Subgroups — #18081579

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563752	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	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)	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
9	#11926299	—	2	1	no	—
10	#11926299	—	2	2	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)	D₄	1	4	yes	—
43	C₄×C₁₉⋊C₈	—	4	2	no	—
44	C₂×Q₈×C₁₉	—	2	4	no	—
45	C₂×Q₈×C₁₉	—	4	4	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	—	4	4	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	—	2	4	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	4	2	no	—
64	C₄²×C₁₉	SD₁₆	1	2	yes	—
65	C₄²×C₁₉	Q₁₆	1	2	yes	—
66	C₄²×C₁₉	C₂×D₄	1	2	yes	—
67	C₄²×C₁₉	#41	1	2	yes	—
68	C₂×C₁₉⋊C₈	—	2	4	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	#9693	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₁₉	—	8	4	no	—
76	Q₈×C₁₉	—	8	2	no	—
77	Q₈×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	#103	1	4	yes	—
89	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₁₉	#121	1	2	yes	—
91	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	4	yes	—
96	C₂×C₄×C₁₉	#137	1	2	yes	—
97	C₁₉⋊C₈	—	4	4	no	—
98	C₁₉⋊C₈	—	8	2	no	—
99	#2862	D₁₉	1	1	yes	characteristic
100	#1831	—	19	1	no	—
101	C₄×C₄⋊C₈	—	19	1	no	—
102	C₂×#333	—	19	2	no	—
103	C₂×#332	—	19	2	no	—
104	C₂²×C₁₉	#390	1	1	yes	characteristic
105	C₂²×C₁₉	#413	1	2	yes	—
106	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
107	C₂²×C₁₉	#416	1	2	yes	—
108	C₂²×C₁₉	#419	1	1	yes	characteristic
109	C₄×C₁₉	—	2	4	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	—	8	2	no	—
113	C₄×C₁₉	—	8	2	no	—
114	C₄×C₁₉	#461	1	2	yes	—
115	C₄×C₁₉	#462	1	2	yes	—
116	C₄×C₁₉	#488	1	2	yes	—
117	C₄×C₁₉	#495	1	2	yes	—
118	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₈	—	19	2	no	—
121	C₂×C₄⋊C₈	—	19	2	no	—
122	C₂×C₄×C₈	—	38	1	no	—
123	#391	—	2	2	no	—
124	#391	Dic₁₉	1	4	yes	—
125	#382	—	2	1	no	—
126	#382	—	2	1	no	—
127	C₄³	C₂×D₁₉	1	1	yes	characteristic
128	#336	—	38	2	no	—
129	#336	—	38	1	no	—
130	#333	—	38	4	no	—
131	#332	—	38	4	no	—
132	C₂×C₁₉	#1542	1	2	yes	—
133	C₂×C₁₉	#1554	1	2	yes	—
134	C₂×C₁₉	#1958	1	1	yes	characteristic
135	C₂×C₁₉	#1967	1	1	yes	characteristic
136	C₂×C₁₉	#1981	1	1	yes	characteristic
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
139	C₂²×C₈	—	38	2	no	—
140	C₂²×C₈	—	38	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
149	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
150	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	19	4	no	—
155	C₄⋊C₈	—	38	2	no	—
156	C₄⋊C₈	—	38	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	C₄×C₈	—	76	2	no	—
159	#95	—	2	4	no	—
160	#95	—	2	4	no	—
161	C₁₉	#9693	1	1	yes	characteristic, complemented, Sylow
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	4	1	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
170	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
171	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
174	C₂×C₈	—	38	4	no	—
175	C₂×C₈	—	76	2	no	—
176	C₂×C₈	—	76	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	4	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	1	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	1	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	4	2	no	—
187	C₄²	#64527	1	2	yes	—
188	C₄²	#64528	1	2	yes	—
189	C₄²	D₄×D₁₉	1	2	yes	—
190	C₄²	#64543	1	2	yes	—
191	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
192	Q₈	—	8	4	no	—
193	Q₈	—	8	2	no	—
194	Q₈	—	8	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	#10597292	1	4	yes	—
206	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
207	C₂×C₄	#10597382	1	1	yes	characteristic
208	C₂×C₄	#10597384	1	2	yes	—
209	C₂×C₄	#10597386	1	1	yes	characteristic
210	C₂×C₄	C₂×#64527	1	1	yes	characteristic
211	C₂×C₄	#10597388	1	2	yes	—
212	C₂×C₄	C₂×#64528	1	1	yes	characteristic
213	C₂×C₄	#10597396	1	4	yes	—
214	C₈	—	76	4	no	—
215	C₈	—	152	2	no	—
216	C₂²	#11926447	1	1	yes	characteristic
217	C₂²	#11926528	1	2	yes	—
218	C₂²	C₂×#10597292	1	1	yes	characteristic
219	C₂²	#11926540	1	2	yes	—
220	C₂²	#11926553	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	2	4	no	—
223	C₄	—	4	2	no	—
224	C₄	—	8	2	no	—
225	C₄	—	8	2	no	—
226	C₄	#11926746	1	2	yes	—
227	C₄	#11926751	1	2	yes	—
228	C₄	#11926898	1	2	yes	—
229	C₄	#11926926	1	2	yes	—
230	C₂	#14562292	1	2	yes	—
231	C₂	#14562345	1	2	yes	—
232	C₂	#14564447	1	1	yes	characteristic
233	C₂	#14564485	1	1	yes	characteristic
234	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	#9693
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
161. C₁₉	#9693	semidirect

Maximal subgroups

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

subgroup	index
#14563752	2
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926293	2
C₂×#11926290	2
C₁₉×#2862	2
#9693	19