Subgroups — #14572202

Order 2432.

484 conjugacy classes of subgroups.

The subgroup lattice has 266 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
2	C₂×#10597347	C₂	1	1	yes	maximal, characteristic
3	#11927012	C₂	1	1	yes	maximal, characteristic
4	#11926571	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926569	C₂	1	2	yes	maximal, complemented
6	#11926569	C₂	1	2	yes	maximal, complemented
7	#11926567	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926566	C₂	1	2	yes	maximal, complemented
9	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×D₁₉	C₂	1	2	yes	maximal, complemented
11	C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#64541	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#10597353	—	2	4	no	—
20	#10597347	—	2	4	no	—
21	C₂×#64515	C₂²	1	2	yes	—
22	C₂×#64515	C₂²	1	2	yes	—
23	C₂×C₈×D₁₉	C₂²	1	2	yes	—
24	C₂×C₈×D₁₉	C₂²	1	2	yes	—
25	#10597339	C₄	1	1	yes	characteristic
26	#10597339	C₄	1	1	yes	characteristic
27	#10597333	C₄	1	1	yes	characteristic
28	#10597333	C₄	1	1	yes	characteristic
29	(C₂²⋊D₁₉)⋊C₄	C₄	1	2	yes	—
30	(C₂²⋊D₁₉)⋊C₄	C₄	1	2	yes	—
31	#10597318	C₂²	1	2	yes	—
32	C₄²×D₁₉	C₂²	1	2	yes	—
33	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
34	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
35	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
36	Dic₁₉⋊C₈	C₂²	1	2	yes	—
37	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
38	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
39	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
40	Dic₁₉⋊C₈	C₂²	1	2	yes	—
41	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
45	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	#64541	D₄	1	4	yes	—
48	#64541	Q₈	1	4	yes	—
49	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄×D₁₉	C₂³	1	2	yes	—
53	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
54	M₁₆×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₁₉	C₂³	1	2	yes	—
59	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₄²×C₁₉	C₂³	1	2	yes	—
63	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
64	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
65	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
66	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
67	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
68	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
69	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
72	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
73	#64520	—	2	2	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
77	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
78	#64515	—	2	4	no	—
79	#64515	—	2	4	no	—
80	C₈×D₁₉	—	2	4	no	—
81	C₈×D₁₉	—	2	4	no	—
82	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
86	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
89	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₁₉	C₄⋊C₄	1	8	yes	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
97	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
98	D₇₆	C₄⋊C₄	1	4	yes	—
99	C₄×D₁₉	—	2	4	no	—
100	C₄×D₁₉	—	4	2	no	—
101	C₄×D₁₉	C₂×D₄	1	4	yes	—
102	C₄×D₁₉	C₂×Q₈	1	4	yes	—
103	Dic₃₈	C₄⋊C₄	1	4	yes	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	2	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₁₉⋊C₈	—	2	1	no	—
108	C₁₉⋊C₈	—	2	2	no	—
109	C₁₉⋊C₈	—	2	1	no	—
110	#2906	—	19	1	no	maximal, Sylow
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
114	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
115	C₂×D₁₉	—	2	2	no	—
116	C₂×D₁₉	—	2	2	no	—
117	C₂×D₁₉	C₂×C₄⋊C₄	1	4	yes	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
121	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
122	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
123	Dic₁₉	—	2	1	no	—
124	Dic₁₉	—	2	1	no	—
125	Dic₁₉	—	2	1	no	—
126	Dic₁₉	C₂×C₄⋊C₄	1	4	yes	—
127	Dic₁₉	#131	1	2	yes	complemented
128	C₂×#131	—	19	1	no	—
129	C₂×#131	—	19	1	no	—
130	C₄×#41	—	19	1	no	—
131	#424	—	19	1	no	—
132	#424	—	19	2	no	—
133	#424	—	19	2	no	—
134	#424	D₁₉	1	1	yes	characteristic, complemented
135	#423	—	19	1	no	—
136	#423	—	19	2	no	—
137	C₂×C₄⋊C₈	—	19	1	no	—
138	C₂×C₄⋊C₈	—	19	2	no	—
139	C₂×C₁₉	—	2	2	no	—
140	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
142	C₂×C₁₉	#568	1	1	yes	characteristic
143	D₁₉	—	2	4	no	—
144	C₂×#41	—	19	1	no	—
145	#131	—	38	4	no	—
146	#131	—	38	4	no	—
147	C₂×M₁₆	—	19	1	no	—
148	C₂×M₁₆	—	19	2	no	—
149	C₂×M₁₆	—	19	2	no	—
150	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
151	C₂²×C₈	—	19	1	no	—
152	C₂²×C₈	—	19	2	no	—
153	C₂²×C₈	—	19	2	no	—
154	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
155	C₄×Q₈	—	19	1	no	—
156	C₄×Q₈	—	19	1	no	—
157	C₄×D₄	—	19	1	no	—
158	C₄×D₄	—	19	1	no	—
159	C₄×D₄	—	19	2	no	—
160	C₄×D₄	—	19	2	no	—
161	#117	—	19	2	no	—
162	#117	C₂×D₁₉	1	1	yes	characteristic
163	C₂×C₄²	—	19	1	no	—
164	C₂×C₄²	—	19	2	no	—
165	C₄⋊C₈	—	19	1	no	—
166	C₄⋊C₈	—	19	2	no	—
167	C₄⋊C₈	—	19	1	no	—
168	C₄⋊C₈	—	19	1	no	—
169	C₄⋊C₈	—	19	1	no	—
170	C₄⋊C₈	—	19	2	no	—
171	C₄⋊C₈	—	19	2	no	—
172	C₄⋊C₈	—	19	2	no	—
173	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
174	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
175	C₁₉	#2906	1	1	yes	characteristic, complemented, Sylow
176	#41	—	19	4	no	—
177	#41	—	19	4	no	—
178	C₂×Q₈	—	19	1	no	—
179	C₂×D₄	—	19	2	no	—
180	C₂×D₄	—	19	1	no	—
181	C₂²×C₄	—	19	2	no	—
182	C₂²×C₄	—	19	1	no	—
183	C₂²×C₄	—	19	1	no	—
184	C₂²×C₄	—	19	2	no	—
185	C₂²×C₄	—	19	2	no	—
186	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
187	M₁₆	—	2	2	no	—
188	M₁₆	—	38	4	no	—
189	M₁₆	—	38	4	no	—
190	M₁₆	—	38	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	19	1	no	—
193	C₂×C₈	—	19	2	no	—
194	C₂×C₈	—	19	1	no	—
195	C₂×C₈	—	38	4	no	—
196	C₂×C₈	—	38	4	no	—
197	C₂×C₈	—	38	2	no	—
198	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
199	C₂×C₈	C₂²×D₁₉	1	2	yes	—
200	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
201	C₄⋊C₄	—	19	2	no	—
202	C₄⋊C₄	—	19	2	no	—
203	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
204	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
205	C₂²⋊C₄	—	19	2	no	—
206	C₂²⋊C₄	—	19	2	no	—
207	C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
208	C₄²	—	19	2	no	—
209	C₄²	—	19	1	no	—
210	C₄²	—	19	2	no	—
211	C₄²	—	19	1	no	—
212	C₄²	—	19	1	no	—
213	C₄²	—	19	1	no	—
214	C₄²	C₂²×D₁₉	1	2	yes	—
215	C₂³	—	19	2	no	—
216	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
217	Q₈	—	19	4	no	—
218	D₄	—	19	8	no	—
219	D₄	—	19	4	no	—
220	C₂×C₄	—	19	1	no	—
221	C₂×C₄	—	19	2	no	—
222	C₂×C₄	—	19	4	no	—
223	C₂×C₄	—	19	4	no	—
224	C₂×C₄	—	19	1	no	—
225	C₂×C₄	—	19	1	no	—
226	C₂×C₄	—	19	1	no	—
227	C₂×C₄	—	38	4	no	—
228	C₂×C₄	—	38	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	76	1	no	—
231	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
232	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
233	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
234	C₂×C₄	D₄×D₁₉	1	2	yes	—
235	C₂×C₄	Q₈×D₁₉	1	2	yes	—
236	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	2	2	no	—
240	C₈	—	38	1	no	—
241	C₈	—	38	2	no	—
242	C₈	—	38	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	19	4	no	—
246	C₂²	—	38	2	no	—
247	C₂²	—	38	2	no	—
248	C₂²	C₄⋊C₄×D₁₉	1	2	yes	—
249	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
250	C₄	—	2	2	no	—
251	C₄	—	2	2	no	—
252	C₄	—	19	2	no	—
253	C₄	—	19	4	no	—
254	C₄	—	38	1	no	—
255	C₄	—	38	1	no	—
256	C₄	—	38	1	no	—
257	C₄	C₄⋊C₄×D₁₉	1	2	yes	—
258	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
259	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
260	C₂	—	2	2	no	—
261	C₂	—	38	4	no	—
262	C₂	C₂×C₄⋊C₄×D₁₉	1	1	yes	characteristic
263	C₂	#131×D₁₉	1	1	yes	characteristic
264	C₂	#11927309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#424	C₂
prime radical	C₂×#64541	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#424	D₁₉
hypocenter	C₁₉	#2906
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
4. #11926571	C₂	semidirect
5. #11926569	C₂	semidirect
6. #11926569	C₂	semidirect
7. #11926567	C₂	semidirect
8. #11926566	C₂	semidirect
9. C₂×Dic₁₉⋊C₈	C₂	semidirect
10. C₄⋊C₈×D₁₉	C₂	semidirect
11. C₁₉×#424	C₂	semidirect
127. Dic₁₉	#131	semidirect
134. #424	D₁₉	semidirect
175. C₁₉	#2906	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×#10597347	2
#11927012	2
#11926571	2
#11926569	2
#11926567	2
#11926566	2
C₂×Dic₁₉⋊C₈	2
C₄⋊C₈×D₁₉	2
C₁₉×#424	2
#2906	19