Subgroups — #18071232

Order 4864.

366 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572017	C₂	1	1	yes	maximal, characteristic
2	#14563752	C₂	1	1	yes	maximal, characteristic
3	#14561460	C₂	1	2	yes	maximal
4	#14561457	C₂	1	2	yes	maximal
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	#11926450	C₄	1	1	yes	characteristic
8	#11926450	C₄	1	1	yes	characteristic
9	#11926450	C₂²	1	1	yes	characteristic
10	#11926442	C₄	1	1	yes	characteristic
11	#11926442	C₄	1	1	yes	characteristic
12	#11926442	C₂²	1	1	yes	characteristic
13	#11926428	—	2	1	no	—
14	#11926428	—	2	1	no	—
15	#11926428	—	2	1	no	—
16	#11926412	—	2	1	no	—
17	#11926299	—	2	1	no	—
18	#11926299	C₂²	1	2	yes	—
19	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
20	C₄³×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	C₂²	1	2	yes	—
23	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×Dic₁₉⋊C₄	—	2	1	no	—
36	C₂×Dic₁₉⋊C₄	—	2	1	no	—
37	C₂×Dic₁₉⋊C₄	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	4	2	no	—
40	C₁₉⋊#95	—	2	1	no	—
41	C₁₉⋊#95	—	2	1	no	—
42	C₁₉⋊#95	—	2	1	no	—
43	C₁₉⋊#95	—	2	1	no	—
44	C₁₉⋊#95	—	2	1	no	—
45	C₁₉⋊#95	—	2	1	no	—
46	C₁₉⋊#95	—	2	1	no	—
47	C₁₉⋊#95	—	2	1	no	—
48	C₁₉⋊#95	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₁₉	—	2	1	no	—
58	C₂²×Dic₁₉	—	2	1	no	—
59	C₂²×Dic₁₉	—	2	1	no	—
60	C₂²×Dic₁₉	—	2	1	no	—
61	C₂×Dic₃₈	—	2	2	no	—
62	C₂×Dic₃₈	—	4	1	no	—
63	C₂×Dic₃₈	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	4	1	no	—
71	C₄²×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	SD₁₆	1	2	yes	—
75	C₄²×C₁₉	Q₁₆	1	2	yes	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	4	1	no	—
78	C₄⋊Dic₁₉	—	4	1	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	Dic₁₉⋊C₄	—	4	2	no	—
81	Dic₁₉⋊C₄	—	4	1	no	—
82	Dic₁₉⋊C₄	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	#7733	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	#103	1	2	yes	—
105	C₂×C₄×C₁₉	#103	1	2	yes	—
106	C₂×C₄×C₁₉	#131	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
111	C₂×Dic₁₉	—	4	1	no	—
112	C₂×Dic₁₉	—	4	1	no	—
113	C₂×Dic₁₉	—	4	1	no	—
114	C₂×Dic₁₉	—	4	1	no	—
115	C₂×Dic₁₉	—	4	1	no	—
116	C₂×Dic₁₉	—	4	1	no	—
117	C₂×Dic₁₉	—	4	1	no	—
118	C₂×Dic₁₉	—	4	1	no	—
119	C₂×Dic₁₉	—	4	1	no	—
120	C₂×Dic₁₉	—	4	1	no	—
121	C₂×Dic₁₉	—	4	1	no	—
122	C₂×Dic₁₉	—	4	1	no	—
123	Dic₃₈	—	8	2	no	—
124	C₈×C₁₉	—	8	2	no	—
125	C₁₉⋊C₈	—	8	2	no	—
126	#2863	—	19	1	no	—
127	#1831	—	19	1	no	—
128	#1831	D₁₉	1	1	yes	characteristic
129	#1272	—	19	2	no	—
130	#1271	—	19	2	no	—
131	C₂²×C₁₉	#408	1	1	yes	characteristic
132	C₂²×C₁₉	#410	1	1	yes	characteristic
133	C₂²×C₁₉	#413	1	1	yes	characteristic
134	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
135	C₂²×C₁₉	#417	1	1	yes	characteristic
136	C₂²×C₁₉	#421	1	1	yes	characteristic
137	C₂²×C₁₉	#421	1	1	yes	characteristic
138	C₄×C₁₉	—	2	2	no	—
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	—	4	1	no	—
147	Dic₁₉	—	8	1	no	—
148	Dic₁₉	—	8	1	no	—
149	Dic₁₉	—	8	1	no	—
150	Dic₁₉	—	8	1	no	—
151	C₂×C₄⋊C₈	—	2	1	no	—
152	C₂×C₄⋊C₈	—	38	1	no	—
153	#391	—	19	1	no	—
154	#391	—	19	1	no	—
155	#391	—	19	1	no	—
156	#389	—	19	1	no	—
157	#389	—	19	1	no	—
158	#389	—	19	1	no	—
159	#387	—	38	1	no	—
160	#387	—	38	1	no	—
161	#387	—	38	1	no	—
162	#383	—	38	1	no	—
163	C₄³	C₂×D₁₉	1	1	yes	characteristic
164	#336	—	2	1	no	—
165	#336	—	19	2	no	—
166	#336	—	38	1	no	—
167	#336	C₂×D₁₉	1	2	yes	—
168	C₂×C₁₉	#1473	1	1	yes	characteristic
169	C₂×C₁₉	#1481	1	1	yes	characteristic
170	C₂×C₁₉	#1495	1	1	yes	characteristic
171	C₂×C₁₉	#1512	1	1	yes	characteristic
172	C₂×C₁₉	#1518	1	1	yes	characteristic
173	C₂×C₁₉	#1535	1	1	yes	characteristic
174	C₂×C₁₉	#1550	1	1	yes	characteristic
175	C₂²×Q₈	—	19	1	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	38	2	no	—
178	C₂×C₄⋊C₄	—	19	1	no	—
179	C₂×C₄⋊C₄	—	19	1	no	—
180	C₂×C₄⋊C₄	—	19	1	no	—
181	C₂×C₄⋊C₄	—	38	1	no	—
182	C₂×C₄⋊C₄	—	38	1	no	—
183	C₂×C₄⋊C₄	—	38	1	no	—
184	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
185	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
186	C₂×C₄²	D₇₆	1	1	yes	characteristic
187	C₂×C₄²	D₇₆	1	1	yes	characteristic
188	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
190	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
191	C₄⋊C₈	—	4	2	no	—
192	C₄⋊C₈	—	76	2	no	—
193	#95	—	38	1	no	—
194	#95	—	38	1	no	—
195	#95	—	38	1	no	—
196	#95	—	38	1	no	—
197	#95	—	38	1	no	—
198	#95	—	38	1	no	—
199	#95	—	38	1	no	—
200	#95	—	38	1	no	—
201	#95	—	38	1	no	—
202	C₁₉	#7733	1	1	yes	characteristic, complemented, Sylow
203	C₂×Q₈	—	38	2	no	—
204	C₂×Q₈	—	76	1	no	—
205	C₂×Q₈	—	76	1	no	—
206	C₂²×C₄	—	38	1	no	—
207	C₂²×C₄	—	38	1	no	—
208	C₂²×C₄	—	38	1	no	—
209	C₂²×C₄	—	38	1	no	—
210	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
214	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
216	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂×C₈	—	4	2	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	—	76	2	no	—
221	C₂×C₈	—	76	2	no	—
222	C₂×C₈	—	76	2	no	—
223	C₄⋊C₄	—	38	2	no	—
224	C₄⋊C₄	—	76	1	no	—
225	C₄⋊C₄	—	76	1	no	—
226	C₄⋊C₄	—	76	2	no	—
227	C₄⋊C₄	—	76	2	no	—
228	C₄⋊C₄	—	76	1	no	—
229	C₄⋊C₄	—	76	1	no	—
230	C₄²	—	2	2	no	—
231	C₄²	—	2	1	no	—
232	C₄²	—	2	1	no	—
233	C₄²	—	4	1	no	—
234	C₄²	—	4	1	no	—
235	C₄²	—	4	1	no	—
236	C₄²	—	4	1	no	—
237	C₄²	#64526	1	2	yes	—
238	C₄²	#64528	1	2	yes	—
239	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
240	Q₈	—	152	2	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	76	1	no	—
258	C₂×C₄	—	76	1	no	—
259	C₂×C₄	—	76	1	no	—
260	C₂×C₄	—	76	1	no	—
261	C₂×C₄	—	76	1	no	—
262	C₂×C₄	—	76	1	no	—
263	C₂×C₄	—	76	1	no	—
264	C₂×C₄	—	76	1	no	—
265	C₂×C₄	—	76	1	no	—
266	C₂×C₄	—	76	1	no	—
267	C₂×C₄	—	76	1	no	—
268	C₂×C₄	—	76	1	no	—
269	C₂×C₄	#10597267	1	2	yes	—
270	C₂×C₄	#10597267	1	2	yes	—
271	C₂×C₄	#10597347	1	2	yes	—
272	C₂×C₄	#10597354	1	1	yes	characteristic
273	C₂×C₄	#10597355	1	1	yes	characteristic
274	C₂×C₄	C₂×#64526	1	1	yes	characteristic
275	C₂×C₄	C₂×#64528	1	1	yes	characteristic
276	C₈	—	8	2	no	—
277	C₈	—	152	2	no	—
278	C₂²	#11926510	1	1	yes	characteristic
279	C₂²	#11926517	1	1	yes	characteristic
280	C₂²	#11926526	1	1	yes	characteristic
281	C₂²	C₂×#10597267	1	1	yes	characteristic
282	C₂²	#11926546	1	1	yes	characteristic
283	C₂²	#11926560	1	1	yes	characteristic
284	C₂²	#11926562	1	1	yes	characteristic
285	C₄	—	2	2	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	—	2	1	no	—
289	C₄	—	2	1	no	—
290	C₄	—	2	2	no	—
291	C₄	—	2	2	no	—
292	C₄	—	4	1	no	—
293	C₄	—	4	1	no	—
294	C₄	—	152	1	no	—
295	C₄	—	152	1	no	—
296	C₄	—	152	1	no	—
297	C₄	—	152	1	no	—
298	C₂	#14562002	1	1	yes	characteristic
299	C₂	#14562037	1	1	yes	characteristic
300	C₂	#14562101	1	1	yes	characteristic
301	C₂	#14562174	1	1	yes	characteristic
302	C₂	#14562198	1	1	yes	characteristic
303	C₂	#14562264	1	1	yes	characteristic
304	C₂	#14562326	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#7733
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
202. C₁₉	#7733	semidirect

Maximal subgroups

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

subgroup	index
#14572017	2
#14563752	2
#14561460	2
#14561457	2
C₁₉×#1831	2
#7733	19