Subgroups — C₂×#11927311 #14578345

Order 2432.

1460 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	#11927311	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10597394	C₂	1	8	yes	maximal, complemented
3	C₂²×#64520	C₂	1	6	yes	maximal, complemented
4	C₂²×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	C₄	1	4	yes	—
6	C₂×#41×C₁₉	C₄	1	8	yes	—
7	C₂×#41×C₁₉	C₂²	1	4	yes	—
8	C₂×#41×C₁₉	C₂²	1	8	yes	—
9	C₂²×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×D₄×C₁₉	C₄	1	3	yes	—
11	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
12	#10597394	C₂²	1	64	yes	complemented
13	C₂×#64520	C₂²	1	4	yes	—
14	C₂×#64520	C₂²	1	12	yes	complemented
15	C₂×#64520	C₂²	1	48	yes	complemented
16	C₂²×C₁₉⋊C₈	C₂²	1	12	yes	complemented
17	C₂⁴×C₁₉	C₂×C₄	1	3	yes	—
18	#41×C₁₉	C₂×C₄	1	16	yes	—
19	#41×C₁₉	C₂×C₄	1	32	yes	—
20	#41×C₁₉	C₂³	1	16	yes	—
21	C₂×Q₈×C₁₉	C₂×C₄	1	4	yes	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	8	yes	—
23	C₂×D₄×C₁₉	C₂×C₄	1	12	yes	—
24	C₂×D₄×C₁₉	C₂×C₄	1	24	yes	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	3	yes	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	6	yes	—
27	C₂²×C₄×C₁₉	C₂×C₄	1	12	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	12	yes	—
31	#64520	C₂³	1	16	yes	—
32	#64520	C₂³	1	48	yes	complemented
33	C₂×C₁₉⋊C₈	C₂³	1	8	yes	—
34	C₂×C₁₉⋊C₈	C₂³	1	48	yes	complemented
35	C₂³×C₁₉	—	4	6	no	—
36	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂³×C₁₉	C₂²×C₄	1	6	yes	—
38	C₂³×C₁₉	C₂²×C₄	1	12	yes	—
39	Q₈×C₁₉	C₂²×C₄	1	16	yes	—
40	D₄×C₁₉	C₂²×C₄	1	48	yes	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
45	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	—
46	C₂×C₄×C₁₉	C₂²×C₄	1	24	yes	—
47	C₂×C₄×C₁₉	C₂⁴	1	12	yes	—
48	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
49	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₁₉⋊C₈	C₂⁴	1	16	yes	—
51	C₂×#568	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	—	2	2	no	—
53	C₂²×C₁₉	—	2	12	no	—
54	C₂²×C₁₉	—	4	12	no	—
55	C₂²×C₁₉	C₂³×C₄	1	2	yes	—
56	C₂²×C₁₉	C₂³×C₄	1	12	yes	—
57	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
58	C₄×C₁₉	C₂³×C₄	1	2	yes	—
59	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
60	C₄×C₁₉	C₂³×C₄	1	12	yes	—
61	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
62	C₂²×#41	D₁₉	1	1	yes	characteristic
63	#568	—	19	16	no	—
64	C₂×#131	—	19	8	no	—
65	C₂²×M₁₆	—	19	6	no	—
66	C₂×C₁₉	—	2	2	no	—
67	C₂×C₁₉	—	2	12	no	—
68	C₂×C₁₉	#568	1	2	yes	complemented
69	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
70	C₂×#41	Dic₁₉	1	4	yes	—
71	C₂×#41	Dic₁₉	1	8	yes	—
72	C₂×#41	C₂×D₁₉	1	4	yes	—
73	C₂×#41	C₂×D₁₉	1	8	yes	—
74	C₂²×Q₈	Dic₁₉	1	1	yes	characteristic
75	C₂²×D₄	Dic₁₉	1	3	yes	—
76	C₂³×C₄	C₂×D₁₉	1	3	yes	—
77	#131	—	19	64	no	—
78	C₂×M₁₆	—	19	4	no	—
79	C₂×M₁₆	—	19	12	no	—
80	C₂×M₁₆	—	19	48	no	—
81	C₂²×C₈	—	19	12	no	—
82	C₁₉	C₂×#568	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	C₂×Dic₁₉	1	3	yes	—
84	#41	C₂×Dic₁₉	1	16	yes	—
85	#41	C₂×Dic₁₉	1	32	yes	—
86	#41	C₂²×D₁₉	1	16	yes	—
87	C₂×Q₈	C₂×Dic₁₉	1	4	yes	—
88	C₂×Q₈	C₂×Dic₁₉	1	8	yes	—
89	C₂×D₄	C₂×Dic₁₉	1	12	yes	—
90	C₂×D₄	C₂×Dic₁₉	1	24	yes	—
91	C₂²×C₄	C₂×Dic₁₉	1	3	yes	—
92	C₂²×C₄	C₂×Dic₁₉	1	6	yes	—
93	C₂²×C₄	C₂×Dic₁₉	1	12	yes	—
94	C₂²×C₄	C₂²×D₁₉	1	12	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
96	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
97	M₁₆	—	19	16	no	—
98	M₁₆	—	19	48	no	—
99	C₂×C₈	—	19	48	no	—
100	C₂×C₈	—	19	8	no	—
101	C₂³	—	4	6	no	—
102	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
103	C₂³	C₂²×Dic₁₉	1	6	yes	—
104	C₂³	C₂²×Dic₁₉	1	12	yes	—
105	Q₈	C₂²×Dic₁₉	1	16	yes	—
106	D₄	C₂²×Dic₁₉	1	48	yes	—
107	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
108	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
109	C₂×C₄	C₂²×Dic₁₉	1	12	yes	—
110	C₂×C₄	C₂²×Dic₁₉	1	6	yes	—
111	C₂×C₄	C₂²×Dic₁₉	1	24	yes	—
112	C₂×C₄	C₂²×Dic₁₉	1	12	yes	—
113	C₂×C₄	C₂³×D₁₉	1	12	yes	—
114	C₂×C₄	C₂³×D₁₉	1	2	yes	—
115	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
116	C₈	—	19	16	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	2	12	no	—
119	C₂²	—	4	12	no	—
120	C₂²	C₂³×Dic₁₉	1	2	yes	—
121	C₂²	C₂³×Dic₁₉	1	12	yes	—
122	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
123	C₄	C₂³×Dic₁₉	1	2	yes	—
124	C₄	C₂³×Dic₁₉	1	1	yes	characteristic
125	C₄	C₂³×Dic₁₉	1	12	yes	—
126	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	12	no	—
129	C₂	#11927311	1	2	yes	direct product factor
130	C₂	C₂⁴×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₉
Fitting, prime radical	C₂²×#41×C₁₉	C₂
socle	C₂²×C₁₉	C₂³×C₄
cosocle	C₄×C₁₉	C₂⁵
hypercenter	C₂²×#41	D₁₉
hypocenter	C₁₉	C₂×#568
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. #11927311	C₂	direct (N × H)
2. C₂×#10597394	C₂	semidirect
3. C₂²×#64520	C₂	semidirect
12. #10597394	C₂²	semidirect
14. C₂×#64520	C₂²	semidirect
15. C₂×#64520	C₂²	semidirect
16. C₂²×C₁₉⋊C₈	C₂²	semidirect
32. #64520	C₂³	semidirect
34. C₂×C₁₉⋊C₈	C₂³	semidirect
68. C₂×C₁₉	#568	semidirect
82. C₁₉	C₂×#568	semidirect
129. C₂	#11927311	direct (N × H)

Maximal subgroups

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

subgroup	index
#11927311	2
C₂×#10597394	2
C₂²×#64520	2
C₂²×#41×C₁₉	2
C₂×#568	19

Subgroups — C2×#11927311 #14578345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927311 #14578345