Subgroups — #18076280

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 174 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×#11926297	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	#11926297	—	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	D₈	1	4	yes	—
43	C₄²×C₁₉	Q₁₆	1	4	yes	—
44	C₄²×C₁₉	C₂×D₄	1	2	yes	—
45	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
46	C₂×C₁₉⋊C₈	—	4	4	no	—
47	C₂×C₁₉⋊C₈	—	4	8	no	—
48	#8806	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
54	C₂×C₄×C₁₉	#107	1	4	yes	—
55	C₂×C₄×C₁₉	#107	1	4	yes	—
56	C₂×C₄×C₁₉	#108	1	4	yes	—
57	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
60	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
65	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
66	C₈×C₁₉	—	2	4	no	—
67	C₈×C₁₉	C₄⋊C₈	1	8	yes	complemented
68	C₁₉⋊C₈	—	8	4	no	—
69	#1842	—	19	2	no	—
70	C₄²×C₈	D₁₉	1	1	yes	characteristic
71	C₂×#335	—	19	4	no	—
72	C₂²×C₁₉	#384	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
74	C₂²×C₁₉	#423	1	1	yes	characteristic
75	C₂²×C₁₉	C₂×#107	1	2	yes	—
76	C₂²×C₁₉	C₂×#108	1	2	yes	—
77	C₄×C₁₉	—	2	4	no	—
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	#335	1	8	yes	complemented
80	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
81	C₄×C₁₉	#423	1	2	yes	—
82	C₄×C₁₉	#493	1	1	yes	characteristic
83	C₄×C₁₉	#494	1	1	yes	characteristic
84	C₄×C₁₉	#500	1	2	yes	—
85	C₂×C₄⋊C₈	—	19	4	no	—
86	C₂×C₄⋊C₈	—	38	4	no	—
87	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
88	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
89	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
91	C₄³	C₂×D₁₉	1	1	yes	characteristic
92	#335	—	38	8	no	—
93	C₂×C₁₉	C₂×#335	1	2	yes	—
94	C₂×C₁₉	#1567	1	2	yes	—
95	C₂×C₁₉	#1842	1	1	yes	characteristic
96	C₂×C₁₉	#1845	1	1	yes	characteristic
97	C₂×C₁₉	#1848	1	1	yes	characteristic
98	C₂²×C₈	—	38	4	no	—
99	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
100	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
101	C₂×C₄²	Dic₃₈	1	2	yes	—
102	C₂×C₄²	D₇₆	1	2	yes	—
103	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
104	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
105	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
106	C₄⋊C₈	—	38	8	no	—
107	C₄⋊C₈	—	76	8	no	—
108	C₄×C₈	—	2	4	no	—
109	C₄×C₈	—	2	2	no	—
110	C₄×C₈	C₁₉⋊C₈	1	4	yes	complemented
111	C₄×C₈	Dic₃₈	1	4	yes	—
112	C₄×C₈	D₇₆	1	4	yes	—
113	C₁₉	#8806	1	1	yes	characteristic, complemented, Sylow
114	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
115	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
116	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
117	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
118	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	76	4	no	—
122	C₂×C₈	—	76	8	no	—
123	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
124	C₂×C₈	#64520	1	4	yes	—
125	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
126	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
127	C₄²	—	2	4	no	—
128	C₄²	—	2	2	no	—
129	C₄²	D₁₅₂	1	4	yes	—
130	C₄²	Dic₇₆	1	4	yes	—
131	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
132	C₄²	#64520	1	2	yes	—
133	C₄²	C₂×Dic₃₈	1	2	yes	—
134	C₄²	C₂×D₇₆	1	2	yes	—
135	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
140	C₂×C₄	#10597275	1	4	yes	—
141	C₂×C₄	#10597275	1	4	yes	—
142	C₂×C₄	#10597276	1	4	yes	—
143	C₂×C₄	#10597315	1	2	yes	—
144	C₂×C₄	#10597315	1	1	yes	characteristic
145	C₂×C₄	#10597320	1	1	yes	characteristic
146	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
147	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
148	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
149	C₂×C₄	C₂×#64520	1	2	yes	—
150	C₂×C₄	C₂×#64520	1	1	yes	characteristic
151	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
152	C₈	—	2	4	no	—
153	C₈	—	152	4	no	—
154	C₈	C₄⋊(C₁₉⋊C₈)	1	8	yes	complemented
155	C₂²	#11926414	1	1	yes	characteristic
156	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
157	C₂²	#11926568	1	1	yes	characteristic
158	C₂²	C₂×#10597275	1	2	yes	—
159	C₂²	C₂×#10597276	1	2	yes	—
160	C₄	—	2	4	no	—
161	C₄	—	2	2	no	—
162	C₄	#11926297	1	8	yes	complemented
163	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
164	C₄	#11926568	1	2	yes	—
165	C₄	#11926921	1	1	yes	characteristic
166	C₄	#11926924	1	1	yes	characteristic
167	C₄	#11926949	1	2	yes	—
168	C₂	C₂×#11926297	1	2	yes	—
169	C₂	#14562394	1	2	yes	—
170	C₂	#14563787	1	1	yes	characteristic
171	C₂	#14563795	1	1	yes	characteristic
172	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	#8806
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
67. C₈×C₁₉	C₄⋊C₈	semidirect
79. C₄×C₁₉	#335	semidirect
110. C₄×C₈	C₁₉⋊C₈	semidirect
113. C₁₉	#8806	semidirect
154. C₈	C₄⋊(C₁₉⋊C₈)	semidirect
162. C₄	#11926297	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×#11926297	2
C₄²×C₈×C₁₉	2
#8806	19