Subgroups — C₂×C₄⋊C₄×Dic₁₉ #14565972

Order 2432.

928 conjugacy classes of subgroups.

The subgroup lattice has 204 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	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₁₉	C₂	1	2	yes	maximal
3	C₂²×C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×Dic₁₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉⋊#95	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Dic₁₉	C₂²	1	2	yes	—
11	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₄	1	8	yes	complemented
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₁₉	C₄	1	8	yes	complemented
15	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	—	2	8	no	—
17	C₂×C₄×Dic₁₉	C₄	1	8	yes	complemented
18	C₂×C₄×Dic₁₉	C₂²	1	8	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	8	yes	—
21	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	2	4	no	—
23	C₂²×C₄×C₁₉	—	2	4	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	8	yes	—
27	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×Dic₁₉	—	2	4	no	—
31	C₂²×Dic₁₉	—	2	2	no	—
32	C₂²×Dic₁₉	—	2	2	no	—
33	C₂²×Dic₁₉	—	2	4	no	—
34	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
35	C₂²×Dic₁₉	C₂×C₄	1	8	yes	—
36	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
37	C₂²×Dic₁₉	D₄	1	4	yes	—
38	C₂²×Dic₁₉	Q₈	1	4	yes	—
39	C₂²×Dic₁₉	C₂³	1	2	yes	—
40	C₂²×Dic₁₉	C₂³	1	4	yes	—
41	C₂²×Dic₁₉	C₂³	1	2	yes	—
42	C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
43	C₄⋊Dic₁₉	C₂×C₄	1	16	yes	complemented
44	C₄×Dic₁₉	—	2	16	no	—
45	C₄×Dic₁₉	C₂×C₄	1	16	yes	complemented
46	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
47	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
48	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
49	C₂³×C₁₉	C₂×D₄	1	2	yes	—
50	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
51	C₂³×C₁₉	#41	1	2	yes	—
52	C₂³×C₁₉	#41	1	2	yes	—
53	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	16	no	—
55	C₂×C₄×C₁₉	—	2	4	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	C₄²	1	16	yes	complemented
58	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
60	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
61	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
62	C₂×Dic₁₉	—	2	8	no	—
63	C₂×Dic₁₉	—	2	16	no	—
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	C₄⋊C₄	1	16	yes	direct product factor
69	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
70	C₂×Dic₁₉	C₂²×C₄	1	8	yes	—
71	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
72	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
73	C₂×Dic₁₉	C₂×Q₈	1	4	yes	—
74	C₂×C₄×C₄⋊C₄	—	19	1	no	maximal, Sylow
75	C₂²×C₁₉	C₂×C₄²	1	4	yes	—
76	C₂²×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
77	C₂²×C₁₉	#117	1	4	yes	—
78	C₂²×C₁₉	C₄×D₄	1	4	yes	—
79	C₂²×C₁₉	C₄×D₄	1	4	yes	—
80	C₂²×C₁₉	C₄×Q₈	1	4	yes	—
81	C₂²×C₁₉	C₄×Q₈	1	4	yes	—
82	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
83	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
84	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
85	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
86	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
87	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
88	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
89	C₄×C₁₉	—	2	8	no	—
90	C₄×C₁₉	C₂×C₄²	1	8	yes	complemented
91	Dic₁₉	—	2	4	no	—
92	Dic₁₉	—	2	8	no	—
93	Dic₁₉	C₂×C₄⋊C₄	1	8	yes	direct product factor
94	C₂²×C₄⋊C₄	—	19	1	no	—
95	C₂²×C₄⋊C₄	D₁₉	1	1	yes	characteristic
96	C₂²×C₄²	—	19	1	no	—
97	C₂²×C₄²	—	19	2	no	—
98	C₄×C₄⋊C₄	—	19	8	no	—
99	C₂×#95	—	19	2	no	—
100	C₂×C₁₉	C₄×C₄⋊C₄	1	8	yes	complemented
101	C₂×C₁₉	C₂²×C₄²	1	1	yes	characteristic
102	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
104	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
105	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
106	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
107	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
108	C₂³×C₄	—	19	1	no	—
109	C₂³×C₄	—	19	2	no	—
110	C₂³×C₄	—	19	1	no	—
111	C₂³×C₄	C₂×D₁₉	1	2	yes	—
112	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
113	C₂×C₄⋊C₄	—	19	8	no	—
114	C₂×C₄⋊C₄	—	19	4	no	—
115	C₂×C₄⋊C₄	Dic₁₉	1	8	yes	direct product factor
116	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
117	C₂×C₄²	—	19	8	no	—
118	C₂×C₄²	—	19	4	no	—
119	C₂×C₄²	—	19	8	no	—
120	C₂×C₄²	—	38	8	no	—
121	#95	—	19	8	no	—
122	C₁₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
123	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
124	C₂²×C₄	—	2	4	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	—	19	4	no	—
127	C₂²×C₄	—	19	4	no	—
128	C₂²×C₄	—	19	4	no	—
129	C₂²×C₄	—	19	2	no	—
130	C₂²×C₄	—	19	4	no	—
131	C₂²×C₄	—	19	8	no	—
132	C₂²×C₄	—	19	2	no	—
133	C₂²×C₄	—	19	4	no	—
134	C₂²×C₄	—	38	4	no	—
135	C₂²×C₄	—	38	2	no	—
136	C₂²×C₄	—	38	2	no	—
137	C₂²×C₄	—	38	4	no	—
138	C₂²×C₄	C₄×D₁₉	1	4	yes	—
139	C₂²×C₄	C₄×D₁₉	1	4	yes	—
140	C₂²×C₄	C₂×Dic₁₉	1	8	yes	—
141	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
142	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
143	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
144	C₄⋊C₄	—	19	16	no	—
145	C₄⋊C₄	C₂×Dic₁₉	1	16	yes	direct product factor
146	C₄²	—	19	16	no	—
147	C₄²	—	38	16	no	—
148	C₂³	C₂×C₄×D₁₉	1	2	yes	—
149	C₂³	C₂×C₄×D₁₉	1	2	yes	—
150	C₂³	D₄×D₁₉	1	2	yes	—
151	C₂³	#64543	1	2	yes	—
152	C₂³	Q₈×D₁₉	1	2	yes	—
153	C₂³	#64545	1	2	yes	—
154	C₂³	C₂²×Dic₁₉	1	2	yes	—
155	C₂³	C₂³×D₁₉	1	1	yes	characteristic
156	C₂×C₄	—	2	16	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	19	4	no	—
160	C₂×C₄	—	19	4	no	—
161	C₂×C₄	—	19	4	no	—
162	C₂×C₄	—	19	16	no	—
163	C₂×C₄	—	19	4	no	—
164	C₂×C₄	—	19	8	no	—
165	C₂×C₄	—	38	4	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	—	38	2	no	—
168	C₂×C₄	—	38	4	no	—
169	C₂×C₄	—	38	8	no	—
170	C₂×C₄	—	38	16	no	—
171	C₂×C₄	C₄×Dic₁₉	1	16	yes	complemented
172	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
173	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
174	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
175	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
176	C₂²	#10597333	1	4	yes	—
177	C₂²	C₄⋊C₄×D₁₉	1	4	yes	—
178	C₂²	#10597338	1	4	yes	—
179	C₂²	#10597339	1	4	yes	—
180	C₂²	C₂×C₄×Dic₁₉	1	4	yes	—
181	C₂²	D₄×Dic₁₉	1	4	yes	—
182	C₂²	Q₈×Dic₁₉	1	4	yes	—
183	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
184	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
185	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
186	C₂²	C₂×#64543	1	1	yes	characteristic
187	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
188	C₂²	C₂×#64545	1	1	yes	characteristic
189	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
190	C₄	—	2	8	no	—
191	C₄	—	19	8	no	—
192	C₄	—	38	4	no	—
193	C₄	—	38	8	no	—
194	C₄	C₂×C₄×Dic₁₉	1	8	yes	complemented
195	C₂	C₄⋊C₄×Dic₁₉	1	8	yes	direct product factor
196	C₂	C₂²×C₄×Dic₁₉	1	1	yes	characteristic
197	C₂	C₂×C₄⋊C₄×D₁₉	1	1	yes	characteristic
198	C₂	C₂×#10597338	1	1	yes	characteristic
199	C₂	C₂×#10597339	1	1	yes	characteristic
200	C₂	C₂×D₄×Dic₁₉	1	1	yes	characteristic
201	C₂	C₂×#10597333	1	1	yes	characteristic
202	C₂	C₂×Q₈×Dic₁₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₄⋊C₄×Dic₁₉	C₂	direct (N × H)
12. C₂×C₄⋊C₄×C₁₉	C₄	semidirect
14. C₂×C₄⋊Dic₁₉	C₄	semidirect
17. C₂×C₄×Dic₁₉	C₄	semidirect
42. C₄⋊C₄×C₁₉	C₂×C₄	semidirect
43. C₄⋊Dic₁₉	C₂×C₄	semidirect
45. C₄×Dic₁₉	C₂×C₄	semidirect
57. C₂×C₄×C₁₉	C₄²	semidirect
68. C₂×Dic₁₉	C₄⋊C₄	direct (N × H)
90. C₄×C₁₉	C₂×C₄²	semidirect
93. Dic₁₉	C₂×C₄⋊C₄	direct (N × H)
100. C₂×C₁₉	C₄×C₄⋊C₄	semidirect
115. C₂×C₄⋊C₄	Dic₁₉	direct (N × H)
122. C₁₉	C₂×C₄×C₄⋊C₄	semidirect
145. C₄⋊C₄	C₂×Dic₁₉	direct (N × H)
171. C₂×C₄	C₄×Dic₁₉	semidirect
194. C₄	C₂×C₄×Dic₁₉	semidirect
195. C₂	C₄⋊C₄×Dic₁₉	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
C₂²×C₄×Dic₁₉	2
C₄⋊C₄×Dic₁₉	2
C₂×C₁₉⋊#95	2
C₂²×C₄⋊C₄×C₁₉	2
C₂×C₄×C₄⋊C₄	19

Subgroups — C2×C4⋊C4×Dic19 #14565972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊C₄×Dic₁₉ #14565972