Subgroups — #18071912

Order 4864.

486 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563381	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	#11926299	C₄	1	4	yes	—
13	#11926299	C₄	1	4	yes	—
14	#11926266	C₄	1	4	yes	complemented
15	#11926266	C₄	1	4	yes	complemented
16	#11926265	C₄	1	4	yes	complemented
17	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₄³×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#336	C₄	1	4	yes	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
37	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
38	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
39	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
40	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
43	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
45	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₉	—	2	4	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	C₄²	1	4	yes	—
51	C₂×C₈×C₁₉	C₄²	1	4	yes	—
52	C₄²×C₁₉	—	2	4	no	—
53	C₄²×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	—	2	4	no	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₁₉⋊C₈	—	2	4	no	—
60	C₂×C₁₉⋊C₈	—	2	4	no	—
61	C₂×C₁₉⋊C₈	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
64	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
65	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
66	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
67	#7845	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	2	4	no	—
72	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#131	1	4	yes	—
79	C₂×C₄×C₁₉	#131	1	4	yes	—
80	C₂×C₄×C₁₉	#131	1	4	yes	—
81	C₈×C₁₉	—	2	4	no	—
82	C₈×C₁₉	—	2	4	no	—
83	C₁₉⋊C₈	—	2	4	no	—
84	C₁₉⋊C₈	—	2	4	no	—
85	C₁₉⋊C₈	—	2	4	no	—
86	C₁₉⋊C₈	—	2	4	no	—
87	#1744	—	19	1	no	—
88	#1744	—	19	1	no	—
89	#1744	D₁₉	1	1	yes	characteristic
90	C₂×#322	—	19	1	no	—
91	C₂×#322	—	19	1	no	—
92	C₂×#322	—	19	1	no	—
93	C₂×C₈²	—	19	1	no	—
94	C₂²×C₁₉	C₄³	1	1	yes	characteristic
95	C₂²×C₁₉	#405	1	2	yes	—
96	C₂²×C₁₉	#405	1	2	yes	—
97	C₂²×C₁₉	#405	1	2	yes	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	#405	1	2	yes	—
100	C₄×C₁₉	#405	1	2	yes	—
101	C₄×C₁₉	#405	1	2	yes	—
102	C₄×C₁₉	#405	1	2	yes	—
103	C₄×C₁₉	#405	1	2	yes	—
104	C₄×C₁₉	#405	1	2	yes	—
105	C₂×C₄×C₈	—	19	1	no	—
106	C₂×C₄×C₈	—	19	1	no	—
107	C₂×C₄×C₈	—	19	1	no	—
108	C₂×C₄×C₈	—	19	1	no	—
109	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₄³	C₂×D₁₉	1	1	yes	characteristic
112	#336	—	19	4	no	—
113	#336	—	19	4	no	—
114	#336	Dic₁₉	1	4	yes	—
115	#322	—	19	4	no	—
116	#322	—	19	4	no	—
117	#322	—	19	4	no	—
118	C₈²	—	19	4	no	—
119	C₂×C₁₉	#1454	1	4	yes	—
120	C₂×C₁₉	#1726	1	1	yes	characteristic
121	C₂×C₁₉	#1726	1	1	yes	characteristic
122	C₂×C₁₉	#1726	1	1	yes	characteristic
123	C₂²×C₈	—	19	2	no	—
124	C₂²×C₈	—	19	2	no	—
125	C₂²×C₈	—	19	2	no	—
126	C₂²×C₈	—	19	2	no	—
127	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
128	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
129	C₂×C₄²	C₄×D₁₉	1	2	yes	—
130	C₂×C₄²	C₄×D₁₉	1	2	yes	—
131	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
132	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
133	C₄×C₈	—	19	2	no	—
134	C₄×C₈	—	19	2	no	—
135	C₄×C₈	—	19	2	no	—
136	C₄×C₈	—	19	2	no	—
137	C₄×C₈	—	19	2	no	—
138	C₄×C₈	—	19	2	no	—
139	C₄×C₈	—	19	2	no	—
140	C₄×C₈	—	19	2	no	—
141	C₄×C₈	C₄×D₁₉	1	2	yes	—
142	C₄×C₈	C₄×D₁₉	1	2	yes	—
143	C₄×C₈	C₄×D₁₉	1	2	yes	—
144	C₄×C₈	C₄×D₁₉	1	2	yes	—
145	C₁₉	#7845	1	1	yes	characteristic, complemented, Sylow
146	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
147	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
149	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	19	4	no	—
153	C₂×C₈	—	19	4	no	—
154	C₂×C₈	—	19	4	no	—
155	C₂×C₈	—	19	4	no	—
156	C₂×C₈	—	38	4	no	—
157	C₂×C₈	—	38	4	no	—
158	C₂×C₈	—	38	4	no	—
159	C₂×C₈	—	38	4	no	—
160	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
161	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
162	C₄²	—	2	4	no	—
163	C₄²	—	2	4	no	—
164	C₄²	—	2	4	no	—
165	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
166	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
167	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
168	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
169	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
174	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
175	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
176	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
177	C₂×C₄	#10597347	1	4	yes	—
178	C₂×C₄	#10597353	1	4	yes	—
179	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
180	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
181	C₂×C₄	#10597394	1	4	yes	—
182	C₈	—	2	4	no	—
183	C₈	—	2	4	no	—
184	C₈	—	38	4	no	—
185	C₈	—	38	4	no	—
186	C₈	—	38	4	no	—
187	C₈	—	38	4	no	—
188	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
189	C₂²	#11926499	1	2	yes	—
190	C₂²	#11926500	1	2	yes	—
191	C₂²	#11926502	1	2	yes	—
192	C₄	—	4	4	no	—
193	C₄	#11926498	1	2	yes	—
194	C₄	#11926498	1	2	yes	—
195	C₄	#11926500	1	2	yes	—
196	C₄	#11926500	1	2	yes	—
197	C₄	#11926501	1	2	yes	—
198	C₄	#11926501	1	2	yes	—
199	C₂	#14561935	1	4	yes	—
200	C₂	#14563321	1	1	yes	characteristic
201	C₂	#14563322	1	1	yes	characteristic
202	C₂	#14563323	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#7845
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1744

Complements

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

N	H ≅ G/N	type
14. #11926266	C₄	semidirect
15. #11926266	C₄	semidirect
16. #11926265	C₄	semidirect
17. C₈×C₁₉⋊C₈	C₄	semidirect
145. C₁₉	#7845	semidirect

Maximal subgroups

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

subgroup	index
#14563381	2
C₂×#11926266	2
C₂×#11926265	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1744	2
#7845	19