Subgroups — D₄₃×#1312 #25005582

Order 11008.

350 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×D₄₃	C₂	1	2	yes	maximal
2	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19132514	C₂	1	2	yes	maximal, complemented
4	#19132513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1312	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₆×D₄₃	C₄	1	4	yes	—
7	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
9	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
11	C₁₆×Dic₄₃	C₄	1	4	yes	—
12	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₁₆×C₄₃	C₂²	1	2	yes	—
16	C₈²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₄₃	C₈	1	2	yes	—
18	C₂×C₈×D₄₃	C₈	1	2	yes	—
19	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
20	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
22	C₁₆×D₄₃	—	2	8	no	—
23	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₄₃	C₈	1	2	yes	—
27	C₈×Dic₄₃	C₈	1	2	yes	—
28	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
29	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
37	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
39	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
41	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
42	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
44	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
45	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
46	C₈×D₄₃	—	2	4	no	—
47	C₈×D₄₃	C₁₆	1	8	yes	complemented
48	C₈×D₄₃	M₁₆	1	8	yes	—
49	C₁₆×C₄₃	—	2	4	no	—
50	C₄₃⋊C₁₆	—	2	4	no	—
51	C₂²×D₄₃	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
54	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
55	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
56	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
57	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
58	C₄×D₄₃	#97	1	4	yes	—
59	C₄×D₄₃	C₂×C₁₆	1	4	yes	—
60	C₄×D₄₃	M₃₂	1	4	yes	—
61	C₈×C₄₃	—	2	2	no	—
62	C₈×C₄₃	C₂×C₁₆	1	4	yes	complemented
63	C₈×C₄₃	C₂×M₁₆	1	4	yes	—
64	C₄₃⋊C₈	—	2	2	no	—
65	C₄₃⋊C₈	#97	1	4	yes	—
66	C₄₃⋊C₈	C₂×C₁₆	1	4	yes	complemented
67	C₂×#1312	—	43	1	no	maximal, Sylow
68	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
69	C₂×D₄₃	#322	1	2	yes	—
70	C₂×D₄₃	C₄×C₁₆	1	2	yes	—
71	C₂×D₄₃	#346	1	2	yes	—
72	C₄×C₄₃	C₂×#97	1	2	yes	—
73	C₄×C₄₃	C₂²×C₁₆	1	2	yes	—
74	C₄×C₄₃	C₂×M₃₂	1	2	yes	—
75	Dic₄₃	#322	1	2	yes	—
76	Dic₄₃	C₄×C₁₆	1	2	yes	—
77	Dic₄₃	#346	1	2	yes	—
78	C₂×C₄×C₁₆	—	43	2	no	—
79	C₂×C₈²	—	43	1	no	—
80	#1312	—	43	2	no	—
81	#1312	—	43	1	no	—
82	#1312	D₄₃	1	1	yes	characteristic, direct product factor
83	C₂×C₄₃	C₂×#322	1	1	yes	characteristic
84	C₂×C₄₃	C₂×C₄×C₁₆	1	1	yes	characteristic
85	C₂×C₄₃	C₂×#346	1	1	yes	characteristic
86	D₄₃	#1312	1	4	yes	direct product factor
87	C₂²×C₁₆	—	43	4	no	—
88	C₂×C₄×C₈	—	43	1	no	—
89	C₂×C₄×C₈	—	43	1	no	—
90	C₂×C₄×C₈	—	43	1	no	—
91	C₄×C₁₆	—	43	4	no	—
92	C₄×C₁₆	—	43	2	no	—
93	C₄×C₁₆	C₂×D₄₃	1	2	yes	—
94	C₈²	—	43	1	no	—
95	C₈²	—	43	1	no	—
96	C₈²	—	43	1	no	—
97	C₈²	C₂×D₄₃	1	1	yes	characteristic
98	C₄₃	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₈	—	43	2	no	—
100	C₂²×C₈	—	43	2	no	—
101	C₂²×C₈	—	43	2	no	—
102	C₂×C₄²	—	43	1	no	—
103	C₂×C₁₆	—	43	4	no	—
104	C₂×C₁₆	—	86	8	no	—
105	C₂×C₁₆	C₄×D₄₃	1	4	yes	—
106	C₄×C₈	—	43	2	no	—
107	C₄×C₈	—	43	2	no	—
108	C₄×C₈	—	43	2	no	—
109	C₄×C₈	—	43	1	no	—
110	C₄×C₈	—	43	1	no	—
111	C₄×C₈	—	43	1	no	—
112	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
113	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
114	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₂²×C₄	—	43	1	no	—
116	C₂²×C₄	—	43	1	no	—
117	C₂²×C₄	—	43	1	no	—
118	C₂×C₈	—	43	2	no	—
119	C₂×C₈	—	43	2	no	—
120	C₂×C₈	—	43	8	no	—
121	C₂×C₈	—	43	8	no	—
122	C₂×C₈	—	43	2	no	—
123	C₂×C₈	—	86	4	no	—
124	C₂×C₈	C₈×D₄₃	1	2	yes	—
125	C₂×C₈	C₈×D₄₃	1	2	yes	—
126	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
127	C₄²	—	43	1	no	—
128	C₄²	—	43	1	no	—
129	C₄²	—	43	1	no	—
130	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
131	C₁₆	—	2	4	no	—
132	C₁₆	—	86	4	no	—
133	C₂³	—	43	1	no	—
134	C₂×C₄	—	43	1	no	—
135	C₂×C₄	—	43	1	no	—
136	C₂×C₄	—	43	1	no	—
137	C₂×C₄	—	43	4	no	—
138	C₂×C₄	—	43	4	no	—
139	C₂×C₄	—	43	4	no	—
140	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
141	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
142	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
143	C₈	—	2	2	no	—
144	C₈	—	43	4	no	—
145	C₈	—	43	4	no	—
146	C₈	—	86	2	no	—
147	C₈	C₁₆×D₄₃	1	4	yes	complemented
148	C₈	M₁₆×D₄₃	1	4	yes	—
149	C₂²	—	43	2	no	—
150	C₂²	—	43	2	no	—
151	C₂²	—	43	2	no	—
152	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
153	C₄	—	43	2	no	—
154	C₄	—	43	2	no	—
155	C₄	—	43	2	no	—
156	C₄	#97×D₄₃	1	2	yes	—
157	C₄	C₂×C₁₆×D₄₃	1	2	yes	—
158	C₄	M₃₂×D₄₃	1	2	yes	—
159	C₂	—	43	4	no	—
160	C₂	#322×D₄₃	1	1	yes	characteristic
161	C₂	C₄×C₁₆×D₄₃	1	1	yes	characteristic
162	C₂	#346×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₁₆
Fitting	C₄₃×#1312	C₂
socle	C₂²×C₄₃	C₂×C₄×C₈
prime radical	C₂²×D₄₃	C₄×C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1312	D₄₃
hypocenter	C₄₃	C₂×#1312
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ #1312

Complements

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

N	H ≅ G/N	type
3. #19132514	C₂	semidirect
4. #19132513	C₂	semidirect
5. C₄₃×#1312	C₂	semidirect
47. C₈×D₄₃	C₁₆	semidirect
62. C₈×C₄₃	C₂×C₁₆	semidirect
66. C₄₃⋊C₈	C₂×C₁₆	semidirect
82. #1312	D₄₃	direct (N × H)
86. D₄₃	#1312	direct (N × H)
98. C₄₃	C₂×#1312	semidirect
147. C₈	C₁₆×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₆×D₄₃	2
C₈²×D₄₃	2
#19132514	2
#19132513	2
C₄₃×#1312	2
C₂×#1312	43

Subgroups — D43×#1312 #25005582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1312 #25005582