Subgroups — C₂²×#10597275 #14572210

Order 2432.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₁₉	C₂	1	2	yes	maximal
2	C₂×#10597275	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂³×Dic₁₉	—	2	2	no	—
6	C₂²×C₈×C₁₉	C₄	1	8	yes	complemented
7	C₂²×C₈×C₁₉	C₂²	1	6	yes	—
8	C₂×C₄⋊Dic₁₉	—	2	6	no	—
9	C₂×C₄⋊Dic₁₉	C₂²	1	12	yes	—
10	#10597275	C₂²	1	16	yes	direct product factor
11	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₁₉	D₄	1	3	yes	—
14	C₂²×C₄×C₁₉	Q₈	1	4	yes	—
15	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
16	C₂²×Dic₁₉	—	2	12	no	—
17	C₂²×Dic₁₉	—	4	8	no	—
18	C₂×C₈×C₁₉	C₂×C₄	1	24	yes	complemented
19	C₂×C₈×C₁₉	C₂³	1	4	yes	—
20	C₄⋊Dic₁₉	—	2	12	no	—
21	C₄⋊Dic₁₉	C₂³	1	8	yes	—
22	C₂³×C₁₉	C₄⋊C₄	1	4	yes	—
23	C₂³×C₁₉	D₈	1	4	yes	—
24	C₂³×C₁₉	Q₁₆	1	4	yes	—
25	C₂³×C₁₉	C₂×D₄	1	3	yes	—
26	C₂×C₄×C₁₉	C₄⋊C₄	1	12	yes	—
27	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
28	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
29	C₂×C₄×C₁₉	C₂×Q₈	1	6	yes	—
30	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
31	C₂×Dic₁₉	—	2	8	no	—
32	C₂×Dic₁₉	—	4	24	no	—
33	C₈×C₁₉	C₂²×C₄	1	8	yes	complemented
34	C₂²×#107	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	#107	1	16	yes	complemented
36	C₂²×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
37	C₂²×C₁₉	C₂×D₈	1	6	yes	—
38	C₂²×C₁₉	C₂×Q₁₆	1	6	yes	—
39	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
41	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
42	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
43	Dic₁₉	—	4	8	no	—
44	C₂³×C₈	D₁₉	1	1	yes	characteristic
45	C₂²×C₄⋊C₄	—	19	2	no	—
46	C₂×#107	—	19	12	no	—
47	C₂×C₁₉	C₂×#107	1	12	yes	complemented
48	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₁₉	C₂²×D₈	1	1	yes	characteristic
50	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
51	C₂³×C₄	—	38	2	no	—
52	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
53	C₂²×C₈	Dic₁₉	1	8	yes	complemented
54	C₂²×C₈	C₂×D₁₉	1	6	yes	—
55	C₂×C₄⋊C₄	—	19	12	no	—
56	C₂×C₄⋊C₄	—	38	6	no	—
57	#107	—	19	16	no	—
58	C₁₉	C₂²×#107	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	D₇₆	1	1	yes	characteristic
60	C₂²×C₄	—	38	12	no	—
61	C₂²×C₄	—	76	8	no	—
62	C₂²×C₄	Dic₃₈	1	4	yes	—
63	C₂²×C₄	D₇₆	1	3	yes	—
64	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
65	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
66	C₂×C₈	C₂×Dic₁₉	1	24	yes	complemented
67	C₂×C₈	C₂²×D₁₉	1	4	yes	—
68	C₄⋊C₄	—	19	8	no	—
69	C₄⋊C₄	—	38	12	no	—
70	C₂³	D₁₅₂	1	4	yes	—
71	C₂³	Dic₇₆	1	4	yes	—
72	C₂³	C₄⋊Dic₁₉	1	4	yes	—
73	C₂³	C₂×D₇₆	1	3	yes	—
74	C₂×C₄	—	38	8	no	—
75	C₂×C₄	—	76	24	no	—
76	C₂×C₄	C₄⋊Dic₁₉	1	12	yes	—
77	C₂×C₄	C₂×Dic₃₈	1	6	yes	—
78	C₂×C₄	C₂×D₇₆	1	3	yes	—
79	C₂×C₄	C₂²×Dic₁₉	1	6	yes	—
80	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
81	C₈	C₂²×Dic₁₉	1	8	yes	complemented
82	C₂²	#10597275	1	16	yes	direct product factor
83	C₂²	C₂×D₁₅₂	1	6	yes	—
84	C₂²	C₂×Dic₇₆	1	6	yes	—
85	C₂²	C₂×C₄⋊Dic₁₉	1	6	yes	—
86	C₂²	C₂²×D₇₆	1	1	yes	characteristic
87	C₄	—	76	8	no	—
88	C₄	C₂×C₄⋊Dic₁₉	1	6	yes	—
89	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
90	C₄	C₂³×Dic₁₉	1	1	yes	characteristic
91	C₂	C₂×#10597275	1	12	yes	direct product factor
92	C₂	C₂²×C₄⋊Dic₁₉	1	1	yes	characteristic
93	C₂	C₂²×D₁₅₂	1	1	yes	characteristic
94	C₂	C₂²×Dic₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₇₆
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂²×#107
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#10597275	C₂	direct (N × H)
6. C₂²×C₈×C₁₉	C₄	semidirect
10. #10597275	C₂²	direct (N × H)
18. C₂×C₈×C₁₉	C₂×C₄	semidirect
33. C₈×C₁₉	C₂²×C₄	semidirect
35. C₂²×C₁₉	#107	semidirect
47. C₂×C₁₉	C₂×#107	semidirect
53. C₂²×C₈	Dic₁₉	semidirect
58. C₁₉	C₂²×#107	semidirect
66. C₂×C₈	C₂×Dic₁₉	semidirect
81. C₈	C₂²×Dic₁₉	semidirect
82. C₂²	#10597275	direct (N × H)
91. C₂	C₂×#10597275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Dic₁₉	2
C₂×#10597275	2
C₂³×C₈×C₁₉	2
C₂²×#107	19

Subgroups — C22×#10597275 #14572210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10597275 #14572210