Subgroups — #18076277

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	#11926295	—	2	8	no	—
7	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	2	yes	—
17	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	—	2	4	no	—
20	C₄×C₈×C₁₉	—	2	4	no	—
21	C₄×C₈×C₁₉	—	2	2	no	—
22	C₄×C₈×C₁₉	C₈	1	4	yes	complemented
23	C₄×C₈×C₁₉	D₄	1	4	yes	—
24	C₄×C₈×C₁₉	Q₈	1	4	yes	—
25	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
26	C₄⋊(C₁₉⋊C₈)	—	4	8	no	—
27	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
28	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
35	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
36	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
38	C₄²×C₁₉	—	2	4	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	C₂×C₈	1	2	yes	—
41	C₄²×C₁₉	M₁₆	1	2	yes	—
42	C₄²×C₁₉	SD₁₆	1	8	yes	—
43	C₄²×C₁₉	C₂×D₄	1	2	yes	—
44	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	C₂×C₁₉⋊C₈	—	4	8	no	—
47	#8805	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
53	C₂×C₄×C₁₉	#106	1	4	yes	—
54	C₂×C₄×C₁₉	#106	1	4	yes	—
55	C₂×C₄×C₁₉	#108	1	4	yes	—
56	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
57	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
59	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
62	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
64	C₈×C₁₉	—	2	4	no	—
65	C₈×C₁₉	C₄⋊C₈	1	8	yes	complemented
66	C₁₉⋊C₈	—	8	4	no	—
67	#1842	—	19	2	no	—
68	C₄²×C₈	D₁₉	1	1	yes	characteristic
69	C₂×#334	—	19	4	no	—
70	C₂²×C₁₉	#384	1	1	yes	characteristic
71	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
72	C₂²×C₁₉	#423	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×#106	1	2	yes	—
74	C₂²×C₁₉	C₂×#108	1	2	yes	—
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	#334	1	8	yes	complemented
78	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
79	C₄×C₁₉	#423	1	2	yes	—
80	C₄×C₁₉	#492	1	2	yes	—
81	C₄×C₁₉	#498	1	2	yes	—
82	C₂×C₄⋊C₈	—	19	4	no	—
83	C₂×C₄⋊C₈	—	38	4	no	—
84	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
85	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
86	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
88	C₄³	C₂×D₁₉	1	1	yes	characteristic
89	#334	—	38	8	no	—
90	C₂×C₁₉	C₂×#334	1	2	yes	—
91	C₂×C₁₉	#1566	1	2	yes	—
92	C₂×C₁₉	#1842	1	1	yes	characteristic
93	C₂×C₁₉	#1844	1	1	yes	characteristic
94	C₂×C₁₉	#1848	1	1	yes	characteristic
95	C₂²×C₈	—	38	4	no	—
96	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
97	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
98	C₂×C₄²	Dic₃₈	1	2	yes	—
99	C₂×C₄²	D₇₆	1	2	yes	—
100	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
101	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
102	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
103	C₄⋊C₈	—	38	8	no	—
104	C₄⋊C₈	—	76	8	no	—
105	C₄×C₈	—	2	4	no	—
106	C₄×C₈	—	2	2	no	—
107	C₄×C₈	C₁₉⋊C₈	1	4	yes	complemented
108	C₄×C₈	Dic₃₈	1	4	yes	—
109	C₄×C₈	D₇₆	1	4	yes	—
110	C₁₉	#8805	1	1	yes	characteristic, complemented, Sylow
111	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
112	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
113	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
114	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
115	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	76	4	no	—
119	C₂×C₈	—	76	8	no	—
120	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
121	C₂×C₈	#64520	1	4	yes	—
122	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
123	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
124	C₄²	—	2	4	no	—
125	C₄²	—	2	2	no	—
126	C₄²	#64516	1	8	yes	—
127	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
128	C₄²	#64520	1	2	yes	—
129	C₄²	C₂×Dic₃₈	1	2	yes	—
130	C₄²	C₂×D₇₆	1	2	yes	—
131	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
136	C₂×C₄	#10597274	1	4	yes	—
137	C₂×C₄	#10597274	1	4	yes	—
138	C₂×C₄	#10597276	1	4	yes	—
139	C₂×C₄	#10597315	1	2	yes	—
140	C₂×C₄	#10597315	1	1	yes	characteristic
141	C₂×C₄	#10597320	1	1	yes	characteristic
142	C₂×C₄	C₂×#64516	1	4	yes	—
143	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
144	C₂×C₄	C₂×#64520	1	2	yes	—
145	C₂×C₄	C₂×#64520	1	1	yes	characteristic
146	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
147	C₈	—	2	4	no	—
148	C₈	—	152	4	no	—
149	C₈	C₄⋊(C₁₉⋊C₈)	1	8	yes	complemented
150	C₂²	#11926414	1	1	yes	characteristic
151	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
152	C₂²	#11926568	1	1	yes	characteristic
153	C₂²	C₂×#10597274	1	2	yes	—
154	C₂²	C₂×#10597276	1	2	yes	—
155	C₄	—	2	4	no	—
156	C₄	—	2	2	no	—
157	C₄	#11926295	1	8	yes	complemented
158	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
159	C₄	#11926568	1	2	yes	—
160	C₄	#11926917	1	2	yes	—
161	C₄	#11926942	1	2	yes	—
162	C₂	C₂×#11926295	1	2	yes	—
163	C₂	#14562391	1	2	yes	—
164	C₂	#14563787	1	1	yes	characteristic
165	C₂	#14563792	1	1	yes	characteristic
166	C₂	#14563807	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	#8805
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
22. C₄×C₈×C₁₉	C₈	semidirect
65. C₈×C₁₉	C₄⋊C₈	semidirect
77. C₄×C₁₉	#334	semidirect
107. C₄×C₈	C₁₉⋊C₈	semidirect
110. C₁₉	#8805	semidirect
149. C₈	C₄⋊(C₁₉⋊C₈)	semidirect
157. C₄	#11926295	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
C₂×#11926295	2
C₄²×C₈×C₁₉	2
#8805	19