋊C₄	—	86	6	no	—
207	C₂²⋊C₄	—	86	3	no	—
208	C₄²	—	43	6	no	—
209	C₄²	—	86	6	no	—
210	C₄²	C₂×C₄×D₄₃	1	6	yes	—
211	C₂³	—	43	3	no	—
212	C₂³	—	43	3	no	—
213	C₂³	—	172	2	no	—
214	C₂³	#41×D₄₃	1	1	yes	characteristic
215	C₂×C₄	—	2	6	no	—
216	C₂×C₄	—	43	3	no	—
217	C₂×C₄	—	43	3	no	—
218	C₂×C₄	—	43	1	no	—
219	C₂×C₄	—	43	3	no	—
220	C₂×C₄	—	43	3	no	—
221	C₂×C₄	—	43	3	no	—
222	C₂×C₄	—	43	6	no	—
223	C₂×C₄	—	86	6	no	—
224	C₂×C₄	—	172	12	no	—
225	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
226	C₂×C₄	#41×D₄₃	1	3	yes	—
227	C₈	—	2	6	no	—
228	C₈	—	43	1	no	—
229	C₈	—	43	3	no	—
230	C₈	—	86	6	no	—
231	C₈	C₄²×D₄₃	1	3	yes	—
232	C₈	C₄²×D₄₃	1	1	yes	characteristic
233	C₂²	—	4	1	no	—
234	C₂²	—	43	1	no	—
235	C₂²	—	43	3	no	—
236	C₂²	—	86	6	no	—
237	C₂²	—	172	3	no	—
238	C₂²	#117×D₄₃	1	3	yes	—
239	C₄	—	4	6	no	—
240	C₄	—	43	1	no	—
241	C₄	—	43	3	no	—
242	C₄	—	172	6	no	—
243	C₄	C₂×C₄²×D₄₃	1	1	yes	characteristic
244	C₄	#117×D₄₃	1	3	yes	—
245	C₂	—	2	3	no	—
246	C₂	—	43	2	no	—
247	C₂	—	86	3	no	—
248	C₂	#376×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄²×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1747	C₂
socle	C₂×C₄₃	C₂×#376
prime radical	C₂³×D₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1747	D₄₃
hypocenter	C₄₃	C₂×#1747
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ #1747

Complements

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

N	H ≅ G/N	type
2. #19134351	C₂	semidirect
3. #19134350	C₂	semidirect
4. #19134349	C₂	semidirect
7. C₄₃×#1747	C₂	semidirect
12. #14582856	C₄	semidirect
15. #14582853	C₄	semidirect
16. #97×D₄₃	C₄	semidirect
17. C₄×C₈×D₄₃	C₄	semidirect
42. #13063236	C₂×C₄	semidirect
43. #13063235	C₂×C₄	semidirect
44. #13063235	C₂×C₄	semidirect
45. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
46. C₈×Dic₄₃	C₂×C₄	semidirect
47. C₈×Dic₄₃	C₂×C₄	semidirect
51. #97×C₄₃	C₂×C₄	semidirect
52. C₄×C₈×C₄₃	C₂×C₄	semidirect
125. #1747	D₄₃	direct (N × H)
131. D₄₃	#1747	direct (N × H)
148. C₄₃	C₂×#1747	semidirect
173. #97	C₄×D₄₃	semidirect
177. C₄×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#405×D₄₃	2
#19134351	2
#19134350	2
#19134349	2
#338×D₄₃	2
H(3,ℤ/4)×D₄₃	2
C₄₃×#1747	2
C₂×#1747	43

Subgroups — D43×#1747 #25094098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1747 #25094098