Subgroups — D₄₃×#2276 #25254818

Order 11008.

3654 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×D₄₃	C₂	1	3	yes	maximal
2	#19136960	C₂	1	3	yes	maximal, complemented
3	#19136959	C₂	1	9	yes	maximal, complemented
4	#19136958	C₂	1	3	yes	maximal, complemented
5	C₄×C₄⋊C₄×D₄₃	C₂	1	9	yes	maximal
6	#376×D₄₃	C₂	1	3	yes	maximal
7	C₄₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×Dic₄₃	C₂²	1	3	yes	—
10	C₂×C₄×Dic₈₆	C₂²	1	9	yes	—
11	C₂×#13063290	C₂²	1	9	yes	—
12	C₄×Q₈×D₄₃	C₄	1	48	yes	complemented
13	C₂×C₄⋊C₄×D₄₃	C₂²	1	9	yes	—
14	C₂×C₄²×D₄₃	C₂²	1	6	yes	—
15	C₂×C₄²×D₄₃	C₂²	1	9	yes	—
16	C₄⋊C₄×Dic₄₃	C₂²	1	18	yes	—
17	C₄×Dic₄₃⋊C₄	C₂²	1	18	yes	—
18	C₄×C₄⋊Dic₄₃	C₂²	1	9	yes	—
19	#14582750	C₂²	1	18	yes	—
20	#14582745	C₂²	1	9	yes	—
21	#14582744	C₂²	1	3	yes	—
22	#14582744	C₂²	1	9	yes	—
23	#95×D₄₃	C₂²	1	1	yes	characteristic
24	#95×D₄₃	C₂²	1	9	yes	—
25	C₂×C₄×Q₈×C₄₃	C₂²	1	3	yes	—
26	C₄×C₄⋊C₄×C₄₃	C₂²	1	9	yes	—
27	C₄₃×#376	C₂²	1	3	yes	—
28	C₂²×Dic₈₆	C₂³	1	3	yes	—
29	C₂×Q₈×D₄₃	C₂×C₄	1	24	yes	—
30	C₂²×C₄×D₄₃	C₂³	1	9	yes	—
31	C₂²×C₄×D₄₃	C₂³	1	3	yes	—
32	C₂²×C₄×D₄₃	C₂³	1	3	yes	—
33	Q₈×Dic₄₃	C₂×C₄	1	24	yes	complemented
34	C₄×Dic₈₆	C₂×C₄	1	72	yes	complemented
35	#13063290	C₂×C₄	1	72	yes	complemented
36	C₂×C₄⋊Dic₄₃	C₂³	1	9	yes	—
37	C₂×Dic₄₃⋊C₄	C₂³	1	18	yes	—
38	C₄⋊C₄×D₄₃	C₂×C₄	1	72	yes	—
39	C₂×C₄×Dic₄₃	C₂³	1	18	yes	—
40	C₂×C₄×Dic₄₃	C₂³	1	9	yes	—
41	C₂×C₄×Dic₄₃	C₂³	1	9	yes	—
42	C₂×C₄×Dic₄₃	C₂³	1	9	yes	—
43	C₄²×D₄₃	—	4	12	no	—
44	C₄²×D₄₃	C₂×C₄	1	72	yes	—
45	C₄₃⋊#95	C₂³	1	3	yes	—
46	C₄₃⋊#95	C₂³	1	9	yes	—
47	C₄₃⋊#95	C₂³	1	18	yes	—
48	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₄×Q₈×C₄₃	C₂×C₄	1	24	yes	complemented
50	C₂×C₄⋊C₄×C₄₃	C₂³	1	9	yes	—
51	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
52	C₂×C₄²×C₄₃	C₂³	1	9	yes	—
53	#95×C₄₃	C₂³	1	1	yes	characteristic
54	#95×C₄₃	C₂³	1	9	yes	—
55	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
56	C₂×Q₈×C₄₃	C₂²×C₄	1	12	yes	—
57	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
58	C₂²×C₄×C₄₃	C₂⁴	1	9	yes	—
59	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
60	C₂²×Dic₄₃	C₂⁴	1	3	yes	—
61	C₂²×Dic₄₃	C₂⁴	1	9	yes	—
62	C₂²×Dic₄₃	C₂⁴	1	3	yes	—
63	Q₈×D₄₃	C₄²	1	64	yes	complemented
64	C₂×C₄×D₄₃	—	2	18	no	—
65	C₂×C₄×D₄₃	—	2	12	no	—
66	C₂×C₄×D₄₃	—	2	18	no	—
67	C₂×C₄×D₄₃	C₂²×C₄	1	12	yes	—
68	C₂×C₄×D₄₃	C₂²×C₄	1	36	yes	—
69	C₂×C₄×D₄₃	C₂²×C₄	1	36	yes	—
70	C₂×Dic₈₆	C₂²×C₄	1	36	yes	—
71	C₄⋊C₄×C₄₃	C₂²×C₄	1	36	yes	—
72	C₄²×C₄₃	—	4	6	no	—
73	C₄²×C₄₃	C₂²×C₄	1	36	yes	—
74	C₄⋊Dic₄₃	C₂²×C₄	1	36	yes	—
75	Dic₄₃⋊C₄	C₂²×C₄	1	72	yes	—
76	C₄×Dic₄₃	—	4	18	no	—
77	C₄×Dic₄₃	C₂²×C₄	1	36	yes	—
78	C₄×Dic₄₃	C₂²×C₄	1	36	yes	—
79	C₄×Dic₄₃	C₂²×C₄	1	36	yes	—
80	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
81	C₂²×D₄₃	C₂³×C₄	1	6	yes	—
82	C₂²×D₄₃	H(5,𝔽₂)	1	2	yes	—
83	C₂²×D₄₃	2₋¹⁺⁴	1	6	yes	—
84	Q₈×C₄₃	C₂×C₄²	1	16	yes	complemented
85	C₂×C₄×C₄₃	—	2	9	no	—
86	C₂×C₄×C₄₃	—	2	6	no	—
87	C₂×C₄×C₄₃	—	2	9	no	—
88	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
89	C₂×C₄×C₄₃	C₂³×C₄	1	18	yes	—
90	C₂×C₄×C₄₃	C₂³×C₄	1	18	yes	—
91	C₂×Dic₄₃	—	2	9	no	—
92	C₂×Dic₄₃	—	2	6	no	—
93	C₂×Dic₄₃	—	2	9	no	—
94	C₂×Dic₄₃	C₂³×C₄	1	6	yes	—
95	C₂×Dic₄₃	C₂³×C₄	1	18	yes	—
96	C₂×Dic₄₃	C₂³×C₄	1	18	yes	—
97	C₄×D₄₃	—	2	24	no	—
98	C₄×D₄₃	—	2	72	no	—
99	C₄×D₄₃	C₂×C₄²	1	48	yes	—
100	Dic₈₆	C₂×C₄²	1	48	yes	complemented
101	C₂×#2276	—	43	1	no	maximal, Sylow
102	C₂²×C₄₃	C₂⁴×C₄	1	3	yes	—
103	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	3	yes	—
105	C₂×D₄₃	C₂²×C₄²	1	4	yes	—
106	C₂×D₄₃	#519	1	12	yes	—
107	C₂×D₄₃	#520	1	12	yes	—
108	C₄×C₄₃	—	2	6	no	—
109	C₄×C₄₃	—	2	18	no	—
110	C₄×C₄₃	C₂²×C₄²	1	12	yes	—
111	Dic₄₃	—	2	6	no	—
112	Dic₄₃	—	2	18	no	—
113	Dic₄₃	C₂²×C₄²	1	12	yes	—
114	C₂²×C₄×Q₈	—	43	3	no	—
115	#2276	—	43	9	no	—
116	#2276	—	43	3	no	—
117	#2276	—	43	3	no	—
118	#2276	D₄₃	1	1	yes	characteristic, direct product factor
119	C₂×C₄×C₄⋊C₄	—	43	9	no	—
120	C₂×#376	—	43	3	no	—
121	C₂×C₄₃	C₂³×C₄²	1	1	yes	characteristic
122	C₂×C₄₃	C₂×#519	1	3	yes	—
123	C₂×C₄₃	C₂×#520	1	3	yes	—
124	D₄₃	#2276	1	8	yes	direct product factor
125	C₂³×Q₈	—	43	1	no	—
126	C₂×C₄×Q₈	—	43	3	no	—
127	C₂×C₄×Q₈	—	43	48	no	—
128	C₂×C₄×Q₈	—	43	9	no	—
129	C₂×C₄×Q₈	—	43	9	no	—
130	C₂×C₄×Q₈	C₂×D₄₃	1	3	yes	—
131	C₂²×C₄⋊C₄	—	43	9	no	—
132	C₂²×C₄²	—	43	9	no	—
133	C₂²×C₄²	—	43	6	no	—
134	C₄×C₄⋊C₄	—	43	18	no	—
135	C₄×C₄⋊C₄	—	43	9	no	—
136	C₄×C₄⋊C₄	—	43	18	no	—
137	C₄×C₄⋊C₄	—	43	18	no	—
138	C₄×C₄⋊C₄	C₂×D₄₃	1	9	yes	—
139	#376	—	43	9	no	—
140	#376	—	43	9	no	—
141	#376	—	43	3	no	—
142	#376	C₂×D₄₃	1	3	yes	—
143	C₂×#95	—	43	1	no	—
144	C₂×#95	—	43	9	no	—
145	C₄₃	C₂×#2276	1	1	yes	characteristic, complemented, Sylow
146	C₂²×Q₈	—	43	24	no	—
147	C₂²×Q₈	—	43	3	no	—
148	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
149	C₂³×C₄	—	43	3	no	—
150	C₂³×C₄	—	43	9	no	—
151	C₂³×C₄	—	43	3	no	—
152	C₄×Q₈	—	43	24	no	—
153	C₄×Q₈	—	43	72	no	—
154	C₄×Q₈	—	43	72	no	—
155	C₄×Q₈	C₄×D₄₃	1	24	yes	complemented
156	C₂×C₄⋊C₄	—	43	18	no	—
157	C₂×C₄⋊C₄	—	43	9	no	—
158	C₂×C₄⋊C₄	—	43	72	no	—
159	C₂×C₄⋊C₄	C₂²×D₄₃	1	9	yes	—
160	C₂×C₄²	—	43	9	no	—
161	C₂×C₄²	—	43	9	no	—
162	C₂×C₄²	—	43	9	no	—
163	C₂×C₄²	—	43	72	no	—
164	C₂×C₄²	—	43	18	no	—
165	C₂×C₄²	—	172	12	no	—
166	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
167	C₂×C₄²	C₂²×D₄₃	1	9	yes	—
168	#95	—	43	3	no	—
169	#95	—	43	18	no	—
170	#95	—	43	9	no	—
171	#95	C₂²×D₄₃	1	1	yes	characteristic
172	#95	C₂²×D₄₃	1	9	yes	—
173	C₂⁴	—	43	1	no	—
174	C₂×Q₈	—	43	64	no	—
175	C₂×Q₈	—	43	36	no	—
176	C₂×Q₈	C₂×C₄×D₄₃	1	12	yes	—
177	C₂²×C₄	—	43	3	no	—
178	C₂²×C₄	—	43	36	no	—
179	C₂²×C₄	—	43	3	no	—
180	C₂²×C₄	—	43	9	no	—
181	C₂²×C₄	—	43	12	no	—
182	C₂²×C₄	—	43	36	no	—
183	C₂²×C₄	—	86	18	no	—
184	C₂²×C₄	—	86	18	no	—
185	C₂²×C₄	—	86	12	no	—
186	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
187	C₂²×C₄	C₂³×D₄₃	1	9	yes	—
188	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
189	C₄⋊C₄	—	43	72	no	—
190	C₄⋊C₄	—	43	36	no	—
191	C₄⋊C₄	C₂×C₄×D₄₃	1	36	yes	—
192	C₄²	—	4	6	no	—
193	C₄²	—	43	36	no	—
194	C₄²	—	43	36	no	—
195	C₄²	—	43	36	no	—
196	C₄²	—	172	18	no	—
197	C₄²	C₂×C₄×D₄₃	1	36	yes	—
198	C₂³	—	43	6	no	—
199	C₂³	—	43	2	no	—
200	C₂³	—	43	6	no	—
201	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
202	Q₈	—	43	48	no	—
203	Q₈	C₄²×D₄₃	1	16	yes	complemented
204	C₂×C₄	—	2	9	no	—
205	C₂×C₄	—	2	6	no	—
206	C₂×C₄	—	2	9	no	—
207	C₂×C₄	—	43	18	no	—
208	C₂×C₄	—	43	48	no	—
209	C₂×C₄	—	43	6	no	—
210	C₂×C₄	—	43	18	no	—
211	C₂×C₄	—	86	24	no	—
212	C₂×C₄	—	86	72	no	—
213	C₂×C₄	—	86	9	no	—
214	C₂×C₄	—	86	6	no	—
215	C₂×C₄	—	86	9	no	—
216	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
217	C₂×C₄	C₂²×C₄×D₄₃	1	18	yes	—
218	C₂×C₄	C₂²×C₄×D₄₃	1	18	yes	—
219	C₂²	—	43	12	no	—
220	C₂²	—	43	12	no	—
221	C₂²	—	43	4	no	—
222	C₂²	C₂³×C₄×D₄₃	1	3	yes	—
223	C₂²	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
224	C₂²	2₋¹⁺⁴×D₄₃	1	3	yes	—
225	C₄	—	2	6	no	—
226	C₄	—	2	18	no	—
227	C₄	—	43	12	no	—
228	C₄	—	86	6	no	—
229	C₄	—	86	18	no	—
230	C₄	C₂×C₄²×D₄₃	1	12	yes	—
231	C₂	—	43	8	no	—
232	C₂	C₂²×C₄²×D₄₃	1	1	yes	characteristic
233	C₂	#519×D₄₃	1	3	yes	—
234	C₂	#520×D₄₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₃
commutator	C₂×C₄₃	C₂³×C₄²
Fitting	C₄₃×#2276	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂³×D₄₃	C₂⁴
hypercenter	#2276	D₄₃
hypocenter	C₄₃	C₂×#2276
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #2276

Complements

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

N	H ≅ G/N	type
2. #19136960	C₂	semidirect
3. #19136959	C₂	semidirect
4. #19136958	C₂	semidirect
7. C₄₃×#2276	C₂	semidirect
12. C₄×Q₈×D₄₃	C₄	semidirect
33. Q₈×Dic₄₃	C₂×C₄	semidirect
34. C₄×Dic₈₆	C₂×C₄	semidirect
35. #13063290	C₂×C₄	semidirect
49. C₄×Q₈×C₄₃	C₂×C₄	semidirect
63. Q₈×D₄₃	C₄²	semidirect
84. Q₈×C₄₃	C₂×C₄²	semidirect
100. Dic₈₆	C₂×C₄²	semidirect
118. #2276	D₄₃	direct (N × H)
124. D₄₃	#2276	direct (N × H)
145. C₄₃	C₂×#2276	semidirect
155. C₄×Q₈	C₄×D₄₃	semidirect
203. Q₈	C₄²×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₈×D₄₃	2
#19136960	2
#19136959	2
#19136958	2
C₄×C₄⋊C₄×D₄₃	2
#376×D₄₃	2
C₄₃×#2276	2
C₂×#2276	43

Subgroups — D43×#2276 #25254818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#2276 #25254818