Subgroups — C₂×#11926307 #14563349

Order 2432.

512 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₁₉	C₂	1	2	yes	maximal
2	#11926307	C₂	1	4	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	—	2	4	no	—
7	C₂²×C₈×C₁₉	C₄	1	4	yes	complemented
8	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	—	2	4	no	—
11	C₂×C₄⋊Dic₁₉	C₄	1	8	yes	complemented
12	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	4	yes	—
18	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	—	2	8	no	—
21	C₂²×Dic₁₉	—	2	4	no	—
22	C₂²×Dic₁₉	—	4	4	no	—
23	C₂²×Dic₁₉	—	4	4	no	—
24	C₂×C₈×C₁₉	—	2	8	no	—
25	C₂×C₈×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
27	C₄⋊Dic₁₉	—	2	8	no	—
28	C₄⋊Dic₁₉	—	2	4	no	—
29	C₄⋊Dic₁₉	C₂×C₄	1	8	yes	complemented
30	C₂³×C₁₉	C₂²⋊C₄	1	4	yes	—
31	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂³×C₁₉	D₈	1	2	yes	—
33	C₂³×C₁₉	SD₁₆	1	4	yes	—
34	C₂³×C₁₉	Q₁₆	1	2	yes	—
35	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₄²	1	4	yes	—
37	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
38	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
39	C₂×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
40	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×Dic₁₉	—	2	8	no	—
46	C₂×Dic₁₉	—	4	16	no	—
47	C₂×Dic₁₉	—	4	4	no	—
48	C₂×Dic₁₉	—	4	4	no	—
49	C₈×C₁₉	—	2	4	no	—
50	C₂×#340	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	#95	1	4	yes	—
52	C₂²×C₁₉	#102	1	8	yes	—
53	C₂²×C₁₉	#103	1	8	yes	—
54	C₂²×C₁₉	#106	1	4	yes	—
55	C₂²×C₁₉	#107	1	4	yes	—
56	C₂²×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
57	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
60	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
61	C₄×C₁₉	#95	1	4	yes	—
62	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
63	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
65	Dic₁₉	—	4	8	no	—
66	C₂³×C₈	D₁₉	1	1	yes	characteristic
67	C₂²×C₄⋊C₄	—	19	2	no	—
68	#340	—	19	4	no	—
69	C₂×C₁₉	#340	1	8	yes	complemented
70	C₂×C₁₉	C₂×#95	1	1	yes	characteristic
71	C₂×C₁₉	C₂×#102	1	2	yes	—
72	C₂×C₁₉	C₂×#103	1	2	yes	—
73	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
74	C₂×C₁₉	C₂×#107	1	1	yes	characteristic
75	C₂³×C₄	—	38	2	no	—
76	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
77	C₂²×C₈	—	2	4	no	—
78	C₂²×C₈	Dic₁₉	1	4	yes	complemented
79	C₂²×C₈	C₂×D₁₉	1	2	yes	—
80	C₂×C₄⋊C₄	—	19	8	no	—
81	C₂×C₄⋊C₄	—	19	4	no	—
82	C₂×C₄⋊C₄	—	38	2	no	—
83	C₂×C₄⋊C₄	—	38	4	no	—
84	C₁₉	C₂×#340	1	1	yes	characteristic, complemented, Sylow
85	C₂⁴	D₇₆	1	1	yes	characteristic
86	C₂²×C₄	—	38	8	no	—
87	C₂²×C₄	—	38	4	no	—
88	C₂²×C₄	—	76	4	no	—
89	C₂²×C₄	—	76	4	no	—
90	C₂²×C₄	Dic₃₈	1	2	yes	—
91	C₂²×C₄	C₄×D₁₉	1	4	yes	—
92	C₂²×C₄	D₇₆	1	1	yes	characteristic
93	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
94	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	C₂×C₈	—	2	8	no	—
97	C₂×C₈	—	2	4	no	—
98	C₂×C₈	C₂×Dic₁₉	1	4	yes	complemented
99	C₄⋊C₄	—	19	8	no	—
100	C₄⋊C₄	—	38	8	no	—
101	C₄⋊C₄	—	38	4	no	—
102	C₂³	#64516	1	4	yes	—
103	C₂³	D₁₅₂	1	2	yes	—
104	C₂³	Dic₇₆	1	2	yes	—
105	C₂³	C₄⋊Dic₁₉	1	2	yes	—
106	C₂³	(C₂×D₁₉)⋊C₄	1	4	yes	—
107	C₂³	C₂×D₇₆	1	1	yes	characteristic
108	C₂×C₄	—	38	8	no	—
109	C₂×C₄	—	76	16	no	—
110	C₂×C₄	—	76	4	no	—
111	C₂×C₄	—	76	4	no	—
112	C₂×C₄	C₄×Dic₁₉	1	4	yes	—
113	C₂×C₄	Dic₁₉⋊C₄	1	8	yes	—
114	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
115	C₂×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
116	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
117	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
119	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
121	C₈	—	2	4	no	—
122	C₂²	#10597273	1	8	yes	—
123	C₂²	#10597274	1	4	yes	—
124	C₂²	#10597275	1	4	yes	—
125	C₂²	#10597278	1	8	yes	—
126	C₂²	C₁₉⋊#95	1	4	yes	—
127	C₂²	C₂×#64516	1	2	yes	—
128	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
129	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
130	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
131	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
132	C₄	—	76	8	no	—
133	C₄	C₁₉⋊#95	1	4	yes	—
134	C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
135	C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
136	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
137	C₂	#11926307	1	8	yes	direct product factor
138	C₂	C₂×C₁₉⋊#95	1	1	yes	characteristic
139	C₂	C₂×#10597278	1	2	yes	—
140	C₂	C₂×#10597273	1	2	yes	—
141	C₂	C₂×#10597274	1	1	yes	characteristic
142	C₂	C₂×#10597275	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₇₆
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂×#340
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. #11926307	C₂	direct (N × H)
7. C₂²×C₈×C₁₉	C₄	semidirect
11. C₂×C₄⋊Dic₁₉	C₄	semidirect
26. C₂×C₈×C₁₉	C₂×C₄	semidirect
29. C₄⋊Dic₁₉	C₂×C₄	semidirect
69. C₂×C₁₉	#340	semidirect
78. C₂²×C₈	Dic₁₉	semidirect
84. C₁₉	C₂×#340	semidirect
98. C₂×C₈	C₂×Dic₁₉	semidirect
137. C₂	#11926307	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
#11926307	2
C₂³×C₈×C₁₉	2
C₂×#340	19

Subgroups — C2×#11926307 #14563349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926307 #14563349