Subgroups — #18069130

Order 4864.

292 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	#14563752	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
8	#11926299	—	2	1	no	—
9	#11926299	C₄	1	2	yes	—
10	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#336	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	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	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	4	1	no	—
25	C₁₉×C₄⋊C₈	—	4	1	no	—
26	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
27	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
28	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
29	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
30	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
32	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
33	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	2	no	—
43	C₄²×C₁₉	—	2	1	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	4	1	no	—
47	C₄²×C₁₉	—	4	1	no	—
48	C₄²×C₁₉	—	4	1	no	—
49	C₄²×C₁₉	D₈	1	1	yes	characteristic
50	C₄²×C₁₉	D₈	1	1	yes	characteristic
51	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
52	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
53	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
54	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
55	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
56	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	4	2	no	—
63	#7040	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	#95	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#108	1	2	yes	—
93	C₈×C₁₉	—	8	2	no	—
94	C₁₉⋊C₈	—	8	2	no	—
95	C₁₉⋊C₈	—	8	2	no	—
96	#1842	—	19	1	no	—
97	#1831	—	19	1	no	—
98	#1831	D₁₉	1	1	yes	characteristic
99	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
100	C₂²×C₁₉	#340	1	1	yes	characteristic
101	C₂²×C₁₉	#340	1	1	yes	characteristic
102	C₂²×C₁₉	#341	1	1	yes	characteristic
103	C₂²×C₁₉	#343	1	1	yes	characteristic
104	C₂²×C₁₉	#344	1	1	yes	characteristic
105	C₂²×C₁₉	#344	1	1	yes	characteristic
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	4	1	no	—
116	C₄×C₁₉	#331	1	1	yes	characteristic
117	C₄×C₁₉	#332	1	1	yes	characteristic
118	C₄×C₁₉	#332	1	1	yes	characteristic
119	C₄×C₁₉	#333	1	1	yes	characteristic
120	C₂×C₄⋊C₈	—	2	1	no	—
121	C₂×C₄⋊C₈	—	19	2	no	—
122	C₂×C₄⋊C₈	—	38	1	no	—
123	C₂×C₄⋊C₈	—	38	1	no	—
124	C₂×C₄⋊C₈	—	38	1	no	—
125	C₄³	C₂×D₁₉	1	1	yes	characteristic
126	#336	—	2	1	no	—
127	#336	—	19	2	no	—
128	#336	—	38	1	no	—
129	#336	Dic₁₉	1	2	yes	—
130	C₂×C₁₉	#1286	1	1	yes	characteristic
131	C₂×C₁₉	#1286	1	1	yes	characteristic
132	C₂×C₁₉	#1290	1	1	yes	characteristic
133	C₂×C₁₉	#1296	1	1	yes	characteristic
134	C₂×C₁₉	#1301	1	1	yes	characteristic
135	C₂×C₁₉	#1301	1	1	yes	characteristic
136	C₂×C₁₉	#1307	1	1	yes	characteristic
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	38	2	no	—
139	C₂²×C₈	—	38	2	no	—
140	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
141	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
142	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
143	C₂×C₄²	D₇₆	1	1	yes	characteristic
144	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
147	C₄⋊C₈	—	4	1	no	—
148	C₄⋊C₈	—	4	1	no	—
149	C₄⋊C₈	—	76	2	no	—
150	C₄⋊C₈	—	76	1	no	—
151	C₄⋊C₈	—	76	1	no	—
152	C₄⋊C₈	—	76	1	no	—
153	C₄⋊C₈	—	76	1	no	—
154	C₄⋊C₈	—	76	1	no	—
155	C₄⋊C₈	—	76	1	no	—
156	C₁₉	#7040	1	1	yes	characteristic, complemented, Sylow
157	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
158	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
159	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
160	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
161	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
162	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
163	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	4	2	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	76	2	no	—
168	C₂×C₈	—	76	2	no	—
169	C₂×C₈	—	76	2	no	—
170	C₂×C₈	—	76	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₂×C₈	—	76	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	—	2	1	no	—
175	C₄²	—	2	1	no	—
176	C₄²	—	4	1	no	—
177	C₄²	—	4	1	no	—
178	C₄²	—	4	1	no	—
179	C₄²	#64516	1	1	yes	characteristic
180	C₄²	#64516	1	1	yes	characteristic
181	C₄²	D₁₅₂	1	1	yes	characteristic
182	C₄²	Dic₇₆	1	1	yes	characteristic
183	C₄²	#64525	1	1	yes	characteristic
184	C₄²	#64526	1	1	yes	characteristic
185	C₄²	#64527	1	1	yes	characteristic
186	C₄²	#64528	1	1	yes	characteristic
187	C₂³	C₁₉⋊#95	1	1	yes	characteristic
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	#10597264	1	1	yes	characteristic
202	C₂×C₄	#10597265	1	1	yes	characteristic
203	C₂×C₄	#10597266	1	1	yes	characteristic
204	C₂×C₄	#10597267	1	1	yes	characteristic
205	C₂×C₄	#10597273	1	1	yes	characteristic
206	C₂×C₄	#10597273	1	1	yes	characteristic
207	C₂×C₄	#10597274	1	1	yes	characteristic
208	C₂×C₄	#10597275	1	1	yes	characteristic
209	C₂×C₄	#10597278	1	1	yes	characteristic
210	C₂×C₄	#10597278	1	1	yes	characteristic
211	C₂×C₄	#10597279	1	2	yes	—
212	C₂×C₄	#10597280	1	1	yes	characteristic
213	C₂×C₄	#10597281	1	1	yes	characteristic
214	C₂×C₄	#10597289	1	1	yes	characteristic
215	C₂×C₄	#10597292	1	1	yes	characteristic
216	C₈	—	8	2	no	—
217	C₈	—	152	2	no	—
218	C₈	—	152	2	no	—
219	C₂²	#11926300	1	1	yes	characteristic
220	C₂²	#11926306	1	1	yes	characteristic
221	C₂²	#11926307	1	1	yes	characteristic
222	C₂²	#11926308	1	1	yes	characteristic
223	C₂²	#11926312	1	1	yes	characteristic
224	C₂²	#11926314	1	1	yes	characteristic
225	C₂²	#11926315	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	2	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	1	no	—
236	C₄	#11926287	1	1	yes	characteristic
237	C₄	#11926289	1	1	yes	characteristic
238	C₄	#11926291	1	1	yes	characteristic
239	C₄	#11926292	1	1	yes	characteristic
240	C₂	#14561493	1	1	yes	characteristic
241	C₂	#14561494	1	1	yes	characteristic
242	C₂	#14561504	1	1	yes	characteristic
243	C₂	#14561519	1	1	yes	characteristic
244	C₂	#14561530	1	1	yes	characteristic
245	C₂	#14561531	1	1	yes	characteristic
246	C₂	#14561545	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#7040
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
156. C₁₉	#7040	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
#14563752	2
C₁₉×#1831	2
#7040	19