Subgroups — C₄₃×#8285 #24928302

Order 11008.

430 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#106×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal
3	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#322	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1279	C₂	1	2	yes	maximal
6	C₂×#106×C₄₃	C₄	1	2	yes	—
7	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	—	2	2	no	—
9	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₄₃×#340	C₄	1	2	yes	—
14	C₄₃×#336	—	2	2	no	—
15	C₄₃×#335	C₄	1	4	yes	complemented
16	C₄₃×#322	C₄	1	4	yes	complemented
17	C₂²×C₈×C₄₃	—	2	2	no	—
18	C₂²×C₈×C₄₃	—	2	1	no	—
19	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	D₄	1	2	yes	—
22	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₄₃	—	2	2	no	—
24	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	#106×C₄₃	C₈	1	8	yes	complemented
26	C₄⋊C₈×C₄₃	—	2	2	no	—
27	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
28	C₄×C₈×C₄₃	—	2	1	no	—
29	C₄×C₈×C₄₃	—	4	4	no	—
30	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₄₃	Q₈	1	2	yes	—
35	#95×C₄₃	—	2	2	no	—
36	C₂²×C₄×C₄₃	—	2	4	no	—
37	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
40	C₂×C₈×C₄₃	—	2	2	no	—
41	C₂×C₈×C₄₃	—	2	2	no	—
42	C₂×C₈×C₄₃	—	2	2	no	—
43	C₂×C₈×C₄₃	—	2	2	no	—
44	C₂×C₈×C₄₃	—	2	4	no	—
45	C₂×C₈×C₄₃	—	4	2	no	—
46	C₂×C₈×C₄₃	—	4	2	no	—
47	C₂×C₈×C₄₃	—	4	2	no	—
48	C₂×C₈×C₄₃	C₄²	1	2	yes	—
49	C₂×C₈×C₄₃	C₄²	1	2	yes	—
50	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
51	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
52	C₄⋊C₄×C₄₃	—	2	4	no	—
53	C₄⋊C₄×C₄₃	C₂×C₈	1	8	yes	—
54	C₄²×C₄₃	—	4	2	no	—
55	C₄²×C₄₃	—	4	2	no	—
56	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₄₃	#41	1	1	yes	characteristic
60	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	8	no	—
63	C₂×C₄×C₄₃	—	4	4	no	—
64	C₂×C₄×C₄₃	—	4	4	no	—
65	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
66	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
71	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
72	C₂×C₄×C₄₃	#131	1	2	yes	—
73	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
74	C₂×C₄×C₄₃	#137	1	2	yes	—
75	C₈×C₄₃	—	2	2	no	—
76	C₈×C₄₃	—	2	4	no	—
77	C₈×C₄₃	—	4	2	no	—
78	C₈×C₄₃	—	4	4	no	—
79	C₈×C₄₃	C₄×C₈	1	4	yes	complemented
80	#8285	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄₃	C₈×D₄	1	2	yes	—
83	C₂²×C₄₃	#440	1	2	yes	—
84	C₂²×C₄₃	#444	1	2	yes	—
85	C₄×C₄₃	—	2	1	no	—
86	C₄×C₄₃	—	2	1	no	—
87	C₄×C₄₃	—	4	8	no	—
88	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
89	C₄×C₄₃	#405	1	1	yes	characteristic
90	C₄×C₄₃	#428	1	2	yes	—
91	C₄×C₄₃	#441	1	1	yes	characteristic
92	C₄×C₄₃	#442	1	1	yes	characteristic
93	C₄×C₄₃	C₈×Q₈	1	2	yes	—
94	C₄×#106	C₂×C₄₃	1	1	yes	characteristic
95	C₈×C₄⋊C₄	C₂×C₄₃	1	2	yes	—
96	C₂×#335	C₂×C₄₃	1	1	yes	characteristic
97	C₂×#322	C₂×C₄₃	1	1	yes	characteristic
98	#1279	C₂×C₄₃	1	2	yes	—
99	C₂×C₄₃	SD₁₆⋊C₈	1	4	yes	—
100	C₂×C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄₃	#1773	1	1	yes	characteristic
102	C₂×C₄₃	#1776	1	1	yes	characteristic
103	C₂×#106	C₄×C₄₃	1	2	yes	—
104	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
105	C₂×C₄×C₈	—	2	2	no	—
106	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
107	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
109	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
110	#340	C₄×C₄₃	1	2	yes	—
111	#336	—	2	2	no	—
112	#335	C₄×C₄₃	1	4	yes	complemented
113	#322	C₄×C₄₃	1	4	yes	complemented
114	C₄₃	#8285	1	1	yes	characteristic, direct product factor, Sylow
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	—	2	1	no	—
117	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
118	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
119	C₂²×C₈	D₄×C₄₃	1	2	yes	—
120	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
121	C₂×C₄²	—	2	2	no	—
122	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
123	#106	C₈×C₄₃	1	8	yes	complemented
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	C₂×C₄×C₄₃	1	4	yes	—
126	C₄×C₈	—	2	1	no	—
127	C₄×C₈	—	4	4	no	—
128	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
129	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
130	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
131	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
132	C₄×C₈	Q₈×C₄₃	1	2	yes	—
133	#95	—	2	2	no	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
136	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
137	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	C₄²×C₄₃	1	2	yes	—
147	C₂×C₈	C₄²×C₄₃	1	2	yes	—
148	C₂×C₈	C₄⋊C₄×C₄₃	1	4	yes	—
149	C₂×C₈	C₂×C₈×C₄₃	1	4	yes	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	C₂×C₈×C₄₃	1	8	yes	—
152	C₄²	—	4	2	no	—
153	C₄²	—	4	2	no	—
154	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
155	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
156	C₄²	C₂×Q₈×C₄₃	1	1	yes	characteristic
157	C₄²	#41×C₄₃	1	1	yes	characteristic
158	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	C₂×C₄²×C₄₃	1	1	yes	characteristic
164	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
165	C₂×C₄	#117×C₄₃	1	1	yes	characteristic
166	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
167	C₂×C₄	C₄×Q₈×C₄₃	1	1	yes	characteristic
168	C₂×C₄	C₄×Q₈×C₄₃	1	1	yes	characteristic
169	C₂×C₄	C₂²×C₈×C₄₃	1	2	yes	—
170	C₂×C₄	#131×C₄₃	1	2	yes	—
171	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
172	C₂×C₄	#137×C₄₃	1	2	yes	—
173	C₈	—	2	2	no	—
174	C₈	—	2	4	no	—
175	C₈	—	4	2	no	—
176	C₈	—	4	4	no	—
177	C₈	C₄×C₈×C₄₃	1	4	yes	complemented
178	C₂²	C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
179	C₂²	C₈×D₄×C₄₃	1	2	yes	—
180	C₂²	C₄₃×#440	1	2	yes	—
181	C₂²	C₄₃×#444	1	2	yes	—
182	C₄	—	2	1	no	—
183	C₄	—	2	1	no	—
184	C₄	—	4	8	no	—
185	C₄	C₂×C₄×C₈×C₄₃	1	1	yes	characteristic
186	C₄	C₄₃×#405	1	1	yes	characteristic
187	C₄	C₄₃×#428	1	2	yes	—
188	C₄	C₄₃×#441	1	1	yes	characteristic
189	C₄	C₄₃×#442	1	1	yes	characteristic
190	C₄	C₈×Q₈×C₄₃	1	2	yes	—
191	C₂	C₄₃×SD₁₆⋊C₈	1	4	yes	—
192	C₂	C₈×C₄⋊C₄×C₄₃	1	1	yes	characteristic
193	C₂	C₄₃×#1773	1	1	yes	characteristic
194	C₂	C₄₃×#1776	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
15. C₄₃×#335	C₄	semidirect
16. C₄₃×#322	C₄	semidirect
25. #106×C₄₃	C₈	semidirect
79. C₈×C₄₃	C₄×C₈	semidirect
80. #8285	C₄₃	direct (N × H)
112. #335	C₄×C₄₃	semidirect
113. #322	C₄×C₄₃	semidirect
114. C₄₃	#8285	direct (N × H)
123. #106	C₈×C₄₃	semidirect
177. C₈	C₄×C₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×#106×C₄₃	2
C₈×C₄⋊C₄×C₄₃	2
C₂×C₄₃×#335	2
C₂×C₄₃×#322	2
C₄₃×#1279	2
#8285	43

Subgroups — C43×#8285 #24928302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8285 #24928302