Subgroups — #18073562

Order 4864.

444 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562297	C₂	1	1	yes	maximal, characteristic
2	#14562227	C₂	1	1	yes	maximal, characteristic
3	#14561924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#64520	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561524	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561524	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₄×#64520	C₂²	1	1	yes	characteristic
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	#11926293	C₄	1	2	yes	—
13	#11926288	C₄	1	2	yes	—
14	#11926284	C₄	1	4	yes	—
15	#11926266	—	2	1	no	—
16	#11926266	—	2	1	no	—
17	#11926265	—	2	1	no	—
18	C₈×C₁₉⋊C₈	—	2	1	no	—
19	C₂×C₁₉×#131	C₄	1	2	yes	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#436	—	2	1	no	—
22	C₁₉×#436	—	2	1	no	—
23	C₈×D₄×C₁₉	—	2	1	no	—
24	C₈×D₄×C₁₉	—	2	1	no	—
25	C₁₉×#423	C₂²	1	1	yes	characteristic
26	C₁₉×#408	C₄	1	2	yes	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
29	C₁₉×#131	—	4	4	no	—
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
37	C₁₉×#124	C₂×C₄	1	2	yes	—
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64520	—	2	1	no	—
44	C₂×#64520	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	C₁₉×C₂²⋊C₈	—	2	2	no	—
49	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
53	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
57	#10597260	C₂×C₄	1	2	yes	—
58	#10597260	C₂×C₄	1	2	yes	—
59	C₄×C₁₉⋊C₈	—	2	1	no	—
60	C₄×C₁₉⋊C₈	—	2	1	no	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	#41×C₁₉	—	4	2	no	—
64	#41×C₁₉	—	4	2	no	—
65	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	C₄²	1	2	yes	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
74	M₁₆×C₁₉	—	4	4	no	—
75	M₁₆×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	—	4	4	no	—
80	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
92	#64520	—	2	4	no	—
93	#64520	—	4	2	no	—
94	C₂×C₁₉⋊C₈	—	2	2	no	—
95	C₂×C₁₉⋊C₈	—	2	2	no	—
96	C₂×C₁₉⋊C₈	—	2	2	no	—
97	C₂×C₁₉⋊C₈	—	2	2	no	—
98	#8245	—	19	1	no	maximal, Sylow
99	C₂³×C₁₉	—	2	2	no	—
100	C₂³×C₁₉	#117	1	1	yes	characteristic
101	Q₈×C₁₉	—	4	2	no	—
102	D₄×C₁₉	—	4	2	no	—
103	D₄×C₁₉	—	4	4	no	—
104	D₄×C₁₉	—	4	2	no	—
105	D₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
119	C₈×C₁₉	—	2	1	no	—
120	C₈×C₁₉	—	2	1	no	—
121	C₈×C₁₉	—	2	1	no	—
122	C₈×C₁₉	—	4	2	no	—
123	C₈×C₁₉	#100	1	2	yes	—
124	C₁₉⋊C₈	—	2	4	no	—
125	C₁₉⋊C₈	—	4	2	no	—
126	C₁₉⋊C₈	—	4	2	no	—
127	C₁₉⋊C₈	—	4	2	no	—
128	#2931	D₁₉	1	1	yes	characteristic
129	#1543	—	19	1	no	—
130	#1525	—	19	1	no	—
131	#1451	—	19	1	no	—
132	C₈×M₁₆	—	19	1	no	—
133	#1299	—	19	1	no	—
134	#1299	—	19	1	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	—	4	2	no	—
139	C₂²×C₁₉	—	4	2	no	—
140	C₂²×C₁₉	—	4	2	no	—
141	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	4	2	no	—
146	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
147	C₄×C₁₉	#413	1	1	yes	characteristic
148	C₄×C₁₉	#443	1	2	yes	—
149	C₄×C₁₉	#444	1	2	yes	—
150	C₂×#131	Dic₁₉	1	2	yes	—
151	#532	C₂×D₁₉	1	1	yes	characteristic
152	#436	—	2	1	no	—
153	#436	—	2	1	no	—
154	C₈×D₄	—	2	1	no	—
155	C₈×D₄	—	2	1	no	—
156	#431	—	19	1	no	—
157	#431	—	19	1	no	—
158	#423	C₂×D₁₉	1	1	yes	characteristic
159	#408	Dic₁₉	1	2	yes	—
160	C₄×M₁₆	—	19	1	no	—
161	C₄×M₁₆	—	19	1	no	—
162	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
163	#333	—	19	2	no	—
164	#331	—	19	2	no	—
165	#329	—	19	4	no	—
166	#322	—	38	1	no	—
167	#322	—	38	1	no	—
168	#322	—	38	1	no	—
169	C₈²	—	38	1	no	—
170	C₂×C₁₉	—	4	1	no	—
171	C₂×C₁₉	—	8	2	no	—
172	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
173	C₂×C₁₉	#1764	1	1	yes	characteristic
174	C₂×C₁₉	#1765	1	1	yes	characteristic
175	C₂×#41	C₂×Dic₁₉	1	2	yes	—
176	#131	—	4	4	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	—	38	1	no	—
179	C₂×M₁₆	—	38	1	no	—
180	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
183	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
184	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
185	#127	C₄×D₁₉	1	1	yes	characteristic
186	#124	C₄×D₁₉	1	2	yes	—
187	#121	—	2	1	no	—
188	#121	—	2	1	no	—
189	C₄×D₄	—	2	1	no	—
190	C₄×D₄	—	2	1	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	C₄⋊C₈	—	2	1	no	—
193	C₄⋊C₈	—	2	1	no	—
194	C₄⋊C₈	—	19	2	no	—
195	C₄⋊C₈	—	19	2	no	—
196	C₂²⋊C₈	—	2	2	no	—
197	C₂²⋊C₈	—	2	2	no	—
198	C₂²⋊C₈	—	38	1	no	—
199	C₂²⋊C₈	—	38	1	no	—
200	#97	—	19	2	no	—
201	#97	—	19	2	no	—
202	C₄×C₈	—	38	1	no	—
203	C₄×C₈	—	38	1	no	—
204	C₄×C₈	—	38	1	no	—
205	C₄×C₈	—	38	1	no	—
206	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
207	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
208	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
209	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
210	C₁₉	#8245	1	1	yes	characteristic, complemented, Sylow
211	#41	—	4	2	no	—
212	#41	—	4	2	no	—
213	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	—	2	1	no	—
216	C₂×D₄	—	2	1	no	—
217	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	#64541	1	1	yes	characteristic
220	C₂²×C₄	#64541	1	1	yes	characteristic
221	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
222	M₁₆	—	4	4	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	38	4	no	—
225	M₁₆	—	76	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	4	1	no	—
229	C₂×C₈	—	4	4	no	—
230	C₂×C₈	—	38	2	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	38	2	no	—
234	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
235	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
236	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
237	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	1	no	—
240	C₂²⋊C₄	—	2	2	no	—
241	C₂²⋊C₄	—	2	2	no	—
242	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
243	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
244	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
245	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂³	—	2	2	no	—
247	C₂³	#10597372	1	1	yes	characteristic
248	Q₈	—	4	2	no	—
249	D₄	—	4	2	no	—
250	D₄	—	4	4	no	—
251	D₄	—	4	2	no	—
252	D₄	—	4	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
261	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
266	C₈	—	2	1	no	—
267	C₈	—	2	1	no	—
268	C₈	—	2	1	no	—
269	C₈	—	4	2	no	—
270	C₈	—	38	4	no	—
271	C₈	—	76	2	no	—
272	C₈	—	76	2	no	—
273	C₈	—	76	2	no	—
274	C₈	#10597290	1	2	yes	—
275	C₂²	—	2	1	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	4	2	no	—
279	C₂²	—	4	2	no	—
280	C₂²	—	4	2	no	—
281	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
282	C₄	—	2	1	no	—
283	C₄	—	2	1	no	—
284	C₄	—	2	1	no	—
285	C₄	—	4	2	no	—
286	C₄	C₂×#10597290	1	1	yes	characteristic
287	C₄	#11926528	1	1	yes	characteristic
288	C₄	#11926659	1	2	yes	—
289	C₄	#11926664	1	2	yes	—
290	C₂	—	4	1	no	—
291	C₂	—	8	2	no	—
292	C₂	C₄×#10597290	1	1	yes	characteristic
293	C₂	#14563470	1	1	yes	characteristic
294	C₂	#14563477	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2931	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2931	D₁₉
hypocenter	C₁₉	#8245
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
3. #14561924	C₂	semidirect
4. C₈×#64520	C₂	semidirect
5. #14561524	C₂	semidirect
6. #14561524	C₂	semidirect
210. C₁₉	#8245	semidirect

Maximal subgroups

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

subgroup	index
#14562297	2
#14562227	2
#14561924	2
C₈×#64520	2
#14561524	2
C₁₉×#2931	2
#8245	19