Subgroups — #18069412

Order 4864.

234 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926320	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	C₄	1	2	yes	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	#11926320	—	2	1	no	—
7	#11926320	—	2	1	no	—
8	#11926295	—	2	1	no	—
9	#11926295	C₄	1	2	yes	—
10	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#334	—	2	1	no	—
13	C₁₉×#334	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	—	4	1	no	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	2	2	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₁₉⋊C₁₆	—	2	2	no	—
26	C₂×C₁₉⋊C₁₆	—	2	2	no	—
27	C₂×C₁₉⋊C₁₆	C₈	1	4	yes	complemented
28	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	—	8	2	no	—
36	C₂×C₈×C₁₉	C₄²	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	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
42	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₄²×C₁₉	D₈	1	1	yes	characteristic
45	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	C₂×C₁₉⋊C₈	—	8	2	no	—
48	C₁₉⋊C₁₆	—	2	4	no	—
49	#7156	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	#106	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
59	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#108	1	2	yes	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	8	2	no	—
64	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
65	C₈×C₁₉	#97	1	1	yes	characteristic
66	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
67	C₁₉⋊C₈	—	8	2	no	—
68	C₂×#346	—	19	1	no	—
69	C₂×#334	—	19	1	no	—
70	C₂×#334	D₁₉	1	1	yes	characteristic
71	C₂²×C₁₉	#334	1	2	yes	—
72	C₂²×C₁₉	#340	1	1	yes	characteristic
73	C₂²×C₁₉	#365	1	2	yes	—
74	C₂²×C₁₉	#365	1	2	yes	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	#335	1	2	yes	—
80	C₄×C₁₉	#336	1	1	yes	characteristic
81	C₄×C₁₉	#341	1	1	yes	characteristic
82	C₂²×C₁₆	—	19	2	no	—
83	C₂×C₄⋊C₈	—	2	1	no	—
84	C₂×C₄⋊C₈	—	38	1	no	—
85	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
86	#346	—	38	1	no	—
87	#346	—	38	1	no	—
88	#334	—	2	1	no	—
89	#334	—	19	2	no	—
90	#334	—	38	1	no	—
91	#334	Dic₁₉	1	2	yes	—
92	C₂×C₁₉	#1277	1	1	yes	characteristic
93	C₂×C₁₉	#1368	1	4	yes	—
94	C₂×C₁₉	#1383	1	1	yes	characteristic
95	C₂×C₁₉	#1383	1	1	yes	characteristic
96	C₂²×C₈	—	4	1	no	—
97	C₂²×C₈	—	76	1	no	—
98	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
99	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
100	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂×C₁₆	—	19	4	no	—
102	C₂×C₁₆	—	38	2	no	—
103	C₂×C₁₆	—	38	2	no	—
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	4	1	no	—
106	C₄⋊C₈	—	38	2	no	—
107	C₄⋊C₈	—	76	1	no	—
108	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
109	C₄×C₈	D₇₆	1	1	yes	characteristic
110	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
111	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₁₉	#7156	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
114	C₂²×C₄	#64526	1	1	yes	characteristic
115	C₂²×C₄	#64527	1	1	yes	characteristic
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	8	2	no	—
119	C₂×C₈	—	76	2	no	—
120	C₂×C₈	—	152	2	no	—
121	C₂×C₈	C₈×D₁₉	1	2	yes	—
122	C₂×C₈	#64515	1	2	yes	—
123	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
124	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
126	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
127	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₄²	#64525	1	1	yes	characteristic
129	C₄²	#64528	1	1	yes	characteristic
130	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₁₆	—	38	4	no	—
132	C₂³	#10597265	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	#10597264	1	1	yes	characteristic
136	C₂×C₄	#10597266	1	1	yes	characteristic
137	C₂×C₄	#10597267	1	1	yes	characteristic
138	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
139	C₂×C₄	#10597279	1	2	yes	—
140	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
141	C₂×C₄	#10597289	1	1	yes	characteristic
142	C₂×C₄	#10597292	1	1	yes	characteristic
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	8	2	no	—
146	C₈	—	152	2	no	—
147	C₈	C₈×Dic₁₉	1	1	yes	characteristic
148	C₈	#10597272	1	1	yes	characteristic
149	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
150	C₂²	#11926294	1	2	yes	—
151	C₂²	#11926306	1	1	yes	characteristic
152	C₂²	#11926366	1	2	yes	—
153	C₂²	#11926368	1	2	yes	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	#11926296	1	2	yes	—
159	C₄	#11926298	1	1	yes	characteristic
160	C₄	#11926308	1	1	yes	characteristic
161	C₂	#14561469	1	1	yes	characteristic
162	C₂	#14561700	1	4	yes	—
163	C₂	#14561733	1	1	yes	characteristic
164	C₂	#14561735	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597265
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#334	C₂
socle, prime radical	C₂³×C₁₉	#106
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#334	D₁₉
hypocenter	C₁₉	#7156
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
27. C₂×C₁₉⋊C₁₆	C₈	semidirect
112. C₁₉	#7156	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926320	2
C₂×#11926295	2
C₂×C₁₉×#334	2
#7156	19