Subgroups — #14572378

Order 2432.

492 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597347	C₂	1	2	yes	maximal, complemented
2	#11927094	C₂	1	1	yes	maximal, characteristic
3	#11926621	C₂	1	2	yes	maximal, complemented
4	#11926614	C₂	1	4	yes	maximal, complemented
5	#11926609	C₂	1	2	yes	maximal, complemented
6	#11926510	C₂	1	2	yes	maximal, complemented
7	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#64541	C₂²	1	2	yes	—
10	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	#10597376	C₄	1	2	yes	—
13	#10597376	C₄	1	2	yes	—
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	C₂×#64520	C₂²	1	1	yes	characteristic
16	#10597347	—	2	8	no	—
17	C₂×#64515	C₂²	1	4	yes	—
18	C₂×C₈×D₁₉	C₂²	1	4	yes	—
19	#10597321	C₄	1	2	yes	—
20	#10597320	C₄	1	1	yes	characteristic
21	C₄×D₇₆	C₂²	1	2	yes	—
22	C₄×D₇₆	C₂²	1	2	yes	—
23	#10597315	C₄	1	1	yes	characteristic
24	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
28	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
29	#10597260	C₂²	1	2	yes	—
30	C₄×C₁₉⋊C₈	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	C₂×C₂²⋊D₁₉	C₂×C₄	1	4	yes	—
35	#64541	—	2	4	no	—
36	#64541	—	2	4	no	—
37	C₂×D₇₆	C₂×C₄	1	2	yes	—
38	C₂×D₇₆	C₂×C₄	1	2	yes	—
39	C₂×D₇₆	C₂×C₄	1	2	yes	—
40	C₂×C₄×D₁₉	C₂³	1	4	yes	—
41	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
42	C₂×C₈×C₁₉	—	2	4	no	—
43	C₂×C₈×C₁₉	C₂³	1	2	yes	—
44	C₂×C₈×C₁₉	C₂³	1	2	yes	—
45	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
50	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
51	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
52	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
53	#64520	—	2	2	no	—
54	#64520	D₄	1	4	yes	complemented
55	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
56	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
57	#64515	—	2	8	no	—
58	C₈×D₁₉	—	2	8	no	—
59	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×D₁₉	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	#41	1	2	yes	—
70	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂²⋊D₁₉	—	2	8	no	—
72	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
73	D₇₆	—	2	4	no	—
74	D₇₆	—	2	4	no	—
75	D₇₆	—	4	2	no	—
76	C₄×D₁₉	—	2	4	no	—
77	C₄×D₁₉	—	2	4	no	—
78	Dic₃₈	—	2	4	no	—
79	C₈×C₁₉	—	2	2	no	—
80	C₈×C₁₉	—	2	2	no	—
81	C₁₉⋊C₈	—	2	2	no	—
82	C₁₉⋊C₈	C₂×D₄	1	4	yes	—
83	#2935	—	19	1	no	maximal, Sylow
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	C₄×D₄	1	2	yes	—
87	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
88	C₂×D₁₉	—	2	4	no	—
89	C₂×D₁₉	—	2	4	no	—
90	C₂×D₁₉	—	2	4	no	—
91	C₄×C₁₉	—	2	1	no	—
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₄×C₁₉	#131	1	2	yes	complemented
96	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
97	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
98	Dic₁₉	—	2	4	no	—
99	C₂×#131	—	19	2	no	—
100	#532	—	19	1	no	—
101	#436	—	19	2	no	—
102	#435	—	19	4	no	—
103	C₈×D₄	—	19	2	no	—
104	C₂×C₄⋊C₈	D₁₉	1	1	yes	characteristic, complemented
105	#408	—	19	2	no	—
106	C₄×M₁₆	—	19	1	no	—
107	C₂×C₁₉	—	2	2	no	—
108	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
109	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
110	C₂×C₁₉	#568	1	1	yes	characteristic
111	D₁₉	—	4	4	no	—
112	C₂×#41	—	19	2	no	—
113	#131	—	38	8	no	—
114	C₂×M₁₆	—	19	1	no	—
115	C₂×M₁₆	—	19	1	no	—
116	C₂×M₁₆	—	19	4	no	—
117	C₂²×C₈	—	19	4	no	—
118	C₂²×C₈	C₂×D₁₉	1	2	yes	—
119	C₄⋊Q₈	—	19	1	no	—
120	#127	—	19	1	no	—
121	#124	—	19	2	no	—
122	#121	—	19	2	no	—
123	#121	—	19	2	no	—
124	C₄×D₄	—	19	2	no	—
125	C₄×D₄	—	19	2	no	—
126	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
127	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
129	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
130	C₂²⋊C₈	—	19	4	no	—
131	C₂²⋊C₈	—	19	4	no	—
132	#97	—	19	2	no	—
133	C₄×C₈	—	19	2	no	—
134	C₁₉	#2935	1	1	yes	characteristic, complemented, Sylow
135	#41	—	38	4	no	—
136	#41	—	38	4	no	—
137	C₂×Q₈	—	19	2	no	—
138	C₂×D₄	—	19	4	no	—
139	C₂×D₄	—	19	2	no	—
140	C₂×D₄	—	19	2	no	—
141	C₂×D₄	—	19	2	no	—
142	C₂²×C₄	—	19	4	no	—
143	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
144	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
146	M₁₆	—	19	4	no	—
147	M₁₆	—	38	8	no	—
148	M₁₆	—	38	2	no	—
149	C₂×C₈	—	2	4	no	—
150	C₂×C₈	—	19	2	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	—	38	8	no	—
153	C₂×C₈	C₂²×D₁₉	1	2	yes	—
154	C₂×C₈	C₂²×D₁₉	1	2	yes	—
155	C₄⋊C₄	—	19	2	no	—
156	C₄⋊C₄	—	19	2	no	—
157	C₂²⋊C₄	—	19	4	no	—
158	C₂²⋊C₄	—	19	4	no	—
159	C₄²	C₄×D₁₉	1	1	yes	characteristic
160	C₄²	C₄×D₁₉	1	1	yes	characteristic
161	C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	C₂³	—	19	4	no	—
164	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
165	Q₈	—	38	4	no	—
166	D₄	—	38	8	no	—
167	D₄	—	38	4	no	—
168	D₄	—	38	4	no	—
169	D₄	—	76	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	4	1	no	—
172	C₂×C₄	—	19	4	no	—
173	C₂×C₄	—	38	4	no	—
174	C₂×C₄	—	38	4	no	—
175	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
179	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
180	C₂×C₄	D₄×D₁₉	1	2	yes	—
181	C₂×C₄	#64545	1	2	yes	—
182	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	—	2	2	no	—
185	C₈	—	19	4	no	—
186	C₈	—	38	2	no	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	38	4	no	—
190	C₂²	—	38	4	no	—
191	C₂²	—	38	4	no	—
192	C₂²	#10597339	1	2	yes	—
193	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
194	C₄	—	2	1	no	—
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	38	4	no	—
198	C₄	#10597339	1	2	yes	—
199	C₄	#10597347	1	2	yes	complemented
200	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
201	C₄	C₂×#64545	1	1	yes	characteristic
202	C₂	—	2	2	no	—
203	C₂	—	76	4	no	—
204	C₂	C₂×#10597339	1	1	yes	characteristic
205	C₂	C₂×#10597347	1	1	yes	characteristic
206	C₂	#11927310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₂×C₁₉×C₄⋊C₈	C₂
prime radical	#11927094	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#2935
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10597347	C₂	semidirect
3. #11926621	C₂	semidirect
4. #11926614	C₂	semidirect
5. #11926609	C₂	semidirect
6. #11926510	C₂	semidirect
7. C₄×#64520	C₂	semidirect
8. C₂×C₁₉×C₄⋊C₈	C₂	semidirect
54. #64520	D₄	semidirect
95. C₄×C₁₉	#131	semidirect
104. C₂×C₄⋊C₈	D₁₉	semidirect
134. C₁₉	#2935	semidirect
199. C₄	#10597347	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597347	2
#11927094	2
#11926621	2
#11926614	2
#11926609	2
#11926510	2
C₄×#64520	2
C₂×C₁₉×C₄⋊C₈	2
#2935	19