Subgroups — #14572350

Order 2432.

484 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597353	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597394	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927090	C₂	1	1	yes	maximal, characteristic
4	#11926618	C₂	1	4	yes	maximal, complemented
5	#11926612	C₂	1	4	yes	maximal, complemented
6	#11926567	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926510	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64541	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597394	—	2	4	no	—
15	#10597393	C₄	1	1	yes	characteristic
16	#10597390	C₄	1	1	yes	characteristic
17	#10597386	C₄	1	1	yes	characteristic
18	#10597385	C₄	1	4	yes	—
19	#10597382	C₄	1	1	yes	characteristic
20	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	—
21	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×#64520	C₂²	1	1	yes	characteristic
23	C₂×#64520	C₂²	1	2	yes	—
24	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
25	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
26	#10597353	—	2	4	no	—
27	C₂×#64515	C₂²	1	2	yes	—
28	C₂×C₈×D₁₉	C₂²	1	2	yes	—
29	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
30	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
31	#10597272	C₂²	1	2	yes	—
32	#10597272	C₂²	1	2	yes	—
33	Dic₁₉⋊C₈	C₂²	1	4	yes	—
34	#41×C₁₉	—	2	2	no	—
35	#41×C₁₉	—	2	2	no	—
36	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊D₁₉	C₂×C₄	1	4	yes	—
43	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
44	#64541	—	2	2	no	—
45	#64541	—	2	2	no	—
46	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₁₉	C₂³	1	2	yes	—
48	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
49	M₁₆×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
54	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
55	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
56	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₉	C₂³	1	2	yes	—
59	#64520	—	2	2	no	—
60	#64520	—	2	4	no	—
61	C₂×C₁₉⋊C₈	—	2	4	no	—
62	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
63	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
64	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
66	#64515	—	2	4	no	—
67	C₈×D₁₉	—	2	4	no	—
68	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
69	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
71	Q₈×C₁₉	—	2	2	no	—
72	D₄×C₁₉	—	2	4	no	—
73	D₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₉	#41	1	2	yes	—
80	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂²⋊D₁₉	—	2	4	no	—
82	C₂²⋊D₁₉	—	4	4	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
85	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
86	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
87	D₇₆	—	2	2	no	—
88	C₄×D₁₉	—	2	2	no	—
89	C₄×D₁₉	—	2	2	no	—
90	Dic₃₈	—	2	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₁₉⋊C₈	—	2	2	no	—
94	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
95	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
96	#2932	—	19	1	no	maximal, Sylow
97	C₂²×C₁₉	—	2	2	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	4	no	—
100	C₂²×C₁₉	C₄×D₄	1	2	yes	—
101	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
102	C₂×D₁₉	—	2	2	no	—
103	C₂×D₁₉	—	2	4	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	C₄×D₄	1	2	yes	—
106	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
107	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
108	Dic₁₉	—	2	2	no	—
109	Dic₁₉	—	2	2	no	—
110	Dic₁₉	—	2	2	no	—
111	C₂×#131	—	19	1	no	—
112	C₂×#131	—	19	1	no	—
113	#532	—	19	1	no	—
114	#435	—	19	4	no	—
115	#435	—	19	4	no	—
116	#423	—	19	1	no	—
117	#408	—	19	1	no	—
118	#408	D₁₉	1	1	yes	characteristic, complemented
119	C₂×#97	—	19	1	no	—
120	C₂×C₁₉	—	2	2	no	—
121	C₂×C₁₉	—	4	2	no	—
122	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
123	C₂×C₁₉	#568	1	2	yes	—
124	D₁₉	—	4	2	no	—
125	C₂×#41	—	19	1	no	—
126	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
127	#131	—	38	4	no	—
128	#131	—	38	4	no	—
129	C₂×M₁₆	—	19	1	no	—
130	C₂×M₁₆	—	19	2	no	—
131	C₂×M₁₆	—	19	2	no	—
132	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
133	C₂²×C₈	—	19	1	no	—
134	C₂²×C₈	—	19	2	no	—
135	C₂²×C₈	—	19	2	no	—
136	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
137	C₄⋊Q₈	—	19	1	no	—
138	#127	—	19	1	no	—
139	#124	—	19	1	no	—
140	#124	—	19	1	no	—
141	#121	—	19	4	no	—
142	C₄×D₄	—	19	4	no	—
143	C₂×C₄²	—	19	1	no	—
144	C₄⋊C₈	—	19	4	no	—
145	C₂²⋊C₈	—	19	4	no	—
146	C₂²⋊C₈	C₂×D₁₉	1	4	yes	—
147	#97	—	19	2	no	—
148	#97	—	19	2	no	—
149	C₁₉	#2932	1	1	yes	characteristic, complemented, Sylow
150	#41	—	2	2	no	—
151	#41	—	2	2	no	—
152	#41	—	38	2	no	—
153	#41	—	38	2	no	—
154	C₂×Q₈	—	19	1	no	—
155	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
156	C₂×D₄	—	19	2	no	—
157	C₂×D₄	—	19	4	no	—
158	C₂×D₄	—	19	1	no	—
159	C₂×D₄	C₄×D₁₉	1	2	yes	—
160	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
161	C₂²×C₄	—	19	2	no	—
162	C₂²×C₄	—	19	2	no	—
163	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
164	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
165	M₁₆	—	2	2	no	—
166	M₁₆	—	38	4	no	—
167	M₁₆	—	38	4	no	—
168	M₁₆	—	38	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	19	4	no	—
171	C₂×C₈	—	19	1	no	—
172	C₂×C₈	—	19	1	no	—
173	C₂×C₈	—	19	2	no	—
174	C₂×C₈	—	38	4	no	—
175	C₂×C₈	—	38	4	no	—
176	C₂×C₈	C₂²×D₁₉	1	2	yes	—
177	C₂×C₈	C₂²×D₁₉	1	2	yes	—
178	C₄⋊C₄	—	19	4	no	—
179	C₂²⋊C₄	—	19	4	no	—
180	C₂²⋊C₄	—	19	4	no	—
181	C₄²	—	19	1	no	—
182	C₄²	—	19	1	no	—
183	C₄²	—	19	2	no	—
184	C₂³	—	19	2	no	—
185	C₂³	C₂×C₄×D₁₉	1	2	yes	—
186	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
187	Q₈	—	2	2	no	—
188	Q₈	—	38	2	no	—
189	D₄	—	2	4	no	—
190	D₄	—	2	2	no	—
191	D₄	—	38	4	no	—
192	D₄	—	38	2	no	—
193	D₄	—	76	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	19	2	no	—
197	C₂×C₄	—	19	2	no	—
198	C₂×C₄	—	19	2	no	—
199	C₂×C₄	—	38	2	no	—
200	C₂×C₄	—	38	2	no	—
201	C₂×C₄	—	76	2	no	—
202	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
203	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
204	C₂×C₄	D₄×D₁₉	1	2	yes	—
205	C₂×C₄	#64543	1	2	yes	—
206	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	2	2	no	—
209	C₈	—	19	2	no	—
210	C₈	—	19	2	no	—
211	C₈	—	38	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	38	4	no	—
216	C₂²	—	38	2	no	—
217	C₂²	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
218	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	38	2	no	—
221	C₄	—	38	2	no	—
222	C₄	—	38	2	no	—
223	C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
224	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
225	C₄	C₂×#64543	1	1	yes	characteristic
226	C₂	—	2	2	no	—
227	C₂	—	4	2	no	—
228	C₂	—	76	2	no	—
229	C₂	C₂×(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
230	C₂	#11927309	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#408	C₂
prime radical	#11927090	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#408	D₁₉
hypocenter	C₁₉	#2932
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
1. C₂×#10597353	C₂	semidirect
2. C₂×#10597394	C₂	semidirect
4. #11926618	C₂	semidirect
5. #11926612	C₂	semidirect
6. #11926567	C₂	semidirect
7. #11926510	C₂	semidirect
8. C₂×#10597272	C₂	semidirect
9. C₁₉×#408	C₂	semidirect
62. C₂×C₁₉⋊C₈	D₄	semidirect
118. #408	D₁₉	semidirect
149. C₁₉	#2932	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597353	2
C₂×#10597394	2
#11927090	2
#11926618	2
#11926612	2
#11926567	2
#11926510	2
C₂×#10597272	2
C₁₉×#408	2
#2932	19