Subgroups — #18075387

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	2	yes	maximal, complemented
3	#14561470	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926295	—	2	4	no	—
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#431	—	2	4	no	—
11	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	—	2	4	no	—
27	C₁₉×C₄⋊C₈	—	2	4	no	—
28	C₁₉×C₂²⋊C₈	—	2	4	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	C₄×C₈×C₁₉	D₄	1	4	yes	—
31	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
34	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	—	2	1	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₄²×C₁₉	—	2	1	no	—
54	C₄²×C₁₉	—	2	1	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₂×C₁₉⋊C₈	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	#8598	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	—	2	1	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	—	2	1	no	—
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	#106	1	2	yes	—
68	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	8	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	#106	1	2	yes	—
81	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₁₉	#131	1	4	yes	—
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
87	C₂×C₄×C₁₉	#135	1	2	yes	—
88	C₈×C₁₉	—	2	4	no	—
89	C₈×C₁₉	—	4	2	no	—
90	C₁₉⋊C₈	—	8	4	no	—
91	C₂×#431	D₁₉	1	1	yes	characteristic
92	#1797	—	19	2	no	—
93	C₂×#334	—	19	2	no	—
94	#1277	—	19	2	no	—
95	C₂²×C₁₉	—	2	2	no	—
96	C₂²×C₁₉	—	2	4	no	—
97	C₂²×C₁₉	—	4	1	no	—
98	C₂²×C₁₉	—	4	1	no	—
99	C₂²×C₁₉	—	4	2	no	—
100	C₂²×C₁₉	#380	1	1	yes	characteristic
101	C₂²×C₁₉	#424	1	2	yes	—
102	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
103	C₂²×C₁₉	#427	1	1	yes	characteristic
104	C₂²×C₁₉	#430	1	2	yes	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	4	1	no	—
108	C₄×C₁₉	—	4	1	no	—
109	C₄×C₁₉	#408	1	2	yes	—
110	C₄×C₁₉	#433	1	2	yes	—
111	C₄×C₁₉	#465	1	4	yes	—
112	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
113	#431	—	2	4	no	—
114	C₂×C₄⋊C₈	—	19	4	no	—
115	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
116	C₂×C₂²⋊C₈	—	38	2	no	—
117	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
118	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
120	#336	—	38	2	no	—
121	#334	—	38	4	no	—
122	C₂×C₁₉	—	4	2	no	—
123	C₂×C₁₉	#1570	1	2	yes	—
124	C₂×C₁₉	#1572	1	2	yes	—
125	C₂×C₁₉	#1798	1	1	yes	characteristic
126	C₂×C₁₉	#1807	1	1	yes	characteristic
127	C₂×C₁₉	#1811	1	1	yes	characteristic
128	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
129	C₂³×C₄	D₇₆	1	1	yes	characteristic
130	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
131	C₂²×C₈	—	38	4	no	—
132	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
133	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
134	C₂×C₄²	—	2	2	no	—
135	C₂×C₄²	—	2	2	no	—
136	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
137	C₂×C₄²	D₇₆	1	1	yes	characteristic
138	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	2	4	no	—
141	C₄⋊C₈	—	38	4	no	—
142	C₄⋊C₈	—	38	4	no	—
143	C₂²⋊C₈	—	2	4	no	—
144	C₂²⋊C₈	—	76	4	no	—
145	C₄×C₈	—	2	2	no	—
146	C₄×C₈	C₂²⋊D₁₉	1	4	yes	—
147	C₁₉	#8598	1	1	yes	characteristic, complemented, Sylow
148	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	—	2	1	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	1	no	—
155	C₂²×C₄	—	4	2	no	—
156	C₂²×C₄	#64516	1	4	yes	—
157	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
159	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
160	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
161	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
162	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	—	2	4	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	76	4	no	—
167	C₂×C₈	—	76	4	no	—
168	C₂×C₈	—	76	4	no	—
169	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
170	C₄²	—	2	2	no	—
171	C₄²	—	2	1	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	1	no	—
174	C₄²	#64541	1	2	yes	—
175	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	1	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	1	no	—
180	C₂³	#10597274	1	2	yes	—
181	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	8	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	#10597274	1	2	yes	—
194	C₂×C₄	C₂×#64516	1	2	yes	—
195	C₂×C₄	#10597350	1	2	yes	—
196	C₂×C₄	#10597370	1	2	yes	—
197	C₂×C₄	#10597372	1	1	yes	characteristic
198	C₂×C₄	#10597376	1	2	yes	—
199	C₂×C₄	#10597394	1	4	yes	—
200	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
201	C₈	—	2	4	no	—
202	C₈	—	4	2	no	—
203	C₈	—	152	4	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	4	no	—
206	C₂²	—	4	1	no	—
207	C₂²	—	4	1	no	—
208	C₂²	—	4	2	no	—
209	C₂²	#11926404	1	1	yes	characteristic
210	C₂²	#11926571	1	2	yes	—
211	C₂²	C₂×#10597274	1	1	yes	characteristic
212	C₂²	#11926582	1	1	yes	characteristic
213	C₂²	#11926593	1	2	yes	—
214	C₄	—	2	2	no	—
215	C₄	—	2	2	no	—
216	C₄	—	4	1	no	—
217	C₄	—	4	1	no	—
218	C₄	#11926511	1	2	yes	—
219	C₄	#11926605	1	2	yes	—
220	C₄	#11926773	1	4	yes	—
221	C₂	—	4	2	no	—
222	C₂	#14562406	1	2	yes	—
223	C₂	#14562415	1	2	yes	—
224	C₂	#14563619	1	1	yes	characteristic
225	C₂	#14563660	1	1	yes	characteristic
226	C₂	#14563677	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#431	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#431	D₁₉
hypocenter	C₁₉	#8598
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. C₂×#11926295	C₂	semidirect
3. #14561470	C₂	semidirect
147. C₁₉	#8598	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₂×#11926295	2
#14561470	2
C₂×C₁₉×#431	2
#8598	19