Subgroups — #18076199

Order 4864.

422 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	C₄²×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14561469	C₂	1	4	yes	maximal
4	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
13	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
27	C₁₉×C₄⋊C₈	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	4	2	no	—
29	C₁₉×C₄⋊C₈	—	4	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
31	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
33	C₄×C₁₉⋊C₈	—	2	2	no	—
34	C₄×C₁₉⋊C₈	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₄×C₁₉⋊C₈	—	2	4	no	—
37	C₄×C₁₉⋊C₈	C₈	1	4	yes	complemented
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₂×C₈×C₁₉	—	4	2	no	—
47	C₂×C₈×C₁₉	—	4	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	2	2	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	C₂×C₈	1	2	yes	—
52	C₄²×C₁₉	M₁₆	1	2	yes	—
53	C₄²×C₁₉	D₈	1	2	yes	—
54	C₄²×C₁₉	SD₁₆	1	2	yes	—
55	C₄²×C₁₉	SD₁₆	1	2	yes	—
56	C₄²×C₁₉	Q₁₆	1	2	yes	—
57	C₄²×C₁₉	#41	1	2	yes	—
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₂×C₁₉⋊C₈	—	2	2	no	—
60	C₂×C₁₉⋊C₈	—	2	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	4	2	no	—
66	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
67	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
68	#8784	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
77	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
78	C₂×C₄×C₁₉	#106	1	2	yes	—
79	C₂×C₄×C₁₉	#106	1	2	yes	—
80	C₂×C₄×C₁₉	#107	1	2	yes	—
81	C₂×C₄×C₁₉	#107	1	2	yes	—
82	C₂×C₄×C₁₉	#108	1	2	yes	—
83	C₂×C₄×C₁₉	#108	1	2	yes	—
84	C₂×C₄×C₁₉	#117	1	2	yes	—
85	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#125	1	2	yes	—
88	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×SD₁₆	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	C₈×C₁₉	—	8	2	no	—
96	C₁₉⋊C₈	—	2	4	no	—
97	C₁₉⋊C₈	—	2	4	no	—
98	C₁₉⋊C₈	—	8	2	no	—
99	#1842	—	19	1	no	—
100	#1842	D₁₉	1	1	yes	characteristic
101	C₄²×C₈	—	19	1	no	—
102	#1277	—	19	4	no	—
103	C₂²×C₁₉	#382	1	1	yes	characteristic
104	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
105	C₂²×C₁₉	#423	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	#334	1	4	yes	—
114	C₄×C₁₉	#335	1	4	yes	—
115	C₄×C₁₉	#431	1	2	yes	—
116	C₄×C₁₉	#432	1	2	yes	—
117	C₄×C₁₉	#486	1	1	yes	characteristic
118	C₄×C₁₉	#486	1	1	yes	characteristic
119	C₄×C₁₉	#487	1	1	yes	characteristic
120	C₄×C₁₉	#487	1	1	yes	characteristic
121	C₂×C₄⋊C₈	—	2	1	no	—
122	C₂×C₄⋊C₈	—	2	1	no	—
123	C₂×C₄⋊C₈	—	19	2	no	—
124	C₂×C₄⋊C₈	—	38	1	no	—
125	C₂×C₄⋊C₈	—	38	1	no	—
126	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
127	C₂×C₄×C₈	—	19	1	no	—
128	C₂×C₄×C₈	—	19	2	no	—
129	C₂×C₄×C₈	—	19	1	no	—
130	C₂×C₄×C₈	—	19	2	no	—
131	C₄³	C₂×D₁₉	1	1	yes	characteristic
132	C₂×C₁₉	C₂×#334	1	1	yes	characteristic
133	C₂×C₁₉	C₂×#335	1	1	yes	characteristic
134	C₂×C₁₉	#1566	1	1	yes	characteristic
135	C₂×C₁₉	#1567	1	1	yes	characteristic
136	C₂×C₁₉	#1831	1	1	yes	characteristic
137	C₂×C₁₉	#1834	1	1	yes	characteristic
138	C₂×C₁₉	#1837	1	1	yes	characteristic
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	19	2	no	—
141	C₂²×C₈	—	19	2	no	—
142	C₂²×C₈	—	38	2	no	—
143	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
144	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
145	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
146	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
147	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
148	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
150	C₄⋊C₈	—	2	4	no	—
151	C₄⋊C₈	—	4	2	no	—
152	C₄⋊C₈	—	4	2	no	—
153	C₄⋊C₈	—	38	4	no	—
154	C₄⋊C₈	—	76	2	no	—
155	C₄⋊C₈	—	76	2	no	—
156	C₄×C₈	—	19	4	no	—
157	C₄×C₈	—	38	4	no	—
158	C₄×C₈	—	38	2	no	—
159	C₄×C₈	—	38	2	no	—
160	C₄×C₈	—	38	2	no	—
161	C₁₉	#8784	1	1	yes	characteristic, complemented, Sylow
162	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
163	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
164	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
165	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
166	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	19	4	no	—
173	C₂×C₈	—	19	4	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	38	2	no	—
176	C₂×C₈	—	38	2	no	—
177	C₂×C₈	—	38	2	no	—
178	C₂×C₈	—	76	2	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	—	76	2	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	C₈×D₁₉	1	2	yes	—
185	C₄²	#64515	1	2	yes	—
186	C₄²	#64525	1	2	yes	—
187	C₄²	#64526	1	2	yes	—
188	C₄²	#64527	1	2	yes	—
189	C₄²	#64528	1	2	yes	—
190	C₄²	#64543	1	2	yes	—
191	C₄²	#64545	1	2	yes	—
192	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	#10597264	1	2	yes	—
200	C₂×C₄	#10597264	1	2	yes	—
201	C₂×C₄	#10597265	1	2	yes	—
202	C₂×C₄	#10597265	1	2	yes	—
203	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
204	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
205	C₂×C₄	#10597279	1	2	yes	—
206	C₂×C₄	#10597279	1	2	yes	—
207	C₂×C₄	#10597336	1	2	yes	—
208	C₂×C₄	#10597338	1	2	yes	—
209	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
210	C₂×C₄	C₂×#64515	1	1	yes	characteristic
211	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
212	C₂×C₄	C₂×#64525	1	1	yes	characteristic
213	C₂×C₄	C₂×#64526	1	1	yes	characteristic
214	C₂×C₄	#10597382	1	1	yes	characteristic
215	C₂×C₄	C₂×#64527	1	1	yes	characteristic
216	C₂×C₄	C₂×#64528	1	1	yes	characteristic
217	C₂×C₄	#10597393	1	1	yes	characteristic
218	C₈	—	8	2	no	—
219	C₈	—	38	4	no	—
220	C₈	—	38	4	no	—
221	C₈	—	152	2	no	—
222	C₂²	#11926409	1	1	yes	characteristic
223	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
224	C₂²	#11926567	1	1	yes	characteristic
225	C₂²	C₂×#10597265	1	1	yes	characteristic
226	C₂²	C₂×#10597264	1	1	yes	characteristic
227	C₂²	C₂×#10597279	1	1	yes	characteristic
228	C₂²	C₂×#10597279	1	1	yes	characteristic
229	C₄	—	2	2	no	—
230	C₄	—	2	2	no	—
231	C₄	—	2	2	no	—
232	C₄	#11926294	1	4	yes	—
233	C₄	#11926296	1	4	yes	—
234	C₄	#11926596	1	2	yes	—
235	C₄	#11926600	1	2	yes	—
236	C₄	#11926890	1	1	yes	characteristic
237	C₄	#11926892	1	1	yes	characteristic
238	C₄	#11926894	1	1	yes	characteristic
239	C₄	#11926896	1	1	yes	characteristic
240	C₂	C₂×#11926294	1	1	yes	characteristic
241	C₂	C₂×#11926296	1	1	yes	characteristic
242	C₂	#14562390	1	1	yes	characteristic
243	C₂	#14562393	1	1	yes	characteristic
244	C₂	#14563751	1	1	yes	characteristic
245	C₂	#14563762	1	1	yes	characteristic
246	C₂	#14563772	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8784
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
37. C₄×C₁₉⋊C₈	C₈	semidirect
161. C₁₉	#8784	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
C₄²×C₁₉⋊C₈	2
#14561469	2
C₁₉×#1842	2
#8784	19