Subgroups — #18069475

Order 4864.

274 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597275	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597275	C₄	1	2	yes	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₄×C₄⋊Dic₁₉	—	2	1	no	—
7	#11926307	—	2	1	no	—
8	#11926295	—	2	1	no	—
9	#11926295	C₄	1	2	yes	complemented
10	C₂²×C₁₆×C₁₉	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#346	—	2	1	no	—
13	C₁₉×#346	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	2	no	—
18	C₂×C₄×Dic₁₉	—	4	1	no	—
19	C₂²×C₁₉⋊C₈	—	4	1	no	—
20	C₂×C₁₆×C₁₉	—	2	4	no	—
21	C₂×C₁₆×C₁₉	—	2	2	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	1	no	—
27	#10597275	—	2	2	no	—
28	#10597275	C₈	1	4	yes	complemented
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	C₄²	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	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
42	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
45	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
46	C₄⋊Dic₁₉	—	2	4	no	—
47	C₄⋊Dic₁₉	—	4	2	no	—
48	C₄×Dic₁₉	—	8	2	no	—
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₂×C₁₉⋊C₈	—	8	2	no	—
51	C₁₆×C₁₉	—	2	4	no	—
52	#7178	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	#102	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
59	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#104	1	2	yes	—
63	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
65	C₂×Dic₁₉	—	4	4	no	—
66	C₂×Dic₁₉	—	8	2	no	—
67	C₂×Dic₁₉	—	8	2	no	—
68	C₈×C₁₉	—	2	1	no	—
69	C₈×C₁₉	—	2	1	no	—
70	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
71	C₈×C₁₉	#97	1	1	yes	characteristic
72	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
73	C₁₉⋊C₈	—	8	2	no	—
74	C₂×#346	D₁₉	1	1	yes	characteristic
75	C₄×#107	—	19	1	no	—
76	C₂×#334	—	19	1	no	—
77	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
78	C₂²×C₁₉	#340	1	1	yes	characteristic
79	C₂²×C₁₉	#360	1	2	yes	—
80	C₂²×C₁₉	#361	1	1	yes	characteristic
81	C₂²×C₁₉	#362	1	1	yes	characteristic
82	C₄×C₁₉	—	2	1	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
87	C₄×C₁₉	#336	1	1	yes	characteristic
88	C₄×C₁₉	#339	1	1	yes	characteristic
89	Dic₁₉	—	8	4	no	—
90	C₂²×C₁₆	—	2	1	no	—
91	C₂×#107	—	19	2	no	—
92	C₂×C₄⋊C₈	—	38	1	no	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₄×C₄⋊C₄	—	38	1	no	—
95	#346	—	2	1	no	—
96	#346	Dic₁₉	1	2	yes	complemented
97	#340	—	38	1	no	—
98	#334	—	19	2	no	—
99	#334	—	38	1	no	—
100	C₂×C₁₉	#1279	1	1	yes	characteristic
101	C₂×C₁₉	#1333	1	2	yes	—
102	C₂×C₁₉	#1334	1	2	yes	—
103	C₂×C₁₉	#1386	1	1	yes	characteristic
104	C₂×C₁₉	#1387	1	1	yes	characteristic
105	C₂²×C₈	—	76	1	no	—
106	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
107	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	C₂×C₄⋊C₄	—	38	2	no	—
109	C₂×C₄²	—	76	1	no	—
110	C₂×C₄²	D₇₆	1	1	yes	characteristic
111	C₂×C₁₆	—	2	4	no	—
112	C₂×C₁₆	—	2	2	no	—
113	#107	—	19	4	no	—
114	#107	—	38	2	no	—
115	C₄⋊C₈	—	38	2	no	—
116	C₄⋊C₈	—	76	1	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	#95	—	76	1	no	—
122	C₁₉	#7178	1	1	yes	characteristic, complemented, Sylow
123	C₂²×C₄	—	76	2	no	—
124	C₂²×C₄	#64516	1	1	yes	characteristic
125	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
126	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	76	2	no	—
129	C₂×C₈	—	152	2	no	—
130	C₂×C₈	C₈×D₁₉	1	2	yes	—
131	C₂×C₈	#64515	1	2	yes	—
132	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
133	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
134	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
135	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
136	C₄⋊C₄	—	38	4	no	—
137	C₄⋊C₄	—	76	2	no	—
138	C₄²	—	152	2	no	—
139	C₄²	#64516	1	1	yes	characteristic
140	C₄²	Dic₇₆	1	1	yes	characteristic
141	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
142	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
143	C₁₆	—	2	4	no	—
144	C₂³	#10597278	1	1	yes	characteristic
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	76	4	no	—
149	C₂×C₄	—	152	2	no	—
150	C₂×C₄	—	152	2	no	—
151	C₂×C₄	#10597262	1	2	yes	—
152	C₂×C₄	#10597273	1	1	yes	characteristic
153	C₂×C₄	#10597273	1	1	yes	characteristic
154	C₂×C₄	#10597274	1	1	yes	characteristic
155	C₂×C₄	#10597275	1	1	yes	characteristic
156	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
157	C₂×C₄	#10597278	1	1	yes	characteristic
158	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
159	C₈	—	2	1	no	—
160	C₈	—	2	1	no	—
161	C₈	—	152	2	no	—
162	C₈	C₈×Dic₁₉	1	1	yes	characteristic
163	C₈	Dic₁₉⋊C₈	1	2	yes	—
164	C₈	#10597272	1	1	yes	characteristic
165	C₂²	#11926273	1	2	yes	—
166	C₂²	#11926307	1	1	yes	characteristic
167	C₂²	#11926355	1	2	yes	—
168	C₂²	#11926358	1	1	yes	characteristic
169	C₂²	#11926361	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	152	4	no	—
175	C₄	#11926276	1	2	yes	—
176	C₄	#11926298	1	1	yes	characteristic
177	C₄	#11926304	1	1	yes	characteristic
178	C₂	#14561475	1	1	yes	characteristic
179	C₂	#14561603	1	2	yes	—
180	C₂	#14561606	1	2	yes	—
181	C₂	#14561741	1	1	yes	characteristic
182	C₂	#14561744	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597278
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#346	C₂
socle, prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#346	D₁₉
hypocenter	C₁₉	#7178
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
9. #11926295	C₄	semidirect
13. C₁₉×#346	C₄	semidirect
28. #10597275	C₈	semidirect
96. #346	Dic₁₉	semidirect
122. C₁₉	#7178	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597275	2
C₂×#11926295	2
C₂×C₁₉×#346	2
#7178	19