Subgroups — #18076308

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563794	C₂	1	2	yes	maximal
2	#14563792	C₂	1	1	yes	maximal, characteristic
3	#14563762	C₂	1	2	yes	maximal
4	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	4	no	—
7	C₂×#10597274	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	2	yes	—
11	#11926306	—	2	4	no	—
12	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₁₉×#106	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
25	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
26	C₁₉×#106	—	4	4	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₉	Q₈	1	2	yes	—
29	#10597274	—	4	4	no	—
30	#10597264	—	4	8	no	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
34	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₁₉	—	4	2	no	—
40	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
41	C₂×C₈×C₁₉	D₈	1	4	yes	—
42	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
43	C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄⋊C₄×C₁₉	—	4	4	no	—
46	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₄⋊Dic₁₉	—	4	4	no	—
51	C₄⋊Dic₁₉	—	4	4	no	—
52	C₄⋊Dic₁₉	—	4	4	no	—
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
55	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
56	C₂×C₁₉⋊C₈	SD₁₆	1	8	yes	—
57	#8814	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	#127	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	8	2	no	—
60	C₂×C₄×C₁₉	—	8	2	no	—
61	C₂×C₄×C₁₉	—	8	2	no	—
62	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
70	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
71	C₂×C₄×C₁₉	#135	1	4	yes	—
72	C₂×Dic₁₉	—	8	2	no	—
73	C₂×Dic₁₉	—	8	2	no	—
74	C₂×Dic₁₉	—	8	2	no	—
75	C₈×C₁₉	#107	1	8	yes	complemented
76	C₁₉⋊C₈	—	2	4	no	—
77	C₁₉⋊C₈	#106	1	8	yes	complemented
78	#1845	—	19	2	no	—
79	#1844	—	19	1	no	—
80	#1844	D₁₉	1	1	yes	characteristic
81	#1834	—	19	2	no	—
82	C₂×C₈²	—	19	1	no	—
83	C₂²×C₁₉	#384	1	1	yes	characteristic
84	C₂²×C₁₉	#492	1	2	yes	—
85	C₂²×C₁₉	#493	1	1	yes	characteristic
86	C₂²×C₁₉	#494	1	1	yes	characteristic
87	C₂²×C₁₉	#495	1	2	yes	—
88	C₄×C₁₉	—	16	2	no	—
89	C₄×C₁₉	C₂×#106	1	2	yes	—
90	C₄×C₁₉	C₂×#107	1	2	yes	—
91	C₄×C₁₉	#427	1	2	yes	—
92	C₄×C₁₉	#498	1	2	yes	—
93	C₄×C₁₉	#499	1	2	yes	—
94	C₄×C₁₉	#500	1	2	yes	—
95	Dic₁₉	—	16	2	no	—
96	C₂×#107	—	38	4	no	—
97	C₂×#106	—	2	2	no	—
98	C₂×#106	—	38	2	no	—
99	C₂×C₄×C₈	—	19	1	no	—
100	C₂×C₄×C₈	—	19	1	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#384	—	19	2	no	—
103	#384	C₂×D₁₉	1	2	yes	—
104	#340	—	38	4	no	—
105	C₈²	—	19	4	no	—
106	C₂×C₁₉	#1706	1	2	yes	—
107	C₂×C₁₉	#1707	1	2	yes	—
108	C₂×C₁₉	#1844	1	1	yes	characteristic
109	C₂×C₁₉	#1845	1	1	yes	characteristic
110	C₂×C₁₉	#1846	1	1	yes	characteristic
111	C₂²×C₈	—	19	2	no	—
112	C₂²×C₈	—	19	2	no	—
113	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	38	2	no	—
118	C₂×C₄⋊C₄	—	38	2	no	—
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	#107	—	76	8	no	—
122	#106	—	4	4	no	—
123	#106	—	76	4	no	—
124	C₄×C₈	—	19	2	no	—
125	C₄×C₈	—	19	2	no	—
126	C₄×C₈	—	19	2	no	—
127	C₄×C₈	—	19	2	no	—
128	C₄×C₈	Dic₃₈	1	2	yes	—
129	C₄×C₈	C₄×D₁₉	1	2	yes	—
130	C₁₉	#8814	1	1	yes	characteristic, complemented, Sylow
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	—	76	2	no	—
133	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
136	C₂×C₈	—	19	4	no	—
137	C₂×C₈	—	19	8	no	—
138	C₂×C₈	—	19	4	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
141	C₂×C₈	#64525	1	4	yes	—
142	C₂×C₈	#64528	1	4	yes	—
143	C₄⋊C₄	—	4	4	no	—
144	C₄⋊C₄	—	4	4	no	—
145	C₄⋊C₄	—	4	4	no	—
146	C₄⋊C₄	—	76	4	no	—
147	C₄⋊C₄	—	76	4	no	—
148	C₄⋊C₄	—	76	4	no	—
149	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
150	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
151	C₄²	Q₈×D₁₉	1	1	yes	characteristic
152	C₄²	Q₈×D₁₉	1	1	yes	characteristic
153	C₂³	#10597386	1	1	yes	characteristic
154	C₂×C₄	—	8	2	no	—
155	C₂×C₄	—	8	2	no	—
156	C₂×C₄	—	8	2	no	—
157	C₂×C₄	—	152	2	no	—
158	C₂×C₄	—	152	2	no	—
159	C₂×C₄	—	152	2	no	—
160	C₂×C₄	#10597334	1	1	yes	characteristic
161	C₂×C₄	#10597334	1	1	yes	characteristic
162	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
163	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
164	C₂×C₄	SD₁₆×D₁₉	1	4	yes	—
165	C₂×C₄	#10597362	1	4	yes	—
166	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
167	C₂×C₄	C₂×#64525	1	2	yes	—
168	C₂×C₄	C₂×#64528	1	2	yes	—
169	C₂×C₄	#10597390	1	1	yes	characteristic
170	C₈	—	19	8	no	—
171	C₈	—	38	4	no	—
172	C₈	#10597264	1	8	yes	complemented
173	C₂²	#11926413	1	1	yes	characteristic
174	C₂²	#11926915	1	2	yes	—
175	C₂²	#11926920	1	1	yes	characteristic
176	C₂²	#11926923	1	1	yes	characteristic
177	C₂²	#11926925	1	2	yes	—
178	C₄	—	16	2	no	—
179	C₄	—	304	2	no	—
180	C₄	#106×D₁₉	1	2	yes	—
181	C₄	C₂×#10597264	1	2	yes	—
182	C₄	#11926579	1	2	yes	—
183	C₄	#11926941	1	2	yes	—
184	C₄	#11926944	1	2	yes	—
185	C₄	#11926947	1	2	yes	—
186	C₂	#14563225	1	2	yes	—
187	C₂	#14563230	1	2	yes	—
188	C₂	#14563790	1	1	yes	characteristic
189	C₂	#14563794	1	1	yes	characteristic
190	C₂	#14563796	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#8814
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
12. C₈×C₁₉⋊C₈	C₄	semidirect
75. C₈×C₁₉	#107	semidirect
77. C₁₉⋊C₈	#106	semidirect
130. C₁₉	#8814	semidirect
172. C₈	#10597264	semidirect

Maximal subgroups

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

subgroup	index
#14563794	2
#14563792	2
#14563762	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1844	2
#8814	19