Subgroups — #18081481

Order 4864.

434 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562383	C₂	1	1	yes	maximal, characteristic
2	#14562030	C₂	1	2	yes	maximal
3	#14561959	C₂	1	2	yes	maximal
4	#14561927	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926597	C₂²	1	1	yes	characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926297	—	2	1	no	—
10	#11926295	—	2	1	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926270	—	2	4	no	—
13	#11926266	—	2	1	no	—
14	#11926266	—	2	1	no	—
15	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₄×Q₁₆×C₁₉	—	2	1	no	—
18	C₄×Q₁₆×C₁₉	—	2	1	no	—
19	C₄×Q₁₆×C₁₉	—	2	1	no	—
20	C₄×Q₁₆×C₁₉	—	2	1	no	—
21	C₂×C₁₉×#107	C₄	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₄	1	2	yes	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×Q₁₆×C₁₉	—	2	4	no	—
26	C₂×Q₁₆×C₁₉	—	2	1	no	—
27	C₂×Q₁₆×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×#107	—	2	1	no	—
39	C₁₉×#107	—	2	1	no	—
40	C₁₉×#103	—	2	2	no	—
41	C₁₉×#103	—	2	2	no	—
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
52	C₄×C₁₉⋊C₈	—	2	1	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×Q₈×C₁₉	—	2	2	no	—
58	C₂×Q₈×C₁₉	—	2	2	no	—
59	C₂×Q₈×C₁₉	—	2	2	no	—
60	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	Q₁₆×C₁₉	—	2	4	no	—
67	Q₁₆×C₁₉	—	2	4	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	#41	1	1	yes	characteristic
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	#9671	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
89	Q₈×C₁₉	—	2	4	no	—
90	Q₈×C₁₉	—	2	4	no	—
91	Q₈×C₁₉	—	4	2	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	4	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	8	2	no	—
100	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
107	C₂×C₄×C₁₉	#131	1	2	yes	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₁₉⋊C₈	—	4	2	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	C₁₉⋊C₈	—	8	2	no	—
115	C₂×C₄×Q₁₆	D₁₉	1	1	yes	characteristic
116	#1564	—	19	1	no	—
117	#1479	—	19	2	no	—
118	#1461	—	19	2	no	—
119	#1452	—	19	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	#390	1	1	yes	characteristic
123	C₂²×C₁₉	#435	1	2	yes	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	4	4	no	—
128	C₄×C₁₉	—	8	2	no	—
129	C₄×C₁₉	#407	1	1	yes	characteristic
130	C₄×C₁₉	#408	1	1	yes	characteristic
131	C₄×C₁₉	#435	1	2	yes	—
132	C₄×C₁₉	#473	1	2	yes	—
133	C₂²×Q₁₆	Dic₁₉	1	1	yes	characteristic
134	C₂×C₄×Q₈	C₂×D₁₉	1	2	yes	—
135	C₄×Q₁₆	—	2	1	no	—
136	C₄×Q₁₆	—	2	1	no	—
137	C₄×Q₁₆	—	2	1	no	—
138	C₄×Q₁₆	—	2	1	no	—
139	#431	—	19	1	no	—
140	#431	—	19	1	no	—
141	#431	—	19	2	no	—
142	C₂×#107	Dic₁₉	1	1	yes	characteristic
143	C₂×#103	Dic₁₉	1	2	yes	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#335	—	38	1	no	—
146	#334	—	38	1	no	—
147	Q₈⋊C₈	—	38	4	no	—
148	#324	—	38	4	no	—
149	#322	—	38	1	no	—
150	#322	—	38	1	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#1955	1	1	yes	characteristic
153	C₂×C₁₉	#1976	1	1	yes	characteristic
154	C₂×C₁₉	#1979	1	1	yes	characteristic
155	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
156	C₂×Q₁₆	—	2	4	no	—
157	C₂×Q₁₆	—	2	1	no	—
158	C₂×Q₁₆	—	2	1	no	—
159	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
160	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
161	C₄×Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
167	C₂×C₄²	—	2	2	no	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	#107	—	2	1	no	—
170	#107	—	2	1	no	—
171	C₄⋊C₈	—	19	2	no	—
172	C₄⋊C₈	—	38	1	no	—
173	C₄⋊C₈	—	38	2	no	—
174	#103	—	2	2	no	—
175	#103	—	2	2	no	—
176	C₂²⋊C₈	—	19	2	no	—
177	C₂²⋊C₈	—	38	1	no	—
178	C₂²⋊C₈	—	38	2	no	—
179	C₄×C₈	—	38	2	no	—
180	C₄×C₈	—	38	1	no	—
181	C₄×C₈	—	38	1	no	—
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
186	C₁₉	#9671	1	1	yes	characteristic, complemented, Sylow
187	C₂×Q₈	—	2	2	no	—
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	2	2	no	—
192	C₂×Q₈	#64520	1	4	yes	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
196	C₂²×C₄	#64543	1	1	yes	characteristic
197	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
198	Q₁₆	—	2	4	no	—
199	Q₁₆	—	2	4	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	76	2	no	—
205	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
206	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
207	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
208	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	4	2	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄²	—	4	2	no	—
214	C₄²	—	4	2	no	—
215	C₄²	D₄×D₁₉	1	1	yes	characteristic
216	C₄²	#64543	1	1	yes	characteristic
217	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
220	Q₈	—	2	4	no	—
221	Q₈	—	2	4	no	—
222	Q₈	—	4	2	no	—
223	Q₈	—	4	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	C₂×#64520	1	2	yes	—
232	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
233	C₂×C₄	#10597382	1	1	yes	characteristic
234	C₂×C₄	#10597384	1	1	yes	characteristic
235	C₂×C₄	#10597384	1	1	yes	characteristic
236	C₂×C₄	#10597386	1	1	yes	characteristic
237	C₂×C₄	#10597394	1	2	yes	—
238	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
239	C₈	—	2	1	no	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	2	1	no	—
243	C₈	—	76	2	no	—
244	C₈	—	76	2	no	—
245	C₈	—	152	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	#11926447	1	1	yes	characteristic
249	C₂²	#11926616	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	4	4	no	—
254	C₄	—	8	2	no	—
255	C₄	#11926508	1	1	yes	characteristic
256	C₄	#11926511	1	1	yes	characteristic
257	C₄	#11926616	1	2	yes	—
258	C₄	#11926816	1	2	yes	—
259	C₂	—	2	2	no	—
260	C₂	#14564434	1	1	yes	characteristic
261	C₂	#14564534	1	1	yes	characteristic
262	C₂	#14564551	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₄×Q₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×Q₁₆	D₁₉
hypocenter	C₁₉	#9671
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
186. C₁₉	#9671	semidirect

Maximal subgroups

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

subgroup	index
#14562383	2
#14562030	2
#14561959	2
#14561927	2
C₂×C₄×Q₁₆×C₁₉	2
#9671	19