Subgroups — #18069717

Order 4864.

222 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926365	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926365	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1846	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597269	—	2	1	no	—
6	#11926365	—	2	1	no	—
7	#11926365	—	2	1	no	—
8	#11926365	C₄	1	2	yes	complemented
9	#11926365	C₄	1	2	yes	complemented
10	C₂×C₁₉×#107	—	2	1	no	—
11	C₂×C₁₉×#106	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#382	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₁₉×#107	—	4	1	no	—
19	C₁₉×#107	—	4	1	no	—
20	C₁₉×#106	—	4	1	no	—
21	C₁₉×#106	—	4	1	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
26	C₁₉×#95	—	4	2	no	—
27	#10597269	—	2	2	no	—
28	#10597269	—	2	2	no	—
29	#10597269	—	4	1	no	—
30	#10597269	—	4	1	no	—
31	C₂×C₁₉⋊C₁₆	—	4	1	no	—
32	C₂×C₁₉⋊C₁₆	—	4	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	4	2	no	—
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₄²×C₁₉	—	2	1	no	—
51	C₄²×C₁₉	C₄²	1	1	yes	characteristic
52	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₁₉⋊C₁₆	—	4	2	no	—
54	C₁₉⋊C₁₆	—	4	2	no	—
55	#7271	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	#100	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	—	8	4	no	—
61	C₂×C₄×C₁₉	—	8	2	no	—
62	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
68	C₈×C₁₉	#102	1	1	yes	characteristic
69	C₈×C₁₉	#102	1	1	yes	characteristic
70	C₈×C₁₉	#103	1	1	yes	characteristic
71	C₈×C₁₉	#103	1	1	yes	characteristic
72	C₈×C₁₉	#106	1	1	yes	characteristic
73	C₈×C₁₉	#106	1	1	yes	characteristic
74	C₈×C₁₉	#107	1	1	yes	characteristic
75	C₈×C₁₉	#107	1	1	yes	characteristic
76	C₂×#364	—	19	1	no	—
77	C₂×#364	—	19	1	no	—
78	#1846	D₁₉	1	1	yes	characteristic
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	#331	1	1	yes	characteristic
81	C₂²×C₁₉	#333	1	1	yes	characteristic
82	C₂²×C₁₉	#343	1	1	yes	characteristic
83	C₄×C₁₉	—	4	1	no	—
84	C₄×C₁₉	—	4	1	no	—
85	C₄×C₁₉	—	16	2	no	—
86	C₄×C₁₉	#332	1	1	yes	characteristic
87	C₄×C₁₉	#332	1	1	yes	characteristic
88	C₄×C₁₉	#340	1	1	yes	characteristic
89	C₄×C₁₉	#340	1	1	yes	characteristic
90	C₂×M₃₂	—	38	1	no	—
91	C₂×M₃₂	—	38	1	no	—
92	C₂×#107	—	2	1	no	—
93	C₂×#106	—	2	1	no	—
94	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
95	#382	Dic₁₉	1	2	yes	—
96	#364	—	19	2	no	—
97	#364	—	19	2	no	—
98	#364	—	38	1	no	—
99	#364	—	38	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	—	2	1	no	—
102	C₂×C₁₉	#1296	1	1	yes	characteristic
103	C₂×C₁₉	#1366	1	2	yes	—
104	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
108	M₃₂	—	38	2	no	—
109	M₃₂	—	38	2	no	—
110	M₃₂	—	76	1	no	—
111	M₃₂	—	76	1	no	—
112	C₂×C₁₆	—	76	1	no	—
113	C₂×C₁₆	—	76	1	no	—
114	#107	—	4	1	no	—
115	#107	—	4	1	no	—
116	#106	—	4	1	no	—
117	#106	—	4	1	no	—
118	C₄×C₈	Dic₃₈	1	1	yes	characteristic
119	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
120	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
121	C₄×C₈	D₇₆	1	1	yes	characteristic
122	#95	—	4	2	no	—
123	C₁₉	#7271	1	1	yes	characteristic, complemented, Sylow
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	—	4	2	no	—
126	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
128	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
129	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
130	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₂×C₈	#64525	1	1	yes	characteristic
132	C₂×C₈	#64525	1	1	yes	characteristic
133	C₂×C₈	#64526	1	1	yes	characteristic
134	C₂×C₈	#64526	1	1	yes	characteristic
135	C₂×C₈	#64527	1	1	yes	characteristic
136	C₂×C₈	#64527	1	1	yes	characteristic
137	C₂×C₈	#64528	1	1	yes	characteristic
138	C₂×C₈	#64528	1	1	yes	characteristic
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄²	—	2	1	no	—
142	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
143	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
144	C₁₆	—	76	2	no	—
145	C₁₆	—	76	2	no	—
146	C₂³	#10597290	1	1	yes	characteristic
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	8	4	no	—
151	C₂×C₄	—	8	2	no	—
152	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
153	C₂×C₄	#10597289	1	1	yes	characteristic
154	C₂×C₄	#10597289	1	1	yes	characteristic
155	C₂×C₄	#10597292	1	1	yes	characteristic
156	C₂×C₄	#10597292	1	1	yes	characteristic
157	C₂×C₄	#10597293	1	1	yes	characteristic
158	C₈	#10597264	1	1	yes	characteristic
159	C₈	#10597264	1	1	yes	characteristic
160	C₈	#10597265	1	1	yes	characteristic
161	C₈	#10597265	1	1	yes	characteristic
162	C₈	#10597266	1	1	yes	characteristic
163	C₈	#10597266	1	1	yes	characteristic
164	C₈	#10597267	1	1	yes	characteristic
165	C₈	#10597267	1	1	yes	characteristic
166	C₂²	—	2	2	no	—
167	C₂²	#11926288	1	1	yes	characteristic
168	C₂²	#11926293	1	1	yes	characteristic
169	C₂²	#11926313	1	1	yes	characteristic
170	C₄	—	4	1	no	—
171	C₄	—	4	1	no	—
172	C₄	—	16	2	no	—
173	C₄	#11926290	1	1	yes	characteristic
174	C₄	#11926290	1	1	yes	characteristic
175	C₄	#11926306	1	1	yes	characteristic
176	C₄	#11926306	1	1	yes	characteristic
177	C₂	—	2	1	no	—
178	C₂	—	2	1	no	—
179	C₂	#14561518	1	1	yes	characteristic
180	C₂	#14561696	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926293
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1846	C₂
socle	C₂²×C₁₉	#333
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1846	D₁₉
hypocenter	C₁₉	#7271
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1846

Complements

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

N	H ≅ G/N	type
8. #11926365	C₄	semidirect
9. #11926365	C₄	semidirect
123. C₁₉	#7271	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926365	2
C₁₉×#1846	2
#7271	19