Subgroups — #14568666

Order 2432.

452 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597336	C₂	1	2	yes	maximal
2	#11926476	C₂	1	4	yes	maximal
3	#11926443	C₂	1	2	yes	maximal
4	#11926442	C₂	1	2	yes	maximal
5	#11926414	C₂	1	2	yes	maximal
6	#11926414	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
8	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
19	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
20	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
21	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
22	#10597336	—	2	8	no	—
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₁₉⋊#95	C₂²	1	2	yes	—
25	C₁₉⋊#95	C₂²	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	C₂³	1	2	yes	—
32	C₂²×Dic₁₉	C₂³	1	2	yes	—
33	C₂²×Dic₁₉	C₂³	1	4	yes	—
34	C₄⋊C₄×C₁₉	D₄	1	4	yes	—
35	C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
36	C₄²×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	Q₈	1	4	yes	—
38	C₄⋊Dic₁₉	—	2	8	no	—
39	C₄⋊Dic₁₉	—	2	4	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	C₄⋊Dic₁₉	—	2	2	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	—	4	4	no	—
44	C₄⋊Dic₁₉	—	4	2	no	—
45	Dic₁₉⋊C₄	—	2	8	no	—
46	C₄×Dic₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
58	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
59	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
61	C₂×C₄×C₁₉	#41	1	2	yes	—
62	C₂×C₄×C₁₉	#41	1	2	yes	—
63	C₂×Dic₁₉	—	2	2	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	C₂×Dic₁₉	—	2	4	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	2	4	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	#2552	—	19	1	no	maximal, Sylow
73	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
74	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
75	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
76	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
78	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
79	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	4	no	—
82	C₄×C₁₉	—	2	4	no	—
83	C₄×C₁₉	#125	1	4	yes	complemented
84	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
85	Dic₁₉	—	4	2	no	—
86	Dic₁₉	—	4	2	no	—
87	Dic₁₉	—	4	4	no	—
88	C₂×#125	—	19	2	no	—
89	#398	—	19	4	no	—
90	#389	—	19	2	no	—
91	#389	—	19	2	no	—
92	#384	—	19	2	no	—
93	#384	—	19	1	no	—
94	C₄×C₄⋊C₄	—	19	1	no	—
95	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
96	C₂×C₁₉	C₂×#125	1	1	yes	characteristic
97	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
98	C₂×C₁₉	#544	1	1	yes	characteristic
99	C₂×C₁₉	#547	1	1	yes	characteristic
100	C₂×C₁₉	#550	1	1	yes	characteristic
101	C₂×C₁₉	#554	1	1	yes	characteristic
102	C₂×C₁₉	#557	1	1	yes	characteristic
103	#125	—	38	8	no	—
104	C₂×C₄⋊C₄	—	19	2	no	—
105	C₂×C₄⋊C₄	—	19	4	no	—
106	C₂×C₄⋊C₄	—	19	4	no	—
107	C₂×C₄⋊C₄	—	19	1	no	—
108	C₂×C₄⋊C₄	—	19	1	no	—
109	C₂×C₄⋊C₄	—	19	2	no	—
110	C₂×C₄⋊C₄	—	19	4	no	—
111	C₂×C₄⋊C₄	—	19	2	no	—
112	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
113	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
114	C₂×C₄²	—	19	2	no	—
115	C₂×C₄²	C₂×D₁₉	1	2	yes	—
116	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
117	#95	—	19	2	no	—
118	#95	—	19	4	no	—
119	#95	C₂×D₁₉	1	2	yes	—
120	C₁₉	#2552	1	1	yes	characteristic, complemented, Sylow
121	C₂²×C₄	—	19	2	no	—
122	C₂²×C₄	—	19	2	no	—
123	C₂²×C₄	—	19	4	no	—
124	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
125	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
126	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
127	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₄	—	38	8	no	—
130	C₄⋊C₄	—	38	8	no	—
131	C₄⋊C₄	—	38	4	no	—
132	C₄⋊C₄	—	38	2	no	—
133	C₄⋊C₄	—	38	2	no	—
134	C₄⋊C₄	—	38	4	no	—
135	C₄⋊C₄	—	76	4	no	—
136	C₄⋊C₄	—	76	2	no	—
137	C₄⋊C₄	Dic₃₈	1	4	yes	—
138	C₄⋊C₄	D₇₆	1	4	yes	—
139	C₄²	—	2	4	no	—
140	C₄²	—	38	4	no	—
141	C₄²	Dic₃₈	1	4	yes	—
142	C₂³	C₂³×D₁₉	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	38	2	no	—
150	C₂×C₄	—	38	2	no	—
151	C₂×C₄	—	38	4	no	—
152	C₂×C₄	—	38	2	no	—
153	C₂×C₄	—	38	2	no	—
154	C₂×C₄	—	38	4	no	—
155	C₂×C₄	—	38	2	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
159	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
160	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
161	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
162	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
163	C₂×C₄	C₂×D₇₆	1	4	yes	—
164	C₂×C₄	C₂×D₇₆	1	2	yes	—
165	C₂×C₄	#64543	1	2	yes	—
166	C₂×C₄	#64545	1	2	yes	—
167	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
168	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
169	C₂²	C₂²×D₇₆	1	1	yes	characteristic
170	C₂²	C₂×#64543	1	1	yes	characteristic
171	C₂²	C₂×#64545	1	1	yes	characteristic
172	C₂²	#10597435	1	1	yes	characteristic
173	C₂²	#10597436	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	2	4	no	—
176	C₄	—	2	4	no	—
177	C₄	—	76	2	no	—
178	C₄	—	76	2	no	—
179	C₄	—	76	4	no	—
180	C₄	#10597315	1	4	yes	—
181	C₄	#10597336	1	4	yes	complemented
182	C₂	C₂×#10597336	1	1	yes	characteristic
183	C₂	C₂×#10597315	1	1	yes	characteristic
184	C₂	#11927172	1	1	yes	characteristic
185	C₂	#11927198	1	1	yes	characteristic
186	C₂	#11927216	1	1	yes	characteristic
187	C₂	#11927251	1	1	yes	characteristic
188	C₂	#11927273	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#2552
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
83. C₄×C₁₉	#125	semidirect
120. C₁₉	#2552	semidirect
181. C₄	#10597336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597336	2
#11926476	2
#11926443	2
#11926442	2
#11926414	2
C₄×C₄⋊Dic₁₉	2
C₄×C₄⋊C₄×C₁₉	2
#2552	19