Subgroups — C₂²×#10597347 #14578339

Order 2432.

1504 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64541	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597347	C₂	1	24	yes	maximal, direct product factor
3	C₂²×#64520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#64515	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×D₁₉	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₂²⋊D₁₉	C₄	1	2	yes	—
9	C₂×#64541	C₄	1	12	yes	—
10	C₂×#64541	C₂²	1	12	yes	—
11	C₂²×D₇₆	C₄	1	1	yes	characteristic
12	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
13	C₂²×Dic₃₈	C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂²	1	12	yes	complemented
17	C₂×#64520	C₂²	1	12	yes	complemented
18	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
19	#10597347	C₂²	1	64	yes	direct product factor
20	C₂×#64515	C₂²	1	24	yes	complemented
21	C₂×C₈×D₁₉	C₂²	1	24	yes	complemented
22	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×D₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₄	1	6	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
28	C₂×C₂²⋊D₁₉	C₂×C₄	1	24	yes	—
29	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
30	#64541	C₂×C₄	1	48	yes	—
31	#64541	C₂³	1	16	yes	—
32	C₂×D₇₆	C₂×C₄	1	12	yes	—
33	C₂×C₄×D₁₉	C₂×C₄	1	12	yes	—
34	C₂×C₄×D₁₉	C₂³	1	12	yes	—
35	C₂×Dic₃₈	C₂×C₄	1	12	yes	—
36	C₂×C₈×C₁₉	C₂³	1	6	yes	—
37	C₂×C₈×C₁₉	C₂³	1	6	yes	—
38	C₂×C₈×C₁₉	C₂³	1	16	yes	complemented
39	#64520	C₂³	1	16	yes	complemented
40	C₂×C₁₉⋊C₈	C₂³	1	12	yes	—
41	#64515	C₂³	1	32	yes	complemented
42	C₈×D₁₉	C₂³	1	32	yes	complemented
43	C₂³×C₁₉	—	2	4	no	—
44	C₂³×C₁₉	C₂²×C₄	1	6	yes	—
45	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₁₉	—	2	8	no	—
47	C₂²×D₁₉	C₂²×C₄	1	12	yes	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	—
51	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
52	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
53	C₂²⋊D₁₉	C₂²×C₄	1	32	yes	—
54	C₂×Dic₁₉	C₂²×C₄	1	12	yes	—
55	D₇₆	C₂²×C₄	1	16	yes	—
56	C₄×D₁₉	C₂²×C₄	1	24	yes	—
57	C₄×D₁₉	C₂⁴	1	8	yes	—
58	Dic₃₈	C₂²×C₄	1	16	yes	—
59	C₈×C₁₉	C₂⁴	1	4	yes	—
60	C₈×C₁₉	C₂⁴	1	4	yes	—
61	C₁₉⋊C₈	C₂⁴	1	8	yes	—
62	C₂²×#131	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	2	12	no	—
64	C₂²×C₁₉	#131	1	4	yes	complemented
65	C₂²×C₁₉	C₂³×C₄	1	4	yes	—
66	C₂²×C₁₉	C₂³×C₄	1	3	yes	—
67	C₂×D₁₉	—	2	24	no	—
68	C₂×D₁₉	C₂³×C₄	1	8	yes	—
69	C₄×C₁₉	C₂³×C₄	1	4	yes	—
70	C₄×C₁₉	C₂³×C₄	1	3	yes	—
71	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
72	Dic₁₉	C₂³×C₄	1	8	yes	—
73	C₂²×#41	—	19	1	no	—
74	C₂×#131	—	19	24	no	—
75	C₂²×M₁₆	—	19	1	no	—
76	C₂²×M₁₆	—	19	2	no	—
77	C₂³×C₈	—	19	2	no	—
78	C₂³×C₈	D₁₉	1	1	yes	characteristic, complemented
79	C₂×C₁₉	—	2	4	no	—
80	C₂×C₁₉	C₂×#131	1	6	yes	complemented
81	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
82	D₁₉	—	2	8	no	—
83	C₂×#41	—	19	12	no	—
84	C₂×#41	—	19	12	no	—
85	C₂²×Q₈	—	19	1	no	—
86	C₂²×D₄	—	19	2	no	—
87	C₂²×D₄	—	19	1	no	—
88	C₂³×C₄	—	19	2	no	—
89	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
90	#131	—	19	64	no	—
91	C₂×M₁₆	—	19	12	no	—
92	C₂×M₁₆	—	19	24	no	—
93	C₂²×C₈	—	19	2	no	—
94	C₂²×C₈	—	19	24	no	—
95	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
96	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
97	C₂²×C₈	C₂×D₁₉	1	12	yes	complemented
98	C₁₉	C₂²×#131	1	1	yes	characteristic, complemented, Sylow
99	C₂⁴	—	19	2	no	—
100	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
101	#41	—	19	48	no	—
102	#41	—	19	16	no	—
103	C₂×Q₈	—	19	12	no	—
104	C₂×D₄	—	19	24	no	—
105	C₂×D₄	—	19	12	no	—
106	C₂²×C₄	—	19	2	no	—
107	C₂²×C₄	—	19	12	no	—
108	C₂²×C₄	—	19	12	no	—
109	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
110	C₂²×C₄	C₄×D₁₉	1	6	yes	—
111	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
113	M₁₆	—	19	16	no	—
114	M₁₆	—	19	32	no	—
115	C₂×C₈	—	19	12	no	—
116	C₂×C₈	—	19	32	no	—
117	C₂×C₈	C₂²×D₁₉	1	6	yes	—
118	C₂×C₈	C₂²×D₁₉	1	6	yes	—
119	C₂×C₈	C₂²×D₁₉	1	16	yes	complemented
120	C₂³	—	2	4	no	—
121	C₂³	—	19	12	no	—
122	C₂³	—	38	8	no	—
123	C₂³	C₂×C₄×D₁₉	1	6	yes	—
124	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
125	Q₈	—	19	16	no	—
126	D₄	—	19	32	no	—
127	D₄	—	19	16	no	—
128	C₂×C₄	—	19	12	no	—
129	C₂×C₄	—	19	24	no	—
130	C₂×C₄	—	19	8	no	—
131	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
132	C₂×C₄	C₂×C₄×D₁₉	1	6	yes	—
133	C₂×C₄	C₂×C₄×D₁₉	1	12	yes	—
134	C₂×C₄	C₂³×D₁₉	1	3	yes	—
135	C₂×C₄	C₂³×D₁₉	1	4	yes	—
136	C₈	—	19	8	no	—
137	C₈	C₂³×D₁₉	1	4	yes	—
138	C₈	C₂³×D₁₉	1	4	yes	—
139	C₂²	—	2	12	no	—
140	C₂²	—	19	8	no	—
141	C₂²	—	38	24	no	—
142	C₂²	#10597347	1	4	yes	direct product factor
143	C₂²	C₂²×C₄×D₁₉	1	4	yes	—
144	C₂²	C₂²×C₄×D₁₉	1	3	yes	—
145	C₄	—	19	8	no	—
146	C₄	C₂²×C₄×D₁₉	1	3	yes	—
147	C₄	C₂²×C₄×D₁₉	1	4	yes	—
148	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
149	C₂	—	2	4	no	—
150	C₂	—	38	8	no	—
151	C₂	C₂×#10597347	1	6	yes	direct product factor
152	C₂	C₂³×C₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂²×#64541	C₂
cosocle	C₄×C₁₉	C₂⁵
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂²×#131
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#10597347	C₂	direct (N × H)
3. C₂²×#64520	C₂	semidirect
4. C₂²×#64515	C₂	semidirect
5. C₂²×C₈×D₁₉	C₂	semidirect
6. C₂³×C₈×C₁₉	C₂	semidirect
16. C₂²×C₈×C₁₉	C₂²	semidirect
17. C₂×#64520	C₂²	semidirect
19. #10597347	C₂²	direct (N × H)
20. C₂×#64515	C₂²	semidirect
21. C₂×C₈×D₁₉	C₂²	semidirect
38. C₂×C₈×C₁₉	C₂³	semidirect
39. #64520	C₂³	semidirect
41. #64515	C₂³	semidirect
42. C₈×D₁₉	C₂³	semidirect
64. C₂²×C₁₉	#131	semidirect
78. C₂³×C₈	D₁₉	semidirect
80. C₂×C₁₉	C₂×#131	semidirect
97. C₂²×C₈	C₂×D₁₉	semidirect
98. C₁₉	C₂²×#131	semidirect
119. C₂×C₈	C₂²×D₁₉	semidirect
142. C₂²	#10597347	direct (N × H)
151. C₂	C₂×#10597347	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×#64541	2
C₂×#10597347	2
C₂²×#64520	2
C₂²×#64515	2
C₂²×C₈×D₁₉	2
C₂³×C₈×C₁₉	2
C₂²×#131	19

Subgroups — C22×#10597347 #14578339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10597347 #14578339