Subgroups — #18069407

Order 4864.

218 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	#14565391	C₂	1	1	yes	maximal, characteristic
2	#14561918	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926597	C₄	1	1	yes	characteristic
6	#11926597	C₄	1	1	yes	characteristic
7	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	C₄⋊(C₁₉⋊C₁₆)	C₄	1	2	yes	—
9	#11926265	—	2	1	no	—
10	C₈×C₁₉⋊C₈	—	2	1	no	—
11	C₂²×C₁₆×C₁₉	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₁₆	—	2	1	no	—
14	C₁₉×C₄⋊C₁₆	C₄	1	2	yes	—
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	—	2	2	no	—
19	C₂×C₁₆×C₁₉	—	4	1	no	—
20	C₂×C₁₆×C₁₉	—	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	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
26	C₂²⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
27	#10597269	—	4	1	no	—
28	#10597269	—	4	1	no	—
29	C₂×C₁₉⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
31	C₄⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
32	C₄×C₁₉⋊C₈	—	2	1	no	—
33	C₄×C₁₉⋊C₈	—	2	1	no	—
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	D₈	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	C₄²×C₁₉	C₄²	1	1	yes	characteristic
48	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
50	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₁₆×C₁₉	—	4	2	no	—
54	C₁₉⋊C₁₆	—	4	2	no	—
55	#7153	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
69	C₈×C₁₉	—	2	1	no	—
70	C₈×C₁₉	—	2	1	no	—
71	C₈×C₁₉	#102	1	1	yes	characteristic
72	C₈×C₁₉	#102	1	1	yes	characteristic
73	C₈×C₁₉	#103	1	1	yes	characteristic
74	C₈×C₁₉	#103	1	1	yes	characteristic
75	C₁₉⋊C₈	—	4	2	no	—
76	C₁₉⋊C₈	—	4	2	no	—
77	#2150	—	19	1	no	—
78	C₂×C₄⋊C₁₆	D₁₉	1	1	yes	characteristic
79	#1450	—	19	1	no	—
80	C₂²×C₁₉	—	2	1	no	—
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	#334	1	1	yes	characteristic
83	C₂²×C₁₉	#335	1	1	yes	characteristic
84	C₂²×C₁₉	#336	1	1	yes	characteristic
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	#334	1	1	yes	characteristic
89	C₄×C₁₉	#335	1	1	yes	characteristic
90	C₄×C₁₉	#340	1	1	yes	characteristic
91	C₄×C₁₉	#341	1	1	yes	characteristic
92	C₄×C₁₉	#350	1	2	yes	—
93	C₂×M₃₂	—	38	1	no	—
94	C₂²×C₁₆	—	2	1	no	—
95	#431	—	19	1	no	—
96	#431	—	19	1	no	—
97	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
98	C₄⋊C₁₆	—	2	1	no	—
99	C₄⋊C₁₆	—	19	2	no	—
100	C₄⋊C₁₆	—	38	1	no	—
101	C₄⋊C₁₆	Dic₁₉	1	2	yes	—
102	#322	—	38	1	no	—
103	C₈²	—	38	1	no	—
104	C₂×C₁₉	—	2	1	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	#1277	1	1	yes	characteristic
107	C₂×C₁₉	#1378	1	1	yes	characteristic
108	C₂×C₁₉	#1379	1	1	yes	characteristic
109	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
110	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
112	M₃₂	—	76	1	no	—
113	M₃₂	—	76	1	no	—
114	C₂×C₁₆	—	2	2	no	—
115	C₂×C₁₆	—	4	1	no	—
116	C₂×C₁₆	—	4	1	no	—
117	C₂×C₁₆	—	38	2	no	—
118	C₄⋊C₈	—	19	2	no	—
119	C₄⋊C₈	—	38	1	no	—
120	C₂²⋊C₈	—	19	2	no	—
121	C₂²⋊C₈	—	38	1	no	—
122	C₄×C₈	—	38	1	no	—
123	C₄×C₈	—	38	1	no	—
124	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
125	C₄×C₈	D₇₆	1	1	yes	characteristic
126	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
127	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₁₉	#7153	1	1	yes	characteristic, complemented, Sylow
129	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	#64515	1	1	yes	characteristic
131	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	2	1	no	—
134	C₂×C₈	—	38	2	no	—
135	C₂×C₈	—	38	2	no	—
136	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
137	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
138	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
139	C₂×C₈	#64525	1	1	yes	characteristic
140	C₂×C₈	#64526	1	1	yes	characteristic
141	C₂×C₈	#64527	1	1	yes	characteristic
142	C₂×C₈	#64528	1	1	yes	characteristic
143	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
144	C₄²	C₈×D₁₉	1	1	yes	characteristic
145	C₄²	#64515	1	1	yes	characteristic
146	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
147	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
148	C₁₆	—	4	2	no	—
149	C₁₆	—	76	2	no	—
150	C₂³	Dic₁₉⋊C₈	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	#10597264	1	1	yes	characteristic
154	C₂×C₄	#10597265	1	1	yes	characteristic
155	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
156	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
157	C₂×C₄	#10597272	1	1	yes	characteristic
158	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
159	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
160	C₂×C₄	#10597279	1	1	yes	characteristic
161	C₂×C₄	#10597279	1	1	yes	characteristic
162	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
163	C₈	—	2	1	no	—
164	C₈	—	2	1	no	—
165	C₈	—	76	2	no	—
166	C₈	—	76	2	no	—
167	C₈	#10597266	1	1	yes	characteristic
168	C₈	#10597267	1	1	yes	characteristic
169	C₈	#10597289	1	1	yes	characteristic
170	C₈	#10597292	1	1	yes	characteristic
171	C₂²	—	2	1	no	—
172	C₂²	—	2	1	no	—
173	C₂²	#11926294	1	1	yes	characteristic
174	C₂²	#11926296	1	1	yes	characteristic
175	C₂²	#11926298	1	1	yes	characteristic
176	C₄	—	2	1	no	—
177	C₄	—	2	1	no	—
178	C₄	—	2	1	no	—
179	C₄	#11926294	1	1	yes	characteristic
180	C₄	#11926296	1	1	yes	characteristic
181	C₄	#11926306	1	1	yes	characteristic
182	C₄	#11926308	1	1	yes	characteristic
183	C₄	#11926327	1	2	yes	—
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	#14561469	1	1	yes	characteristic
187	C₂	#14561722	1	1	yes	characteristic
188	C₂	#14561723	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×C₄⋊C₁₆	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×C₄⋊C₁₆	D₁₉
hypocenter	C₁₉	#7153
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
128. C₁₉	#7153	semidirect

Maximal subgroups

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

subgroup	index
#14565391	2
#14561918	2
C₂×C₁₉×C₄⋊C₁₆	2
#7153	19