Subgroups — #18073728

Order 4864.

438 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563488	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	2	yes	maximal
3	#14561470	C₂	1	2	yes	maximal
4	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	C₂×#10597260	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926295	C₄	1	8	yes	complemented
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	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	4	no	—
23	C₄×C₈×C₁₉	—	2	4	no	—
24	C₄×C₈×C₁₉	—	2	4	no	—
25	C₄×C₈×C₁₉	—	2	2	no	—
26	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
27	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
28	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
29	#10597260	—	4	4	no	—
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	C₄²	1	2	yes	—
39	C₂×C₈×C₁₉	C₄²	1	2	yes	—
40	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
41	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
42	C₄²×C₁₉	—	2	4	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	C₄²×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	SD₁₆	1	4	yes	—
47	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
48	C₄²×C₁₉	#41	1	2	yes	—
49	C₂×C₁₉⋊C₈	—	2	8	no	—
50	C₂×C₁₉⋊C₈	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	4	4	no	—
52	#8273	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	#106	1	4	yes	—
60	C₂×C₄×C₁₉	#108	1	4	yes	—
61	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
64	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
65	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
67	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
68	C₂×C₄×C₁₉	#135	1	2	yes	—
69	C₈×C₁₉	—	2	2	no	—
70	C₈×C₁₉	—	2	4	no	—
71	C₈×C₁₉	#97	1	4	yes	complemented
72	C₁₉⋊C₈	—	4	8	no	—
73	#1767	—	19	2	no	—
74	C₄²×C₈	D₁₉	1	1	yes	characteristic
75	C₂×#334	—	19	2	no	—
76	#1277	—	19	2	no	—
77	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₁₉	#423	1	2	yes	—
79	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
80	C₂²×C₁₉	#427	1	1	yes	characteristic
81	C₂²×C₁₉	C₂×#108	1	2	yes	—
82	C₄×C₁₉	—	2	4	no	—
83	C₄×C₁₉	—	2	4	no	—
84	C₄×C₁₉	—	2	2	no	—
85	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
86	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
87	C₄×C₁₉	#432	1	2	yes	—
88	C₄×C₁₉	C₄×SD₁₆	1	4	yes	—
89	C₂×C₄⋊C₈	—	19	4	no	—
90	C₂×#97	—	38	2	no	—
91	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
92	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
95	C₄³	C₂×D₁₉	1	1	yes	characteristic
96	#336	—	38	2	no	—
97	#334	—	19	8	no	—
98	C₂×C₁₉	#1566	1	2	yes	—
99	C₂×C₁₉	#1568	1	2	yes	—
100	C₂×C₁₉	#1767	1	1	yes	characteristic
101	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
102	C₂×C₁₉	C₄×#108	1	1	yes	characteristic
103	C₂²×C₈	—	38	4	no	—
104	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
105	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
106	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
107	C₂×C₄²	Dic₃₈	1	2	yes	—
108	C₂×C₄²	D₇₆	1	1	yes	characteristic
109	C₂×C₄²	D₇₆	1	1	yes	characteristic
110	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
111	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	C₄⋊C₈	—	19	8	no	—
113	C₄⋊C₈	—	38	4	no	—
114	#97	—	76	4	no	—
115	C₄×C₈	—	2	4	no	—
116	C₄×C₈	—	2	4	no	—
117	C₄×C₈	—	2	2	no	—
118	C₄×C₈	C₄×D₁₉	1	4	yes	—
119	C₁₉	#8273	1	1	yes	characteristic, complemented, Sylow
120	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
121	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
122	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
123	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
124	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	38	8	no	—
129	C₂×C₈	—	76	4	no	—
130	C₂×C₈	—	76	4	no	—
131	C₂×C₈	#64520	1	4	yes	—
132	C₂×C₈	#64520	1	4	yes	—
133	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
134	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
135	C₄²	—	2	4	no	—
136	C₄²	—	2	2	no	—
137	C₄²	—	2	2	no	—
138	C₄²	—	2	2	no	—
139	C₄²	#64516	1	4	yes	—
140	C₄²	C₂×C₄×D₁₉	1	2	yes	—
141	C₄²	#64541	1	2	yes	—
142	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	#10597274	1	4	yes	—
149	C₂×C₄	#10597276	1	4	yes	—
150	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
151	C₂×C₄	C₄×D₇₆	1	2	yes	—
152	C₂×C₄	C₂×#64516	1	2	yes	—
153	C₂×C₄	#10597350	1	2	yes	—
154	C₂×C₄	C₂×#64520	1	2	yes	—
155	C₂×C₄	C₂×#64520	1	2	yes	—
156	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
157	C₂×C₄	#10597372	1	1	yes	characteristic
158	C₈	—	2	4	no	—
159	C₈	—	2	2	no	—
160	C₈	—	76	8	no	—
161	C₈	#10597260	1	4	yes	complemented
162	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
163	C₂²	#11926568	1	2	yes	—
164	C₂²	C₂×#10597274	1	1	yes	characteristic
165	C₂²	#11926582	1	1	yes	characteristic
166	C₂²	C₂×#10597276	1	2	yes	—
167	C₄	—	2	4	no	—
168	C₄	—	2	4	no	—
169	C₄	—	2	2	no	—
170	C₄	C₂×#10597260	1	1	yes	characteristic
171	C₄	C₄×#64520	1	1	yes	characteristic
172	C₄	#11926601	1	2	yes	—
173	C₄	C₄×#64516	1	4	yes	—
174	C₂	#14562391	1	2	yes	—
175	C₂	#14562398	1	2	yes	—
176	C₂	#14563488	1	1	yes	characteristic
177	C₂	C₄×#10597274	1	1	yes	characteristic
178	C₂	C₄×#10597276	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
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	#8273
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
8. #11926295	C₄	semidirect
71. C₈×C₁₉	#97	semidirect
119. C₁₉	#8273	semidirect
161. C₈	#10597260	semidirect

Maximal subgroups

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

subgroup	index
#14563488	2
C₂×#11926295	2
#14561470	2
C₄²×C₈×C₁₉	2
#8273	19