Subgroups — #18072687

Order 4864.

524 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926601	C₂	1	2	yes	maximal
2	#14561522	C₂	1	4	yes	maximal
3	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
4	#11926601	—	2	2	no	—
5	#11926601	—	2	2	no	—
6	#11926601	C₄	1	4	yes	—
7	#11926601	C₄	1	4	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
10	C₂×#10597260	—	2	2	no	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#432	—	2	2	no	—
13	C₁₉×#431	—	2	2	no	—
14	C₁₉×#423	C₄	1	2	yes	—
15	C₁₉×#407	C₂²	1	2	yes	—
16	C₄×M₁₆×C₁₉	C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	2	4	no	—
29	C₁₉×C₂²⋊C₈	—	2	4	no	—
30	C₁₉×#97	—	2	2	no	—
31	C₄×C₈×C₁₉	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
33	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
34	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	#10597260	—	2	4	no	—
37	#10597260	—	2	4	no	—
38	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	—	4	2	no	—
40	C₂²×C₄×C₁₉	—	4	4	no	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	M₁₆×C₁₉	—	4	4	no	—
52	C₂×C₈×C₁₉	—	2	4	no	—
53	C₄²×C₁₉	C₄²	1	2	yes	—
54	C₄²×C₁₉	C₄²	1	1	yes	characteristic
55	C₄²×C₁₉	C₄²	1	1	yes	characteristic
56	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₁₉⋊C₈	—	2	8	no	—
64	C₂×C₁₉⋊C₈	—	4	8	no	—
65	#8056	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	—	2	4	no	—
67	C₂³×C₁₉	—	4	1	no	—
68	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
69	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	2	4	no	—
72	C₂×C₄×C₁₉	—	2	4	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	#95	1	2	yes	—
81	C₂×C₄×C₁₉	#95	1	2	yes	—
82	C₂×C₄×C₁₉	#95	1	2	yes	—
83	C₂×C₄×C₁₉	#95	1	2	yes	—
84	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
87	C₈×C₁₉	—	4	4	no	—
88	C₁₉⋊C₈	—	4	8	no	—
89	#2920	D₁₉	1	1	yes	characteristic
90	C₂×#432	—	19	2	no	—
91	#1298	—	19	4	no	—
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	—	2	1	no	—
96	C₂²×C₁₉	—	4	4	no	—
97	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
98	C₂²×C₁₉	#430	1	4	yes	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	#410	1	2	yes	—
106	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
107	#432	—	2	2	no	—
108	#432	—	19	4	no	—
109	#432	—	19	4	no	—
110	#432	—	38	2	no	—
111	#432	—	38	2	no	—
112	#431	—	2	2	no	—
113	#423	Dic₁₉	1	2	yes	—
114	C₂×C₄⋊C₈	—	38	2	no	—
115	#407	C₂×D₁₉	1	2	yes	—
116	C₂×C₂²⋊C₈	—	19	4	no	—
117	C₄×M₁₆	Dic₁₉	1	2	yes	—
118	C₂×#97	—	38	2	no	—
119	C₂×C₁₉	—	2	4	no	—
120	C₂×C₁₉	—	4	1	no	—
121	C₂×C₁₉	#1738	1	2	yes	—
122	C₂×C₁₉	#1740	1	1	yes	characteristic
123	C₂³×C₄	Dic₃₈	1	2	yes	—
124	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
125	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
126	C₂²×C₈	—	38	4	no	—
127	C₂×C₄²	C₄×D₁₉	1	2	yes	—
128	C₂×C₄²	C₄×D₁₉	1	2	yes	—
129	C₂×C₄²	D₇₆	1	2	yes	—
130	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
131	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
132	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
133	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
134	C₄⋊C₈	—	2	4	no	—
135	C₄⋊C₈	—	38	4	no	—
136	C₄⋊C₈	—	38	4	no	—
137	C₂²⋊C₈	—	2	4	no	—
138	C₂²⋊C₈	—	19	8	no	—
139	C₂²⋊C₈	—	38	4	no	—
140	#97	—	2	2	no	—
141	#97	—	38	4	no	—
142	#97	—	38	4	no	—
143	C₄×C₈	—	2	2	no	—
144	C₁₉	#8056	1	1	yes	characteristic, complemented, Sylow
145	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	4	no	—
148	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
149	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
150	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
151	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
152	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
153	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
154	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
155	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
156	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
158	M₁₆	—	4	4	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	38	8	no	—
161	C₂×C₈	—	76	8	no	—
162	C₄²	C₄×Dic₁₉	1	2	yes	—
163	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
164	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
165	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
166	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
167	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
168	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
169	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
170	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
171	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
172	C₂³	—	2	4	no	—
173	C₂³	—	4	1	no	—
174	C₂³	C₂×Dic₁₉⋊C₄	1	2	yes	—
175	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	1	no	—
186	C₂×C₄	C₁₉⋊#95	1	2	yes	—
187	C₂×C₄	C₁₉⋊#95	1	2	yes	—
188	C₂×C₄	C₁₉⋊#95	1	2	yes	—
189	C₂×C₄	C₁₉⋊#95	1	2	yes	—
190	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
191	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
192	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
193	C₈	—	4	4	no	—
194	C₈	—	76	8	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	4	4	no	—
200	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
201	C₂²	#11926592	1	4	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	—	2	1	no	—
208	C₄	#11926518	1	2	yes	—
209	C₂	—	2	4	no	—
210	C₂	—	4	1	no	—
211	C₂	#14563361	1	2	yes	—
212	C₂	#14563368	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2920	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2920	D₁₉
hypocenter	C₁₉	#8056
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
144. C₁₉	#8056	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926601	2
#14561522	2
C₁₉×#2920	2
#8056	19