Subgroups — C₄×#11926266 #18071888

Order 4864.

654 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	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926266	C₂	1	4	yes	maximal
4	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926266	C₄	1	16	yes	direct product factor
10	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₉	—	2	8	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	8	yes	—
22	C₄×C₁₉⋊C₈	—	2	8	no	—
23	C₄×C₁₉⋊C₈	C₈	1	16	yes	complemented
24	C₄×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
25	C₄×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
26	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
27	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	—	2	8	no	—
31	C₂×C₈×C₁₉	C₄²	1	8	yes	—
32	C₄²×C₁₉	C₂×C₈	1	8	yes	—
33	C₄²×C₁₉	M₁₆	1	8	yes	—
34	C₄²×C₁₉	M₁₆	1	8	yes	—
35	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
36	C₂×C₁₉⋊C₈	—	2	8	no	—
37	C₂×C₁₉⋊C₈	C₄²	1	8	yes	—
38	C₂×C₁₉⋊C₈	C₄²	1	8	yes	—
39	C₂×C₁₉⋊C₈	C₂×C₈	1	16	yes	—
40	C₄×#322	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₄×C₈	1	8	yes	—
43	C₂×C₄×C₁₉	#97	1	8	yes	—
44	C₂×C₄×C₁₉	#97	1	8	yes	—
45	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
48	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
49	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
50	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
51	C₈×C₁₉	—	2	8	no	—
52	C₁₉⋊C₈	—	2	8	no	—
53	C₁₉⋊C₈	C₄×C₈	1	16	yes	complemented
54	C₄²×C₈	—	19	1	no	—
55	C₄²×C₈	—	19	1	no	—
56	C₄²×C₈	D₁₉	1	1	yes	characteristic
57	C₂×#322	—	19	4	no	—
58	C₂²×C₁₉	C₄³	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×C₄×C₈	1	2	yes	—
60	C₂²×C₁₉	C₂×#97	1	2	yes	—
61	C₂²×C₁₉	C₂×#97	1	2	yes	—
62	C₄×C₁₉	#322	1	16	yes	complemented
63	C₄×C₁₉	C₂×C₄×C₈	1	4	yes	—
64	C₄×C₁₉	C₄×M₁₆	1	4	yes	—
65	C₄×C₁₉	C₄×M₁₆	1	4	yes	—
66	C₂×C₄×C₈	—	19	4	no	—
67	C₂×C₄×C₈	—	19	2	no	—
68	C₂×C₄×C₈	—	19	2	no	—
69	C₂×C₄×C₈	—	19	4	no	—
70	C₂×C₄×C₈	Dic₁₉	1	4	yes	—
71	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
72	C₄³	C₂×D₁₉	1	1	yes	characteristic
73	#322	—	19	16	no	—
74	C₂×C₁₉	C₂×#322	1	4	yes	—
75	C₂×C₁₉	C₄²×C₈	1	1	yes	characteristic
76	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
77	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
78	C₂²×C₈	—	19	4	no	—
79	C₂²×C₈	—	19	4	no	—
80	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
81	C₂×C₄²	C₄×D₁₉	1	2	yes	—
82	C₂×C₄²	C₄×D₁₉	1	2	yes	—
83	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
84	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
85	C₄×C₈	—	2	8	no	—
86	C₄×C₈	—	19	16	no	—
87	C₄×C₈	—	19	8	no	—
88	C₄×C₈	—	19	8	no	—
89	C₄×C₈	—	38	8	no	—
90	C₄×C₈	C₄×D₁₉	1	8	yes	—
91	C₁₉	C₄×#322	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
93	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
94	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
95	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
96	C₂×C₈	—	2	8	no	—
97	C₂×C₈	—	19	8	no	—
98	C₂×C₈	—	19	16	no	—
99	C₂×C₈	—	19	8	no	—
100	C₂×C₈	—	38	8	no	—
101	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
102	C₄²	C₈×D₁₉	1	8	yes	—
103	C₄²	#64515	1	8	yes	—
104	C₄²	#64520	1	8	yes	—
105	C₄²	C₂×C₄×D₁₉	1	4	yes	—
106	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
107	C₂×C₄	#10597260	1	8	yes	—
108	C₂×C₄	C₈×Dic₁₉	1	8	yes	—
109	C₂×C₄	#10597272	1	8	yes	—
110	C₂×C₄	C₄²×D₁₉	1	2	yes	—
111	C₂×C₄	C₄²×D₁₉	1	2	yes	—
112	C₂×C₄	C₂×C₈×D₁₉	1	4	yes	—
113	C₂×C₄	C₂×#64515	1	4	yes	—
114	C₂×C₄	C₂×#64520	1	4	yes	—
115	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
116	C₈	—	2	8	no	—
117	C₈	—	19	16	no	—
118	C₈	—	38	8	no	—
119	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
120	C₂²	C₂×C₈×Dic₁₉	1	2	yes	—
121	C₂²	C₂×#10597272	1	2	yes	—
122	C₂²	C₂×#10597260	1	2	yes	—
123	C₄	#11926266	1	16	yes	direct product factor
124	C₄	C₄×C₈×D₁₉	1	4	yes	—
125	C₄	C₄×#64515	1	4	yes	—
126	C₄	C₄×#64520	1	4	yes	—
127	C₂	C₂×#11926266	1	4	yes	—
128	C₂	C₄×C₈×Dic₁₉	1	1	yes	characteristic
129	C₂	C₄×#10597272	1	1	yes	characteristic
130	C₂	C₄×#10597260	1	1	yes	characteristic

	subgroup	G/H
center	C₄³	C₂×D₁₉
commutator	C₂×C₁₉	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	C₄×#322
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
9. #11926266	C₄	direct (N × H)
23. C₄×C₁₉⋊C₈	C₈	semidirect
53. C₁₉⋊C₈	C₄×C₈	semidirect
62. C₄×C₁₉	#322	semidirect
91. C₁₉	C₄×#322	semidirect
123. C₄	#11926266	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₁₉⋊C₈	2
C₂×#11926266	2
C₄²×C₈×C₁₉	2
C₄×#322	19

Subgroups — C4×#11926266 #18071888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926266 #18071888