Subgroups — #18075391

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	#14563615	C₂	1	2	yes	maximal
2	C₂×#11926297	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	#11926297	—	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	D₈	1	2	yes	—
46	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	4	no	—
53	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
54	C₄²×C₁₉	—	2	1	no	—
55	C₄²×C₁₉	—	2	1	no	—
56	C₄²×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	C₂×D₄	1	2	yes	—
59	C₄²×C₁₉	#41	1	2	yes	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	C₂×C₁₉⋊C₈	—	4	4	no	—
63	#8599	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	—	2	1	no	—
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	1	no	—
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	#107	1	2	yes	—
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	2	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	#107	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#121	1	2	yes	—
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	#131	1	4	yes	—
88	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₈×C₁₉	—	2	4	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₁₉⋊C₈	—	8	4	no	—
94	C₂×#431	D₁₉	1	1	yes	characteristic
95	#1797	—	19	2	no	—
96	C₂×#335	—	19	2	no	—
97	#1277	—	19	2	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	4	no	—
100	C₂²×C₁₉	—	4	1	no	—
101	C₂²×C₁₉	—	4	1	no	—
102	C₂²×C₁₉	—	4	2	no	—
103	C₂²×C₁₉	#380	1	1	yes	characteristic
104	C₂²×C₁₉	#424	1	2	yes	—
105	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
106	C₂²×C₁₉	#427	1	1	yes	characteristic
107	C₂²×C₁₉	#430	1	2	yes	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	4	1	no	—
111	C₄×C₁₉	—	4	1	no	—
112	C₄×C₁₉	#408	1	2	yes	—
113	C₄×C₁₉	#433	1	2	yes	—
114	C₄×C₁₉	#466	1	2	yes	—
115	C₄×C₁₉	#467	1	2	yes	—
116	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
117	#431	—	2	4	no	—
118	C₂×C₄⋊C₈	—	19	4	no	—
119	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
120	C₂×C₂²⋊C₈	—	38	2	no	—
121	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
122	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#336	—	38	2	no	—
125	#335	—	38	4	no	—
126	C₂×C₁₉	—	4	2	no	—
127	C₂×C₁₉	#1571	1	2	yes	—
128	C₂×C₁₉	#1572	1	2	yes	—
129	C₂×C₁₉	#1798	1	1	yes	characteristic
130	C₂×C₁₉	#1808	1	1	yes	characteristic
131	C₂×C₁₉	#1811	1	1	yes	characteristic
132	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
133	C₂³×C₄	D₇₆	1	1	yes	characteristic
134	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
135	C₂²×C₈	—	38	4	no	—
136	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
137	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
138	C₂×C₄²	—	2	2	no	—
139	C₂×C₄²	—	2	2	no	—
140	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
141	C₂×C₄²	D₇₆	1	1	yes	characteristic
142	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	4	no	—
145	C₄⋊C₈	—	38	4	no	—
146	C₄⋊C₈	—	38	4	no	—
147	C₂²⋊C₈	—	2	4	no	—
148	C₂²⋊C₈	—	76	4	no	—
149	C₄×C₈	—	2	2	no	—
150	C₄×C₈	C₂²⋊D₁₉	1	4	yes	—
151	C₁₉	#8599	1	1	yes	characteristic, complemented, Sylow
152	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	2	1	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	D₁₅₂	1	2	yes	—
161	C₂²×C₄	Dic₇₆	1	2	yes	—
162	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
163	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
164	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
165	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
167	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	76	4	no	—
172	C₂×C₈	—	76	4	no	—
173	C₂×C₈	—	76	4	no	—
174	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
175	C₄²	—	2	2	no	—
176	C₄²	—	2	1	no	—
177	C₄²	—	2	2	no	—
178	C₄²	—	2	1	no	—
179	C₄²	#64541	1	2	yes	—
180	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	1	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	1	no	—
185	C₂³	#10597275	1	2	yes	—
186	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#10597275	1	2	yes	—
200	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
201	C₂×C₄	#10597350	1	2	yes	—
202	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
203	C₂×C₄	#10597370	1	2	yes	—
204	C₂×C₄	#10597372	1	1	yes	characteristic
205	C₂×C₄	#10597376	1	2	yes	—
206	C₂×C₄	#10597394	1	4	yes	—
207	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
208	C₈	—	2	4	no	—
209	C₈	—	4	2	no	—
210	C₈	—	152	4	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	4	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	—	4	2	no	—
216	C₂²	#11926404	1	1	yes	characteristic
217	C₂²	#11926571	1	2	yes	—
218	C₂²	C₂×#10597275	1	1	yes	characteristic
219	C₂²	#11926582	1	1	yes	characteristic
220	C₂²	#11926593	1	2	yes	—
221	C₄	—	2	2	no	—
222	C₄	—	2	2	no	—
223	C₄	—	4	1	no	—
224	C₄	—	4	1	no	—
225	C₄	#11926511	1	2	yes	—
226	C₄	#11926605	1	2	yes	—
227	C₄	#11926780	1	2	yes	—
228	C₄	#11926785	1	2	yes	—
229	C₂	—	4	2	no	—
230	C₂	#14562410	1	2	yes	—
231	C₂	#14562415	1	2	yes	—
232	C₂	#14563619	1	1	yes	characteristic
233	C₂	#14563664	1	1	yes	characteristic
234	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	#8599
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×#11926297	C₂	semidirect
3. #14561470	C₂	semidirect
151. C₁₉	#8599	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×#11926297	2
#14561470	2
C₂×C₁₉×#431	2
#8599	19