Subgroups — #18069477

Order 4864.

274 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563514	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	C₄	1	1	yes	characteristic
5	#11926582	C₄	1	1	yes	characteristic
6	#11926499	—	2	1	no	—
7	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
8	#11926304	—	2	1	no	—
9	C₈×C₁₉⋊C₈	—	2	1	no	—
10	C₈×C₁₉⋊C₈	C₄	1	2	yes	complemented
11	C₂×C₁₉×M₃₂	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#364	—	2	1	no	—
14	C₁₉×#364	C₄	1	2	yes	complemented
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
18	#10597372	—	2	1	no	—
19	C₂×#64520	—	2	1	no	—
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	C₁₉×M₃₂	—	2	2	no	—
22	C₁₉×M₃₂	—	4	1	no	—
23	C₂×C₁₆×C₁₉	—	4	1	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
28	#10597276	—	2	1	no	—
29	#10597276	C₈	1	2	yes	complemented
30	#10597275	C₈	1	2	yes	complemented
31	#10597274	—	2	1	no	—
32	#10597272	—	4	1	no	—
33	C₈×Dic₁₉	—	4	1	no	—
34	C₄×C₁₉⋊C₈	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
44	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
47	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
50	C₄²×C₁₉	—	2	1	no	—
51	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₂²⋊Dic₁₉	—	4	1	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄×Dic₁₉	—	4	1	no	—
56	#64520	—	2	2	no	—
57	#64520	—	4	1	no	—
58	C₂×C₁₉⋊C₈	—	2	4	no	—
59	C₂×C₁₉⋊C₈	—	2	8	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	C₁₆×C₁₉	—	4	2	no	—
62	#7179	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#104	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
73	C₂×Dic₁₉	—	4	2	no	—
74	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
75	C₈×C₁₉	#97	1	1	yes	characteristic
76	C₈×C₁₉	#102	1	1	yes	characteristic
77	C₈×C₁₉	#103	1	1	yes	characteristic
78	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
79	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
80	C₈×C₁₉	#106	1	1	yes	characteristic
81	C₈×C₁₉	#107	1	1	yes	characteristic
82	C₁₉⋊C₈	—	2	8	no	—
83	C₁₉⋊C₈	—	4	2	no	—
84	C₂×#364	D₁₉	1	1	yes	characteristic
85	#1772	—	19	1	no	—
86	C₂×C₈²	—	19	1	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
89	C₂²×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
90	C₂²×C₁₉	#339	1	1	yes	characteristic
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
94	C₄×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
95	C₄×C₁₉	#336	1	1	yes	characteristic
96	C₄×C₁₉	#340	1	1	yes	characteristic
97	Dic₁₉	—	8	2	no	—
98	C₂×M₃₂	—	2	1	no	—
99	C₂×#108	—	19	1	no	—
100	#427	—	19	1	no	—
101	#405	—	38	1	no	—
102	C₂×C₄×C₈	—	38	1	no	—
103	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
104	#364	—	2	1	no	—
105	#364	Dic₁₉	1	2	yes	complemented
106	#339	—	38	1	no	—
107	C₈²	—	19	2	no	—
108	C₈²	—	38	1	no	—
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	—	2	1	no	—
111	C₂×C₁₉	#1279	1	1	yes	characteristic
112	C₂×C₁₉	#1335	1	2	yes	—
113	C₂×M₁₆	—	38	1	no	—
114	C₂²×C₈	—	38	2	no	—
115	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
116	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
117	#117	—	38	1	no	—
118	C₂×C₄²	D₇₆	1	1	yes	characteristic
119	M₃₂	—	2	2	no	—
120	M₃₂	—	4	1	no	—
121	C₂×C₁₆	—	4	1	no	—
122	#108	—	19	2	no	—
123	#108	—	38	1	no	—
124	#107	—	19	2	no	—
125	#106	—	38	1	no	—
126	#97	—	76	1	no	—
127	C₄×C₈	—	38	2	no	—
128	C₄×C₈	—	38	2	no	—
129	C₄×C₈	—	76	1	no	—
130	C₄×C₈	Dic₃₈	1	1	yes	characteristic
131	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
133	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
134	C₁₉	#7179	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
137	M₁₆	—	38	2	no	—
138	M₁₆	—	76	1	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	—	38	8	no	—
141	C₂×C₈	—	76	1	no	—
142	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
143	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
144	C₂×C₈	#64515	1	1	yes	characteristic
145	C₂×C₈	#64515	1	1	yes	characteristic
146	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
147	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
148	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
149	C₂×C₈	#64525	1	1	yes	characteristic
150	C₂×C₈	#64526	1	1	yes	characteristic
151	C₂×C₈	#64527	1	1	yes	characteristic
152	C₂×C₈	#64528	1	1	yes	characteristic
153	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
154	C₄⋊C₄	—	38	2	no	—
155	C₂²⋊C₄	—	76	1	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	76	1	no	—
158	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
159	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
160	C₁₆	—	4	2	no	—
161	C₂³	#10597282	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	76	2	no	—
166	C₂×C₄	#10597266	1	1	yes	characteristic
167	C₂×C₄	#10597267	1	1	yes	characteristic
168	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
169	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
170	C₂×C₄	#10597282	1	1	yes	characteristic
171	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
172	C₈	—	38	8	no	—
173	C₈	—	76	2	no	—
174	C₈	#10597264	1	1	yes	characteristic
175	C₈	#10597265	1	1	yes	characteristic
176	C₈	C₈×Dic₁₉	1	1	yes	characteristic
177	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
178	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
179	C₈	#10597272	1	1	yes	characteristic
180	C₈	#10597289	1	1	yes	characteristic
181	C₈	#10597292	1	1	yes	characteristic
182	C₂²	—	2	2	no	—
183	C₂²	#11926271	1	1	yes	characteristic
184	C₂²	#11926274	1	1	yes	characteristic
185	C₂²	#11926305	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	—	152	2	no	—
189	C₄	#11926271	1	1	yes	characteristic
190	C₄	#11926274	1	1	yes	characteristic
191	C₄	#11926298	1	1	yes	characteristic
192	C₄	#11926306	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	#14561474	1	1	yes	characteristic
196	C₂	#14561607	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	#64525
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#364	C₂
socle	C₂²×C₁₉	D₄⋊C₈
prime radical	C₂³×C₁₉	#104
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#364	D₁₉
hypocenter	C₁₉	#7179
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
10. C₈×C₁₉⋊C₈	C₄	semidirect
14. C₁₉×#364	C₄	semidirect
29. #10597276	C₈	semidirect
30. #10597275	C₈	semidirect
105. #364	Dic₁₉	semidirect
134. C₁₉	#7179	semidirect

Maximal subgroups

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

subgroup	index
#14563514	2
C₂×C₈×C₁₉⋊C₈	2
C₂×C₁₉×#364	2
#7179	19