Subgroups — #18071908

Order 4864.

518 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563380	C₂	1	1	yes	maximal, characteristic
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	C₄×#10597272	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597272	C₄	1	4	yes	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926298	C₄	1	4	yes	—
14	#11926298	C₄	1	4	yes	—
15	#11926266	C₄	1	4	yes	complemented
16	#11926266	C₄	1	4	yes	complemented
17	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#322	C₄	1	4	yes	complemented
22	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	#10597272	—	2	8	no	—
39	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
40	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
43	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×Dic₁₉	C₄²	1	4	yes	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	C₄²	1	4	yes	—
53	C₂×C₈×C₁₉	C₄²	1	4	yes	—
54	C₂×C₈×C₁₉	C₄²	1	4	yes	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₄×Dic₁₉	—	2	4	no	—
60	C₄×Dic₁₉	—	2	4	no	—
61	C₄×Dic₁₉	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
65	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
66	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
67	C₂×C₁₉⋊C₈	M₁₆	1	8	yes	—
68	#7844	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
77	C₂×C₄×C₁₉	#131	1	4	yes	—
78	C₂×C₄×C₁₉	#131	1	4	yes	—
79	C₂×Dic₁₉	—	2	4	no	—
80	C₂×Dic₁₉	—	2	4	no	—
81	C₂×Dic₁₉	—	2	4	no	—
82	C₈×C₁₉	—	2	4	no	—
83	C₈×C₁₉	—	2	4	no	—
84	C₈×C₁₉	—	2	4	no	—
85	C₁₉⋊C₈	—	2	4	no	—
86	C₁₉⋊C₈	—	2	4	no	—
87	C₁₉⋊C₈	#97	1	8	yes	—
88	#1744	—	19	1	no	—
89	#1744	—	19	1	no	—
90	C₄×#97	—	19	1	no	—
91	C₂×#322	—	19	1	no	—
92	C₂×#322	—	19	1	no	—
93	C₂×#322	D₁₉	1	1	yes	characteristic
94	C₂×C₈²	—	19	1	no	—
95	C₂²×C₁₉	C₄³	1	1	yes	characteristic
96	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
97	C₂²×C₁₉	#405	1	2	yes	—
98	C₂²×C₁₉	#405	1	2	yes	—
99	C₄×C₁₉	C₂×#97	1	2	yes	—
100	C₄×C₁₉	C₄×M₁₆	1	2	yes	—
101	C₄×C₁₉	#405	1	2	yes	—
102	C₄×C₁₉	#405	1	2	yes	—
103	C₄×C₁₉	#405	1	2	yes	—
104	C₄×C₁₉	#405	1	2	yes	—
105	Dic₁₉	—	4	4	no	—
106	C₂×#97	—	19	4	no	—
107	C₂×C₄×C₈	—	19	1	no	—
108	C₂×C₄×C₈	—	19	1	no	—
109	C₂×C₄×C₈	—	19	1	no	—
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
113	C₄³	—	19	1	no	—
114	#336	—	19	4	no	—
115	#336	—	19	4	no	—
116	#322	—	19	4	no	—
117	#322	—	19	4	no	—
118	#322	Dic₁₉	1	4	yes	complemented
119	C₈²	—	19	4	no	—
120	C₂×C₁₉	#1453	1	4	yes	—
121	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
122	C₂×C₁₉	#1726	1	1	yes	characteristic
123	C₂×C₁₉	#1726	1	1	yes	characteristic
124	C₂²×C₈	—	19	2	no	—
125	C₂²×C₈	—	19	2	no	—
126	C₂²×C₈	—	19	2	no	—
127	C₂²×C₈	C₄×D₁₉	1	2	yes	—
128	C₂²×C₈	C₄×D₁₉	1	2	yes	—
129	C₂²×C₈	C₄×D₁₉	1	2	yes	—
130	C₂×C₄²	—	19	2	no	—
131	C₂×C₄²	—	19	2	no	—
132	C₂×C₄²	—	19	2	no	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	#97	—	38	8	no	—
135	C₄×C₈	—	19	2	no	—
136	C₄×C₈	—	19	2	no	—
137	C₄×C₈	—	19	2	no	—
138	C₄×C₈	—	19	2	no	—
139	C₄×C₈	—	19	2	no	—
140	C₄×C₈	—	19	2	no	—
141	C₄×C₈	C₄×D₁₉	1	2	yes	—
142	C₄×C₈	C₄×D₁₉	1	2	yes	—
143	C₄×C₈	C₄×D₁₉	1	2	yes	—
144	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
145	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
146	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
147	C₁₉	#7844	1	1	yes	characteristic, complemented, Sylow
148	C₂²×C₄	—	19	4	no	—
149	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	—	19	4	no	—
156	C₂×C₈	—	19	8	no	—
157	C₂×C₈	—	19	4	no	—
158	C₂×C₈	—	19	4	no	—
159	C₂×C₈	—	38	4	no	—
160	C₂×C₈	—	38	4	no	—
161	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
162	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
163	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
164	C₄²	—	38	4	no	—
165	C₄²	—	38	4	no	—
166	C₄²	—	38	4	no	—
167	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
168	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
169	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
170	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
171	C₂³	C₄²×D₁₉	1	1	yes	characteristic
172	C₂×C₄	—	38	4	no	—
173	C₂×C₄	—	38	4	no	—
174	C₂×C₄	—	38	4	no	—
175	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
176	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
177	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
178	C₂×C₄	#10597347	1	4	yes	—
179	C₂×C₄	M₁₆×D₁₉	1	4	yes	—
180	C₂×C₄	#10597353	1	4	yes	—
181	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
182	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
184	C₈	—	2	4	no	—
185	C₈	—	2	4	no	—
186	C₈	—	2	4	no	—
187	C₈	—	19	8	no	—
188	C₈	—	38	4	no	—
189	C₈	—	38	4	no	—
190	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
191	C₂²	#11926496	1	2	yes	—
192	C₂²	#11926498	1	2	yes	—
193	C₂²	#11926501	1	2	yes	—
194	C₄	—	76	4	no	—
195	C₄	#97×D₁₉	1	2	yes	—
196	C₄	M₁₆×Dic₁₉	1	2	yes	—
197	C₄	#11926498	1	2	yes	—
198	C₄	#11926499	1	2	yes	—
199	C₄	#11926501	1	2	yes	—
200	C₄	#11926502	1	2	yes	—
201	C₂	#14561931	1	4	yes	—
202	C₂	#97×Dic₁₉	1	1	yes	characteristic
203	C₂	#14563321	1	1	yes	characteristic
204	C₂	#14563323	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#7844
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
15. #11926266	C₄	semidirect
16. #11926266	C₄	semidirect
17. C₈×C₁₉⋊C₈	C₄	semidirect
21. C₁₉×#322	C₄	semidirect
118. #322	Dic₁₉	semidirect
147. C₁₉	#7844	semidirect

Maximal subgroups

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

subgroup	index
#14563380	2
C₄×#10597272	2
C₂×#11926266	2
C₂×C₈×C₁₉⋊C₈	2
C₂×C₁₉×#322	2
#7844	19