Subgroups — C₄₃×#7912 #24927929

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#432	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1280	C₂	1	4	yes	maximal
4	C₂²×C₄⋊C₄×C₄₃	C₄	1	2	yes	—
5	C₂²×C₄²×C₄₃	C₄	1	2	yes	—
6	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×#432	—	2	4	no	—
8	C₄₃×#432	C₄	1	8	yes	complemented
9	C₂×C₄⋊C₈×C₄₃	—	2	2	no	—
10	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
11	C₂×#97×C₄₃	—	2	2	no	—
12	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
13	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
14	C₂×#95×C₄₃	C₂²	1	2	yes	—
15	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	—	2	4	no	—
20	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
21	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
22	C₂×C₄²×C₄₃	—	2	2	no	—
23	C₂×C₄²×C₄₃	—	2	2	no	—
24	C₂×C₄²×C₄₃	—	4	4	no	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₄₃	D₄	1	2	yes	—
27	C₂×C₄²×C₄₃	D₄	1	2	yes	—
28	C₂×C₄²×C₄₃	D₄	1	2	yes	—
29	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
30	C₄⋊C₈×C₄₃	—	2	8	no	—
31	C₂²⋊C₈×C₄₃	—	2	4	no	—
32	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
33	#97×C₄₃	—	2	8	no	—
34	#95×C₄₃	—	2	4	no	—
35	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	—	2	2	no	—
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	4	no	—
39	C₂²×C₄×C₄₃	—	2	4	no	—
40	C₂²×C₄×C₄₃	—	2	4	no	—
41	C₂²×C₄×C₄₃	—	4	2	no	—
42	C₂²×C₄×C₄₃	—	4	4	no	—
43	C₂²×C₄×C₄₃	—	4	4	no	—
44	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
45	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
46	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₄₃	M₁₆	1	8	yes	—
52	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₈×C₄₃	—	2	8	no	—
57	C₂×C₈×C₄₃	—	4	8	no	—
58	C₄⋊C₄×C₄₃	—	2	16	no	—
59	C₄²×C₄₃	—	4	4	no	—
60	C₄²×C₄₃	—	4	4	no	—
61	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
62	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
63	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
64	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
65	C₂³×C₄₃	—	2	2	no	—
66	C₂³×C₄₃	—	2	1	no	—
67	C₂³×C₄₃	—	2	1	no	—
68	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
69	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂³×C₄₃	C₂×M₁₆	1	4	yes	—
72	C₂×C₄×C₄₃	—	2	4	no	—
73	C₂×C₄×C₄₃	—	2	4	no	—
74	C₂×C₄×C₄₃	—	2	4	no	—
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	1	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	2	4	no	—
80	C₂×C₄×C₄₃	—	2	8	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	—	4	1	no	—
83	C₂×C₄×C₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	—	4	8	no	—
85	C₂×C₄×C₄₃	—	4	4	no	—
86	C₂×C₄×C₄₃	—	4	4	no	—
87	C₂×C₄×C₄₃	—	4	8	no	—
88	C₂×C₄×C₄₃	#95	1	4	yes	—
89	C₂×C₄×C₄₃	#95	1	2	yes	—
90	C₂×C₄×C₄₃	#95	1	2	yes	—
91	C₂×C₄×C₄₃	#100	1	2	yes	—
92	C₂×C₄×C₄₃	#101	1	2	yes	—
93	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
94	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
95	C₈×C₄₃	—	4	8	no	—
96	#7912	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂²×C₄₃	—	2	4	no	—
98	C₂²×C₄₃	—	2	4	no	—
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	—	2	1	no	—
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
104	C₂²×C₄₃	C₄×M₁₆	1	2	yes	—
105	C₂²×C₄₃	#407	1	2	yes	—
106	C₂²×C₄₃	#410	1	2	yes	—
107	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
108	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
109	C₂²×C₄₃	#423	1	2	yes	—
110	C₄×C₄₃	—	2	4	no	—
111	C₄×C₄₃	—	2	2	no	—
112	C₄×C₄₃	—	2	2	no	—
113	C₄×C₄₃	—	2	2	no	—
114	C₄×C₄₃	—	4	8	no	—
115	C₄×C₄₃	#343	1	4	yes	—
116	C₂×#432	C₂×C₄₃	1	2	yes	—
117	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
118	#1280	C₂×C₄₃	1	4	yes	—
119	C₂×C₄₃	—	2	2	no	—
120	C₂×C₄₃	—	2	2	no	—
121	C₂×C₄₃	#1466	1	2	yes	—
122	C₂×C₄₃	#1467	1	2	yes	—
123	C₂×C₄₃	#1728	1	1	yes	characteristic
124	C₂×C₄₃	#1740	1	1	yes	characteristic
125	C₂×C₄₃	C₂×#343	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	C₄×C₄₃	1	2	yes	—
127	C₂²×C₄²	C₄×C₄₃	1	2	yes	—
128	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
129	#432	—	2	4	no	—
130	#432	C₄×C₄₃	1	8	yes	complemented
131	C₂×C₄⋊C₈	—	2	2	no	—
132	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
133	C₂×#97	—	2	2	no	—
134	C₄×C₄⋊C₄	—	2	2	no	—
135	C₄×C₄⋊C₄	—	2	2	no	—
136	C₂×#95	C₂²×C₄₃	1	2	yes	—
137	C₄₃	#7912	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
139	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
140	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
141	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
142	C₂²×C₈	—	2	4	no	—
143	C₂×C₄⋊C₄	—	2	4	no	—
144	C₂×C₄⋊C₄	—	2	8	no	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	—	2	2	no	—
147	C₂×C₄²	—	4	4	no	—
148	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
149	C₂×C₄²	D₄×C₄₃	1	2	yes	—
150	C₂×C₄²	D₄×C₄₃	1	2	yes	—
151	C₂×C₄²	D₄×C₄₃	1	2	yes	—
152	C₂×C₄²	Q₈×C₄₃	1	2	yes	—
153	C₄⋊C₈	—	2	8	no	—
154	C₂²⋊C₈	—	2	4	no	—
155	C₂²⋊C₈	C₂×C₄×C₄₃	1	8	yes	—
156	#97	—	2	8	no	—
157	#95	—	2	4	no	—
158	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	4	2	no	—
165	C₂²×C₄	—	4	4	no	—
166	C₂²×C₄	—	4	4	no	—
167	C₂²×C₄	C₄²×C₄₃	1	2	yes	—
168	C₂²×C₄	C₄²×C₄₃	1	2	yes	—
169	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
170	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
171	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
172	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
173	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
174	C₂²×C₄	M₁₆×C₄₃	1	8	yes	—
175	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
176	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
177	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
179	C₂×C₈	—	2	8	no	—
180	C₂×C₈	—	4	8	no	—
181	C₄⋊C₄	—	2	16	no	—
182	C₄²	—	4	4	no	—
183	C₄²	—	4	4	no	—
184	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
185	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
186	C₄²	C₄⋊C₄×C₄₃	1	4	yes	—
187	C₄²	C₄⋊C₄×C₄₃	1	4	yes	—
188	C₂³	—	2	2	no	—
189	C₂³	—	2	1	no	—
190	C₂³	—	2	1	no	—
191	C₂³	C₂×C₄²×C₄₃	1	1	yes	characteristic
192	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
193	C₂³	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
194	C₂³	C₂×M₁₆×C₄₃	1	4	yes	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	8	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	8	no	—
211	C₂×C₄	#95×C₄₃	1	4	yes	—
212	C₂×C₄	#95×C₄₃	1	2	yes	—
213	C₂×C₄	#95×C₄₃	1	2	yes	—
214	C₂×C₄	#100×C₄₃	1	2	yes	—
215	C₂×C₄	#101×C₄₃	1	2	yes	—
216	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
217	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
218	C₈	—	4	8	no	—
219	C₂²	—	2	4	no	—
220	C₂²	—	2	4	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	C₂×#95×C₄₃	1	1	yes	characteristic
226	C₂²	C₄×M₁₆×C₄₃	1	2	yes	—
227	C₂²	C₄₃×#407	1	2	yes	—
228	C₂²	C₄₃×#410	1	2	yes	—
229	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
230	C₂²	C₂×#101×C₄₃	1	1	yes	characteristic
231	C₂²	C₄₃×#423	1	2	yes	—
232	C₄	—	2	4	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	4	8	no	—
237	C₄	C₄₃×#343	1	4	yes	—
238	C₂	—	2	2	no	—
239	C₂	—	2	2	no	—
240	C₂	C₄₃×#1466	1	2	yes	—
241	C₂	C₄₃×#1467	1	2	yes	—
242	C₂	C₄₃×#1728	1	1	yes	characteristic
243	C₂	C₄₃×#1740	1	1	yes	characteristic
244	C₂	C₂×C₄₃×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₄₃×#432	C₄	semidirect
96. #7912	C₄₃	direct (N × H)
130. #432	C₄×C₄₃	semidirect
137. C₄₃	#7912	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#432	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1280	2
#7912	43

Subgroups — C43×#7912 #24927929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#7912 #24927929