Subgroups — #18069736

Order 4864.

246 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14565391	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926597	—	2	1	no	—
6	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	C₄⋊(C₁₉⋊C₁₆)	C₄	1	2	yes	complemented
8	#11926297	C₄	1	2	yes	complemented
9	#11926295	—	2	1	no	—
10	C₂×C₁₉×#106	—	2	1	no	—
11	C₂×C₁₉×#106	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#384	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
18	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₁₉×#106	—	4	1	no	—
21	C₁₉×#106	—	4	1	no	—
22	C₁₉×#106	—	4	2	no	—
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
27	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
28	#10597269	—	4	1	no	—
29	#10597269	—	4	1	no	—
30	C₂×C₁₉⋊C₁₆	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	4	1	no	—
33	C₂²×C₄×C₁₉	—	4	2	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
44	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	8	2	no	—
50	C₄⋊C₄×C₁₉	—	8	2	no	—
51	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
54	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
55	C₂×C₁₉⋊C₈	—	4	2	no	—
56	C₁₉⋊C₁₆	—	4	2	no	—
57	#7278	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	#102	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	8	2	no	—
62	C₂×C₄×C₁₉	—	8	2	no	—
63	C₂×C₄×C₁₉	—	8	2	no	—
64	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
74	C₈×C₁₉	—	2	1	no	—
75	C₈×C₁₉	—	2	1	no	—
76	C₈×C₁₉	#102	1	1	yes	characteristic
77	C₈×C₁₉	#103	1	1	yes	characteristic
78	C₈×C₁₉	#106	1	1	yes	characteristic
79	C₈×C₁₉	#107	1	1	yes	characteristic
80	C₁₉⋊C₈	—	8	2	no	—
81	#2150	—	19	1	no	—
82	#1844	D₁₉	1	1	yes	characteristic
83	#1564	—	19	1	no	—
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	#331	1	1	yes	characteristic
87	C₂²×C₁₉	#332	1	1	yes	characteristic
88	C₂²×C₁₉	#340	1	1	yes	characteristic
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	—	16	2	no	—
92	C₄×C₁₉	#332	1	1	yes	characteristic
93	C₄×C₁₉	#333	1	1	yes	characteristic
94	C₄×C₁₉	#340	1	1	yes	characteristic
95	C₄×C₁₉	#343	1	1	yes	characteristic
96	C₄×C₁₉	#360	1	2	yes	—
97	C₄×C₁₉	#365	1	2	yes	—
98	C₂×M₃₂	—	38	1	no	—
99	#431	—	38	1	no	—
100	C₂×#106	—	2	1	no	—
101	C₂×#106	Dic₁₉	1	2	yes	—
102	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
103	#384	—	2	1	no	—
104	C₄⋊C₁₆	—	19	2	no	—
105	C₄⋊C₁₆	—	38	1	no	—
106	#335	—	19	2	no	—
107	#334	—	38	1	no	—
108	C₂×C₁₉	—	2	1	no	—
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	#1296	1	1	yes	characteristic
111	C₂×C₁₉	#1383	1	1	yes	characteristic
112	C₂×C₁₉	#1386	1	1	yes	characteristic
113	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
114	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄⋊C₄	—	4	1	no	—
117	C₂×C₄⋊C₄	—	4	1	no	—
118	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
119	M₃₂	—	76	1	no	—
120	M₃₂	—	76	1	no	—
121	C₂×C₁₆	—	38	2	no	—
122	#106	—	4	1	no	—
123	#106	—	4	1	no	—
124	#106	—	4	2	no	—
125	C₄⋊C₈	—	38	2	no	—
126	C₂²⋊C₈	—	76	1	no	—
127	C₄×C₈	—	76	1	no	—
128	C₄×C₈	Dic₃₈	1	1	yes	characteristic
129	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
130	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
131	C₄×C₈	D₇₆	1	1	yes	characteristic
132	C₁₉	#7278	1	1	yes	characteristic, complemented, Sylow
133	C₂²×C₄	—	4	2	no	—
134	C₂²×C₄	#64525	1	1	yes	characteristic
135	C₂²×C₄	#64526	1	1	yes	characteristic
136	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	—	76	2	no	—
140	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
141	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
142	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
143	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
144	C₂×C₈	#64525	1	1	yes	characteristic
145	C₂×C₈	#64526	1	1	yes	characteristic
146	C₂×C₈	#64527	1	1	yes	characteristic
147	C₂×C₈	#64528	1	1	yes	characteristic
148	C₄⋊C₄	—	4	2	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	8	2	no	—
151	C₄⋊C₄	—	8	2	no	—
152	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
153	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
154	C₄²	#64527	1	1	yes	characteristic
155	C₄²	#64528	1	1	yes	characteristic
156	C₁₆	—	76	2	no	—
157	C₂³	#10597289	1	1	yes	characteristic
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	—	8	2	no	—
162	C₂×C₄	—	8	2	no	—
163	C₂×C₄	#10597264	1	1	yes	characteristic
164	C₂×C₄	#10597265	1	1	yes	characteristic
165	C₂×C₄	#10597266	1	1	yes	characteristic
166	C₂×C₄	#10597267	1	1	yes	characteristic
167	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
168	C₂×C₄	#10597289	1	1	yes	characteristic
169	C₂×C₄	#10597290	1	1	yes	characteristic
170	C₂×C₄	#10597292	1	1	yes	characteristic
171	C₂×C₄	#10597292	1	1	yes	characteristic
172	C₂×C₄	#10597293	1	1	yes	characteristic
173	C₈	—	2	1	no	—
174	C₈	—	2	1	no	—
175	C₈	—	152	2	no	—
176	C₈	#10597264	1	1	yes	characteristic
177	C₈	#10597265	1	1	yes	characteristic
178	C₈	#10597266	1	1	yes	characteristic
179	C₈	#10597267	1	1	yes	characteristic
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	#11926288	1	1	yes	characteristic
183	C₂²	#11926290	1	1	yes	characteristic
184	C₂²	#11926306	1	1	yes	characteristic
185	C₄	—	2	1	no	—
186	C₄	—	2	1	no	—
187	C₄	—	16	2	no	—
188	C₄	#11926290	1	1	yes	characteristic
189	C₄	#11926293	1	1	yes	characteristic
190	C₄	#11926306	1	1	yes	characteristic
191	C₄	#11926313	1	1	yes	characteristic
192	C₄	#11926353	1	2	yes	—
193	C₄	#11926366	1	2	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	#14561518	1	1	yes	characteristic
197	C₂	#14561733	1	1	yes	characteristic
198	C₂	#14561742	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926306
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1844	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#7278
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1844

Complements

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

N	H ≅ G/N	type
7. C₄⋊(C₁₉⋊C₁₆)	C₄	semidirect
8. #11926297	C₄	semidirect
132. C₁₉	#7278	semidirect

Maximal subgroups

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

subgroup	index
#14565391	2
#14562383	2
C₁₉×#1844	2
#7278	19