Subgroups — #18069721

Order 4864.

208 conjugacy classes of subgroups.

The subgroup lattice has 178 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	#14563807	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597276	—	2	1	no	—
6	C₂×#10597276	—	2	1	no	—
7	#11926568	C₄	1	2	yes	—
8	#11926365	—	2	1	no	—
9	#11926365	C₄	1	2	yes	—
10	C₂×C₁₉×M₃₂	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#364	—	2	1	no	—
13	C₁₉×#364	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×#64520	—	2	2	no	—
18	C₁₉×M₃₂	—	2	2	no	—
19	C₁₉×M₃₂	—	4	1	no	—
20	C₂×C₁₆×C₁₉	—	4	1	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
25	#10597276	—	4	1	no	—
26	#10597276	—	4	1	no	—
27	#10597276	—	4	1	no	—
28	#10597276	—	4	1	no	—
29	#10597269	—	2	2	no	—
30	#10597269	—	4	1	no	—
31	C₂×C₁₉⋊C₁₆	—	4	1	no	—
32	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
40	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₈×C₁₉	SD₁₆	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	Q₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
47	C₄²×C₁₉	—	2	1	no	—
48	C₄²×C₁₉	C₄²	1	1	yes	characteristic
49	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	#64520	—	4	2	no	—
51	#64520	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	4	2	no	—
53	C₁₆×C₁₉	—	4	2	no	—
54	C₁₉⋊C₁₆	—	4	2	no	—
55	#7272	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	#101	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	#95	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
66	C₈×C₁₉	#102	1	1	yes	characteristic
67	C₈×C₁₉	#102	1	1	yes	characteristic
68	C₈×C₁₉	#103	1	1	yes	characteristic
69	C₈×C₁₉	#103	1	1	yes	characteristic
70	C₈×C₁₉	#106	1	1	yes	characteristic
71	C₈×C₁₉	#106	1	1	yes	characteristic
72	C₈×C₁₉	#107	1	1	yes	characteristic
73	C₈×C₁₉	#107	1	1	yes	characteristic
74	C₁₉⋊C₈	—	8	2	no	—
75	C₂×#364	—	19	1	no	—
76	C₂×#364	D₁₉	1	1	yes	characteristic
77	#1848	—	19	1	no	—
78	C₂²×C₁₉	—	4	1	no	—
79	C₂²×C₁₉	#332	1	1	yes	characteristic
80	C₂²×C₁₉	#332	1	1	yes	characteristic
81	C₂²×C₁₉	#343	1	1	yes	characteristic
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	4	1	no	—
84	C₄×C₁₉	#331	1	1	yes	characteristic
85	C₄×C₁₉	#333	1	1	yes	characteristic
86	C₄×C₁₉	#340	1	1	yes	characteristic
87	C₄×C₁₉	#340	1	1	yes	characteristic
88	C₂×M₃₂	—	2	1	no	—
89	C₂×M₃₂	—	38	1	no	—
90	C₂×#108	—	38	1	no	—
91	C₂×#108	—	38	1	no	—
92	#423	—	19	2	no	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	#364	—	2	1	no	—
95	#364	—	19	2	no	—
96	#364	—	38	1	no	—
97	#364	Dic₁₉	1	2	yes	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	#1296	1	1	yes	characteristic
102	C₂×M₁₆	—	38	2	no	—
103	C₂²×C₈	D₇₆	1	1	yes	characteristic
104	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
106	M₃₂	—	2	2	no	—
107	M₃₂	—	4	1	no	—
108	M₃₂	—	38	2	no	—
109	M₃₂	—	76	1	no	—
110	C₂×C₁₆	—	4	1	no	—
111	C₂×C₁₆	—	76	1	no	—
112	#108	—	76	1	no	—
113	#108	—	76	1	no	—
114	#108	—	76	1	no	—
115	#108	—	76	1	no	—
116	C₄⋊C₈	—	76	2	no	—
117	C₄×C₈	Dic₃₈	1	1	yes	characteristic
118	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
119	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
120	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
121	C₁₉	#7272	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	—	2	1	no	—
123	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
124	M₁₆	—	76	2	no	—
125	M₁₆	—	76	2	no	—
126	C₂×C₈	—	76	2	no	—
127	C₂×C₈	#64516	1	1	yes	characteristic
128	C₂×C₈	#64516	1	1	yes	characteristic
129	C₂×C₈	D₁₅₂	1	1	yes	characteristic
130	C₂×C₈	Dic₇₆	1	1	yes	characteristic
131	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
132	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
133	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
134	C₂×C₈	#64525	1	1	yes	characteristic
135	C₂×C₈	#64526	1	1	yes	characteristic
136	C₂×C₈	#64527	1	1	yes	characteristic
137	C₂×C₈	#64528	1	1	yes	characteristic
138	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
139	C₄²	—	2	1	no	—
140	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
141	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
142	C₁₆	—	4	2	no	—
143	C₁₆	—	76	2	no	—
144	C₂³	#10597281	1	1	yes	characteristic
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	#10597266	1	1	yes	characteristic
149	C₂×C₄	#10597267	1	1	yes	characteristic
150	C₂×C₄	#10597273	1	1	yes	characteristic
151	C₂×C₄	#10597278	1	1	yes	characteristic
152	C₂×C₄	#10597280	1	1	yes	characteristic
153	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
154	C₈	—	152	2	no	—
155	C₈	#10597264	1	1	yes	characteristic
156	C₈	#10597265	1	1	yes	characteristic
157	C₈	#10597273	1	1	yes	characteristic
158	C₈	#10597274	1	1	yes	characteristic
159	C₈	#10597275	1	1	yes	characteristic
160	C₈	#10597278	1	1	yes	characteristic
161	C₈	#10597289	1	1	yes	characteristic
162	C₈	#10597292	1	1	yes	characteristic
163	C₂²	—	4	1	no	—
164	C₂²	#11926289	1	1	yes	characteristic
165	C₂²	#11926291	1	1	yes	characteristic
166	C₂²	#11926312	1	1	yes	characteristic
167	C₄	—	2	2	no	—
168	C₄	—	4	1	no	—
169	C₄	#11926287	1	1	yes	characteristic
170	C₄	#11926292	1	1	yes	characteristic
171	C₄	#11926306	1	1	yes	characteristic
172	C₄	#11926307	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	—	2	1	no	—
176	C₂	#14561519	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926292
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#364	C₂
socle	C₂×C₁₉	#1296
prime radical	C₂³×C₁₉	#101
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#364	D₁₉
hypocenter	C₁₉	#7272
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
121. C₁₉	#7272	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
#14563807	2
C₂×C₁₉×#364	2
#7272	19