Subgroups — #18076189

Order 4864.

310 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562383	C₂	1	2	yes	maximal
2	#14561480	C₂	1	2	yes	maximal
3	#14561464	C₂	1	2	yes	maximal
4	C₁₉×#1726	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	—	2	2	no	—
7	#11926295	—	2	2	no	—
8	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
9	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
10	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#376	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₁₉×#97	—	2	2	no	—
23	C₁₉×#97	—	2	2	no	—
24	C₁₉×#97	C₈	1	4	yes	complemented
25	C₄×C₈×C₁₉	—	2	2	no	—
26	C₄×C₈×C₁₉	—	2	2	no	—
27	C₄×C₈×C₁₉	D₄	1	2	yes	—
28	C₄×C₈×C₁₉	Q₈	1	2	yes	—
29	C₁₉×#95	—	2	2	no	—
30	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
32	C₄×C₁₉⋊C₈	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	#41	1	2	yes	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
49	C₄²×C₁₉	—	2	1	no	—
50	C₄²×C₁₉	—	2	1	no	—
51	C₄²×C₁₉	C₂×C₈	1	2	yes	—
52	C₄²×C₁₉	M₁₆	1	2	yes	—
53	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₄²×C₁₉	#41	1	2	yes	—
56	C₂×C₁₉⋊C₈	—	4	4	no	—
57	#8781	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	#117	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	4	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#124	1	2	yes	—
67	C₂×C₄×C₁₉	#125	1	2	yes	—
68	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
72	C₈×C₁₉	—	2	2	no	—
73	C₈×C₁₉	—	2	2	no	—
74	C₈×C₁₉	—	2	2	no	—
75	C₈×C₁₉	C₄⋊C₈	1	4	yes	—
76	C₁₉⋊C₈	—	8	4	no	—
77	#1726	D₁₉	1	1	yes	characteristic
78	#1564	—	19	2	no	—
79	#1281	—	19	2	no	—
80	#1274	—	19	2	no	—
81	C₂²×C₁₉	—	2	2	no	—
82	C₂²×C₁₉	#382	1	1	yes	characteristic
83	C₂²×C₁₉	#431	1	1	yes	characteristic
84	C₂²×C₁₉	#432	1	1	yes	characteristic
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	4	2	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
90	C₄×C₁₉	#423	1	1	yes	characteristic
91	C₄×C₁₉	#431	1	1	yes	characteristic
92	C₄×C₁₉	#432	1	1	yes	characteristic
93	#431	—	19	4	no	—
94	C₂×#97	Dic₁₉	1	1	yes	characteristic
95	C₂×#97	Dic₁₉	1	1	yes	characteristic
96	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
97	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
98	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	#376	C₂×D₁₉	1	1	yes	characteristic
101	#335	—	38	2	no	—
102	#334	—	38	2	no	—
103	C₂×C₁₉	—	2	1	no	—
104	C₂×C₁₉	—	2	1	no	—
105	C₂×C₁₉	#1831	1	1	yes	characteristic
106	C₂×C₁₉	#1833	1	2	yes	—
107	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
108	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
109	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
110	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
111	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
112	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
113	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	C₄⋊C₈	—	38	4	no	—
115	C₂²⋊C₈	—	38	4	no	—
116	#97	—	2	2	no	—
117	#97	—	2	2	no	—
118	#97	C₁₉⋊C₈	1	4	yes	complemented
119	C₄×C₈	—	2	2	no	—
120	C₄×C₈	—	2	2	no	—
121	C₄×C₈	—	38	4	no	—
122	C₄×C₈	Dic₃₈	1	2	yes	—
123	C₄×C₈	D₇₆	1	2	yes	—
124	#95	—	2	2	no	—
125	C₁₉	#8781	1	1	yes	characteristic, complemented, Sylow
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	—	2	1	no	—
128	C₂²×C₄	#64541	1	2	yes	—
129	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	2	1	no	—
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	76	4	no	—
137	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
138	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
139	C₂×C₈	#64520	1	2	yes	—
140	C₂×C₈	#64520	1	2	yes	—
141	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
142	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
143	C₄²	—	2	1	no	—
144	C₄²	—	2	1	no	—
145	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
146	C₄²	#64520	1	2	yes	—
147	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
148	C₄²	C₂×D₇₆	1	1	yes	characteristic
149	C₄²	#64541	1	2	yes	—
150	C₂³	#10597372	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	#10597316	1	2	yes	—
157	C₂×C₄	#10597321	1	2	yes	—
158	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
159	C₂×C₄	C₂×#64520	1	1	yes	characteristic
160	C₂×C₄	C₂×#64520	1	1	yes	characteristic
161	C₂×C₄	C₂×#64520	1	1	yes	characteristic
162	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
163	C₂×C₄	#10597372	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	2	2	no	—
166	C₈	—	2	2	no	—
167	C₈	—	152	4	no	—
168	C₈	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
169	C₂²	—	2	2	no	—
170	C₂²	#11926410	1	1	yes	characteristic
171	C₂²	#11926597	1	1	yes	characteristic
172	C₂²	#11926601	1	1	yes	characteristic
173	C₄	—	2	2	no	—
174	C₄	—	2	2	no	—
175	C₄	—	4	2	no	—
176	C₄	—	4	2	no	—
177	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
178	C₄	#11926568	1	1	yes	characteristic
179	C₄	#11926597	1	1	yes	characteristic
180	C₄	#11926601	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	#14563752	1	1	yes	characteristic
184	C₂	#14563759	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1726	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1726	D₁₉
hypocenter	C₁₉	#8781
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1726

Complements

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

N	H ≅ G/N	type
24. C₁₉×#97	C₈	semidirect
118. #97	C₁₉⋊C₈	semidirect
125. C₁₉	#8781	semidirect

Maximal subgroups

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

subgroup	index
#14562383	2
#14561480	2
#14561464	2
C₁₉×#1726	2
#8781	19