Subgroups — #18076202

Order 4864.

382 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563752	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14561469	C₂	1	4	yes	maximal
4	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
10	#11926299	—	2	2	no	—
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#336	—	2	2	no	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊C₈	—	2	4	no	—
24	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄×C₁₉⋊C₈	—	2	2	no	—
26	C₄×C₁₉⋊C₈	—	2	2	no	—
27	C₄×C₁₉⋊C₈	—	2	2	no	—
28	C₄×C₁₉⋊C₈	—	2	4	no	—
29	C₄×C₁₉⋊C₈	C₈	1	4	yes	complemented
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	4	no	—
37	C₄²×C₁₉	—	2	4	no	—
38	C₄²×C₁₉	—	2	2	no	—
39	C₄²×C₁₉	—	2	4	no	—
40	C₄²×C₁₉	C₂×C₈	1	2	yes	—
41	C₄²×C₁₉	M₁₆	1	2	yes	—
42	C₄²×C₁₉	#41	1	2	yes	—
43	C₄²×C₁₉	#41	1	2	yes	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	2	2	no	—
47	C₂×C₁₉⋊C₈	—	2	2	no	—
48	C₂×C₁₉⋊C₈	—	4	2	no	—
49	C₂×C₁₉⋊C₈	—	4	4	no	—
50	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
51	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
52	#8785	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
60	C₂×C₄×C₁₉	#108	1	4	yes	—
61	C₂×C₄×C₁₉	#117	1	2	yes	—
62	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#125	1	2	yes	—
65	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
68	C₂×C₄×C₁₉	#135	1	4	yes	—
69	C₈×C₁₉	—	8	2	no	—
70	C₁₉⋊C₈	—	2	4	no	—
71	C₁₉⋊C₈	—	2	4	no	—
72	C₁₉⋊C₈	—	8	2	no	—
73	#1831	—	19	1	no	—
74	#1831	D₁₉	1	1	yes	characteristic
75	C₄²×C₈	—	19	1	no	—
76	#1277	—	19	4	no	—
77	C₂²×C₁₉	#382	1	1	yes	characteristic
78	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
79	C₂²×C₁₉	#423	1	1	yes	characteristic
80	C₂²×C₁₉	#427	1	2	yes	—
81	C₂²×C₁₉	C₂×#108	1	2	yes	—
82	C₄×C₁₉	—	2	4	no	—
83	C₄×C₁₉	—	2	4	no	—
84	C₄×C₁₉	—	2	2	no	—
85	C₄×C₁₉	#431	1	2	yes	—
86	C₄×C₁₉	#432	1	2	yes	—
87	C₄×C₁₉	#488	1	2	yes	—
88	C₄×C₁₉	#488	1	2	yes	—
89	C₂×C₄⋊C₈	—	19	2	no	—
90	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
91	C₂×C₄×C₈	—	19	1	no	—
92	C₂×C₄×C₈	—	19	2	no	—
93	C₂×C₄×C₈	—	19	1	no	—
94	C₂×C₄×C₈	—	19	2	no	—
95	C₄³	C₂×D₁₉	1	1	yes	characteristic
96	#336	—	2	2	no	—
97	#336	—	38	2	no	—
98	C₂×C₁₉	#1564	1	2	yes	—
99	C₂×C₁₉	#1568	1	2	yes	—
100	C₂×C₁₉	#1831	1	1	yes	characteristic
101	C₂×C₁₉	#1835	1	1	yes	characteristic
102	C₂×C₁₉	#1837	1	1	yes	characteristic
103	C₂²×C₈	—	2	2	no	—
104	C₂²×C₈	—	19	2	no	—
105	C₂²×C₈	—	19	2	no	—
106	C₂²×C₈	—	38	2	no	—
107	C₂×C₄²	Dic₃₈	1	2	yes	—
108	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
109	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
110	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
111	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	C₄⋊C₈	—	2	4	no	—
113	C₄⋊C₈	—	38	4	no	—
114	C₄×C₈	—	19	4	no	—
115	C₄×C₈	—	38	4	no	—
116	C₄×C₈	—	38	2	no	—
117	C₄×C₈	—	38	2	no	—
118	C₄×C₈	—	38	2	no	—
119	C₁₉	#8785	1	1	yes	characteristic, complemented, Sylow
120	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
121	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
122	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
123	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
124	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₂×C₈	—	4	2	no	—
126	C₂×C₈	—	4	4	no	—
127	C₂×C₈	—	19	4	no	—
128	C₂×C₈	—	19	4	no	—
129	C₂×C₈	—	38	2	no	—
130	C₂×C₈	—	38	2	no	—
131	C₂×C₈	—	38	2	no	—
132	C₂×C₈	—	38	2	no	—
133	C₂×C₈	—	76	2	no	—
134	C₂×C₈	—	76	4	no	—
135	C₄²	—	2	4	no	—
136	C₄²	—	2	4	no	—
137	C₄²	—	2	2	no	—
138	C₄²	C₈×D₁₉	1	2	yes	—
139	C₄²	#64515	1	2	yes	—
140	C₄²	#64543	1	2	yes	—
141	C₄²	#64545	1	2	yes	—
142	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
149	C₂×C₄	#10597279	1	4	yes	—
150	C₂×C₄	#10597336	1	2	yes	—
151	C₂×C₄	#10597338	1	2	yes	—
152	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
153	C₂×C₄	C₂×#64515	1	1	yes	characteristic
154	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
155	C₂×C₄	#10597382	1	1	yes	characteristic
156	C₂×C₄	#10597393	1	1	yes	characteristic
157	C₂×C₄	#10597396	1	4	yes	—
158	C₈	—	8	2	no	—
159	C₈	—	38	4	no	—
160	C₈	—	38	4	no	—
161	C₈	—	152	2	no	—
162	C₂²	#11926409	1	1	yes	characteristic
163	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
164	C₂²	#11926567	1	1	yes	characteristic
165	C₂²	#11926580	1	2	yes	—
166	C₂²	C₂×#10597279	1	2	yes	—
167	C₄	—	2	4	no	—
168	C₄	—	2	4	no	—
169	C₄	—	2	2	no	—
170	C₄	#11926596	1	2	yes	—
171	C₄	#11926600	1	2	yes	—
172	C₄	#11926898	1	2	yes	—
173	C₄	#11926901	1	2	yes	—
174	C₂	#14562381	1	2	yes	—
175	C₂	#14562396	1	2	yes	—
176	C₂	#14563751	1	1	yes	characteristic
177	C₂	#14563765	1	1	yes	characteristic
178	C₂	#14563772	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#8785
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
29. C₄×C₁₉⋊C₈	C₈	semidirect
119. C₁₉	#8785	semidirect

Maximal subgroups

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

subgroup	index
#14563752	2
C₄²×C₁₉⋊C₈	2
#14561469	2
C₁₉×#1831	2
#8785	19