Subgroups — #18076346

Order 4864.

322 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563772	C₂	1	2	yes	maximal
2	#14562394	C₂	1	1	yes	maximal, characteristic
3	#14562390	C₂	1	2	yes	maximal
4	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926308	—	2	4	no	—
10	#11926297	—	2	2	no	—
11	#11926294	—	2	4	no	—
12	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
15	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#335	—	2	2	no	—
19	C₂×M₁₆×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×#64520	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
24	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	D₄	1	2	yes	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
37	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	M₁₆×C₁₉	—	4	4	no	—
42	C₂×C₈×C₁₉	—	2	4	no	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	#64520	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
57	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
59	#8824	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#135	1	2	yes	—
70	C₂×C₄×C₁₉	#135	1	2	yes	—
71	C₈×C₁₉	—	2	2	no	—
72	C₈×C₁₉	—	8	2	no	—
73	C₈×C₁₉	#108	1	4	yes	—
74	C₁₉⋊C₈	—	2	2	no	—
75	C₁₉⋊C₈	—	2	2	no	—
76	C₁₉⋊C₈	—	2	2	no	—
77	C₁₉⋊C₈	—	8	2	no	—
78	C₁₉⋊C₈	#108	1	4	yes	—
79	#1837	—	19	2	no	—
80	#1567	—	19	1	no	—
81	#1567	D₁₉	1	1	yes	characteristic
82	#1566	—	19	2	no	—
83	C₂×C₈²	—	19	1	no	—
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	#384	1	1	yes	characteristic
87	C₂²×C₁₉	#499	1	2	yes	—
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	#427	1	2	yes	—
91	C₄×C₁₉	C₂×#108	1	2	yes	—
92	C₄×C₁₉	C₂×#108	1	2	yes	—
93	C₄×C₁₉	#495	1	1	yes	characteristic
94	C₄×C₁₉	#495	1	1	yes	characteristic
95	#423	—	19	2	no	—
96	#423	C₂×D₁₉	1	2	yes	—
97	C₂×C₄×C₈	—	19	1	no	—
98	C₂×C₄×C₈	—	19	1	no	—
99	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	#341	—	38	4	no	—
101	#335	—	2	2	no	—
102	#335	—	38	2	no	—
103	#334	—	38	4	no	—
104	C₈²	—	19	1	no	—
105	C₈²	—	19	1	no	—
106	C₈²	—	19	1	no	—
107	C₈²	—	19	1	no	—
108	C₂×C₁₉	—	2	2	no	—
109	C₂×C₁₉	#1846	1	1	yes	characteristic
110	C₂×C₁₉	#1848	1	1	yes	characteristic
111	C₂×C₁₉	#1848	1	1	yes	characteristic
112	C₂×M₁₆	—	2	2	no	—
113	C₂×M₁₆	—	38	2	no	—
114	C₂²×C₈	—	19	2	no	—
115	C₂²×C₈	—	19	2	no	—
116	C₂²×C₈	Dic₃₈	1	2	yes	—
117	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
118	C₄⋊C₈	—	2	2	no	—
119	C₄⋊C₈	—	2	2	no	—
120	C₄⋊C₈	—	38	2	no	—
121	C₄⋊C₈	—	38	2	no	—
122	C₄×C₈	—	19	1	no	—
123	C₄×C₈	—	19	1	no	—
124	C₄×C₈	—	19	1	no	—
125	C₄×C₈	—	19	1	no	—
126	C₄×C₈	—	19	2	no	—
127	C₄×C₈	—	19	2	no	—
128	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
129	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
130	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
131	C₁₉	#8824	1	1	yes	characteristic, complemented, Sylow
132	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
133	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
135	M₁₆	—	4	4	no	—
136	M₁₆	—	76	4	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	19	2	no	—
140	C₂×C₈	—	19	2	no	—
141	C₂×C₈	—	19	2	no	—
142	C₂×C₈	—	19	2	no	—
143	C₂×C₈	—	38	4	no	—
144	C₂×C₈	—	38	2	no	—
145	C₂×C₈	—	38	2	no	—
146	C₂×C₈	—	76	2	no	—
147	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
148	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
149	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
150	C₄²	D₄×D₁₉	1	1	yes	characteristic
151	C₄²	Q₈×D₁₉	1	1	yes	characteristic
152	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂³	#10597334	1	1	yes	characteristic
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	#10597334	1	1	yes	characteristic
157	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
158	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
159	C₂×C₄	#10597358	1	2	yes	—
160	C₂×C₄	#10597365	1	2	yes	—
161	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
162	C₂×C₄	#10597386	1	1	yes	characteristic
163	C₂×C₄	#10597390	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	8	2	no	—
166	C₈	—	19	4	no	—
167	C₈	—	38	2	no	—
168	C₈	—	38	2	no	—
169	C₈	—	38	2	no	—
170	C₈	—	152	2	no	—
171	C₈	#10597279	1	4	yes	—
172	C₂²	—	2	1	no	—
173	C₂²	—	2	1	no	—
174	C₂²	#11926413	1	1	yes	characteristic
175	C₂²	#11926945	1	2	yes	—
176	C₄	—	2	1	no	—
177	C₄	—	2	1	no	—
178	C₄	#11926581	1	2	yes	—
179	C₄	#108×D₁₉	1	2	yes	—
180	C₄	C₂×#10597279	1	2	yes	—
181	C₄	#11926927	1	1	yes	characteristic
182	C₄	#11926929	1	1	yes	characteristic
183	C₂	—	2	2	no	—
184	C₂	#14563798	1	1	yes	characteristic
185	C₂	#14563805	1	1	yes	characteristic
186	C₂	#14563806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#8824
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
131. C₁₉	#8824	semidirect

Maximal subgroups

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

subgroup	index
#14563772	2
#14562394	2
#14562390	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1567	2
#8824	19