Subgroups — C₄₃×#17114 #24937131

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#398	C₂	1	6	yes	maximal
2	C₄₃×#1444	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1444	C₂	1	3	yes	maximal
4	C₄₃×#1443	C₂	1	2	yes	maximal
5	C₄₃×#1442	C₂	1	3	yes	maximal
6	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
7	C₂²×C₄⋊C₄×C₄₃	C₂²	1	6	yes	—
8	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×#398	—	2	24	no	—
11	C₂×#95×C₄₃	C₂²	1	6	yes	—
12	C₂×#95×C₄₃	C₂²	1	6	yes	—
13	C₂×#95×C₄₃	C₂²	1	3	yes	—
14	C₂×#95×C₄₃	C₂²	1	3	yes	—
15	C₂×#95×C₄₃	C₂²	1	3	yes	—
16	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
18	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂³×C₄×C₄₃	C₂³	1	6	yes	—
20	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
21	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
23	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
24	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
25	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
26	C₂×C₄⋊C₄×C₄₃	—	4	3	no	—
27	C₂×C₄⋊C₄×C₄₃	—	4	3	no	—
28	C₂×C₄⋊C₄×C₄₃	—	4	6	no	—
29	C₂×C₄⋊C₄×C₄₃	—	4	3	no	—
30	#95×C₄₃	—	2	12	no	—
31	#95×C₄₃	—	2	12	no	—
32	#95×C₄₃	—	2	6	no	—
33	#95×C₄₃	—	4	3	no	—
34	#95×C₄₃	D₄	1	12	yes	—
35	#95×C₄₃	Q₈	1	4	yes	—
36	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	—	2	6	no	—
38	C₂²×C₄×C₄₃	—	2	6	no	—
39	C₂²×C₄×C₄₃	—	2	6	no	—
40	C₂²×C₄×C₄₃	—	2	6	no	—
41	C₂²×C₄×C₄₃	—	2	6	no	—
42	C₂²×C₄×C₄₃	—	2	3	no	—
43	C₂²×C₄×C₄₃	—	2	3	no	—
44	C₂²×C₄×C₄₃	—	2	3	no	—
45	C₂²×C₄×C₄₃	—	2	6	no	—
46	C₂²×C₄×C₄₃	—	2	6	no	—
47	C₂²×C₄×C₄₃	—	2	6	no	—
48	C₂²×C₄×C₄₃	—	2	6	no	—
49	C₂²×C₄×C₄₃	—	2	3	no	—
50	C₂²×C₄×C₄₃	—	2	6	no	—
51	C₂²×C₄×C₄₃	—	2	6	no	—
52	C₂²×C₄×C₄₃	—	2	3	no	—
53	C₂²×C₄×C₄₃	—	2	6	no	—
54	C₂²×C₄×C₄₃	—	2	3	no	—
55	C₂²×C₄×C₄₃	—	2	2	no	—
56	C₂²×C₄×C₄₃	C₂×D₄	1	12	yes	—
57	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
58	C₂²×C₄×C₄₃	C₂×Q₈	1	6	yes	—
59	C₂²×C₄×C₄₃	#41	1	2	yes	—
60	C₄⋊C₄×C₄₃	—	4	12	no	—
61	C₄⋊C₄×C₄₃	—	4	12	no	—
62	C₄⋊C₄×C₄₃	—	4	24	no	—
63	C₄⋊C₄×C₄₃	—	4	4	no	—
64	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
65	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
66	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
67	C₂³×C₄₃	H(5,𝔽₂)	1	3	yes	—
68	C₂³×C₄₃	2₋¹⁺⁴	1	3	yes	—
69	C₂³×C₄₃	2₋¹⁺⁴	1	3	yes	—
70	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
71	C₂×C₄×C₄₃	—	2	12	no	—
72	C₂×C₄×C₄₃	—	2	6	no	—
73	C₂×C₄×C₄₃	—	2	6	no	—
74	C₂×C₄×C₄₃	—	2	6	no	—
75	C₂×C₄×C₄₃	—	2	12	no	—
76	C₂×C₄×C₄₃	—	2	12	no	—
77	C₂×C₄×C₄₃	—	2	12	no	—
78	C₂×C₄×C₄₃	—	2	12	no	—
79	C₂×C₄×C₄₃	—	4	6	no	—
80	C₂×C₄×C₄₃	—	4	6	no	—
81	C₂×C₄×C₄₃	—	4	6	no	—
82	C₂×C₄×C₄₃	—	4	6	no	—
83	C₂×C₄×C₄₃	—	4	3	no	—
84	C₂×C₄×C₄₃	—	4	3	no	—
85	C₂×C₄×C₄₃	—	4	6	no	—
86	C₂×C₄×C₄₃	—	4	1	no	—
87	C₂×C₄×C₄₃	—	4	3	no	—
88	C₂×C₄×C₄₃	—	4	3	no	—
89	C₂×C₄×C₄₃	—	4	3	no	—
90	C₂×C₄×C₄₃	—	4	6	no	—
91	C₂×C₄×C₄₃	—	4	6	no	—
92	C₂×C₄×C₄₃	—	4	6	no	—
93	C₂×C₄×C₄₃	—	4	2	no	—
94	#17114	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂²×C₄₃	#536	1	6	yes	—
96	C₂²×C₄₃	#537	1	3	yes	—
97	C₂²×C₄₃	#539	1	3	yes	—
98	C₂²×C₄₃	#544	1	3	yes	—
99	C₂²×C₄₃	D₄²	1	3	yes	—
100	C₂²×C₄₃	#547	1	3	yes	—
101	C₂²×C₄₃	D₄×Q₈	1	3	yes	—
102	C₂²×C₄₃	#557	1	1	yes	characteristic
103	C₂²×C₄₃	#560	1	1	yes	characteristic
104	C₂²×C₄₃	#563	1	3	yes	—
105	C₂²×C₄₃	#563	1	3	yes	—
106	C₂²×C₄₃	#564	1	3	yes	—
107	C₄×C₄₃	—	4	2	no	—
108	C₄×C₄₃	—	4	6	no	—
109	C₄×C₄₃	—	4	6	no	—
110	C₄×C₄₃	—	4	12	no	—
111	C₄×C₄₃	—	8	2	no	—
112	C₂×#398	C₂×C₄₃	1	6	yes	—
113	#1444	C₂×C₄₃	1	1	yes	characteristic
114	#1444	C₂×C₄₃	1	3	yes	—
115	#1443	C₂×C₄₃	1	2	yes	—
116	#1442	C₂×C₄₃	1	3	yes	—
117	C₂×C₄₃	#2675	1	1	yes	characteristic
118	C₂×C₄₃	#2677	1	3	yes	—
119	C₂×C₄₃	#2680	1	3	yes	—
120	C₂×C₄₃	#2726	1	3	yes	—
121	C₂×C₄₃	#2822	1	3	yes	—
122	C₂×C₄₃	#2834	1	1	yes	characteristic
123	C₂×C₄₃	#2843	1	1	yes	characteristic
124	C₂²×C₄⋊C₄	C₂²×C₄₃	1	3	yes	—
125	C₂²×C₄⋊C₄	C₂²×C₄₃	1	6	yes	—
126	C₂²×C₄⋊C₄	C₂²×C₄₃	1	3	yes	—
127	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
128	#398	—	2	24	no	—
129	C₂×#95	C₂²×C₄₃	1	6	yes	—
130	C₂×#95	C₂²×C₄₃	1	6	yes	—
131	C₂×#95	C₂²×C₄₃	1	3	yes	—
132	C₂×#95	C₂²×C₄₃	1	3	yes	—
133	C₂×#95	C₂²×C₄₃	1	3	yes	—
134	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
135	C₄₃	#17114	1	1	yes	characteristic, direct product factor, Sylow
136	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
137	C₂³×C₄	C₂³×C₄₃	1	3	yes	—
138	C₂³×C₄	C₂³×C₄₃	1	6	yes	—
139	C₂³×C₄	C₂³×C₄₃	1	3	yes	—
140	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
141	C₂×C₄⋊C₄	—	2	12	no	—
142	C₂×C₄⋊C₄	—	2	12	no	—
143	C₂×C₄⋊C₄	—	2	12	no	—
144	C₂×C₄⋊C₄	—	2	12	no	—
145	C₂×C₄⋊C₄	—	4	3	no	—
146	C₂×C₄⋊C₄	—	4	3	no	—
147	C₂×C₄⋊C₄	—	4	6	no	—
148	C₂×C₄⋊C₄	—	4	3	no	—
149	#95	—	2	12	no	—
150	#95	—	2	12	no	—
151	#95	—	2	6	no	—
152	#95	—	4	3	no	—
153	#95	D₄×C₄₃	1	12	yes	—
154	#95	Q₈×C₄₃	1	4	yes	—
155	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
156	C₂²×C₄	—	2	6	no	—
157	C₂²×C₄	—	2	6	no	—
158	C₂²×C₄	—	2	6	no	—
159	C₂²×C₄	—	2	6	no	—
160	C₂²×C₄	—	2	3	no	—
161	C₂²×C₄	—	2	3	no	—
162	C₂²×C₄	—	2	3	no	—
163	C₂²×C₄	—	2	6	no	—
164	C₂²×C₄	—	2	6	no	—
165	C₂²×C₄	—	2	6	no	—
166	C₂²×C₄	—	2	6	no	—
167	C₂²×C₄	—	2	3	no	—
168	C₂²×C₄	—	2	3	no	—
169	C₂²×C₄	—	2	3	no	—
170	C₂²×C₄	—	2	6	no	—
171	C₂²×C₄	—	2	6	no	—
172	C₂²×C₄	—	2	6	no	—
173	C₂²×C₄	—	2	6	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂×D₄×C₄₃	1	12	yes	—
176	C₂²×C₄	C₂×D₄×C₄₃	1	6	yes	—
177	C₂²×C₄	C₂×Q₈×C₄₃	1	6	yes	—
178	C₂²×C₄	#41×C₄₃	1	2	yes	—
179	C₄⋊C₄	—	4	12	no	—
180	C₄⋊C₄	—	4	12	no	—
181	C₄⋊C₄	—	4	24	no	—
182	C₄⋊C₄	—	4	4	no	—
183	C₂³	C₂²×D₄×C₄₃	1	3	yes	—
184	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
185	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
186	C₂³	H(5,𝔽₂)×C₄₃	1	3	yes	—
187	C₂³	2₋¹⁺⁴×C₄₃	1	3	yes	—
188	C₂³	2₋¹⁺⁴×C₄₃	1	3	yes	—
189	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
190	C₂×C₄	—	2	12	no	—
191	C₂×C₄	—	2	6	no	—
192	C₂×C₄	—	2	6	no	—
193	C₂×C₄	—	2	6	no	—
194	C₂×C₄	—	2	12	no	—
195	C₂×C₄	—	2	12	no	—
196	C₂×C₄	—	2	12	no	—
197	C₂×C₄	—	2	12	no	—
198	C₂×C₄	—	4	6	no	—
199	C₂×C₄	—	4	6	no	—
200	C₂×C₄	—	4	6	no	—
201	C₂×C₄	—	4	6	no	—
202	C₂×C₄	—	4	3	no	—
203	C₂×C₄	—	4	3	no	—
204	C₂×C₄	—	4	6	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	3	no	—
207	C₂×C₄	—	4	3	no	—
208	C₂×C₄	—	4	3	no	—
209	C₂×C₄	—	4	6	no	—
210	C₂×C₄	—	4	6	no	—
211	C₂×C₄	—	4	6	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂²	C₄₃×#536	1	6	yes	—
214	C₂²	C₄₃×#537	1	3	yes	—
215	C₂²	C₄₃×#539	1	3	yes	—
216	C₂²	C₄₃×#544	1	3	yes	—
217	C₂²	D₄²×C₄₃	1	3	yes	—
218	C₂²	C₄₃×#547	1	3	yes	—
219	C₂²	D₄×Q₈×C₄₃	1	3	yes	—
220	C₂²	C₄₃×#557	1	1	yes	characteristic
221	C₂²	C₄₃×#560	1	1	yes	characteristic
222	C₂²	C₄₃×#563	1	3	yes	—
223	C₂²	C₄₃×#563	1	3	yes	—
224	C₂²	C₄₃×#564	1	3	yes	—
225	C₄	—	4	2	no	—
226	C₄	—	4	6	no	—
227	C₄	—	4	6	no	—
228	C₄	—	4	12	no	—
229	C₄	—	8	2	no	—
230	C₂	C₄₃×#2675	1	1	yes	characteristic
231	C₂	C₄₃×#2677	1	3	yes	—
232	C₂	C₄₃×#2680	1	3	yes	—
233	C₂	C₄₃×#2726	1	3	yes	—
234	C₂	C₄₃×#2822	1	3	yes	—
235	C₂	C₄₃×#2834	1	1	yes	characteristic
236	C₂	C₄₃×#2843	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
94. #17114	C₄₃	direct (N × H)
135. C₄₃	#17114	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×#398	2
C₄₃×#1444	2
C₄₃×#1443	2
C₄₃×#1442	2
#17114	43

Subgroups — C43×#17114 #24937131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17114 #24937131