Subgroups — #14572064

Order 2432.

556 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597353	C₂	1	2	yes	maximal
2	C₄×#64541	C₂	1	1	yes	maximal, characteristic
3	#11926502	C₂	1	2	yes	maximal, complemented
4	#11926498	C₂	1	4	yes	maximal, complemented
5	#11926496	C₂	1	2	yes	maximal, complemented
6	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
7	#97×D₁₉	C₂	1	2	yes	maximal, complemented
8	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#64541	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×C₂²⋊D₁₉	C₄	1	4	yes	—
13	#10597372	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597353	C₄	1	16	yes	complemented
16	C₂×#64515	C₂²	1	4	yes	—
17	C₂×C₈×D₁₉	C₂²	1	4	yes	—
18	C₄×D₇₆	C₄	1	2	yes	—
19	#10597318	C₂²	1	2	yes	—
20	C₄²×D₁₉	C₂²	1	2	yes	—
21	C₄×Dic₃₈	C₄	1	2	yes	—
22	C₁₉×#97	C₂²	1	2	yes	—
23	C₄×C₈×C₁₉	C₂²	1	2	yes	—
24	#10597272	C₂²	1	4	yes	—
25	C₈×Dic₁₉	C₂²	1	4	yes	—
26	#10597260	C₂²	1	1	yes	characteristic
27	#10597260	C₂²	1	1	yes	characteristic
28	#10597260	C₂²	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
32	#64541	C₂×C₄	1	8	yes	—
33	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₉	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₁₉	C₂³	1	2	yes	—
36	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
37	M₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
38	C₂×C₈×C₁₉	C₂³	1	4	yes	—
39	C₄²×C₁₉	C₂×C₄	1	2	yes	—
40	C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
43	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
44	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
45	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
46	C₄×Dic₁₉	C₂×C₄	1	4	yes	—
47	C₄×Dic₁₉	C₂³	1	2	yes	—
48	C₂×C₁₉⋊C₈	C₂×C₄	1	8	yes	complemented
49	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
50	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
51	#64515	C₂×C₄	1	16	yes	complemented
52	C₈×D₁₉	C₂×C₄	1	16	yes	complemented
53	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
60	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
61	C₂²⋊D₁₉	C₄²	1	8	yes	—
62	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
63	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
64	D₇₆	C₄²	1	4	yes	—
65	C₄×D₁₉	—	4	4	no	—
66	C₄×D₁₉	C₂²×C₄	1	8	yes	—
67	Dic₃₈	C₄²	1	4	yes	—
68	C₈×C₁₉	C₂²×C₄	1	8	yes	—
69	C₁₉⋊C₈	C₂²×C₄	1	4	yes	—
70	C₁₉⋊C₈	C₂²×C₄	1	4	yes	—
71	#2875	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	C₂×C₄²	1	2	yes	—
74	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
75	C₂×D₁₉	—	2	4	no	—
76	C₂×D₁₉	C₂×C₄²	1	4	yes	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	C₂×C₄²	1	2	yes	—
80	C₄×C₁₉	C₂³×C₄	1	2	yes	—
81	Dic₁₉	—	2	4	no	—
82	Dic₁₉	C₂×C₄²	1	4	yes	—
83	C₂×#131	—	19	2	no	—
84	C₄×#41	—	19	1	no	—
85	#405	—	19	2	no	—
86	#405	—	19	4	no	—
87	C₄×M₁₆	—	19	2	no	—
88	C₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
89	C₂×#97	—	19	1	no	—
90	C₂×#97	—	19	2	no	—
91	C₂×C₁₉	—	2	2	no	—
92	C₂×C₁₉	C₂²×C₄²	1	1	yes	characteristic
93	C₂×C₁₉	#568	1	2	yes	—
94	D₁₉	—	2	4	no	—
95	C₂×#41	—	19	1	no	—
96	#131	—	19	16	no	—
97	C₂×M₁₆	—	19	4	no	—
98	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
99	C₂²×C₈	—	19	2	no	—
100	C₂²×C₈	—	19	4	no	—
101	C₄×Q₈	—	19	2	no	—
102	C₄×D₄	—	19	4	no	—
103	C₄×D₄	—	19	2	no	—
104	#117	—	19	1	no	—
105	#117	—	19	2	no	—
106	C₂×C₄²	—	19	2	no	—
107	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
108	#97	—	19	4	no	—
109	#97	—	19	1	no	—
110	#97	—	19	1	no	—
111	#97	—	19	2	no	—
112	#97	C₂×D₁₉	1	2	yes	—
113	C₄×C₈	—	19	4	no	—
114	C₄×C₈	C₂×D₁₉	1	2	yes	—
115	C₁₉	#2875	1	1	yes	characteristic, complemented, Sylow
116	#41	—	19	8	no	—
117	C₂×Q₈	—	19	1	no	—
118	C₂×D₄	—	19	2	no	—
119	C₂×D₄	—	19	1	no	—
120	C₂²×C₄	—	19	2	no	—
121	C₂²×C₄	—	19	4	no	—
122	C₂²×C₄	C₄×D₁₉	1	2	yes	—
123	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
124	M₁₆	—	19	16	no	—
125	M₁₆	C₄×D₁₉	1	8	yes	complemented
126	C₂×C₈	—	19	8	no	—
127	C₂×C₈	—	19	2	no	—
128	C₂×C₈	—	19	2	no	—
129	C₂×C₈	—	19	16	no	—
130	C₂×C₈	C₂²×D₁₉	1	4	yes	—
131	C₄⋊C₄	—	19	4	no	—
132	C₄⋊C₄	—	19	2	no	—
133	C₂²⋊C₄	—	19	2	no	—
134	C₂²⋊C₄	—	19	4	no	—
135	C₄²	—	19	4	no	—
136	C₄²	—	19	2	no	—
137	C₄²	C₄×D₁₉	1	2	yes	—
138	C₄²	C₂²×D₁₉	1	1	yes	characteristic
139	C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₂³	—	19	2	no	—
141	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
142	Q₈	—	19	4	no	—
143	D₄	—	19	8	no	—
144	D₄	—	19	4	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	19	2	no	—
147	C₂×C₄	—	19	8	no	—
148	C₂×C₄	—	19	4	no	—
149	C₂×C₄	—	76	4	no	—
150	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
152	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
154	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
155	C₈	—	19	4	no	—
156	C₈	—	19	4	no	—
157	C₈	C₂×C₄×D₁₉	1	8	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	19	4	no	—
160	C₂²	—	38	4	no	—
161	C₂²	C₄²×D₁₉	1	2	yes	—
162	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	2	2	no	—
165	C₄	—	19	4	no	—
166	C₄	—	38	4	no	—
167	C₄	C₄²×D₁₉	1	2	yes	—
168	C₄	C₂²×C₄×D₁₉	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	38	4	no	—
171	C₂	C₂×C₄²×D₁₉	1	1	yes	characteristic
172	C₂	#11927310	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator	C₂×C₁₉	C₂²×C₄²
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂×#64541	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	#2875
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #11926502	C₂	semidirect
4. #11926498	C₂	semidirect
5. #11926496	C₂	semidirect
6. C₂×#10597260	C₂	semidirect
7. #97×D₁₉	C₂	semidirect
8. C₄×M₁₆×C₁₉	C₂	semidirect
15. #10597353	C₄	semidirect
37. M₁₆×C₁₉	C₂×C₄	semidirect
48. C₂×C₁₉⋊C₈	C₂×C₄	semidirect
51. #64515	C₂×C₄	semidirect
52. C₈×D₁₉	C₂×C₄	semidirect
88. C₄×M₁₆	D₁₉	semidirect
115. C₁₉	#2875	semidirect
125. M₁₆	C₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597353	2
C₄×#64541	2
#11926502	2
#11926498	2
#11926496	2
C₂×#10597260	2
#97×D₁₉	2
C₄×M₁₆×C₁₉	2
#2875	19