Subgroups — #18081617

Order 4864.

486 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926293	C₂	1	2	yes	maximal
4	C₂×#11926290	C₂	1	2	yes	maximal
5	C₁₉×#2862	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×#10597260	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926293	—	2	4	no	—
12	#11926290	—	2	4	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#391	—	2	2	no	—
16	C₁₉×#391	C₄	1	4	yes	—
17	C₁₉×#382	—	2	1	no	—
18	C₁₉×#382	—	2	1	no	—
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₁₉⋊C₈	—	2	2	no	—
37	C₁₉×#95	—	2	4	no	—
38	C₁₉×#95	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
44	#10597260	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	2	4	no	—
46	C₂×Q₈×C₁₉	—	4	4	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	SD₁₆	1	2	yes	—
68	C₄²×C₁₉	Q₁₆	1	2	yes	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	#41	1	2	yes	—
71	C₂×C₁₉⋊C₈	—	2	4	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	4	no	—
76	#9701	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Q₈×C₁₉	—	8	4	no	—
79	Q₈×C₁₉	—	8	2	no	—
80	Q₈×C₁₉	—	8	1	no	—
81	Q₈×C₁₉	—	8	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	#103	1	4	yes	—
93	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₉	#121	1	2	yes	—
95	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₂×C₄×C₁₉	#137	1	2	yes	—
101	C₂×C₄×C₁₉	#137	1	2	yes	—
102	C₁₉⋊C₈	—	4	4	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	#2862	D₁₉	1	1	yes	characteristic
105	#1842	—	19	1	no	—
106	#1767	—	19	1	no	—
107	C₂×#333	—	19	2	no	—
108	C₂×#332	—	19	2	no	—
109	C₂²×C₁₉	#390	1	1	yes	characteristic
110	C₂²×C₁₉	#413	1	2	yes	—
111	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
112	C₂²×C₁₉	#417	1	2	yes	—
113	C₂²×C₁₉	#419	1	1	yes	characteristic
114	C₄×C₁₉	—	2	4	no	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	—	8	2	no	—
118	C₄×C₁₉	—	8	2	no	—
119	C₄×C₁₉	#461	1	2	yes	—
120	C₄×C₁₉	#462	1	2	yes	—
121	C₄×C₁₉	#489	1	2	yes	—
122	C₄×C₁₉	#496	1	1	yes	characteristic
123	C₄×C₁₉	#497	1	1	yes	characteristic
124	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	19	2	no	—
127	C₂×C₄⋊C₈	—	19	2	no	—
128	C₂×C₄⋊C₈	—	38	2	no	—
129	C₂×#97	—	38	1	no	—
130	#391	—	2	2	no	—
131	#391	Dic₁₉	1	4	yes	—
132	#382	—	2	1	no	—
133	#382	—	2	1	no	—
134	C₄³	C₂×D₁₉	1	1	yes	characteristic
135	#336	—	38	1	no	—
136	#333	—	38	4	no	—
137	#332	—	38	4	no	—
138	C₂×C₁₉	#1550	1	2	yes	—
139	C₂×C₁₉	#1559	1	2	yes	—
140	C₂×C₁₉	#1959	1	1	yes	characteristic
141	C₂×C₁₉	#1967	1	1	yes	characteristic
142	C₂×C₁₉	#1981	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
145	C₂²×C₈	—	38	2	no	—
146	C₂²×C₈	—	38	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
155	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
156	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
158	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
159	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
160	C₄⋊C₈	—	19	4	no	—
161	C₄⋊C₈	—	38	2	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	—	38	2	no	—
164	C₄⋊C₈	—	76	4	no	—
165	#97	—	76	2	no	—
166	#95	—	2	4	no	—
167	#95	—	2	4	no	—
168	C₁₉	#9701	1	1	yes	characteristic, complemented, Sylow
169	C₂×Q₈	—	2	4	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×Q₈	—	4	1	no	—
172	C₂×Q₈	—	4	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂×Q₈	—	4	2	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
178	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
179	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
182	C₂×C₈	—	38	4	no	—
183	C₂×C₈	—	76	2	no	—
184	C₂×C₈	—	76	2	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	—	76	4	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	2	2	no	—
194	C₄²	—	2	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	#64527	1	2	yes	—
197	C₄²	#64528	1	2	yes	—
198	C₄²	D₄×D₁₉	1	2	yes	—
199	C₄²	#64543	1	2	yes	—
200	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
201	Q₈	—	8	4	no	—
202	Q₈	—	8	2	no	—
203	Q₈	—	8	1	no	—
204	Q₈	—	8	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	#10597292	1	4	yes	—
216	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
217	C₂×C₄	#10597382	1	1	yes	characteristic
218	C₂×C₄	#10597384	1	2	yes	—
219	C₂×C₄	#10597386	1	1	yes	characteristic
220	C₂×C₄	C₂×#64527	1	1	yes	characteristic
221	C₂×C₄	#10597388	1	2	yes	—
222	C₂×C₄	C₂×#64528	1	1	yes	characteristic
223	C₂×C₄	#10597395	1	2	yes	—
224	C₂×C₄	#10597397	1	2	yes	—
225	C₈	—	76	4	no	—
226	C₈	—	152	2	no	—
227	C₂²	#11926447	1	1	yes	characteristic
228	C₂²	#11926528	1	2	yes	—
229	C₂²	C₂×#10597292	1	1	yes	characteristic
230	C₂²	#11926545	1	2	yes	—
231	C₂²	#11926553	1	1	yes	characteristic
232	C₄	—	2	4	no	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	2	no	—
236	C₄	—	8	2	no	—
237	C₄	#11926746	1	2	yes	—
238	C₄	#11926751	1	2	yes	—
239	C₄	#11926903	1	2	yes	—
240	C₄	#11926934	1	1	yes	characteristic
241	C₄	#11926939	1	1	yes	characteristic
242	C₂	#14562325	1	2	yes	—
243	C₂	#14562365	1	2	yes	—
244	C₂	#14564452	1	1	yes	characteristic
245	C₂	#14564485	1	1	yes	characteristic
246	C₂	#14564559	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2862	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2862	D₁₉
hypocenter	C₁₉	#9701
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

Complements

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

N	H ≅ G/N	type
168. C₁₉	#9701	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
#14563488	2
C₂×#11926293	2
C₂×#11926290	2
C₁₉×#2862	2
#9701	19