Subgroups — #14572722

Order 2432.

364 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×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#11926674	C₂	1	2	yes	maximal, complemented
3	#11926673	C₂	1	4	yes	maximal, complemented
4	C₈×Dic₃₈	C₂	1	2	yes	maximal, complemented
5	#11926601	C₂	1	1	yes	maximal, characteristic
6	#11926598	C₂	1	2	yes	maximal
7	#11926594	C₂	1	2	yes	maximal
8	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₃₈	C₄	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
14	C₄×Dic₃₈	C₄	1	1	yes	characteristic
15	C₄×Dic₃₈	C₄	1	2	yes	—
16	C₄×Dic₃₈	C₄	1	1	yes	characteristic
17	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
18	C₄×Dic₃₈	C₂²	1	2	yes	—
19	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
20	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂²	1	2	yes	—
24	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
25	#10597272	C₂²	1	4	yes	—
26	Dic₁₉⋊C₈	C₂²	1	4	yes	—
27	Dic₁₉⋊C₈	C₂²	1	4	yes	—
28	C₈×Dic₁₉	C₂²	1	4	yes	—
29	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
30	#10597260	C₂²	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
35	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
36	C₂×Dic₃₈	—	2	4	no	—
37	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
38	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
39	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂³	1	2	yes	—
41	C₂×C₈×C₁₉	C₂³	1	2	yes	—
42	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄²×C₁₉	C₂³	1	1	yes	characteristic
45	C₄²×C₁₉	C₂³	1	1	yes	characteristic
46	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
47	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
49	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
50	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
51	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
52	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
53	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
54	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₉	C₂³	1	2	yes	—
56	C₄×Dic₁₉	C₂³	1	2	yes	—
57	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
58	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
68	C₂×Dic₁₉	—	2	4	no	—
69	C₂×Dic₁₉	—	2	4	no	—
70	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
71	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
72	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
73	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
74	Dic₃₈	—	2	2	no	—
75	Dic₃₈	—	2	4	no	—
76	Dic₃₈	M₁₆	1	4	yes	—
77	C₈×C₁₉	—	2	2	no	—
78	C₈×C₁₉	—	2	2	no	—
79	C₁₉⋊C₈	—	2	4	no	—
80	#2984	—	19	1	no	maximal, Sylow
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	#131	1	2	yes	—
84	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
90	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
91	Dic₁₉	—	2	2	no	—
92	Dic₁₉	—	2	2	no	—
93	Dic₁₉	—	2	2	no	—
94	Dic₁₉	C₂×M₁₆	1	4	yes	—
95	C₂×C₄×Q₈	—	19	1	no	—
96	#446	—	19	4	no	—
97	#446	—	19	2	no	—
98	C₈×Q₈	—	19	2	no	—
99	#432	—	19	1	no	—
100	#432	—	19	2	no	—
101	#431	—	19	2	no	—
102	#431	D₁₉	1	1	yes	characteristic
103	C₂×C₁₉	—	2	2	no	—
104	C₂×C₁₉	#519	1	1	yes	characteristic
105	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
106	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
107	C₂²×Q₈	—	19	1	no	—
108	C₄×Q₈	—	19	1	no	—
109	C₄×Q₈	—	19	2	no	—
110	C₄×Q₈	—	19	1	no	—
111	C₄×Q₈	—	19	1	no	—
112	C₄×Q₈	—	19	2	no	—
113	C₄×Q₈	—	19	1	no	—
114	C₂×C₄⋊C₄	—	19	2	no	—
115	C₂×C₄⋊C₄	—	19	1	no	—
116	C₂×C₄²	—	19	2	no	—
117	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
118	C₄⋊C₈	—	19	4	no	—
119	C₄⋊C₈	—	19	4	no	—
120	C₄⋊C₈	—	19	2	no	—
121	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
122	C₂²⋊C₈	—	19	2	no	—
123	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
124	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
125	#97	—	19	4	no	—
126	#97	—	19	2	no	—
127	C₄×C₈	—	19	4	no	—
128	C₄×C₈	C₂×D₁₉	1	2	yes	—
129	C₁₉	#2984	1	1	yes	characteristic, complemented, Sylow
130	C₂×Q₈	—	19	1	no	—
131	C₂×Q₈	—	19	2	no	—
132	C₂×Q₈	—	19	1	no	—
133	C₂×Q₈	—	38	4	no	—
134	C₂²×C₄	—	19	2	no	—
135	C₂²×C₄	—	19	2	no	—
136	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	C₂×C₈	—	19	4	no	—
140	C₂×C₈	C₂²×D₁₉	1	2	yes	—
141	C₂×C₈	C₂²×D₁₉	1	2	yes	—
142	C₄⋊C₄	—	19	2	no	—
143	C₄⋊C₄	—	19	2	no	—
144	C₄⋊C₄	—	19	2	no	—
145	C₄⋊C₄	—	19	2	no	—
146	C₄⋊C₄	—	19	2	no	—
147	C₄⋊C₄	—	19	1	no	—
148	C₄⋊C₄	—	19	1	no	—
149	C₄²	—	19	2	no	—
150	C₄²	—	19	2	no	—
151	C₄²	—	19	2	no	—
152	C₄²	—	19	2	no	—
153	C₄²	C₄×D₁₉	1	1	yes	characteristic
154	C₄²	C₄×D₁₉	1	1	yes	characteristic
155	C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄²	C₂²×D₁₉	1	1	yes	characteristic
157	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
158	Q₈	—	19	4	no	—
159	Q₈	—	38	4	no	—
160	Q₈	—	38	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	19	2	no	—
165	C₂×C₄	—	19	2	no	—
166	C₂×C₄	—	19	2	no	—
167	C₂×C₄	—	19	2	no	—
168	C₂×C₄	—	38	4	no	—
169	C₂×C₄	—	38	4	no	—
170	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
171	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
172	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
173	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
175	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	2	no	—
178	C₈	—	38	4	no	—
179	C₂²	—	2	1	no	—
180	C₂²	—	2	1	no	—
181	C₂²	#10597347	1	2	yes	—
182	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
183	C₄	—	2	1	no	—
184	C₄	—	2	1	no	—
185	C₄	—	2	1	no	—
186	C₄	—	2	1	no	—
187	C₄	—	19	4	no	—
188	C₄	—	38	2	no	—
189	C₄	—	38	2	no	—
190	C₄	—	38	2	no	—
191	C₄	M₁₆×D₁₉	1	2	yes	—
192	C₄	#10597436	1	2	yes	—
193	C₂	—	2	2	no	—
194	C₂	#11927021	1	1	yes	characteristic
195	C₂	C₂×M₁₆×D₁₉	1	1	yes	characteristic
196	C₂	C₂×#10597347	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#431	C₂
prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#431	D₁₉
hypocenter	C₁₉	#2984
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
2. #11926674	C₂	semidirect
3. #11926673	C₂	semidirect
4. C₈×Dic₃₈	C₂	semidirect
129. C₁₉	#2984	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926674	2
#11926673	2
C₈×Dic₃₈	2
#11926601	2
#11926598	2
#11926594	2
C₁₉×#431	2
#2984	19