Subgroups — #18073734

Order 4864.

438 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563490	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
4	#14561469	C₂	1	2	yes	maximal
5	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597272	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
10	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
11	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926298	—	2	2	no	—
13	#11926297	C₄	1	4	yes	complemented
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#335	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
25	C₂²×C₁₉⋊C₈	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
31	#10597272	—	4	4	no	—
32	C₈×Dic₁₉	—	2	4	no	—
33	C₈×Dic₁₉	—	2	4	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
36	C₄×C₁₉⋊C₈	—	2	1	no	—
37	C₄×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	4	no	—
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₂×C₈×C₁₉	—	4	2	no	—
47	C₂×C₈×C₁₉	C₄²	1	2	yes	—
48	C₂×C₈×C₁₉	C₄²	1	2	yes	—
49	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
50	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	1	yes	characteristic
53	C₄²×C₁₉	#41	1	1	yes	characteristic
54	C₄×Dic₁₉	—	2	2	no	—
55	C₄×Dic₁₉	—	2	2	no	—
56	C₄×Dic₁₉	—	2	1	no	—
57	C₄×Dic₁₉	—	2	1	no	—
58	C₄×Dic₁₉	—	2	4	no	—
59	C₄×Dic₁₉	D₈	1	2	yes	—
60	C₄×Dic₁₉	Q₁₆	1	2	yes	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	4	2	no	—
66	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
67	#8274	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
77	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	2	2	no	—
84	C₂×Dic₁₉	—	2	2	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	#107	1	4	yes	—
87	C₂×Dic₁₉	#108	1	4	yes	—
88	C₈×C₁₉	—	2	2	no	—
89	C₈×C₁₉	—	4	4	no	—
90	C₈×C₁₉	#97	1	4	yes	complemented
91	C₁₉⋊C₈	—	2	4	no	—
92	C₁₉⋊C₈	—	4	4	no	—
93	#1767	—	19	2	no	—
94	C₄²×C₈	—	19	1	no	—
95	C₂×#335	—	19	1	no	—
96	C₂×#335	D₁₉	1	1	yes	characteristic
97	#1277	—	19	2	no	—
98	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₉	#423	1	2	yes	—
100	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
101	C₂²×C₁₉	#427	1	1	yes	characteristic
102	C₂²×C₁₉	C₂×#108	1	2	yes	—
103	C₄×C₁₉	—	2	1	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
106	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
107	C₄×C₁₉	#432	1	2	yes	—
108	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
109	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
110	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
111	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
112	Dic₁₉	—	2	4	no	—
113	Dic₁₉	—	2	4	no	—
114	C₂×C₄⋊C₈	—	19	2	no	—
115	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
116	C₂×#97	—	38	2	no	—
117	C₂×C₄×C₈	—	19	2	no	—
118	C₂×C₄×C₈	—	19	2	no	—
119	C₂×C₄×C₈	—	19	1	no	—
120	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
121	C₄³	—	19	1	no	—
122	#336	—	38	2	no	—
123	#335	—	19	4	no	—
124	#335	Dic₁₉	1	4	yes	complemented
125	C₂×C₁₉	#1567	1	2	yes	—
126	C₂×C₁₉	#1568	1	2	yes	—
127	C₂×C₁₉	#1767	1	1	yes	characteristic
128	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
129	C₂×C₁₉	C₄×#108	1	1	yes	characteristic
130	C₂²×C₈	—	2	2	no	—
131	C₂²×C₈	—	19	2	no	—
132	C₂²×C₈	—	38	2	no	—
133	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
134	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄²	—	19	1	no	—
136	C₂×C₄²	—	19	2	no	—
137	C₂×C₄²	—	19	1	no	—
138	C₂×C₄²	—	19	2	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	19	4	no	—
142	C₄⋊C₈	—	38	2	no	—
143	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
144	#97	—	76	4	no	—
145	C₄×C₈	—	38	4	no	—
146	C₄×C₈	—	38	4	no	—
147	C₄×C₈	—	38	1	no	—
148	C₄×C₈	—	38	1	no	—
149	C₄×C₈	C₄×D₁₉	1	2	yes	—
150	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
151	C₁₉	#8274	1	1	yes	characteristic, complemented, Sylow
152	C₂²×C₄	—	19	2	no	—
153	C₂²×C₄	—	19	2	no	—
154	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
155	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
156	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	19	4	no	—
162	C₂×C₈	—	38	2	no	—
163	C₂×C₈	—	38	2	no	—
164	C₂×C₈	—	38	4	no	—
165	C₂×C₈	—	76	2	no	—
166	C₂×C₈	—	76	2	no	—
167	C₂×C₈	#64515	1	4	yes	—
168	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
169	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
170	C₄²	—	19	2	no	—
171	C₄²	—	19	2	no	—
172	C₄²	—	38	4	no	—
173	C₄²	—	38	2	no	—
174	C₄²	—	38	2	no	—
175	C₄²	—	38	1	no	—
176	C₄²	—	38	1	no	—
177	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₄²	#64543	1	1	yes	characteristic
179	C₄²	#64545	1	1	yes	characteristic
180	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
181	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	19	4	no	—
184	C₂×C₄	—	19	4	no	—
185	C₂×C₄	—	38	2	no	—
186	C₂×C₄	—	38	2	no	—
187	C₂×C₄	—	38	2	no	—
188	C₂×C₄	—	38	2	no	—
189	C₂×C₄	#10597333	1	1	yes	characteristic
190	C₂×C₄	#10597338	1	1	yes	characteristic
191	C₂×C₄	#10597339	1	1	yes	characteristic
192	C₂×C₄	C₂×#64515	1	2	yes	—
193	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
194	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
195	C₂×C₄	#10597358	1	1	yes	characteristic
196	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
197	C₂×C₄	#10597365	1	1	yes	characteristic
198	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
199	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
200	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
201	C₈	—	2	2	no	—
202	C₈	—	4	4	no	—
203	C₈	—	38	4	no	—
204	C₈	—	76	4	no	—
205	C₈	#10597272	1	4	yes	complemented
206	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
207	C₂²	#11926566	1	2	yes	—
208	C₂²	#107×D₁₉	1	1	yes	characteristic
209	C₂²	#11926581	1	1	yes	characteristic
210	C₂²	#108×D₁₉	1	2	yes	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	38	4	no	—
214	C₄	—	38	4	no	—
215	C₄	C₂×#10597272	1	1	yes	characteristic
216	C₄	M₁₆×Dic₁₉	1	1	yes	characteristic
217	C₄	#11926600	1	2	yes	—
218	C₄	#11926626	1	1	yes	characteristic
219	C₄	D₈×Dic₁₉	1	1	yes	characteristic
220	C₄	#11926638	1	1	yes	characteristic
221	C₄	Q₁₆×Dic₁₉	1	1	yes	characteristic
222	C₂	#14562392	1	2	yes	—
223	C₂	#14562397	1	2	yes	—
224	C₂	#14563490	1	1	yes	characteristic
225	C₂	#107×Dic₁₉	1	1	yes	characteristic
226	C₂	#108×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#335	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#8274
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
13. #11926297	C₄	semidirect
16. C₁₉×#335	C₄	semidirect
90. C₈×C₁₉	#97	semidirect
124. #335	Dic₁₉	semidirect
151. C₁₉	#8274	semidirect
205. C₈	#10597272	semidirect

Maximal subgroups

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

subgroup	index
#14563490	2
C₄×C₈×Dic₁₉	2
C₂×#11926297	2
#14561469	2
C₂×C₁₉×#335	2
#8274	19