Subgroups — C₄₃×#8296 #24928313

Order 11008.

342 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#108×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1564	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1451	C₂	1	1	yes	maximal, characteristic
4	C₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×#322	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1278	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1278	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#431	C₂²	1	1	yes	characteristic
9	C₄₃×#431	C₂²	1	1	yes	characteristic
10	C₂×#108×C₄₃	C₄	1	2	yes	—
11	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#341	C₄	1	2	yes	—
17	C₄₃×#335	C₄	1	2	yes	—
18	C₄₃×#334	C₄	1	2	yes	—
19	C₄₃×#322	—	2	1	no	—
20	C₄₃×#322	—	2	1	no	—
21	C₄₃×#322	—	2	1	no	—
22	C₄₃×#322	C₄	1	2	yes	—
23	C₄₃×#322	C₄	1	2	yes	—
24	C₈²×C₄₃	—	2	1	no	—
25	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
26	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₄₃	—	2	1	no	—
28	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₄₃	Q₈	1	2	yes	—
31	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	#108×C₄₃	—	2	4	no	—
33	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
34	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₂²⋊C₈×C₄₃	—	2	1	no	—
36	C₂²⋊C₈×C₄₃	—	2	1	no	—
37	#97×C₄₃	—	2	1	no	—
38	#97×C₄₃	—	2	1	no	—
39	C₄×C₈×C₄₃	—	2	1	no	—
40	C₄×C₈×C₄₃	—	2	1	no	—
41	C₄×C₈×C₄₃	—	2	1	no	—
42	C₄×C₈×C₄₃	—	2	1	no	—
43	C₄×C₈×C₄₃	—	2	1	no	—
44	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
45	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
51	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
55	M₁₆×C₄₃	—	2	2	no	—
56	M₁₆×C₄₃	—	2	2	no	—
57	M₁₆×C₄₃	—	2	2	no	—
58	M₁₆×C₄₃	M₁₆	1	4	yes	—
59	C₂×C₈×C₄₃	—	2	4	no	—
60	C₂×C₈×C₄₃	—	2	2	no	—
61	C₂×C₈×C₄₃	—	2	2	no	—
62	C₂×C₈×C₄₃	—	2	2	no	—
63	C₂×C₈×C₄₃	—	2	2	no	—
64	C₂×C₈×C₄₃	—	2	2	no	—
65	C₂×C₈×C₄₃	—	2	2	no	—
66	C₂×C₈×C₄₃	—	2	2	no	—
67	C₂×C₈×C₄₃	—	4	2	no	—
68	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
69	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
71	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
72	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
73	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
74	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₄₃	#41	1	1	yes	characteristic
78	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₄₃	#131	1	2	yes	—
89	C₈×C₄₃	—	2	4	no	—
90	C₈×C₄₃	—	2	1	no	—
91	C₈×C₄₃	—	2	1	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	—	2	2	no	—
95	C₈×C₄₃	—	2	2	no	—
96	C₈×C₄₃	—	2	4	no	—
97	C₈×C₄₃	—	4	2	no	—
98	C₈×C₄₃	—	4	2	no	—
99	C₈×C₄₃	—	4	2	no	—
100	#8296	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄₃	#446	1	2	yes	—
105	C₄×C₄₃	—	2	1	no	—
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
108	C₄×C₄₃	#405	1	1	yes	characteristic
109	C₄×C₄₃	#430	1	2	yes	—
110	C₄×C₄₃	#435	1	2	yes	—
111	C₄×C₄₃	#443	1	2	yes	—
112	C₄×#108	C₂×C₄₃	1	1	yes	characteristic
113	#1564	C₂×C₄₃	1	1	yes	characteristic
114	#1451	C₂×C₄₃	1	1	yes	characteristic
115	C₈×M₁₆	C₂×C₄₃	1	1	yes	characteristic
116	C₂×#322	C₂×C₄₃	1	1	yes	characteristic
117	#1278	C₂×C₄₃	1	1	yes	characteristic
118	#1278	C₂×C₄₃	1	1	yes	characteristic
119	C₂×C₄₃	—	2	2	no	—
120	C₂×C₄₃	#1771	1	1	yes	characteristic
121	C₂×C₄₃	#1772	1	1	yes	characteristic
122	C₂×C₄₃	#1778	1	1	yes	characteristic
123	#431	C₂²×C₄₃	1	1	yes	characteristic
124	#431	C₂²×C₄₃	1	1	yes	characteristic
125	C₂×#108	C₄×C₄₃	1	2	yes	—
126	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
127	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
131	#341	C₄×C₄₃	1	2	yes	—
132	#335	C₄×C₄₃	1	2	yes	—
133	#334	C₄×C₄₃	1	2	yes	—
134	#322	—	2	1	no	—
135	#322	—	2	1	no	—
136	#322	—	2	1	no	—
137	#322	C₄×C₄₃	1	2	yes	—
138	#322	C₄×C₄₃	1	2	yes	—
139	C₈²	—	2	1	no	—
140	C₄₃	#8296	1	1	yes	characteristic, direct product factor, Sylow
141	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	—
142	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
145	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
146	C₂²×C₈	Q₈×C₄₃	1	2	yes	—
147	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
148	#108	—	2	4	no	—
149	C₄⋊C₈	C₂×C₄×C₄₃	1	2	yes	—
150	C₄⋊C₈	C₂×C₄×C₄₃	1	2	yes	—
151	C₂²⋊C₈	—	2	1	no	—
152	C₂²⋊C₈	—	2	1	no	—
153	#97	—	2	1	no	—
154	#97	—	2	1	no	—
155	C₄×C₈	—	2	1	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
161	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
162	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
163	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
164	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
165	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
166	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
167	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
168	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
169	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
170	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
171	M₁₆	—	2	2	no	—
172	M₁₆	—	2	2	no	—
173	M₁₆	—	2	2	no	—
174	M₁₆	M₁₆×C₄₃	1	4	yes	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	C₄²×C₄₃	1	1	yes	characteristic
185	C₂×C₈	C₄²×C₄₃	1	1	yes	characteristic
186	C₂×C₈	C₄²×C₄₃	1	1	yes	characteristic
187	C₂×C₈	C₄²×C₄₃	1	1	yes	characteristic
188	C₂×C₈	C₄⋊C₄×C₄₃	1	2	yes	—
189	C₂×C₈	C₄⋊C₄×C₄₃	1	2	yes	—
190	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
191	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
192	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
193	C₄²	#41×C₄₃	1	1	yes	characteristic
194	C₂³	C₄×Q₈×C₄₃	1	1	yes	characteristic
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	C₂×C₄²×C₄₃	1	1	yes	characteristic
198	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
199	C₂×C₄	#117×C₄₃	1	1	yes	characteristic
200	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
201	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
202	C₂×C₄	C₄×Q₈×C₄₃	1	1	yes	characteristic
203	C₂×C₄	C₂×M₁₆×C₄₃	1	2	yes	—
204	C₂×C₄	#131×C₄₃	1	2	yes	—
205	C₈	—	2	4	no	—
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	2	1	no	—
209	C₈	—	2	1	no	—
210	C₈	—	2	2	no	—
211	C₈	—	2	2	no	—
212	C₈	—	2	4	no	—
213	C₈	—	4	2	no	—
214	C₈	—	4	2	no	—
215	C₈	—	4	2	no	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
219	C₂²	C₄₃×#446	1	2	yes	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	C₄×M₁₆×C₄₃	1	1	yes	characteristic
223	C₄	C₄₃×#405	1	1	yes	characteristic
224	C₄	C₄₃×#430	1	2	yes	—
225	C₄	C₄₃×#435	1	2	yes	—
226	C₄	C₄₃×#443	1	2	yes	—
227	C₂	—	2	2	no	—
228	C₂	C₄₃×#1771	1	1	yes	characteristic
229	C₂	C₄₃×#1772	1	1	yes	characteristic
230	C₂	C₄₃×#1778	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂²×C₄₃	C₄×C₄⋊C₄
prime radical	C₂³×C₄₃	C₄×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₄₃ ◁ C₂×C₄×C₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
100. #8296	C₄₃	direct (N × H)
140. C₄₃	#8296	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#108×C₄₃	2
C₄₃×#1564	2
C₄₃×#1451	2
C₈×M₁₆×C₄₃	2
C₂×C₄₃×#322	2
C₄₃×#1278	2
#8296	43

Subgroups — C43×#8296 #24928313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8296 #24928313