Subgroups — C₂×#11926622 #14572322

Order 2432.

552 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64520	C₂	1	2	yes	maximal, complemented
2	#11926622	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
9	C₄×D₄×C₁₉	C₄	1	4	yes	—
10	C₄×D₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	—	2	8	no	—
15	C₂×#64520	C₂²	1	8	yes	complemented
16	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
17	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²⋊(C₁₉⋊C₈)	C₂²	1	8	yes	complemented
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	complemented
21	C₄×C₁₉⋊C₈	C₂²	1	4	yes	complemented
22	C₂⁴×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×D₄×C₁₉	—	2	4	no	—
24	C₂×D₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₉	—	2	4	no	—
26	C₂²×C₄×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
34	C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
35	C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₄²×C₁₉	C₂³	1	2	yes	—
37	#64520	—	2	16	no	—
38	C₂×C₁₉⋊C₈	—	2	4	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
41	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
42	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
43	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
44	C₂³×C₁₉	—	2	4	no	—
45	C₂³×C₁₉	—	2	4	no	—
46	C₂³×C₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂²×C₄	1	4	yes	—
48	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	D₄×C₁₉	—	2	8	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	8	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	M₁₆	1	4	yes	complemented
56	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
58	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	#41	1	2	yes	—
62	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
63	C₁₉⋊C₈	—	2	4	no	—
64	C₁₉⋊C₈	—	2	2	no	—
65	C₁₉⋊C₈	C₂×D₄	1	4	yes	complemented
66	C₂×#436	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	2	4	no	—
68	C₂²×C₁₉	—	2	4	no	—
69	C₂²×C₁₉	—	2	4	no	—
70	C₂²×C₁₉	—	4	8	no	—
71	C₂²×C₁₉	C₄×D₄	1	2	yes	—
72	C₂²×C₁₉	C₂×M₁₆	1	2	yes	—
73	C₂²×C₁₉	#131	1	2	yes	—
74	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	C₄×D₄	1	2	yes	—
78	C₄×C₁₉	C₂×M₁₆	1	4	yes	complemented
79	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
80	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
81	C₂²×M₁₆	—	19	2	no	—
82	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic
83	#436	—	19	8	no	—
84	C₂×C₄⋊C₈	—	19	1	no	—
85	C₂×C₂²⋊C₈	—	19	2	no	—
86	C₂×C₄×C₈	—	19	1	no	—
87	C₂×C₁₉	—	4	4	no	—
88	C₂×C₁₉	#436	1	4	yes	complemented
89	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
90	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
91	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
92	C₂²×D₄	Dic₁₉	1	1	yes	characteristic
93	C₂³×C₄	C₂×D₁₉	1	2	yes	—
94	C₂×M₁₆	—	19	8	no	—
95	C₂×M₁₆	—	38	8	no	—
96	C₂²×C₈	—	19	1	no	—
97	C₂²×C₈	—	19	2	no	—
98	C₂²×C₈	—	19	1	no	—
99	C₄×D₄	Dic₁₉	1	4	yes	—
100	C₄×D₄	C₂×D₁₉	1	4	yes	—
101	C₂×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
102	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
103	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
104	C₄⋊C₈	—	19	4	no	—
105	C₂²⋊C₈	—	19	8	no	—
106	C₄×C₈	—	19	4	no	—
107	C₁₉	C₂×#436	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	C₂×Dic₁₉	1	2	yes	—
109	C₂×D₄	—	2	4	no	—
110	C₂×D₄	C₂×Dic₁₉	1	4	yes	—
111	C₂²×C₄	—	2	4	no	—
112	C₂²×C₄	—	2	4	no	—
113	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
115	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
116	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	M₁₆	—	38	16	no	—
120	C₂×C₈	—	19	4	no	—
121	C₂×C₈	—	19	2	no	—
122	C₂×C₈	—	19	2	no	—
123	C₂×C₈	—	19	4	no	—
124	C₂×C₈	—	38	4	no	—
125	C₂×C₈	—	38	2	no	—
126	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
127	C₂²⋊C₄	C₂×Dic₁₉	1	8	yes	—
128	C₄²	C₂×Dic₁₉	1	2	yes	—
129	C₄²	C₂²×D₁₉	1	2	yes	—
130	C₂³	—	2	4	no	—
131	C₂³	—	2	4	no	—
132	C₂³	—	2	4	no	—
133	C₂³	C₂²×Dic₁₉	1	4	yes	—
134	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
135	D₄	—	2	8	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	8	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	#64520	1	4	yes	complemented
142	C₂×C₄	D₄×D₁₉	1	2	yes	—
143	C₂×C₄	#64543	1	2	yes	—
144	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
145	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
146	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
147	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
148	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
149	C₈	—	19	4	no	—
150	C₈	—	38	4	no	—
151	C₈	—	38	2	no	—
152	C₂²	—	2	4	no	—
153	C₂²	—	2	4	no	—
154	C₂²	—	2	4	no	—
155	C₂²	—	4	8	no	—
156	C₂²	C₂×#64520	1	2	yes	—
157	C₂²	D₄×Dic₁₉	1	2	yes	—
158	C₂²	#10597394	1	2	yes	—
159	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	2	4	no	—
162	C₄	C₂×#64520	1	4	yes	complemented
163	C₄	D₄×Dic₁₉	1	2	yes	—
164	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
165	C₄	C₂×#64543	1	1	yes	characteristic
166	C₂	—	4	4	no	—
167	C₂	#11926622	1	4	yes	direct product factor
168	C₂	C₂×D₄×Dic₁₉	1	1	yes	characteristic
169	C₂	C₂²×#64520	1	1	yes	characteristic
170	C₂	C₂×#10597394	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×D₄×C₁₉	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂²×D₄×C₁₉	C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	C₂×#436
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#64520	C₂	semidirect
2. #11926622	C₂	direct (N × H)
3. C₂×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. C₂×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
5. C₂×C₄×C₁₉⋊C₈	C₂	semidirect
15. C₂×#64520	C₂²	semidirect
19. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
20. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
21. C₄×C₁₉⋊C₈	C₂²	semidirect
40. C₂×C₁₉⋊C₈	D₄	semidirect
55. C₂×C₄×C₁₉	M₁₆	semidirect
65. C₁₉⋊C₈	C₂×D₄	semidirect
78. C₄×C₁₉	C₂×M₁₆	semidirect
88. C₂×C₁₉	#436	semidirect
107. C₁₉	C₂×#436	semidirect
141. C₂×C₄	#64520	semidirect
162. C₄	C₂×#64520	semidirect
167. C₂	#11926622	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×#64520	2
#11926622	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
C₂×C₄×C₁₉⋊C₈	2
C₂×C₄×D₄×C₁₉	2
C₂×#436	19

Subgroups — C2×#11926622 #14572322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926622 #14572322