Subgroups — #18073780

Order 4864.

414 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563504	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	2	yes	maximal
5	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597260	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926299	—	2	2	no	—
11	#11926295	C₄	1	4	yes	complemented
12	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₁₉×#106	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#340	C₄	1	2	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	1	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
26	C₁₉×#106	—	2	4	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₁₉×#95	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
32	#10597260	—	4	4	no	—
33	C₄×C₁₉⋊C₈	—	2	1	no	—
34	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
37	C₂²×C₄×C₁₉	—	2	4	no	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
41	C₂×C₈×C₁₉	—	2	2	no	—
42	C₂×C₈×C₁₉	C₄²	1	2	yes	—
43	C₂×C₈×C₁₉	C₄²	1	2	yes	—
44	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
45	C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	4	2	no	—
48	C₄²×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	1	yes	characteristic
53	C₂×C₁₉⋊C₈	—	2	4	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	2	2	no	—
56	C₂×C₁₉⋊C₈	—	2	4	no	—
57	C₂×C₁₉⋊C₈	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
60	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
62	#8283	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	—	4	4	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
75	C₂×C₄×C₁₉	#131	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
77	C₂×C₄×C₁₉	#135	1	2	yes	—
78	C₈×C₁₉	—	2	2	no	—
79	C₈×C₁₉	#97	1	4	yes	complemented
80	C₁₉⋊C₈	—	2	4	no	—
81	C₁₉⋊C₈	—	2	2	no	—
82	C₁₉⋊C₈	—	4	4	no	—
83	C₁₉⋊C₈	#106	1	4	yes	complemented
84	C₄×#106	D₁₉	1	1	yes	characteristic
85	#1770	—	19	2	no	—
86	C₂×#334	—	19	1	no	—
87	C₂×C₈²	—	19	1	no	—
88	#1279	—	19	2	no	—
89	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₁₉	#436	1	2	yes	—
91	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
92	C₂²×C₁₉	#443	1	2	yes	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	8	4	no	—
96	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
97	C₄×C₁₉	#405	1	1	yes	characteristic
98	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
99	C₄×C₁₉	#427	1	1	yes	characteristic
100	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
101	C₄×C₁₉	#446	1	2	yes	—
102	C₂×#106	Dic₁₉	1	2	yes	—
103	C₂×C₄⋊C₈	—	19	2	no	—
104	C₂×#97	—	38	2	no	—
105	C₂×C₄×C₈	—	19	1	no	—
106	C₂×C₄×C₈	—	19	1	no	—
107	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
108	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
109	#340	Dic₁₉	1	2	yes	—
110	#336	—	38	2	no	—
111	#334	—	19	4	no	—
112	C₈²	—	19	4	no	—
113	C₂×C₁₉	#1590	1	4	yes	—
114	C₂×C₁₉	#1770	1	1	yes	characteristic
115	C₂×C₁₉	#1772	1	1	yes	characteristic
116	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
117	C₂²×C₈	—	19	1	no	—
118	C₂²×C₈	—	19	1	no	—
119	C₂²×C₈	—	38	1	no	—
120	C₂²×C₈	—	38	2	no	—
121	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
122	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
123	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
124	C₂×C₄²	—	2	2	no	—
125	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
126	#106	—	2	4	no	—
127	C₄⋊C₈	—	19	4	no	—
128	C₄⋊C₈	—	38	2	no	—
129	#97	—	76	4	no	—
130	C₄×C₈	—	19	2	no	—
131	C₄×C₈	—	19	2	no	—
132	C₄×C₈	—	19	2	no	—
133	C₄×C₈	—	38	1	no	—
134	C₄×C₈	C₄×D₁₉	1	2	yes	—
135	C₄×C₈	C₄×D₁₉	1	2	yes	—
136	#95	—	2	2	no	—
137	C₁₉	#8283	1	1	yes	characteristic, complemented, Sylow
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
140	C₂²×C₄	#64543	1	1	yes	characteristic
141	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	19	2	no	—
144	C₂×C₈	—	19	4	no	—
145	C₂×C₈	—	19	2	no	—
146	C₂×C₈	—	38	4	no	—
147	C₂×C₈	—	38	2	no	—
148	C₂×C₈	—	38	2	no	—
149	C₂×C₈	—	38	4	no	—
150	C₂×C₈	—	76	2	no	—
151	C₂×C₈	—	76	2	no	—
152	C₂×C₈	#64520	1	4	yes	—
153	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
154	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
155	C₄⋊C₄	—	2	4	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄²	—	4	2	no	—
158	C₄²	—	4	2	no	—
159	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
160	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₄²	Q₈×D₁₉	1	1	yes	characteristic
162	C₄²	#64545	1	1	yes	characteristic
163	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	4	4	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	#10597333	1	1	yes	characteristic
169	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
170	C₂×C₄	#10597338	1	1	yes	characteristic
171	C₂×C₄	#10597339	1	1	yes	characteristic
172	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
173	C₂×C₄	#10597362	1	2	yes	—
174	C₂×C₄	C₂×#64520	1	2	yes	—
175	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
177	C₂×C₄	#10597394	1	2	yes	—
178	C₈	—	2	2	no	—
179	C₈	—	19	4	no	—
180	C₈	—	38	4	no	—
181	C₈	—	38	2	no	—
182	C₈	—	76	4	no	—
183	C₈	#10597260	1	4	yes	complemented
184	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
185	C₂²	#11926622	1	2	yes	—
186	C₂²	SD₁₆×Dic₁₉	1	2	yes	—
187	C₂²	#11926661	1	2	yes	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	8	4	no	—
191	C₄	C₂×#10597260	1	1	yes	characteristic
192	C₄	#11926500	1	1	yes	characteristic
193	C₄	#106×D₁₉	1	1	yes	characteristic
194	C₄	#11926579	1	1	yes	characteristic
195	C₄	#11926631	1	2	yes	—
196	C₄	#11926675	1	2	yes	—
197	C₂	#14562526	1	4	yes	—
198	C₂	#14563504	1	1	yes	characteristic
199	C₂	#14563516	1	1	yes	characteristic
200	C₂	#106×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#106	D₁₉
hypocenter	C₁₉	#8283
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#106

Complements

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

N	H ≅ G/N	type
11. #11926295	C₄	semidirect
12. C₈×C₁₉⋊C₈	C₄	semidirect
79. C₈×C₁₉	#97	semidirect
83. C₁₉⋊C₈	#106	semidirect
137. C₁₉	#8283	semidirect
183. C₈	#10597260	semidirect

Maximal subgroups

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

subgroup	index
#14563504	2
C₂×#11926295	2
C₂×C₈×C₁₉⋊C₈	2
#14561476	2
C₄×C₁₉×#106	2
#8283	19