Subgroups — #18076342

Order 4864.

354 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563806	C₂	1	2	yes	maximal
2	#14562394	C₂	1	1	yes	maximal, characteristic
3	#14562393	C₂	1	2	yes	maximal
4	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597279	—	2	4	no	—
7	#11926568	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926297	—	2	2	no	—
11	#11926296	—	2	4	no	—
12	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
15	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#335	—	2	2	no	—
19	C₂×M₁₆×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×#64520	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
24	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	D₄	1	2	yes	—
30	#10597279	—	4	8	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
38	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	M₁₆×C₁₉	—	4	4	no	—
43	C₂×C₈×C₁₉	—	2	4	no	—
44	C₂×C₈×C₁₉	—	4	2	no	—
45	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	#64520	—	4	4	no	—
52	C₂×C₁₉⋊C₈	—	2	4	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
55	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
57	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₁₉⋊C₈	D₈	1	4	yes	—
59	C₂×C₁₉⋊C₈	Q₁₆	1	4	yes	—
60	#8823	—	19	1	no	maximal, Sylow
61	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
72	C₈×C₁₉	—	2	2	no	—
73	C₈×C₁₉	—	8	2	no	—
74	C₈×C₁₉	#108	1	4	yes	complemented
75	C₁₉⋊C₈	—	2	2	no	—
76	C₁₉⋊C₈	—	8	2	no	—
77	C₁₉⋊C₈	#107	1	4	yes	—
78	C₁₉⋊C₈	#107	1	4	yes	—
79	C₁₉⋊C₈	#108	1	4	yes	complemented
80	#1848	—	19	2	no	—
81	#1567	—	19	2	no	—
82	#1567	—	19	1	no	—
83	#1567	D₁₉	1	1	yes	characteristic
84	C₂×C₈²	—	19	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	#384	1	1	yes	characteristic
88	C₂²×C₁₉	#500	1	2	yes	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	C₂×#107	1	2	yes	—
92	C₄×C₁₉	C₂×#108	1	2	yes	—
93	C₄×C₁₉	C₂×#108	1	2	yes	—
94	C₄×C₁₉	#493	1	1	yes	characteristic
95	C₄×C₁₉	#494	1	1	yes	characteristic
96	C₂×#108	—	38	4	no	—
97	#423	—	19	2	no	—
98	#423	C₂×D₁₉	1	2	yes	—
99	C₂×C₄×C₈	—	19	1	no	—
100	C₂×C₄×C₈	—	19	1	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#335	—	2	2	no	—
103	#335	—	38	4	no	—
104	#335	—	38	2	no	—
105	C₈²	—	19	1	no	—
106	C₈²	—	19	1	no	—
107	C₈²	—	19	1	no	—
108	C₈²	—	19	1	no	—
109	C₂×C₁₉	—	2	2	no	—
110	C₂×C₁₉	#1845	1	1	yes	characteristic
111	C₂×C₁₉	#1848	1	1	yes	characteristic
112	C₂×C₁₉	#1848	1	1	yes	characteristic
113	C₂×M₁₆	—	2	2	no	—
114	C₂×M₁₆	—	38	2	no	—
115	C₂²×C₈	—	19	2	no	—
116	C₂²×C₈	—	19	2	no	—
117	C₂²×C₈	Dic₃₈	1	2	yes	—
118	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
119	#108	—	76	8	no	—
120	C₄⋊C₈	—	2	2	no	—
121	C₄⋊C₈	—	2	2	no	—
122	C₄⋊C₈	—	38	2	no	—
123	C₄⋊C₈	—	38	2	no	—
124	C₄×C₈	—	19	1	no	—
125	C₄×C₈	—	19	1	no	—
126	C₄×C₈	—	19	1	no	—
127	C₄×C₈	—	19	1	no	—
128	C₄×C₈	—	19	2	no	—
129	C₄×C₈	—	19	2	no	—
130	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
131	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
133	C₁₉	#8823	1	1	yes	characteristic, complemented, Sylow
134	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
135	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
136	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
137	M₁₆	—	4	4	no	—
138	M₁₆	—	76	4	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	19	2	no	—
142	C₂×C₈	—	19	2	no	—
143	C₂×C₈	—	19	2	no	—
144	C₂×C₈	—	19	4	no	—
145	C₂×C₈	—	19	4	no	—
146	C₂×C₈	—	19	2	no	—
147	C₂×C₈	—	38	4	no	—
148	C₂×C₈	—	76	2	no	—
149	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
150	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
151	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
152	C₄²	D₄×D₁₉	1	1	yes	characteristic
153	C₄²	Q₈×D₁₉	1	1	yes	characteristic
154	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂³	#10597334	1	1	yes	characteristic
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	#10597334	1	1	yes	characteristic
159	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
160	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
161	C₂×C₄	D₈×D₁₉	1	2	yes	—
162	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
163	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
164	C₂×C₄	#10597386	1	1	yes	characteristic
165	C₂×C₄	#10597390	1	1	yes	characteristic
166	C₈	—	2	2	no	—
167	C₈	—	8	2	no	—
168	C₈	—	19	4	no	—
169	C₈	—	19	4	no	—
170	C₈	—	19	4	no	—
171	C₈	—	38	2	no	—
172	C₈	—	152	2	no	—
173	C₈	#10597279	1	4	yes	complemented
174	C₂²	—	2	1	no	—
175	C₂²	—	2	1	no	—
176	C₂²	#11926413	1	1	yes	characteristic
177	C₂²	#11926948	1	2	yes	—
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	#107×D₁₉	1	2	yes	—
181	C₄	#108×D₁₉	1	2	yes	—
182	C₄	C₂×#10597279	1	2	yes	—
183	C₄	#11926919	1	1	yes	characteristic
184	C₄	#11926922	1	1	yes	characteristic
185	C₂	—	2	2	no	—
186	C₂	#14563793	1	1	yes	characteristic
187	C₂	#14563805	1	1	yes	characteristic
188	C₂	#14563806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#8823
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
74. C₈×C₁₉	#108	semidirect
79. C₁₉⋊C₈	#108	semidirect
133. C₁₉	#8823	semidirect
173. C₈	#10597279	semidirect

Maximal subgroups

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

subgroup	index
#14563806	2
#14562394	2
#14562393	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1567	2
#8823	19