Subgroups — #18069488

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	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
6	#11926365	—	2	1	no	—
7	#11926365	C₄	1	2	yes	complemented
8	#11926265	—	2	1	no	—
9	#11926265	C₄	1	2	yes	complemented
10	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
11	C₁₉×#427	C₄	1	1	yes	characteristic
12	C₁₉×#405	—	2	1	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#339	—	2	1	no	—
15	C₂×M₁₆×C₁₉	—	2	1	no	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉×#117	—	2	1	no	—
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	C₁₉×#108	—	2	1	no	—
22	C₁₉×#108	C₈	1	2	yes	complemented
23	C₁₉×#107	C₈	1	2	yes	complemented
24	C₁₉×#106	—	2	1	no	—
25	C₁₉×#97	—	4	1	no	—
26	C₄×C₈×C₁₉	—	4	1	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
30	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
31	#10597269	—	2	2	no	—
32	#10597269	—	4	1	no	—
33	C₂×C₁₉⋊C₁₆	—	4	1	no	—
34	C₄×C₁₉⋊C₈	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	M₁₆×C₁₉	—	2	2	no	—
39	M₁₆×C₁₉	—	4	1	no	—
40	C₂×C₈×C₁₉	—	4	1	no	—
41	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
50	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
52	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂²⋊C₄×C₁₉	—	4	1	no	—
55	C₄²×C₁₉	—	2	1	no	—
56	C₄²×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₁₉⋊C₈	—	2	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	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	—	4	2	no	—
68	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
74	C₈×C₁₉	—	4	2	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	4	no	—
84	C₂×#364	—	19	1	no	—
85	#1772	D₁₉	1	1	yes	characteristic
86	C₂×#322	—	19	1	no	—
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	—	8	2	no	—
94	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
95	C₄×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
96	C₄×C₁₉	#336	1	1	yes	characteristic
97	C₄×C₁₉	#340	1	1	yes	characteristic
98	C₂×M₃₂	—	38	1	no	—
99	C₂×#108	Dic₁₉	1	1	yes	characteristic
100	#427	Dic₁₉	1	1	yes	characteristic
101	#405	—	2	1	no	—
102	C₂×C₄×C₈	—	38	1	no	—
103	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
104	#364	—	19	2	no	—
105	#364	—	38	1	no	—
106	#339	—	2	1	no	—
107	#322	—	19	2	no	—
108	#322	—	38	1	no	—
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	—	2	1	no	—
114	C₂²×C₈	—	38	2	no	—
115	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
116	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
117	#117	—	2	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	—	2	1	no	—
123	#108	C₁₉⋊C₈	1	2	yes	complemented
124	#107	C₁₉⋊C₈	1	2	yes	complemented
125	#106	—	2	1	no	—
126	#97	—	4	1	no	—
127	C₄×C₈	—	4	1	no	—
128	C₄×C₈	—	38	2	no	—
129	C₄×C₈	—	38	2	no	—
130	C₄×C₈	Dic₃₈	1	1	yes	characteristic
131	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
133	C₄×C₈	D₇₆	1	1	yes	characteristic
134	C₁₉	#7182	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
137	M₁₆	—	2	2	no	—
138	M₁₆	—	4	1	no	—
139	C₂×C₈	—	4	1	no	—
140	C₂×C₈	—	38	4	no	—
141	C₂×C₈	—	76	4	no	—
142	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
143	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
144	C₂×C₈	#64520	1	1	yes	characteristic
145	C₂×C₈	#64520	1	1	yes	characteristic
146	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
147	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
148	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
149	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
150	C₂×C₈	#64525	1	1	yes	characteristic
151	C₂×C₈	#64526	1	1	yes	characteristic
152	C₂×C₈	#64527	1	1	yes	characteristic
153	C₂×C₈	#64528	1	1	yes	characteristic
154	C₄⋊C₄	—	2	2	no	—
155	C₂²⋊C₄	—	4	1	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	4	1	no	—
158	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
159	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
160	C₁₆	—	76	2	no	—
161	C₂³	#10597294	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	—	4	2	no	—
166	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
167	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
168	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
169	C₂×C₄	#10597289	1	1	yes	characteristic
170	C₂×C₄	#10597292	1	1	yes	characteristic
171	C₂×C₄	#10597294	1	1	yes	characteristic
172	C₈	—	4	2	no	—
173	C₈	—	76	4	no	—
174	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
175	C₈	#10597260	1	1	yes	characteristic
176	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
177	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
178	C₈	#10597264	1	1	yes	characteristic
179	C₈	#10597265	1	1	yes	characteristic
180	C₈	#10597266	1	1	yes	characteristic
181	C₈	#10597267	1	1	yes	characteristic
182	C₂²	—	2	2	no	—
183	C₂²	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
184	C₂²	Q₈⋊(C₁₉⋊C₈)	1	1	yes	characteristic
185	C₂²	#11926303	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	—	8	2	no	—
189	C₄	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
190	C₄	Q₈⋊(C₁₉⋊C₈)	1	1	yes	characteristic
191	C₄	#11926299	1	1	yes	characteristic
192	C₄	#11926306	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	#14561476	1	1	yes	characteristic
196	C₂	#14561611	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597289
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1772	C₂
socle	C₂²×C₁₉	D₄⋊C₈
prime radical	C₂³×C₁₉	#104
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1772	D₁₉
hypocenter	C₁₉	#7182
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
7. #11926365	C₄	semidirect
9. #11926265	C₄	semidirect
22. C₁₉×#108	C₈	semidirect
23. C₁₉×#107	C₈	semidirect
123. #108	C₁₉⋊C₈	semidirect
124. #107	C₁₉⋊C₈	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
C₂×#11926265	2
C₁₉×#1772	2
#7182	19