Subgroups — C₂²×#14582675 #25249223

Order 11008.

942 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₂×#14582675	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₁₆	C₄	1	16	yes	complemented
5	C₂²×C₄₃⋊C₁₆	C₂²	1	12	yes	—
6	#14582675	C₂²	1	16	yes	direct product factor
7	C₂³×C₈×C₄₃	C₄	1	1	yes	characteristic
8	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₃	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₄₃	C₄	1	6	yes	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	6	yes	—
12	C₂×C₄₃⋊C₁₆	C₂×C₄	1	48	yes	complemented
13	C₂×C₄₃⋊C₁₆	C₂³	1	8	yes	—
14	C₂³×C₄×C₄₃	C₈	1	2	yes	—
15	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₄₃	C₈	1	8	yes	—
17	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	—
18	C₂²×C₈×C₄₃	C₂×C₄	1	3	yes	—
19	C₂²×C₈×C₄₃	C₂×C₄	1	6	yes	—
20	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
21	C₂×C₄²×C₄₃	C₈	1	6	yes	—
22	C₂×C₄²×C₄₃	C₂×C₄	1	6	yes	—
23	C₄×C₈×C₄₃	C₂×C₄	1	12	yes	—
24	C₄×C₈×C₄₃	C₂³	1	4	yes	—
25	C₂⁴×C₄₃	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	—	2	8	no	—
27	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
28	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	—
29	C₂²×C₄×C₄₃	C₂×C₈	1	12	yes	—
30	C₂²×C₄×C₄₃	C₂×C₈	1	3	yes	—
31	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
32	C₂×C₈×C₄₃	C₄²	1	12	yes	—
33	C₂×C₈×C₄₃	C₂×C₈	1	24	yes	—
34	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	—
35	C₂×C₈×C₄₃	C₂²×C₄	1	3	yes	—
36	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
37	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₄²×C₄₃	C₂×C₈	1	12	yes	—
39	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
40	C₄₃⋊C₁₆	C₂²×C₄	1	16	yes	complemented
41	C₂³×C₄₃	C₄×C₈	1	4	yes	—
42	C₂³×C₄₃	M₃₂	1	8	yes	—
43	C₂³×C₄₃	C₂²×C₈	1	3	yes	—
44	C₂×C₄×C₄₃	—	2	24	no	—
45	C₂×C₄×C₄₃	C₄×C₈	1	12	yes	—
46	C₂×C₄×C₄₃	C₂×C₄²	1	6	yes	—
47	C₂×C₄×C₄₃	C₂²×C₈	1	8	yes	—
48	C₂×C₄×C₄₃	C₂²×C₈	1	6	yes	—
49	C₂×C₄×C₄₃	C₂²×C₈	1	3	yes	—
50	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
51	C₈×C₄₃	C₂×C₄²	1	6	yes	—
52	C₈×C₄₃	C₂²×C₈	1	8	yes	—
53	C₈×C₄₃	C₂³×C₄	1	2	yes	—
54	C₂²×#346	—	43	1	no	maximal, Sylow
55	C₂²×C₄₃	#346	1	16	yes	complemented
56	C₂²×C₄₃	C₂×C₄×C₈	1	6	yes	—
57	C₂²×C₄₃	C₂×M₃₂	1	12	yes	—
58	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
59	C₄×C₄₃	—	2	8	no	—
60	C₄×C₄₃	C₂×C₄×C₈	1	6	yes	—
61	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
62	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
63	C₂³×C₁₆	—	43	2	no	—
64	C₂²×C₄×C₈	D₄₃	1	1	yes	characteristic
65	C₂×#346	—	43	12	no	—
66	C₂×C₄₃	C₂×#346	1	12	yes	complemented
67	C₂×C₄₃	C₂²×C₄×C₈	1	1	yes	characteristic
68	C₂×C₄₃	C₂²×M₃₂	1	2	yes	—
69	C₂³×C₈	Dic₄₃	1	1	yes	characteristic
70	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
71	C₂²×C₄²	Dic₄₃	1	1	yes	characteristic
72	C₂²×C₁₆	—	43	12	no	—
73	C₂²×C₁₆	—	43	16	no	—
74	C₂×C₄×C₈	Dic₄₃	1	6	yes	—
75	C₂×C₄×C₈	C₂×D₄₃	1	6	yes	—
76	#346	—	43	16	no	—
77	C₄₃	C₂²×#346	1	1	yes	characteristic, complemented, Sylow
78	C₂³×C₄	C₄₃⋊C₈	1	2	yes	—
79	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
80	C₂²×C₈	C₄₃⋊C₈	1	8	yes	—
81	C₂²×C₈	C₄×D₄₃	1	8	yes	—
82	C₂²×C₈	C₂×Dic₄₃	1	6	yes	—
83	C₂²×C₈	C₂×Dic₄₃	1	3	yes	—
84	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
85	C₂×C₄²	C₄₃⋊C₈	1	6	yes	—
86	C₂×C₄²	C₂×Dic₄₃	1	6	yes	—
87	C₂×C₁₆	—	43	48	no	—
88	C₂×C₁₆	—	43	8	no	—
89	C₄×C₈	C₂×Dic₄₃	1	12	yes	—
90	C₄×C₈	C₂²×D₄₃	1	4	yes	—
91	C₂⁴	C₂×C₄₃⋊C₈	1	1	yes	characteristic
92	C₂²×C₄	—	2	8	no	—
93	C₂²×C₄	C₂×C₄₃⋊C₈	1	12	yes	—
94	C₂²×C₄	C₂×C₄₃⋊C₈	1	3	yes	—
95	C₂²×C₄	C₂×C₄₃⋊C₈	1	4	yes	—
96	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
97	C₂²×C₄	C₂²×Dic₄₃	1	3	yes	—
98	C₂×C₈	C₂×C₄₃⋊C₈	1	24	yes	—
99	C₂×C₈	C₄×Dic₄₃	1	12	yes	—
100	C₂×C₈	C₂×C₄×D₄₃	1	12	yes	—
101	C₂×C₈	C₂²×Dic₄₃	1	3	yes	—
102	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
103	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
104	C₄²	C₂×C₄₃⋊C₈	1	12	yes	—
105	C₄²	C₂²×Dic₄₃	1	4	yes	—
106	C₁₆	—	43	16	no	—
107	C₂³	C₄×C₄₃⋊C₈	1	4	yes	—
108	C₂³	#13063265	1	8	yes	—
109	C₂³	C₂²×C₄₃⋊C₈	1	3	yes	—
110	C₂×C₄	—	2	24	no	—
111	C₂×C₄	C₄×C₄₃⋊C₈	1	12	yes	—
112	C₂×C₄	C₂×C₄×Dic₄₃	1	6	yes	—
113	C₂×C₄	C₂²×C₄₃⋊C₈	1	8	yes	—
114	C₂×C₄	C₂²×C₄₃⋊C₈	1	3	yes	—
115	C₂×C₄	C₂²×C₄₃⋊C₈	1	6	yes	—
116	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
117	C₈	C₂×C₄×Dic₄₃	1	6	yes	—
118	C₈	C₂²×C₄₃⋊C₈	1	8	yes	—
119	C₈	C₂²×C₄×D₄₃	1	2	yes	—
120	C₂²	#14582675	1	16	yes	direct product factor
121	C₂²	C₂×C₄×C₄₃⋊C₈	1	6	yes	—
122	C₂²	C₂×#13063265	1	12	yes	—
123	C₂²	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
124	C₄	—	2	8	no	—
125	C₄	C₂×C₄×C₄₃⋊C₈	1	6	yes	—
126	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
127	C₄	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
128	C₂	C₂×#14582675	1	12	yes	direct product factor
129	C₂	C₂²×C₄×C₄₃⋊C₈	1	1	yes	characteristic
130	C₂	C₂²×#13063265	1	2	yes	—

	subgroup	G/H
center	C₂³×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂²×C₄×C₈×C₄₃	C₂
socle, prime radical	C₂⁴×C₄₃	C₂×C₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂²×#346
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₈ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#14582675	C₂	direct (N × H)
4. C₂²×C₄₃⋊C₁₆	C₄	semidirect
6. #14582675	C₂²	direct (N × H)
12. C₂×C₄₃⋊C₁₆	C₂×C₄	semidirect
40. C₄₃⋊C₁₆	C₂²×C₄	semidirect
55. C₂²×C₄₃	#346	semidirect
66. C₂×C₄₃	C₂×#346	semidirect
77. C₄₃	C₂²×#346	semidirect
120. C₂²	#14582675	direct (N × H)
128. C₂	C₂×#14582675	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄₃⋊C₁₆	2
C₂×#14582675	2
C₂²×C₄×C₈×C₄₃	2
C₂²×#346	43

Subgroups — C22×#14582675 #25249223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14582675 #25249223