Subgroups — #18075244

Order 4864.

492 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566112	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926274	C₂	1	2	yes	maximal
4	#14561474	C₂	1	2	yes	maximal
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926450	C₄	1	1	yes	characteristic
10	#11926450	C₄	1	1	yes	characteristic
11	#11926442	C₄	1	1	yes	characteristic
12	#11926442	C₄	1	1	yes	characteristic
13	#11926428	—	2	1	no	—
14	#11926428	—	2	1	no	—
15	C₄×Dic₁₉⋊C₄	—	2	1	no	—
16	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	#11926390	—	2	1	no	—
18	#11926299	—	2	1	no	—
19	#11926274	—	2	4	no	—
20	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
21	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂×C₄	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	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂³	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×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×Dic₁₉⋊C₄	—	2	1	no	—
37	C₂×Dic₁₉⋊C₄	—	2	1	no	—
38	C₂×Dic₁₉⋊C₄	—	2	1	no	—
39	C₂×C₄×Dic₁₉	—	2	1	no	—
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂²×C₁₉⋊C₈	—	2	2	no	—
42	C₄×Dic₃₈	—	2	1	no	—
43	C₄×Dic₃₈	—	2	1	no	—
44	C₄×Dic₃₈	D₄	1	2	yes	—
45	C₄×Dic₃₈	Q₈	1	2	yes	—
46	C₁₉×C₄⋊C₈	—	2	2	no	—
47	C₁₉×C₄⋊C₈	—	2	2	no	—
48	C₁₉×C₄⋊C₈	—	4	2	no	—
49	C₁₉×C₄⋊C₈	—	4	2	no	—
50	C₁₉⋊#95	—	2	1	no	—
51	C₁₉⋊#95	—	2	1	no	—
52	C₁₉⋊#95	—	2	1	no	—
53	C₁₉⋊#95	—	2	1	no	—
54	C₁₉⋊#95	—	2	1	no	—
55	C₁₉⋊#95	—	2	1	no	—
56	C₁₉⋊#95	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
58	C₄×C₁₉⋊C₈	—	2	2	no	—
59	C₄×C₁₉⋊C₈	—	2	2	no	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	2	1	no	—
68	C₂²×Dic₁₉	—	2	1	no	—
69	C₂²×Dic₁₉	—	2	1	no	—
70	C₂²×Dic₁₉	—	2	1	no	—
71	C₂×Dic₃₈	—	2	2	no	—
72	C₂×Dic₃₈	—	2	2	no	—
73	C₂×Dic₃₈	—	2	1	no	—
74	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
75	C₂×C₈×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	4	2	no	—
77	C₂×C₈×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	—	2	2	no	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	—	2	1	no	—
83	C₄²×C₁₉	—	4	1	no	—
84	C₄²×C₁₉	SD₁₆	1	2	yes	—
85	C₄²×C₁₉	Q₁₆	1	2	yes	—
86	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	C₄²×C₁₉	#41	1	1	yes	characteristic
89	C₄²×C₁₉	#41	1	1	yes	characteristic
90	C₄⋊Dic₁₉	—	2	1	no	—
91	C₄⋊Dic₁₉	—	2	2	no	—
92	C₄⋊Dic₁₉	—	2	2	no	—
93	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
94	Dic₁₉⋊C₄	—	2	2	no	—
95	Dic₁₉⋊C₄	—	2	2	no	—
96	Dic₁₉⋊C₄	—	4	2	no	—
97	Dic₁₉⋊C₄	—	4	2	no	—
98	C₄×Dic₁₉	—	2	2	no	—
99	C₄×Dic₁₉	—	2	2	no	—
100	C₄×Dic₁₉	—	4	1	no	—
101	C₄×Dic₁₉	—	4	1	no	—
102	C₂×C₁₉⋊C₈	—	2	4	no	—
103	C₂×C₁₉⋊C₈	—	4	2	no	—
104	C₂×C₁₉⋊C₈	—	4	2	no	—
105	#8568	—	19	1	no	maximal, Sylow
106	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	#103	1	2	yes	—
119	C₂×C₄×C₁₉	#103	1	2	yes	—
120	C₂×C₄×C₁₉	#104	1	2	yes	—
121	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
124	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#131	1	2	yes	—
128	C₂×C₄×C₁₉	#131	1	2	yes	—
129	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
131	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
133	C₂×Dic₁₉	—	2	2	no	—
134	C₂×Dic₁₉	—	2	2	no	—
135	C₂×Dic₁₉	—	4	1	no	—
136	C₂×Dic₁₉	—	4	1	no	—
137	C₂×Dic₁₉	—	4	1	no	—
138	C₂×Dic₁₉	—	4	1	no	—
139	C₂×Dic₁₉	—	4	1	no	—
140	C₂×Dic₁₉	—	4	1	no	—
141	C₂×Dic₁₉	—	4	1	no	—
142	C₂×Dic₁₉	—	4	1	no	—
143	C₂×Dic₁₉	—	4	1	no	—
144	C₂×Dic₁₉	—	4	1	no	—
145	Dic₃₈	—	2	4	no	—
146	Dic₃₈	—	4	2	no	—
147	C₈×C₁₉	—	8	2	no	—
148	C₁₉⋊C₈	—	4	4	no	—
149	#2295	—	19	1	no	—
150	#1842	D₁₉	1	1	yes	characteristic
151	C₄×C₄⋊C₈	—	19	1	no	—
152	C₂×Q₈⋊C₈	—	19	2	no	—
153	#1279	—	19	2	no	—
154	C₂²×C₁₉	#380	1	1	yes	characteristic
155	C₂²×C₁₉	#408	1	1	yes	characteristic
156	C₂²×C₁₉	#408	1	1	yes	characteristic
157	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
158	C₂²×C₁₉	#417	1	1	yes	characteristic
159	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
160	C₂²×C₁₉	#421	1	1	yes	characteristic
161	C₄×C₁₉	—	2	1	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	2	2	no	—
164	C₄×C₁₉	—	2	2	no	—
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	4	1	no	—
167	C₄×C₁₉	#424	1	2	yes	—
168	C₄×C₁₉	#433	1	2	yes	—
169	C₄×C₁₉	#460	1	1	yes	characteristic
170	C₄×C₁₉	#462	1	1	yes	characteristic
171	C₄×C₁₉	#475	1	1	yes	characteristic
172	C₄×C₁₉	#477	1	1	yes	characteristic
173	Dic₁₉	—	4	2	no	—
174	Dic₁₉	—	4	2	no	—
175	Dic₁₉	—	8	1	no	—
176	Dic₁₉	—	8	1	no	—
177	C₂×C₄×Q₈	—	19	1	no	—
178	C₂×C₄⋊C₈	—	2	1	no	—
179	C₂×C₄⋊C₈	—	2	1	no	—
180	C₂×C₄⋊C₈	—	38	1	no	—
181	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
182	C₂×C₄×C₈	—	19	2	no	—
183	#391	—	19	1	no	—
184	#391	—	19	1	no	—
185	#389	—	19	1	no	—
186	#389	—	19	1	no	—
187	#387	—	38	1	no	—
188	#387	—	38	1	no	—
189	C₄×C₄⋊C₄	—	19	1	no	—
190	C₄×C₄⋊C₄	—	38	1	no	—
191	#376	—	38	1	no	—
192	C₄³	C₂×D₁₉	1	1	yes	characteristic
193	#336	—	38	1	no	—
194	Q₈⋊C₈	—	38	4	no	—
195	C₂×C₁₉	#1481	1	1	yes	characteristic
196	C₂×C₁₉	#1483	1	1	yes	characteristic
197	C₂×C₁₉	#1493	1	1	yes	characteristic
198	C₂×C₁₉	#1495	1	1	yes	characteristic
199	C₂×C₁₉	#1798	1	1	yes	characteristic
200	C₂×C₁₉	#1803	1	1	yes	characteristic
201	C₂×C₁₉	#1806	1	1	yes	characteristic
202	C₂²×Q₈	—	19	1	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	38	2	no	—
205	C₄×Q₈	—	19	2	no	—
206	C₄×Q₈	—	19	2	no	—
207	C₄×Q₈	—	38	1	no	—
208	C₄×Q₈	—	38	1	no	—
209	C₂×C₄⋊C₄	—	19	1	no	—
210	C₂×C₄⋊C₄	—	19	1	no	—
211	C₂×C₄⋊C₄	—	19	1	no	—
212	C₂×C₄⋊C₄	—	38	1	no	—
213	C₂×C₄⋊C₄	—	38	1	no	—
214	C₂×C₄⋊C₄	—	38	1	no	—
215	C₂×C₄²	—	38	1	no	—
216	C₂×C₄²	—	38	1	no	—
217	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
219	C₂×C₄²	D₇₆	1	1	yes	characteristic
220	C₂×C₄²	D₇₆	1	1	yes	characteristic
221	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
222	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	—	4	2	no	—
227	C₄⋊C₈	—	4	2	no	—
228	C₄⋊C₈	—	38	4	no	—
229	C₄×C₈	—	38	2	no	—
230	C₄×C₈	—	38	2	no	—
231	#95	—	38	1	no	—
232	#95	—	38	1	no	—
233	#95	—	38	1	no	—
234	#95	—	38	1	no	—
235	#95	—	38	1	no	—
236	#95	—	38	1	no	—
237	#95	—	38	1	no	—
238	C₁₉	#8568	1	1	yes	characteristic, complemented, Sylow
239	C₂×Q₈	—	19	2	no	—
240	C₂×Q₈	—	38	1	no	—
241	C₂×Q₈	—	38	2	no	—
242	C₂×Q₈	—	38	2	no	—
243	C₂²×C₄	—	38	1	no	—
244	C₂²×C₄	—	38	1	no	—
245	C₂²×C₄	—	38	1	no	—
246	C₂²×C₄	—	38	1	no	—
247	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
253	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	4	2	no	—
256	C₂×C₈	—	4	2	no	—
257	C₂×C₈	—	38	4	no	—
258	C₂×C₈	—	76	2	no	—
259	C₂×C₈	—	76	2	no	—
260	C₄⋊C₄	—	19	2	no	—
261	C₄⋊C₄	—	38	1	no	—
262	C₄⋊C₄	—	38	2	no	—
263	C₄⋊C₄	—	38	2	no	—
264	C₄⋊C₄	—	38	2	no	—
265	C₄⋊C₄	—	38	2	no	—
266	C₄⋊C₄	—	76	2	no	—
267	C₄⋊C₄	—	76	2	no	—
268	C₄²	—	2	1	no	—
269	C₄²	—	2	1	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	4	1	no	—
274	C₄²	—	38	2	no	—
275	C₄²	—	38	2	no	—
276	C₄²	—	76	1	no	—
277	C₄²	—	76	1	no	—
278	C₄²	#64526	1	2	yes	—
279	C₄²	#64528	1	2	yes	—
280	C₄²	D₄×D₁₉	1	1	yes	characteristic
281	C₄²	#64543	1	1	yes	characteristic
282	C₄²	Q₈×D₁₉	1	1	yes	characteristic
283	C₄²	#64545	1	1	yes	characteristic
284	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
285	Q₈	—	38	4	no	—
286	Q₈	—	76	2	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	38	2	no	—
299	C₂×C₄	—	38	2	no	—
300	C₂×C₄	—	76	1	no	—
301	C₂×C₄	—	76	1	no	—
302	C₂×C₄	—	76	1	no	—
303	C₂×C₄	—	76	1	no	—
304	C₂×C₄	—	76	1	no	—
305	C₂×C₄	—	76	1	no	—
306	C₂×C₄	—	76	1	no	—
307	C₂×C₄	—	76	1	no	—
308	C₂×C₄	—	76	1	no	—
309	C₂×C₄	—	76	1	no	—
310	C₂×C₄	#10597267	1	2	yes	—
311	C₂×C₄	#10597267	1	2	yes	—
312	C₂×C₄	#10597282	1	2	yes	—
313	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
314	C₂×C₄	#10597338	1	1	yes	characteristic
315	C₂×C₄	#10597341	1	1	yes	characteristic
316	C₂×C₄	#10597343	1	1	yes	characteristic
317	C₂×C₄	#10597347	1	2	yes	—
318	C₂×C₄	#10597353	1	2	yes	—
319	C₂×C₄	#10597378	1	1	yes	characteristic
320	C₂×C₄	C₂×#64526	1	1	yes	characteristic
321	C₂×C₄	#10597384	1	1	yes	characteristic
322	C₂×C₄	#10597388	1	1	yes	characteristic
323	C₂×C₄	C₂×#64528	1	1	yes	characteristic
324	C₂×C₄	#10597392	1	1	yes	characteristic
325	C₈	—	8	2	no	—
326	C₈	—	76	4	no	—
327	C₂²	#11926401	1	1	yes	characteristic
328	C₂²	#11926510	1	1	yes	characteristic
329	C₂²	#11926512	1	1	yes	characteristic
330	C₂²	C₂×#10597267	1	1	yes	characteristic
331	C₂²	#11926543	1	1	yes	characteristic
332	C₂²	C₂×#10597282	1	1	yes	characteristic
333	C₂²	#11926560	1	1	yes	characteristic
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	4	1	no	—
340	C₄	—	76	2	no	—
341	C₄	—	76	2	no	—
342	C₄	—	152	1	no	—
343	C₄	—	152	1	no	—
344	C₄	#11926569	1	2	yes	—
345	C₄	#11926604	1	2	yes	—
346	C₄	#11926741	1	1	yes	characteristic
347	C₄	#11926751	1	1	yes	characteristic
348	C₄	#11926826	1	1	yes	characteristic
349	C₄	#11926836	1	1	yes	characteristic
350	C₂	#14562037	1	1	yes	characteristic
351	C₂	#14562046	1	1	yes	characteristic
352	C₂	#14562089	1	1	yes	characteristic
353	C₂	#14562098	1	1	yes	characteristic
354	C₂	#14563616	1	1	yes	characteristic
355	C₂	#14563637	1	1	yes	characteristic
356	C₂	#14563652	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8568
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
238. C₁₉	#8568	semidirect

Maximal subgroups

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

subgroup	index
#14566112	2
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926274	2
#14561474	2
C₁₉×#1842	2
#8568	19