Subgroups — #18076296

Order 4864.

362 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563751	C₂	1	2	yes	maximal
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	2	yes	maximal
4	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
9	#11926298	—	2	4	no	—
10	#11926298	C₄	1	2	yes	—
11	#11926298	C₄	1	2	yes	—
12	#11926296	—	2	4	no	—
13	#11926295	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#334	—	2	2	no	—
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
23	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
24	C₂²×C₁₉⋊C₈	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	D₄	1	2	yes	—
29	C₄×C₈×C₁₉	Q₈	1	2	yes	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
33	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
37	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	4	4	no	—
42	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
48	C₄×Dic₁₉	—	2	2	no	—
49	C₄×Dic₁₉	—	2	2	no	—
50	C₄×Dic₁₉	—	2	4	no	—
51	C₄×Dic₁₉	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	C₂×C₁₉⋊C₈	—	4	4	no	—
56	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
57	#8811	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#131	1	2	yes	—
67	C₂×C₄×C₁₉	#131	1	2	yes	—
68	C₂×C₄×C₁₉	#135	1	4	yes	—
69	C₂×Dic₁₉	—	2	4	no	—
70	C₂×Dic₁₉	—	2	4	no	—
71	C₂×Dic₁₉	—	2	4	no	—
72	C₈×C₁₉	—	2	2	no	—
73	C₈×C₁₉	—	2	2	no	—
74	C₈×C₁₉	—	8	2	no	—
75	C₁₉⋊C₈	—	2	4	no	—
76	C₁₉⋊C₈	—	8	2	no	—
77	#1831	—	19	2	no	—
78	#1744	—	19	1	no	—
79	C₂×#335	—	19	2	no	—
80	C₂×#334	—	19	1	no	—
81	C₂×#334	D₁₉	1	1	yes	characteristic
82	C₂²×C₁₉	#384	1	1	yes	characteristic
83	C₂²×C₁₉	#424	1	2	yes	—
84	C₂²×C₁₉	#427	1	2	yes	—
85	C₂²×C₁₉	#430	1	2	yes	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	#424	1	2	yes	—
89	C₄×C₁₉	#424	1	1	yes	characteristic
90	C₄×C₁₉	#424	1	1	yes	characteristic
91	C₄×C₁₉	#495	1	2	yes	—
92	C₄×C₁₉	#499	1	2	yes	—
93	Dic₁₉	—	4	4	no	—
94	C₂×C₄⋊C₈	—	19	2	no	—
95	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
96	C₂×C₄×C₈	—	19	1	no	—
97	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
98	C₄³	—	19	1	no	—
99	#336	—	19	2	no	—
100	#336	—	19	2	no	—
101	#336	—	38	4	no	—
102	#335	—	38	4	no	—
103	#334	—	2	2	no	—
104	#334	—	38	2	no	—
105	C₂×C₁₉	#1572	1	4	yes	—
106	C₂×C₁₉	#1843	1	1	yes	characteristic
107	C₂×C₁₉	#1846	1	1	yes	characteristic
108	C₂×C₁₉	#1849	1	1	yes	characteristic
109	C₂²×C₈	—	2	2	no	—
110	C₂²×C₈	—	19	2	no	—
111	C₂²×C₈	—	38	2	no	—
112	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
113	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
114	C₂×C₄²	—	19	2	no	—
115	C₂×C₄²	—	19	2	no	—
116	C₂×C₄²	—	19	2	no	—
117	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
118	C₄⋊C₈	—	2	2	no	—
119	C₄⋊C₈	—	2	2	no	—
120	C₄⋊C₈	—	38	2	no	—
121	C₄⋊C₈	—	38	2	no	—
122	C₄×C₈	—	19	2	no	—
123	C₄×C₈	—	19	2	no	—
124	C₄×C₈	Dic₃₈	1	2	yes	—
125	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
126	C₁₉	#8811	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₄	—	19	4	no	—
128	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	4	4	no	—
135	C₂×C₈	—	19	4	no	—
136	C₂×C₈	—	38	2	no	—
137	C₂×C₈	—	38	2	no	—
138	C₂×C₈	—	76	2	no	—
139	C₂×C₈	—	76	4	no	—
140	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
141	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
142	C₄²	—	38	2	no	—
143	C₄²	—	38	2	no	—
144	C₄²	—	38	4	no	—
145	C₄²	—	76	2	no	—
146	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
147	C₄²	D₄×D₁₉	1	1	yes	characteristic
148	C₄²	Q₈×D₁₉	1	1	yes	characteristic
149	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	38	4	no	—
153	C₂×C₄	—	38	4	no	—
154	C₂×C₄	—	38	4	no	—
155	C₂×C₄	#10597334	1	1	yes	characteristic
156	C₂×C₄	#10597334	1	1	yes	characteristic
157	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
158	C₂×C₄	#10597347	1	2	yes	—
159	C₂×C₄	#10597353	1	2	yes	—
160	C₂×C₄	#10597362	1	4	yes	—
161	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
162	C₂×C₄	#10597386	1	1	yes	characteristic
163	C₂×C₄	#10597390	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	2	2	no	—
166	C₈	—	8	2	no	—
167	C₈	—	38	4	no	—
168	C₈	—	152	2	no	—
169	C₂²	#11926413	1	1	yes	characteristic
170	C₂²	#11926569	1	2	yes	—
171	C₂²	#11926579	1	2	yes	—
172	C₂²	#11926591	1	2	yes	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	76	4	no	—
176	C₄	#11926569	1	2	yes	—
177	C₄	#11926570	1	1	yes	characteristic
178	C₄	#11926572	1	1	yes	characteristic
179	C₄	#11926925	1	2	yes	—
180	C₄	#11926944	1	2	yes	—
181	C₂	#14562412	1	4	yes	—
182	C₂	#14563788	1	1	yes	characteristic
183	C₂	#14563796	1	1	yes	characteristic
184	C₂	#14563808	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#334	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#334	D₁₉
hypocenter	C₁₉	#8811
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
126. C₁₉	#8811	semidirect

Maximal subgroups

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

subgroup	index
#14563751	2
#14563380	2
C₂×#11926296	2
C₂×#11926295	2
C₂×C₁₉×#334	2
#8811	19