Subgroups — #18081442

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564572	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926299	—	2	4	no	—
10	#11926295	—	2	2	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926266	—	2	2	no	—
13	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₄×Q₁₆×C₁₉	—	2	2	no	—
16	C₄×Q₁₆×C₁₉	—	2	2	no	—
17	C₂×C₁₉×#107	C₄	1	1	yes	characteristic
18	C₂×C₁₉×#103	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×Q₁₆×C₁₉	—	2	4	no	—
22	C₂×Q₁₆×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	2	no	—
35	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×#103	—	2	4	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	1	no	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₄×C₁₉⋊C₈	—	2	1	no	—
45	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	Q₁₆×C₁₉	—	2	8	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₂×C₁₉⋊C₈	—	2	4	no	—
73	C₂×C₁₉⋊C₈	—	2	2	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	4	no	—
78	#9664	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	2	4	no	—
81	Q₈×C₁₉	—	2	4	no	—
82	Q₈×C₁₉	—	4	2	no	—
83	Q₈×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	#131	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	4	yes	—
99	C₈×C₁₉	—	2	2	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₁₉⋊C₈	—	2	4	no	—
102	C₁₉⋊C₈	—	4	2	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	C₂×C₄×Q₁₆	D₁₉	1	1	yes	characteristic
105	#1984	—	19	2	no	—
106	C₂×#334	—	19	1	no	—
107	C₂×Q₈⋊C₈	—	19	2	no	—
108	C₂×#322	—	19	1	no	—
109	C₂²×C₁₉	#390	1	1	yes	characteristic
110	C₂²×C₁₉	#435	1	2	yes	—
111	C₂²×C₁₉	#441	1	2	yes	—
112	C₂²×C₁₉	#443	1	2	yes	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	4	4	no	—
116	C₄×C₁₉	—	8	2	no	—
117	C₄×C₁₉	#407	1	1	yes	characteristic
118	C₄×C₁₉	#408	1	1	yes	characteristic
119	C₄×C₁₉	#435	1	2	yes	—
120	C₄×C₁₉	#470	1	2	yes	—
121	C₄×C₁₉	#497	1	2	yes	—
122	C₂²×Q₁₆	Dic₁₉	1	1	yes	characteristic
123	C₂×C₄×Q₈	C₂×D₁₉	1	2	yes	—
124	C₄×Q₁₆	—	2	2	no	—
125	C₄×Q₁₆	—	2	2	no	—
126	C₂×#107	Dic₁₉	1	1	yes	characteristic
127	C₂×C₄⋊C₈	—	19	2	no	—
128	C₂×#103	Dic₁₉	1	2	yes	—
129	C₂×C₄×C₈	—	19	1	no	—
130	C₂×C₄×C₈	—	19	1	no	—
131	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
132	#336	—	38	4	no	—
133	#334	—	38	2	no	—
134	Q₈⋊C₈	—	38	4	no	—
135	#322	—	38	2	no	—
136	C₂×C₁₉	#1587	1	4	yes	—
137	C₂×C₁₉	#1955	1	1	yes	characteristic
138	C₂×C₁₉	#1971	1	1	yes	characteristic
139	C₂×C₁₉	#1974	1	1	yes	characteristic
140	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
141	C₂×Q₁₆	—	2	4	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂²×C₈	—	19	2	no	—
144	C₂²×C₈	—	38	1	no	—
145	C₂²×C₈	—	38	2	no	—
146	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
147	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
148	C₄×Q₈	—	2	2	no	—
149	C₄×Q₈	—	2	2	no	—
150	C₄×Q₈	—	2	2	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
154	C₂×C₄²	—	2	2	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	#107	—	2	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	#103	—	2	4	no	—
160	C₄×C₈	—	19	2	no	—
161	C₄×C₈	—	38	1	no	—
162	C₄×C₈	—	38	1	no	—
163	C₄×C₈	—	38	1	no	—
164	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
165	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
166	C₁₉	#9664	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	#64520	1	4	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	#64543	1	1	yes	characteristic
177	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
178	Q₁₆	—	2	8	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	38	4	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	38	2	no	—
184	C₂×C₈	—	38	4	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	—	76	4	no	—
187	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
188	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄²	—	4	2	no	—
194	C₄²	—	4	2	no	—
195	C₄²	D₄×D₁₉	1	1	yes	characteristic
196	C₄²	#64543	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
200	Q₈	—	2	4	no	—
201	Q₈	—	2	4	no	—
202	Q₈	—	4	2	no	—
203	Q₈	—	4	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	#10597364	1	4	yes	—
211	C₂×C₄	C₂×#64520	1	2	yes	—
212	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
213	C₂×C₄	#10597382	1	1	yes	characteristic
214	C₂×C₄	#10597384	1	1	yes	characteristic
215	C₂×C₄	#10597384	1	1	yes	characteristic
216	C₂×C₄	#10597386	1	1	yes	characteristic
217	C₂×C₄	#10597394	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
219	C₈	—	2	2	no	—
220	C₈	—	2	2	no	—
221	C₈	—	38	4	no	—
222	C₈	—	76	2	no	—
223	C₈	—	152	2	no	—
224	C₂²	#11926447	1	1	yes	characteristic
225	C₂²	#11926616	1	2	yes	—
226	C₂²	#11926651	1	2	yes	—
227	C₂²	#11926661	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	4	4	no	—
231	C₄	—	8	2	no	—
232	C₄	#11926508	1	1	yes	characteristic
233	C₄	#11926511	1	1	yes	characteristic
234	C₄	#11926616	1	2	yes	—
235	C₄	#11926799	1	2	yes	—
236	C₄	#11926937	1	2	yes	—
237	C₂	#14562507	1	4	yes	—
238	C₂	#14564434	1	1	yes	characteristic
239	C₂	#14564507	1	1	yes	characteristic
240	C₂	#14564524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₄×Q₁₆×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×Q₁₆	D₁₉
hypocenter	C₁₉	#9664
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
166. C₁₉	#9664	semidirect

Maximal subgroups

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

subgroup	index
#14564572	2
C₂×#11926295	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926266	2
C₂×C₄×Q₁₆×C₁₉	2
#9664	19