Subgroups — #18075302

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563488	C₂	1	2	yes	maximal, complemented
2	C₂×#11926284	C₂	1	2	yes	maximal
3	#14561516	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×#10597260	C₂²	1	4	yes	—
7	#11926299	—	2	2	no	—
8	#11926284	—	2	4	no	—
9	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
12	C₁₉×#391	C₄	1	1	yes	characteristic
13	C₁₉×#390	C₄	1	1	yes	characteristic
14	C₁₉×#388	—	2	2	no	—
15	C₁₉×#382	C₂²	1	1	yes	characteristic
16	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₁₉×#124	D₄	1	2	yes	—
23	C₁₉×#124	Q₈	1	2	yes	—
24	C₄×Q₈×C₁₉	—	4	2	no	—
25	C₄×D₄×C₁₉	—	4	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	D₄	1	2	yes	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₁₉⋊C₈	—	2	4	no	—
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
42	#10597260	—	2	4	no	—
43	#10597260	—	2	4	no	—
44	C₂⁴×C₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂×D₄×C₁₉	—	2	1	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	4	1	no	—
52	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	—	4	4	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂²⋊C₄×C₁₉	—	4	4	no	—
69	C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	4	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₄²×C₁₉	#41	1	2	yes	—
78	C₂×C₁₉⋊C₈	—	2	8	no	—
79	C₂×C₁₉⋊C₈	—	4	4	no	—
80	C₂×C₁₉⋊C₈	—	4	4	no	—
81	#8579	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	—	4	2	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	D₄×C₁₉	—	4	2	no	—
91	D₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	8	4	no	—
109	C₂×C₄×C₁₉	#100	1	2	yes	—
110	C₂×C₄×C₁₉	#104	1	4	yes	—
111	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
115	C₁₉⋊C₈	—	4	8	no	—
116	C₄×#124	D₁₉	1	1	yes	characteristic
117	#1767	—	19	2	no	—
118	C₂×#329	—	19	2	no	—
119	#1295	—	19	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	4	no	—
122	C₂²×C₁₉	—	8	1	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	#380	1	1	yes	characteristic
126	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
127	C₂²×C₁₉	#413	1	1	yes	characteristic
128	C₂²×C₁₉	C₂×#104	1	2	yes	—
129	C₂²×C₁₉	#421	1	2	yes	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	2	no	—
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	—	4	2	no	—
136	C₄×C₁₉	—	4	2	no	—
137	C₄×C₁₉	—	8	1	no	—
138	C₄×C₁₉	—	8	1	no	—
139	C₄×C₁₉	#329	1	4	yes	complemented
140	C₂×#124	C₂×D₁₉	1	1	yes	characteristic
141	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
142	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
143	C₂×C₄⋊C₈	—	38	2	no	—
144	C₂×#97	—	19	4	no	—
145	#391	Dic₁₉	1	1	yes	characteristic
146	#390	Dic₁₉	1	1	yes	characteristic
147	#388	—	2	2	no	—
148	#382	C₂×D₁₉	1	1	yes	characteristic
149	C₄×C₂²⋊C₄	—	2	2	no	—
150	C₄³	C₂×D₁₉	1	1	yes	characteristic
151	#336	—	38	2	no	—
152	#329	—	38	4	no	—
153	C₂×C₁₉	—	8	2	no	—
154	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
155	C₂×C₁₉	#1529	1	2	yes	—
156	C₂×C₁₉	#1536	1	1	yes	characteristic
157	C₂×C₁₉	#1800	1	1	yes	characteristic
158	C₂×C₁₉	#1806	1	2	yes	—
159	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
160	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
161	C₂³×C₄	—	2	1	no	—
162	C₂²×C₈	—	38	4	no	—
163	#124	—	2	2	no	—
164	#124	Dic₃₈	1	2	yes	—
165	#124	D₇₆	1	2	yes	—
166	C₄×Q₈	—	4	2	no	—
167	C₄×D₄	—	4	2	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	—	2	2	no	—
172	C₂×C₂²⋊C₄	—	2	1	no	—
173	C₂×C₂²⋊C₄	—	2	2	no	—
174	C₂×C₄²	—	2	1	no	—
175	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
177	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
178	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
179	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
180	C₄⋊C₈	—	38	8	no	—
181	#97	—	38	4	no	—
182	#97	—	38	4	no	—
183	#95	—	2	2	no	—
184	#95	—	2	2	no	—
185	C₁₉	#8579	1	1	yes	characteristic, complemented, Sylow
186	C₂⁴	—	2	1	no	—
187	C₂×Q₈	—	2	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×Q₈	—	4	1	no	—
190	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
191	C₂×D₄	—	2	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	4	no	—
200	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
201	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
205	C₂×C₈	—	38	8	no	—
206	C₂×C₈	—	76	4	no	—
207	C₂×C₈	—	76	4	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₂²⋊C₄	—	2	4	no	—
212	C₂²⋊C₄	—	2	4	no	—
213	C₂²⋊C₄	—	4	4	no	—
214	C₂²⋊C₄	—	4	2	no	—
215	C₄²	—	2	2	no	—
216	C₄²	—	2	4	no	—
217	C₄²	—	4	1	no	—
218	C₄²	—	4	2	no	—
219	C₄²	—	4	2	no	—
220	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
221	C₄²	C₂×D₇₆	1	1	yes	characteristic
222	C₄²	#64541	1	2	yes	—
223	C₂³	—	2	2	no	—
224	C₂³	—	4	1	no	—
225	C₂³	—	4	2	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	1	no	—
228	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
229	Q₈	—	4	2	no	—
230	Q₈	—	4	2	no	—
231	D₄	—	4	2	no	—
232	D₄	—	4	2	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	8	4	no	—
250	C₂×C₄	#10597290	1	2	yes	—
251	C₂×C₄	#10597294	1	4	yes	—
252	C₂×C₄	#10597370	1	2	yes	—
253	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
254	C₂×C₄	#10597372	1	1	yes	characteristic
255	C₂×C₄	#10597376	1	2	yes	—
256	C₈	—	76	8	no	—
257	C₂²	—	4	2	no	—
258	C₂²	—	4	4	no	—
259	C₂²	—	8	1	no	—
260	C₂²	—	8	2	no	—
261	C₂²	—	8	1	no	—
262	C₂²	#11926404	1	1	yes	characteristic
263	C₂²	C₂×#10597290	1	1	yes	characteristic
264	C₂²	#11926528	1	1	yes	characteristic
265	C₂²	C₂×#10597294	1	2	yes	—
266	C₂²	#11926561	1	2	yes	—
267	C₄	—	2	1	no	—
268	C₄	—	2	1	no	—
269	C₄	—	2	2	no	—
270	C₄	—	2	2	no	—
271	C₄	—	4	2	no	—
272	C₄	—	4	2	no	—
273	C₄	—	4	1	no	—
274	C₄	—	8	1	no	—
275	C₄	—	8	1	no	—
276	C₄	#11926284	1	4	yes	complemented
277	C₂	—	8	2	no	—
278	C₂	C₂×#11926284	1	1	yes	characteristic
279	C₂	#14562242	1	2	yes	—
280	C₂	#14562270	1	1	yes	characteristic
281	C₂	#14563627	1	1	yes	characteristic
282	C₂	#14563655	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#124	D₁₉
hypocenter	C₁₉	#8579
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. #14563488	C₂	semidirect
3. #14561516	C₂	semidirect
139. C₄×C₁₉	#329	semidirect
185. C₁₉	#8579	semidirect
276. C₄	#11926284	semidirect

Maximal subgroups

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

subgroup	index
#14563488	2
C₂×#11926284	2
#14561516	2
C₄×C₁₉×#124	2
#8579	19