Subgroups — #18081648

Order 4864.

486 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926290	C₂	1	2	yes	maximal
4	C₂×#11926290	C₂	1	2	yes	maximal
5	C₁₉×#2862	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×#10597260	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926290	—	2	4	no	—
12	#11926290	—	2	4	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#391	—	2	1	no	—
16	C₁₉×#391	—	2	2	no	—
17	C₁₉×#391	—	2	1	no	—
18	C₁₉×#382	C₄	1	4	yes	—
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₁₉⋊C₈	—	2	2	no	—
37	C₁₉×#95	—	2	4	no	—
38	C₁₉×#95	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
44	#10597260	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	4	2	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	1	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	—	2	4	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	1	no	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	#41	1	2	yes	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	4	no	—
78	#9708	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	8	2	no	—
81	Q₈×C₁₉	—	8	2	no	—
82	Q₈×C₁₉	—	8	2	no	—
83	Q₈×C₁₉	—	8	1	no	—
84	Q₈×C₁₉	—	8	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	4	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	#101	1	4	yes	—
97	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₉	#121	1	2	yes	—
99	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#135	1	2	yes	—
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#137	1	2	yes	—
106	C₁₉⋊C₈	—	4	4	no	—
107	C₁₉⋊C₈	—	8	2	no	—
108	#2862	D₁₉	1	1	yes	characteristic
109	#1842	—	19	1	no	—
110	#1767	—	19	1	no	—
111	C₂×#332	—	19	2	no	—
112	C₂×#332	—	19	2	no	—
113	C₂²×C₁₉	#390	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#101	1	2	yes	—
115	C₂²×C₁₉	#416	1	1	yes	characteristic
116	C₂²×C₁₉	#417	1	2	yes	—
117	C₂²×C₁₉	#417	1	1	yes	characteristic
118	C₄×C₁₉	—	2	4	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	8	2	no	—
122	C₄×C₁₉	—	8	2	no	—
123	C₄×C₁₉	#463	1	2	yes	—
124	C₄×C₁₉	#464	1	2	yes	—
125	C₄×C₁₉	#489	1	2	yes	—
126	C₄×C₁₉	#496	1	1	yes	characteristic
127	C₄×C₁₉	#497	1	1	yes	characteristic
128	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
129	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	19	2	no	—
131	C₂×C₄⋊C₈	—	19	2	no	—
132	C₂×C₄⋊C₈	—	38	2	no	—
133	C₂×#97	—	38	1	no	—
134	#391	—	2	1	no	—
135	#391	—	2	1	no	—
136	#391	—	2	2	no	—
137	#382	Dic₁₉	1	4	yes	—
138	C₄³	C₂×D₁₉	1	1	yes	characteristic
139	#336	—	38	1	no	—
140	#332	—	38	4	no	—
141	#332	—	38	4	no	—
142	C₂×C₁₉	#1552	1	2	yes	—
143	C₂×C₁₉	#1561	1	2	yes	—
144	C₂×C₁₉	#1959	1	1	yes	characteristic
145	C₂×C₁₉	#1966	1	1	yes	characteristic
146	C₂×C₁₉	#1983	1	1	yes	characteristic
147	C₂²×Q₈	—	2	1	no	—
148	C₂²×Q₈	—	2	1	no	—
149	C₂²×C₈	—	38	2	no	—
150	C₂²×C₈	—	38	2	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
158	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
159	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
160	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
161	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
162	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
163	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	19	4	no	—
165	C₄⋊C₈	—	38	2	no	—
166	C₄⋊C₈	—	38	2	no	—
167	C₄⋊C₈	—	38	2	no	—
168	C₄⋊C₈	—	76	4	no	—
169	#97	—	76	2	no	—
170	#95	—	2	4	no	—
171	#95	—	2	4	no	—
172	C₁₉	#9708	1	1	yes	characteristic, complemented, Sylow
173	C₂×Q₈	—	4	1	no	—
174	C₂×Q₈	—	4	2	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	4	2	no	—
180	C₂×Q₈	—	4	1	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
184	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
185	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂×C₈	—	38	4	no	—
189	C₂×C₈	—	76	2	no	—
190	C₂×C₈	—	76	2	no	—
191	C₂×C₈	—	76	2	no	—
192	C₂×C₈	—	76	4	no	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	1	no	—
198	C₄²	—	2	1	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	1	no	—
203	C₄²	—	2	4	no	—
204	C₄²	D₄×D₁₉	1	2	yes	—
205	C₄²	#64543	1	2	yes	—
206	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
207	Q₈	—	8	2	no	—
208	Q₈	—	8	1	no	—
209	Q₈	—	8	1	no	—
210	Q₈	—	8	2	no	—
211	Q₈	—	8	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	#10597293	1	4	yes	—
224	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
225	C₂×C₄	#10597382	1	1	yes	characteristic
226	C₂×C₄	#10597384	1	2	yes	—
227	C₂×C₄	#10597386	1	1	yes	characteristic
228	C₂×C₄	#10597395	1	2	yes	—
229	C₂×C₄	#10597395	1	1	yes	characteristic
230	C₂×C₄	#10597396	1	2	yes	—
231	C₂×C₄	#10597397	1	2	yes	—
232	C₂×C₄	#10597397	1	1	yes	characteristic
233	C₈	—	76	4	no	—
234	C₈	—	152	2	no	—
235	C₂²	#11926447	1	1	yes	characteristic
236	C₂²	C₂×#10597293	1	2	yes	—
237	C₂²	#11926540	1	1	yes	characteristic
238	C₂²	#11926545	1	2	yes	—
239	C₂²	#11926545	1	1	yes	characteristic
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	8	2	no	—
244	C₄	—	8	2	no	—
245	C₄	#11926756	1	2	yes	—
246	C₄	#11926763	1	2	yes	—
247	C₄	#11926903	1	2	yes	—
248	C₄	#11926934	1	1	yes	characteristic
249	C₄	#11926939	1	1	yes	characteristic
250	C₂	#14562335	1	2	yes	—
251	C₂	#14562373	1	2	yes	—
252	C₂	#14564452	1	1	yes	characteristic
253	C₂	#14564480	1	1	yes	characteristic
254	C₂	#14564568	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2862	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2862	D₁₉
hypocenter	C₁₉	#9708
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

Complements

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

N	H ≅ G/N	type
172. C₁₉	#9708	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
#14563488	2
C₂×#11926290	2
C₁₉×#2862	2
#9708	19