Subgroups — C₂×#19136889 #25254706

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136889	C₂	1	8	yes	maximal, direct product factor
2	C₂×#14582733	C₂	1	3	yes	maximal, complemented
3	C₂²×C₄₃⋊C₃₂	C₂	1	3	yes	maximal, complemented
4	C₂×C₄₃×#504	C₂	1	1	yes	maximal, characteristic
5	#14582733	C₂²	1	12	yes	complemented
6	C₂×C₄₃⋊C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₄₃⋊C₃₂	C₂²	1	3	yes	—
8	C₂×C₄₃⋊C₃₂	C₂²	1	12	yes	complemented
9	C₂×#131×C₄₃	C₄	1	1	yes	characteristic
10	C₄₃×#504	C₄	1	4	yes	—
11	C₄₃×#504	C₂²	1	4	yes	—
12	C₂×M₃₂×C₄₃	C₄	1	3	yes	—
13	C₂²×C₁₆×C₄₃	C₂²	1	3	yes	—
14	C₄₃⋊C₃₂	C₂³	1	2	yes	—
15	C₄₃⋊C₃₂	C₂³	1	6	yes	—
16	C₂×#41×C₄₃	C₈	1	1	yes	characteristic
17	#131×C₄₃	C₈	1	4	yes	—
18	#131×C₄₃	C₂×C₄	1	4	yes	—
19	C₂×M₁₆×C₄₃	C₈	1	3	yes	—
20	C₂²×C₈×C₄₃	C₂×C₄	1	3	yes	—
21	M₃₂×C₄₃	C₂×C₄	1	12	yes	—
22	C₂×C₁₆×C₄₃	C₂×C₄	1	3	yes	—
23	C₂×C₁₆×C₄₃	C₂×C₄	1	6	yes	—
24	C₂×C₁₆×C₄₃	C₂³	1	6	yes	—
25	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
26	#41×C₄₃	C₁₆	1	4	yes	—
27	#41×C₄₃	C₂×C₈	1	4	yes	—
28	C₂×Q₈×C₄₃	C₁₆	1	1	yes	characteristic
29	C₂×D₄×C₄₃	C₁₆	1	3	yes	—
30	C₂²×C₄×C₄₃	C₂×C₈	1	3	yes	—
31	M₁₆×C₄₃	C₂×C₈	1	12	yes	—
32	C₂×C₈×C₄₃	C₂×C₈	1	3	yes	—
33	C₂×C₈×C₄₃	C₂×C₈	1	6	yes	—
34	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₂²×C₄	1	6	yes	—
36	C₁₆×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₁₆×C₄₃	C₂²×C₄	1	6	yes	—
38	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
39	C₂³×C₄₃	C₂×C₁₆	1	3	yes	—
40	Q₈×C₄₃	C₂×C₁₆	1	4	yes	—
41	D₄×C₄₃	C₂×C₁₆	1	12	yes	—
42	C₂×C₄×C₄₃	C₂×C₁₆	1	3	yes	—
43	C₂×C₄×C₄₃	C₂×C₁₆	1	6	yes	—
44	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂²×C₈	1	6	yes	—
46	C₈×C₄₃	C₂²×C₈	1	1	yes	characteristic
47	C₈×C₄₃	C₂²×C₈	1	6	yes	—
48	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
49	C₂×#2258	—	43	1	no	maximal, Sylow
50	C₂²×C₄₃	—	2	6	no	—
51	C₂²×C₄₃	C₂²×C₁₆	1	6	yes	—
52	C₂²×C₄₃	C₂²×C₁₆	1	1	yes	characteristic
53	C₄×C₄₃	C₂²×C₁₆	1	1	yes	characteristic
54	C₄×C₄₃	C₂²×C₁₆	1	6	yes	—
55	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
56	C₂×#504	D₄₃	1	1	yes	characteristic
57	#2258	—	43	8	no	—
58	C₂×M₆₄	—	43	3	no	—
59	C₂²×C₃₂	—	43	3	no	—
60	C₂×C₄₃	—	2	6	no	—
61	C₂×C₄₃	#2258	1	2	yes	complemented
62	C₂×C₄₃	C₂³×C₁₆	1	1	yes	characteristic
63	C₂×#131	Dic₄₃	1	1	yes	characteristic
64	#504	Dic₄₃	1	4	yes	—
65	#504	C₂×D₄₃	1	4	yes	—
66	C₂×M₃₂	Dic₄₃	1	3	yes	—
67	C₂²×C₁₆	C₂×D₄₃	1	3	yes	—
68	M₆₄	—	43	12	no	—
69	C₂×C₃₂	—	43	12	no	—
70	C₂×C₃₂	—	43	1	no	—
71	C₂×C₃₂	—	43	3	no	—
72	C₄₃	C₂×#2258	1	1	yes	characteristic, complemented, Sylow
73	C₂×#41	C₄₃⋊C₈	1	1	yes	characteristic
74	#131	C₄₃⋊C₈	1	4	yes	—
75	#131	C₂×Dic₄₃	1	4	yes	—
76	C₂×M₁₆	C₄₃⋊C₈	1	3	yes	—
77	C₂²×C₈	C₂×Dic₄₃	1	3	yes	—
78	M₃₂	C₂×Dic₄₃	1	12	yes	—
79	C₂×C₁₆	C₂×Dic₄₃	1	3	yes	—
80	C₂×C₁₆	C₂×Dic₄₃	1	6	yes	—
81	C₂×C₁₆	C₂²×D₄₃	1	6	yes	—
82	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
83	C₃₂	—	43	2	no	—
84	C₃₂	—	43	6	no	—
85	#41	C₄₃⋊C₁₆	1	4	yes	—
86	#41	C₂×C₄₃⋊C₈	1	4	yes	—
87	C₂×Q₈	C₄₃⋊C₁₆	1	1	yes	characteristic
88	C₂×D₄	C₄₃⋊C₁₆	1	3	yes	—
89	C₂²×C₄	C₂×C₄₃⋊C₈	1	3	yes	—
90	M₁₆	C₂×C₄₃⋊C₈	1	12	yes	—
91	C₂×C₈	C₂×C₄₃⋊C₈	1	3	yes	—
92	C₂×C₈	C₂×C₄₃⋊C₈	1	6	yes	—
93	C₂×C₈	C₂²×Dic₄₃	1	6	yes	—
94	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
95	C₁₆	C₂²×Dic₄₃	1	6	yes	—
96	C₁₆	C₂²×Dic₄₃	1	1	yes	characteristic
97	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
98	C₂³	C₂×C₄₃⋊C₁₆	1	3	yes	—
99	Q₈	C₂×C₄₃⋊C₁₆	1	4	yes	—
100	D₄	C₂×C₄₃⋊C₁₆	1	12	yes	—
101	C₂×C₄	C₂×C₄₃⋊C₁₆	1	3	yes	—
102	C₂×C₄	C₂×C₄₃⋊C₁₆	1	6	yes	—
103	C₂×C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
104	C₂×C₄	C₂²×C₄₃⋊C₈	1	6	yes	—
105	C₈	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
106	C₈	C₂²×C₄₃⋊C₈	1	6	yes	—
107	C₈	C₂³×Dic₄₃	1	1	yes	characteristic
108	C₂²	—	2	6	no	—
109	C₂²	C₂²×C₄₃⋊C₁₆	1	6	yes	—
110	C₂²	C₂²×C₄₃⋊C₁₆	1	1	yes	characteristic
111	C₄	C₂²×C₄₃⋊C₁₆	1	1	yes	characteristic
112	C₄	C₂²×C₄₃⋊C₁₆	1	6	yes	—
113	C₄	C₂³×C₄₃⋊C₈	1	1	yes	characteristic
114	C₂	—	2	6	no	—
115	C₂	#19136889	1	2	yes	direct product factor
116	C₂	C₂³×C₄₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₁₆
Frattini	C₁₆	C₂³×D₄₃
Fitting	C₂×C₄₃×#504	C₂
socle	C₂²×C₄₃	C₂²×C₁₆
prime radical	C₂×#41×C₄₃	C₈
cosocle	C₁₆×C₄₃	C₂⁴
hypercenter	C₂×#504	D₄₃
hypocenter	C₄₃	C₂×#2258
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. #19136889	C₂	direct (N × H)
2. C₂×#14582733	C₂	semidirect
3. C₂²×C₄₃⋊C₃₂	C₂	semidirect
5. #14582733	C₂²	semidirect
8. C₂×C₄₃⋊C₃₂	C₂²	semidirect
61. C₂×C₄₃	#2258	semidirect
72. C₄₃	C₂×#2258	semidirect
115. C₂	#19136889	direct (N × H)

Maximal subgroups

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

subgroup	index
#19136889	2
C₂×#14582733	2
C₂²×C₄₃⋊C₃₂	2
C₂×C₄₃×#504	2
C₂×#2258	43

Subgroups — C2×#19136889 #25254706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136889 #25254706