Subgroups — C₂×#11926594 #14572248

Order 2432.

528 conjugacy classes of subgroups.

The subgroup lattice has 182 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	#11926594	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×Dic₁₉	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×Dic₁₉	C₄	1	1	yes	characteristic
9	C₂³×Dic₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₄	1	4	yes	—
13	C₂×C₄×Dic₁₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
19	C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
20	Dic₁₉⋊C₈	C₂²	1	8	yes	complemented
21	C₈×Dic₁₉	C₂²	1	8	yes	complemented
22	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	2	4	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	4	no	—
29	C₂²×Dic₁₉	C₈	1	8	yes	complemented
30	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
32	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
35	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	2	4	no	—
37	C₂×C₈×C₁₉	C₂³	1	4	yes	—
38	C₄×Dic₁₉	C₂×C₄	1	4	yes	—
39	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
40	C₄×Dic₁₉	C₂×C₄	1	4	yes	—
41	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
42	C₄×Dic₁₉	C₂³	1	2	yes	—
43	C₄×Dic₁₉	C₂³	1	2	yes	—
44	C₂×C₁₉⋊C₈	—	2	4	no	—
45	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	C₂×C₈	1	4	yes	—
49	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
50	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	4	yes	—
57	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	2	8	no	—
60	C₂×Dic₁₉	C₂×C₈	1	4	yes	—
61	C₂×Dic₁₉	C₂×C₈	1	4	yes	—
62	C₂×Dic₁₉	C₂×C₈	1	16	yes	complemented
63	C₂×Dic₁₉	M₁₆	1	4	yes	—
64	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
65	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
66	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
67	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
68	C₈×C₁₉	—	2	4	no	—
69	C₁₉⋊C₈	—	2	4	no	—
70	C₂×#431	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	—	2	2	no	—
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	—	2	8	no	—
74	C₂²×C₁₉	#117	1	2	yes	—
75	C₂²×C₁₉	C₂²×C₈	1	4	yes	—
76	C₂²×C₁₉	C₂²×C₈	1	2	yes	—
77	C₂²×C₁₉	C₂×M₁₆	1	2	yes	—
78	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	#117	1	2	yes	—
81	C₄×C₁₉	C₂×#41	1	2	yes	—
82	Dic₁₉	—	2	2	no	—
83	Dic₁₉	C₂²×C₈	1	4	yes	—
84	Dic₁₉	C₂²×C₈	1	4	yes	—
85	Dic₁₉	C₂×M₁₆	1	4	yes	—
86	C₂²×C₄²	—	19	1	no	—
87	#431	—	19	8	no	—
88	C₂×C₄⋊C₈	—	19	2	no	—
89	C₂×C₂²⋊C₈	—	19	1	no	—
90	C₂×C₂²⋊C₈	D₁₉	1	1	yes	characteristic
91	C₂×C₄×C₈	—	19	2	no	—
92	C₂×C₁₉	—	2	4	no	—
93	C₂×C₁₉	#431	1	4	yes	complemented
94	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
95	C₂×C₁₉	C₂³×C₈	1	1	yes	characteristic
96	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
97	C₂³×C₄	—	19	1	no	—
98	C₂³×C₄	—	19	1	no	—
99	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
100	C₂²×C₈	—	19	2	no	—
101	C₂²×C₈	C₂×D₁₉	1	2	yes	—
102	C₂×C₄²	—	19	1	no	—
103	C₂×C₄²	—	19	4	no	—
104	C₂×C₄²	—	19	1	no	—
105	C₂×C₄²	—	19	4	no	—
106	C₂×C₄²	—	19	1	no	—
107	C₂×C₄²	—	19	1	no	—
108	C₄⋊C₈	—	19	8	no	—
109	C₂²⋊C₈	—	19	4	no	—
110	C₂²⋊C₈	C₂×D₁₉	1	4	yes	—
111	C₄×C₈	—	19	8	no	—
112	C₁₉	C₂×#431	1	1	yes	characteristic, complemented, Sylow
113	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
114	C₂²×C₄	—	2	4	no	—
115	C₂²×C₄	—	19	8	no	—
116	C₂²×C₄	—	19	1	no	—
117	C₂²×C₄	—	19	1	no	—
118	C₂²×C₄	—	19	4	no	—
119	C₂²×C₄	—	19	1	no	—
120	C₂²×C₄	—	19	4	no	—
121	C₂²×C₄	—	19	1	no	—
122	C₂²×C₄	—	38	4	no	—
123	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
124	C₂²×C₄	C₄×D₁₉	1	2	yes	—
125	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
126	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
127	C₂×C₈	—	2	4	no	—
128	C₂×C₈	—	19	4	no	—
129	C₂×C₈	—	38	4	no	—
130	C₂×C₈	C₂²×D₁₉	1	4	yes	—
131	C₄²	—	19	4	no	—
132	C₄²	—	19	2	no	—
133	C₄²	—	19	4	no	—
134	C₄²	—	19	2	no	—
135	C₄²	—	19	2	no	—
136	C₄²	—	19	2	no	—
137	C₂³	—	2	2	no	—
138	C₂³	—	2	2	no	—
139	C₂³	C₈×D₁₉	1	4	yes	—
140	C₂³	C₂×C₄×D₁₉	1	2	yes	—
141	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	19	2	no	—
146	C₂×C₄	—	19	2	no	—
147	C₂×C₄	—	19	2	no	—
148	C₂×C₄	—	19	4	no	—
149	C₂×C₄	—	19	4	no	—
150	C₂×C₄	—	19	16	no	—
151	C₂×C₄	—	19	4	no	—
152	C₂×C₄	—	19	2	no	—
153	C₂×C₄	—	38	8	no	—
154	C₂×C₄	—	38	2	no	—
155	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
156	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
157	C₂×C₄	#64543	1	4	yes	—
158	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
159	C₈	—	2	4	no	—
160	C₈	—	38	4	no	—
161	C₂²	—	2	2	no	—
162	C₂²	—	2	8	no	—
163	C₂²	—	2	2	no	—
164	C₂²	#10597323	1	2	yes	—
165	C₂²	C₂×C₈×D₁₉	1	4	yes	—
166	C₂²	C₂×C₈×D₁₉	1	2	yes	—
167	C₂²	M₁₆×D₁₉	1	2	yes	—
168	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
169	C₄	—	2	2	no	—
170	C₄	—	19	4	no	—
171	C₄	—	19	4	no	—
172	C₄	—	19	4	no	—
173	C₄	—	38	2	no	—
174	C₄	#10597323	1	2	yes	—
175	C₄	C₂×#64543	1	2	yes	—
176	C₂	—	2	4	no	—
177	C₂	#11926594	1	4	yes	direct product factor
178	C₂	C₂×#10597323	1	1	yes	characteristic
179	C₂	C₂²×C₈×D₁₉	1	1	yes	characteristic
180	C₂	C₂×M₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂×C₁₉	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×C₂²⋊C₈	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×C₂²⋊C₈	D₁₉
hypocenter	C₁₉	C₂×#431
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11926594	C₂	direct (N × H)
3. C₂×Dic₁₉⋊C₈	C₂	semidirect
5. C₂×C₈×Dic₁₉	C₂	semidirect
20. Dic₁₉⋊C₈	C₂²	semidirect
21. C₈×Dic₁₉	C₂²	semidirect
29. C₂²×Dic₁₉	C₈	semidirect
62. C₂×Dic₁₉	C₂×C₈	semidirect
93. C₂×C₁₉	#431	semidirect
112. C₁₉	C₂×#431	semidirect
177. C₂	#11926594	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
#11926594	2
C₂×Dic₁₉⋊C₈	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
C₂×C₈×Dic₁₉	2
C₂×C₁₉×C₂²⋊C₈	2
C₂×#431	19

Subgroups — C2×#11926594 #14572248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926594 #14572248