Subgroups — #18069487

Order 4864.

258 conjugacy classes of subgroups.

The subgroup lattice has 198 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	#14563514	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597276	C₄	1	1	yes	characteristic
6	#11926582	C₄	1	1	yes	characteristic
7	#11926499	—	2	1	no	—
8	#11926365	—	2	1	no	—
9	#11926365	C₄	1	2	yes	complemented
10	#11926304	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#322	—	2	1	no	—
14	C₁₉×#322	C₄	1	2	yes	complemented
15	C₂²×C₈×C₁₉	—	2	2	no	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	#10597372	—	2	1	no	—
20	C₂×#64520	—	2	1	no	—
21	C₄×C₈×C₁₉	—	2	2	no	—
22	C₄×C₈×C₁₉	—	2	2	no	—
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
27	#10597276	—	2	1	no	—
28	#10597276	C₈	1	2	yes	complemented
29	#10597275	C₈	1	2	yes	complemented
30	#10597274	—	2	1	no	—
31	#10597272	—	4	1	no	—
32	C₈×Dic₁₉	—	4	1	no	—
33	#10597269	—	2	2	no	—
34	#10597269	—	4	1	no	—
35	C₂×C₁₉⋊C₁₆	—	4	1	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	—	2	4	no	—
39	C₂×C₈×C₁₉	—	4	4	no	—
40	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
49	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
50	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
52	C₄²×C₁₉	—	2	1	no	—
53	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂²⋊Dic₁₉	—	4	1	no	—
56	C₄⋊Dic₁₉	—	2	2	no	—
57	C₄×Dic₁₉	—	4	1	no	—
58	#64520	—	2	2	no	—
59	#64520	—	4	1	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	C₁₉⋊C₁₆	—	4	2	no	—
62	#7182	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#104	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
73	C₂×Dic₁₉	—	4	2	no	—
74	C₈×C₁₉	—	4	4	no	—
75	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
76	C₈×C₁₉	#97	1	1	yes	characteristic
77	C₈×C₁₉	#102	1	1	yes	characteristic
78	C₈×C₁₉	#103	1	1	yes	characteristic
79	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
80	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
81	C₈×C₁₉	#106	1	1	yes	characteristic
82	C₈×C₁₉	#107	1	1	yes	characteristic
83	C₁₉⋊C₈	—	4	2	no	—
84	C₂×#364	—	19	1	no	—
85	#1772	—	19	1	no	—
86	C₂×#322	D₁₉	1	1	yes	characteristic
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
89	C₂²×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
90	C₂²×C₁₉	#339	1	1	yes	characteristic
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
94	C₄×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
95	C₄×C₁₉	#336	1	1	yes	characteristic
96	C₄×C₁₉	#340	1	1	yes	characteristic
97	Dic₁₉	—	8	2	no	—
98	C₂×M₃₂	—	38	1	no	—
99	C₂×#108	—	19	1	no	—
100	#427	—	19	1	no	—
101	#405	—	38	1	no	—
102	C₂×C₄×C₈	—	2	1	no	—
103	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
104	#364	—	19	2	no	—
105	#364	—	38	1	no	—
106	#339	—	38	1	no	—
107	#322	—	2	1	no	—
108	#322	Dic₁₉	1	2	yes	complemented
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	—	2	1	no	—
111	C₂×C₁₉	#1279	1	1	yes	characteristic
112	C₂×C₁₉	#1336	1	2	yes	—
113	C₂×M₁₆	—	38	1	no	—
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
116	C₂²×C₈	D₇₆	1	1	yes	characteristic
117	#117	—	38	1	no	—
118	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
119	M₃₂	—	38	2	no	—
120	M₃₂	—	76	1	no	—
121	C₂×C₁₆	—	76	1	no	—
122	#108	—	19	2	no	—
123	#108	—	38	1	no	—
124	#107	—	19	2	no	—
125	#106	—	38	1	no	—
126	#97	—	76	1	no	—
127	C₄×C₈	—	2	2	no	—
128	C₄×C₈	—	2	2	no	—
129	C₄×C₈	—	76	1	no	—
130	C₄×C₈	Dic₃₈	1	1	yes	characteristic
131	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
133	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
134	C₁₉	#7182	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
137	M₁₆	—	38	2	no	—
138	M₁₆	—	76	1	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	4	4	no	—
141	C₂×C₈	—	76	1	no	—
142	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
143	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
144	C₂×C₈	#64515	1	1	yes	characteristic
145	C₂×C₈	#64515	1	1	yes	characteristic
146	C₂×C₈	#64516	1	1	yes	characteristic
147	C₂×C₈	#64516	1	1	yes	characteristic
148	C₂×C₈	D₁₅₂	1	1	yes	characteristic
149	C₂×C₈	Dic₇₆	1	1	yes	characteristic
150	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
151	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
152	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
153	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
154	C₄⋊C₄	—	38	2	no	—
155	C₂²⋊C₄	—	76	1	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	76	1	no	—
158	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
159	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
160	C₁₆	—	76	2	no	—
161	C₂³	#10597262	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	76	2	no	—
166	C₂×C₄	#10597262	1	1	yes	characteristic
167	C₂×C₄	#10597273	1	1	yes	characteristic
168	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
169	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
170	C₂×C₄	#10597278	1	1	yes	characteristic
171	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
172	C₈	—	4	4	no	—
173	C₈	—	76	2	no	—
174	C₈	C₈×Dic₁₉	1	1	yes	characteristic
175	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
176	C₈	Dic₁₉⋊C₈	1	1	yes	characteristic
177	C₈	#10597272	1	1	yes	characteristic
178	C₈	#10597273	1	1	yes	characteristic
179	C₈	#10597274	1	1	yes	characteristic
180	C₈	#10597275	1	1	yes	characteristic
181	C₈	#10597278	1	1	yes	characteristic
182	C₂²	—	2	2	no	—
183	C₂²	#11926273	1	1	yes	characteristic
184	C₂²	#11926276	1	1	yes	characteristic
185	C₂²	#11926304	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	—	152	2	no	—
189	C₄	#11926273	1	1	yes	characteristic
190	C₄	#11926276	1	1	yes	characteristic
191	C₄	#11926298	1	1	yes	characteristic
192	C₄	#11926307	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	#14561475	1	1	yes	characteristic
196	C₂	#14561612	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597278
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	D₄⋊C₈
prime radical	C₂³×C₁₉	#104
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#7182
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
9. #11926365	C₄	semidirect
14. C₁₉×#322	C₄	semidirect
28. #10597276	C₈	semidirect
29. #10597275	C₈	semidirect
108. #322	Dic₁₉	semidirect
134. C₁₉	#7182	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
#14563514	2
C₂×C₁₉×#322	2
#7182	19