Subgroups — #18069713

Order 4864.

238 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926365	C₂	1	1	yes	maximal, characteristic
2	#14563795	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597275	—	2	1	no	—
6	C₂×#10597275	—	2	1	no	—
7	#11926414	C₄	1	2	yes	—
8	#11926365	—	2	1	no	—
9	#11926365	C₄	1	2	yes	complemented
10	C₂×C₁₉×M₃₂	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#364	—	2	1	no	—
13	C₁₉×#364	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	2	no	—
18	C₂×C₄⋊Dic₁₉	—	4	2	no	—
19	C₁₉×M₃₂	—	2	2	no	—
20	C₁₉×M₃₂	—	4	1	no	—
21	C₂×C₁₆×C₁₉	—	4	1	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
26	#10597275	—	4	1	no	—
27	#10597275	—	4	1	no	—
28	#10597275	—	4	1	no	—
29	#10597275	—	4	1	no	—
30	#10597269	—	2	2	no	—
31	#10597269	—	4	1	no	—
32	C₂×C₁₉⋊C₁₆	—	4	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×Dic₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
48	C₄²×C₁₉	—	2	1	no	—
49	C₄²×C₁₉	C₄²	1	1	yes	characteristic
50	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₄⋊Dic₁₉	—	4	2	no	—
52	C₄⋊Dic₁₉	—	4	2	no	—
53	C₄⋊Dic₁₉	—	8	4	no	—
54	C₁₆×C₁₉	—	4	2	no	—
55	C₁₉⋊C₁₆	—	4	2	no	—
56	#7269	—	19	1	no	maximal, Sylow
57	C₂³×C₁₉	#100	1	1	yes	characteristic
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
68	C₂×Dic₁₉	—	8	4	no	—
69	C₂×Dic₁₉	—	8	2	no	—
70	C₈×C₁₉	#102	1	1	yes	characteristic
71	C₈×C₁₉	#102	1	1	yes	characteristic
72	C₈×C₁₉	#103	1	1	yes	characteristic
73	C₈×C₁₉	#103	1	1	yes	characteristic
74	C₈×C₁₉	#106	1	1	yes	characteristic
75	C₈×C₁₉	#106	1	1	yes	characteristic
76	C₈×C₁₉	#107	1	1	yes	characteristic
77	C₈×C₁₉	#107	1	1	yes	characteristic
78	C₂×#364	—	19	1	no	—
79	C₂×#364	D₁₉	1	1	yes	characteristic
80	#1845	—	19	1	no	—
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	#331	1	1	yes	characteristic
84	C₂²×C₁₉	#333	1	1	yes	characteristic
85	C₂²×C₁₉	#343	1	1	yes	characteristic
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	#332	1	1	yes	characteristic
89	C₄×C₁₉	#332	1	1	yes	characteristic
90	C₄×C₁₉	#340	1	1	yes	characteristic
91	C₄×C₁₉	#340	1	1	yes	characteristic
92	Dic₁₉	—	16	2	no	—
93	C₂×M₃₂	—	2	1	no	—
94	C₂×M₃₂	—	38	1	no	—
95	C₂×#107	—	38	1	no	—
96	C₂×#107	—	38	1	no	—
97	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
98	#384	—	19	2	no	—
99	#364	—	2	1	no	—
100	#364	—	19	2	no	—
101	#364	—	38	1	no	—
102	#364	Dic₁₉	1	2	yes	complemented
103	C₂×C₁₉	—	2	1	no	—
104	C₂×C₁₉	—	2	1	no	—
105	C₂×C₁₉	#1296	1	1	yes	characteristic
106	C₂×C₁₉	#1357	1	1	yes	characteristic
107	C₂×C₁₉	#1358	1	1	yes	characteristic
108	C₂²×C₈	D₇₆	1	1	yes	characteristic
109	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	38	2	no	—
111	C₂×C₄⋊C₄	—	76	2	no	—
112	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
113	M₃₂	—	2	2	no	—
114	M₃₂	—	4	1	no	—
115	M₃₂	—	38	2	no	—
116	M₃₂	—	76	1	no	—
117	C₂×C₁₆	—	4	1	no	—
118	C₂×C₁₆	—	76	1	no	—
119	#107	—	76	1	no	—
120	#107	—	76	1	no	—
121	#107	—	76	1	no	—
122	#107	—	76	1	no	—
123	C₄×C₈	Dic₃₈	1	1	yes	characteristic
124	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
125	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
126	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
127	C₁₉	#7269	1	1	yes	characteristic, complemented, Sylow
128	C₂²×C₄	—	2	1	no	—
129	C₂²×C₄	—	76	2	no	—
130	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₂×C₈	#64516	1	1	yes	characteristic
132	C₂×C₈	#64516	1	1	yes	characteristic
133	C₂×C₈	D₁₅₂	1	1	yes	characteristic
134	C₂×C₈	Dic₇₆	1	1	yes	characteristic
135	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
136	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
137	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
138	C₂×C₈	#64525	1	1	yes	characteristic
139	C₂×C₈	#64526	1	1	yes	characteristic
140	C₂×C₈	#64527	1	1	yes	characteristic
141	C₂×C₈	#64528	1	1	yes	characteristic
142	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₄⋊C₄	—	76	2	no	—
144	C₄⋊C₄	—	76	2	no	—
145	C₄⋊C₄	—	152	4	no	—
146	C₄²	—	2	1	no	—
147	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
148	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
149	C₁₆	—	4	2	no	—
150	C₁₆	—	76	2	no	—
151	C₂³	#10597280	1	1	yes	characteristic
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	152	4	no	—
157	C₂×C₄	—	152	2	no	—
158	C₂×C₄	#10597266	1	1	yes	characteristic
159	C₂×C₄	#10597267	1	1	yes	characteristic
160	C₂×C₄	#10597273	1	1	yes	characteristic
161	C₂×C₄	#10597278	1	1	yes	characteristic
162	C₂×C₄	#10597281	1	1	yes	characteristic
163	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
164	C₈	#10597264	1	1	yes	characteristic
165	C₈	#10597265	1	1	yes	characteristic
166	C₈	#10597273	1	1	yes	characteristic
167	C₈	#10597274	1	1	yes	characteristic
168	C₈	#10597275	1	1	yes	characteristic
169	C₈	#10597278	1	1	yes	characteristic
170	C₈	#10597289	1	1	yes	characteristic
171	C₈	#10597292	1	1	yes	characteristic
172	C₂²	—	2	1	no	—
173	C₂²	—	2	1	no	—
174	C₂²	#11926287	1	1	yes	characteristic
175	C₂²	#11926292	1	1	yes	characteristic
176	C₂²	#11926312	1	1	yes	characteristic
177	C₄	—	2	2	no	—
178	C₄	—	2	2	no	—
179	C₄	—	304	2	no	—
180	C₄	#11926289	1	1	yes	characteristic
181	C₄	#11926291	1	1	yes	characteristic
182	C₄	#11926306	1	1	yes	characteristic
183	C₄	#11926307	1	1	yes	characteristic
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	#14561519	1	1	yes	characteristic
187	C₂	#14561671	1	1	yes	characteristic
188	C₂	#14561673	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926287
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#364	C₂
socle	C₂²×C₁₉	#331
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#364	D₁₉
hypocenter	C₁₉	#7269
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
9. #11926365	C₄	semidirect
13. C₁₉×#364	C₄	semidirect
102. #364	Dic₁₉	semidirect
127. C₁₉	#7269	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926365	2
#14563795	2
C₂×C₁₉×#364	2
#7269	19