Subgroups — C₈×C₄⋊(C₁₉⋊C₈) #18073660

Order 4864.

550 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₉⋊C₈	C₂	1	2	yes	maximal
3	C₁₉⋊#1273	C₂	1	2	yes	maximal
4	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
7	#11926299	C₄	1	4	yes	—
8	C₈×C₁₉⋊C₈	—	2	4	no	—
9	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
22	C₄×C₈×C₁₉	—	2	4	no	—
23	C₄×C₈×C₁₉	—	2	2	no	—
24	C₄×C₈×C₁₉	C₈	1	8	yes	complemented
25	C₄×C₈×C₁₉	D₄	1	2	yes	—
26	C₄×C₈×C₁₉	Q₈	1	2	yes	—
27	C₄⋊(C₁₉⋊C₈)	C₈	1	16	yes	direct product factor
28	C₄×C₁₉⋊C₈	—	2	4	no	—
29	C₄×C₁₉⋊C₈	—	2	4	no	—
30	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
32	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
38	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
39	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
40	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	2	4	no	—
43	C₄²×C₁₉	C₂×C₈	1	8	yes	—
44	C₄²×C₁₉	C₂×C₈	1	4	yes	—
45	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₄²×C₁₉	#41	1	2	yes	—
48	C₂×C₁₉⋊C₈	—	2	8	no	—
49	C₂×C₁₉⋊C₈	—	2	8	no	—
50	C₂×C₁₉⋊C₈	C₂×C₈	1	16	yes	—
51	C₈×C₄⋊C₈	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
58	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
59	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
60	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
63	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
64	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
65	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
67	C₂×C₄×C₁₉	#131	1	4	yes	—
68	C₈×C₁₉	—	2	4	no	—
69	C₈×C₁₉	C₄⋊C₈	1	8	yes	complemented
70	C₁₉⋊C₈	—	2	16	no	—
71	C₄×C₄⋊C₈	—	19	2	no	—
72	C₄²×C₈	D₁₉	1	1	yes	characteristic
73	C₂×C₈²	—	19	2	no	—
74	#1273	—	19	2	no	—
75	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₁₉	C₂×C₄×C₈	1	2	yes	—
77	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
78	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
79	C₂²×C₁₉	#405	1	2	yes	—
80	C₄×C₁₉	—	2	4	no	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	C₈²	1	4	yes	complemented
83	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
84	C₄×C₁₉	#431	1	2	yes	—
85	C₄×C₁₉	C₈×D₄	1	4	yes	—
86	C₄×C₁₉	C₈×Q₈	1	4	yes	—
87	C₂×C₄⋊C₈	—	19	4	no	—
88	C₂×C₄×C₈	—	19	4	no	—
89	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
90	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
91	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
93	C₄³	C₂×D₁₉	1	1	yes	characteristic
94	#336	—	19	4	no	—
95	C₈²	—	38	4	no	—
96	C₂×C₁₉	C₂×C₈²	1	1	yes	characteristic
97	C₂×C₁₉	C₈×M₁₆	1	2	yes	—
98	C₂×C₁₉	#1450	1	1	yes	characteristic
99	C₂×C₁₉	C₄×C₄⋊C₈	1	1	yes	characteristic
100	C₂×C₁₉	C₈×C₄⋊C₄	1	2	yes	—
101	C₂²×C₈	—	19	8	no	—
102	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
103	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
104	C₂×C₄²	C₄×D₁₉	1	2	yes	—
105	C₂×C₄²	C₄×D₁₉	1	2	yes	—
106	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
107	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
108	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
109	C₄⋊C₈	—	19	16	no	—
110	C₄×C₈	—	2	4	no	—
111	C₄×C₈	—	2	2	no	—
112	C₄×C₈	—	38	4	no	—
113	C₄×C₈	—	38	4	no	—
114	C₄×C₈	C₁₉⋊C₈	1	8	yes	complemented
115	C₄×C₈	Dic₃₈	1	2	yes	—
116	C₄×C₈	D₇₆	1	2	yes	—
117	C₁₉	C₈×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
119	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
120	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
121	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
122	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
123	C₂×C₈	—	2	2	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	19	16	no	—
126	C₂×C₈	—	38	8	no	—
127	C₂×C₈	—	38	8	no	—
128	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
129	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
130	C₂×C₈	#64520	1	4	yes	—
131	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
132	C₄²	—	2	4	no	—
133	C₄²	—	2	2	no	—
134	C₄²	C₈×D₁₉	1	8	yes	—
135	C₄²	C₂×C₁₉⋊C₈	1	4	yes	—
136	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
137	C₄²	C₂×D₇₆	1	1	yes	characteristic
138	C₄²	#64541	1	2	yes	—
139	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	C₄×C₁₉⋊C₈	1	2	yes	—
144	C₂×C₄	C₄×C₁₉⋊C₈	1	2	yes	—
145	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
146	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
147	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
148	C₂×C₄	C₄×D₇₆	1	2	yes	—
149	C₂×C₄	C₂×C₈×D₁₉	1	4	yes	—
150	C₂×C₄	#10597347	1	4	yes	—
151	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
152	C₂×C₄	C₂×#64520	1	2	yes	—
153	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
154	C₂×C₄	#10597372	1	1	yes	characteristic
155	C₈	—	2	4	no	—
156	C₈	—	38	16	no	—
157	C₈	C₄⋊(C₁₉⋊C₈)	1	8	yes	direct product factor
158	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
159	C₂²	C₂×C₈×Dic₁₉	1	2	yes	—
160	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
161	C₂²	C₄×#64520	1	1	yes	characteristic
162	C₂²	#11926499	1	2	yes	—
163	C₄	—	2	4	no	—
164	C₄	—	2	2	no	—
165	C₄	C₈×C₁₉⋊C₈	1	4	yes	complemented
166	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
167	C₄	#11926597	1	2	yes	—
168	C₄	C₈×D₇₆	1	4	yes	—
169	C₄	C₈×Dic₃₈	1	4	yes	—
170	C₂	C₂×C₈×C₁₉⋊C₈	1	1	yes	characteristic
171	C₂	C₈×#64520	1	2	yes	—
172	C₂	#14561918	1	1	yes	characteristic
173	C₂	C₄×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
174	C₂	C₈×C₄⋊Dic₁₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₈²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	C₈×C₄⋊C₈
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
24. C₄×C₈×C₁₉	C₈	semidirect
27. C₄⋊(C₁₉⋊C₈)	C₈	direct (N × H)
69. C₈×C₁₉	C₄⋊C₈	semidirect
82. C₄×C₁₉	C₈²	semidirect
114. C₄×C₈	C₁₉⋊C₈	semidirect
117. C₁₉	C₈×C₄⋊C₈	semidirect
157. C₈	C₄⋊(C₁₉⋊C₈)	direct (N × H)
165. C₄	C₈×C₁₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉⋊#1273	2
C₄²×C₈×C₁₉	2
C₈×C₄⋊C₈	19

Subgroups — C8×C4⋊(C19⋊C8) #18073660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₄⋊(C₁₉⋊C₈) #18073660