Subgroups — Dic₁₉⋊#338 #18088345

Order 4864.

762 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926567	C₂	1	2	yes	maximal
2	C₂×M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊#338	C₂	1	2	yes	maximal
5	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂²×#64520	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	#11926567	—	2	4	no	—
10	#11926567	—	2	2	no	—
11	#11926567	—	2	2	no	—
12	C₂×Dic₁₉⋊C₈	C₄	1	8	yes	—
13	M₁₆×Dic₁₉	—	2	2	no	—
14	M₁₆×Dic₁₉	—	2	2	no	—
15	C₂×#10597272	C₄	1	2	yes	—
16	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
17	C₁₉⋊#338	—	2	4	no	—
18	C₁₉⋊#338	—	2	2	no	—
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#338	—	2	2	no	—
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×Dic₁₉	Q₈	1	2	yes	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	—	2	2	no	—
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂×M₁₆×C₁₉	—	2	2	no	—
28	C₂×M₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
35	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	—
37	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
40	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
41	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
42	C₂×#64520	—	2	2	no	—
43	C₂×#64520	—	2	2	no	—
44	C₂×#64520	—	2	2	no	—
45	C₂×#64520	—	2	2	no	—
46	C₂×#64520	—	2	2	no	—
47	C₂×#64520	—	2	2	no	—
48	C₂×#64520	—	2	2	no	—
49	C₂×#64520	—	2	2	no	—
50	C₂×#64520	D₄	1	2	yes	—
51	C₂×#64520	Q₈	1	2	yes	—
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
53	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
54	#10597272	—	2	4	no	—
55	Dic₁₉⋊C₈	—	2	8	no	—
56	Dic₁₉⋊C₈	—	2	8	no	—
57	C₈×Dic₁₉	—	2	2	no	—
58	C₈×Dic₁₉	—	2	2	no	—
59	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	#41	1	2	yes	—
69	C₂²×C₄×C₁₉	#41	1	2	yes	—
70	C₂²×Dic₁₉	—	4	4	no	—
71	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
72	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
73	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
74	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
75	M₁₆×C₁₉	—	2	4	no	—
76	M₁₆×C₁₉	—	2	4	no	—
77	M₁₆×C₁₉	—	4	2	no	—
78	M₁₆×C₁₉	—	4	2	no	—
79	M₁₆×C₁₉	—	4	2	no	—
80	M₁₆×C₁₉	—	4	2	no	—
81	C₂×C₈×C₁₉	—	2	2	no	—
82	C₂×C₈×C₁₉	—	2	2	no	—
83	C₂×C₈×C₁₉	—	2	4	no	—
84	C₂×C₈×C₁₉	—	2	4	no	—
85	C₂×C₈×C₁₉	—	2	4	no	—
86	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
87	C₄×Dic₁₉	C₄²	1	2	yes	—
88	C₄×Dic₁₉	C₄²	1	2	yes	—
89	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
92	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
93	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
94	#64520	—	2	4	no	—
95	#64520	—	2	4	no	—
96	#64520	—	4	2	no	—
97	#64520	—	4	2	no	—
98	#64520	—	4	2	no	—
99	#64520	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	2	2	no	—
101	C₂×C₁₉⋊C₈	—	2	2	no	—
102	C₂×C₁₉⋊C₈	—	2	4	no	—
103	C₂×C₁₉⋊C₈	—	2	4	no	—
104	C₂×C₁₉⋊C₈	—	2	4	no	—
105	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
106	C₄⋊#338	—	19	1	no	maximal, Sylow
107	C₂³×C₁₉	—	4	2	no	—
108	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
110	C₂³×C₁₉	#125	1	2	yes	—
111	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
112	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
121	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
123	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₁₉	#121	1	2	yes	—
125	C₂×C₄×C₁₉	#121	1	2	yes	—
126	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
127	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
128	C₂×C₄×C₁₉	#124	1	2	yes	—
129	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
131	C₂×Dic₁₉	—	2	4	no	—
132	C₂×Dic₁₉	—	2	8	no	—
133	C₂×Dic₁₉	—	4	2	no	—
134	C₂×Dic₁₉	—	4	4	no	—
135	C₂×Dic₁₉	#95	1	2	yes	—
136	C₂×Dic₁₉	#95	1	4	yes	—
137	C₂×Dic₁₉	#95	1	2	yes	—
138	C₈×C₁₉	—	2	4	no	—
139	C₈×C₁₉	—	4	4	no	—
140	C₁₉⋊C₈	—	2	4	no	—
141	C₁₉⋊C₈	—	4	4	no	—
142	C₂×#423	—	19	2	no	—
143	C₂×C₄×M₁₆	—	19	1	no	—
144	C₂×#338	—	19	2	no	—
145	C₂×#338	—	19	1	no	—
146	C₂×#338	D₁₉	1	1	yes	characteristic
147	C₂²×C₁₉	—	2	2	no	—
148	C₂²×C₁₉	—	2	4	no	—
149	C₂²×C₁₉	—	4	2	no	—
150	C₂²×C₁₉	—	4	1	no	—
151	C₂²×C₁₉	—	4	1	no	—
152	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
153	C₂²×C₁₉	#382	1	1	yes	characteristic
154	C₂²×C₁₉	#384	1	1	yes	characteristic
155	C₂²×C₁₉	#389	1	2	yes	—
156	C₂²×C₁₉	#389	1	2	yes	—
157	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
158	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
159	C₄×C₁₉	#380	1	1	yes	characteristic
160	C₄×C₁₉	#380	1	1	yes	characteristic
161	C₄×C₁₉	#390	1	2	yes	—
162	C₄×C₁₉	#391	1	2	yes	—
163	Dic₁₉	—	2	2	no	—
164	Dic₁₉	—	2	4	no	—
165	Dic₁₉	#338	1	4	yes	complemented
166	C₂²×M₁₆	—	19	1	no	—
167	C₂²×M₁₆	—	19	2	no	—
168	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
169	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
170	C₂²×C₄²	—	19	1	no	—
171	#423	—	38	2	no	—
172	#423	—	38	2	no	—
173	#423	—	38	4	no	—
174	C₂×C₄⋊C₈	—	19	8	no	—
175	C₄×M₁₆	—	38	2	no	—
176	C₄×M₁₆	—	38	2	no	—
177	C₂×#97	—	19	2	no	—
178	C₂×C₄×C₈	—	19	2	no	—
179	#338	—	2	2	no	—
180	#338	—	38	4	no	—
181	#338	—	38	2	no	—
182	C₂×C₁₉	—	2	1	no	—
183	C₂×C₁₉	—	2	1	no	—
184	C₂×C₁₉	—	2	2	no	—
185	C₂×C₁₉	—	2	2	no	—
186	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
187	C₂×C₁₉	C₂×#338	1	2	yes	—
188	C₂³×C₄	—	19	2	no	—
189	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	19	2	no	—
199	C₂×M₁₆	—	19	2	no	—
200	C₂×M₁₆	—	38	2	no	—
201	C₂×M₁₆	—	38	2	no	—
202	C₂×M₁₆	—	38	2	no	—
203	C₂×M₁₆	—	38	2	no	—
204	C₂×M₁₆	—	38	2	no	—
205	C₂×M₁₆	—	38	2	no	—
206	C₂×M₁₆	—	38	2	no	—
207	C₂×M₁₆	—	38	2	no	—
208	C₂×M₁₆	Dic₃₈	1	2	yes	—
209	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
210	C₂²×C₈	—	19	2	no	—
211	C₂²×C₈	—	19	4	no	—
212	C₂²×C₈	C₄×D₁₉	1	4	yes	—
213	C₂²×C₈	C₄×D₁₉	1	2	yes	—
214	C₂×C₄²	—	19	1	no	—
215	C₂×C₄²	—	19	1	no	—
216	C₂×C₄²	—	19	4	no	—
217	C₂×C₄²	—	19	2	no	—
218	C₂×C₄²	—	19	2	no	—
219	C₂×C₄²	—	19	2	no	—
220	C₄⋊C₈	—	38	8	no	—
221	C₄⋊C₈	—	38	8	no	—
222	#97	—	38	4	no	—
223	C₄×C₈	—	38	2	no	—
224	C₄×C₈	—	38	2	no	—
225	C₁₉	C₄⋊#338	1	1	yes	characteristic, complemented, Sylow
226	C₂⁴	Q₈×D₁₉	1	1	yes	characteristic
227	C₂²×C₄	—	19	2	no	—
228	C₂²×C₄	—	19	4	no	—
229	C₂²×C₄	—	19	2	no	—
230	C₂²×C₄	—	19	4	no	—
231	C₂²×C₄	—	76	4	no	—
232	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
234	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
235	C₂²×C₄	#64541	1	2	yes	—
236	C₂²×C₄	D₄×D₁₉	1	2	yes	—
237	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
238	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
239	C₂²×C₄	#64543	1	2	yes	—
240	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
242	M₁₆	—	2	4	no	—
243	M₁₆	—	2	4	no	—
244	M₁₆	—	4	2	no	—
245	M₁₆	—	4	2	no	—
246	M₁₆	—	4	2	no	—
247	M₁₆	—	4	2	no	—
248	M₁₆	—	38	4	no	—
249	M₁₆	—	38	4	no	—
250	M₁₆	—	76	2	no	—
251	M₁₆	—	76	2	no	—
252	M₁₆	—	76	2	no	—
253	M₁₆	—	76	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	19	4	no	—
260	C₂×C₈	—	38	2	no	—
261	C₂×C₈	—	38	2	no	—
262	C₂×C₈	—	38	4	no	—
263	C₂×C₈	—	38	4	no	—
264	C₂×C₈	—	38	4	no	—
265	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
266	C₄²	—	19	2	no	—
267	C₄²	—	19	2	no	—
268	C₄²	—	19	1	no	—
269	C₄²	—	19	1	no	—
270	C₄²	—	19	2	no	—
271	C₄²	—	19	4	no	—
272	C₄²	—	19	4	no	—
273	C₂³	—	4	2	no	—
274	C₂³	#10597334	1	1	yes	characteristic
275	C₂³	#10597335	1	2	yes	—
276	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
277	C₂³	C₄⋊C₄×D₁₉	1	2	yes	—
278	C₂³	#10597390	1	1	yes	characteristic
279	C₂×C₄	—	19	2	no	—
280	C₂×C₄	—	19	2	no	—
281	C₂×C₄	—	19	4	no	—
282	C₂×C₄	—	38	4	no	—
283	C₂×C₄	—	38	8	no	—
284	C₂×C₄	—	76	2	no	—
285	C₂×C₄	—	76	4	no	—
286	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
287	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
288	C₂×C₄	#10597318	1	1	yes	characteristic
289	C₂×C₄	#10597323	1	1	yes	characteristic
290	C₂×C₄	#10597324	1	2	yes	—
291	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
292	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
293	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
294	C₂×C₄	#10597330	1	2	yes	—
295	C₂×C₄	#10597331	1	2	yes	—
296	C₂×C₄	#10597333	1	2	yes	—
297	C₂×C₄	#10597334	1	1	yes	characteristic
298	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
299	C₂×C₄	#10597342	1	2	yes	—
300	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
301	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
302	C₂×C₄	#10597385	1	2	yes	—
303	C₂×C₄	#10597386	1	1	yes	characteristic
304	C₈	—	2	4	no	—
305	C₈	—	4	4	no	—
306	C₈	—	38	4	no	—
307	C₈	—	76	4	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	4	1	no	—
311	C₂²	—	4	1	no	—
312	C₂²	—	4	2	no	—
313	C₂²	#95×D₁₉	1	1	yes	characteristic
314	C₂²	#11926408	1	1	yes	characteristic
315	C₂²	#11926413	1	1	yes	characteristic
316	C₂²	#11926439	1	2	yes	—
317	C₂²	#11926441	1	2	yes	—
318	C₄	—	19	4	no	—
319	C₄	—	38	2	no	—
320	C₄	—	38	4	no	—
321	C₄	#11926395	1	1	yes	characteristic
322	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
323	C₄	#11926402	1	1	yes	characteristic
324	C₄	#11926403	1	1	yes	characteristic
325	C₄	#11926444	1	2	yes	—
326	C₄	#11926448	1	2	yes	—
327	C₂	—	2	1	no	—
328	C₂	—	2	1	no	—
329	C₂	—	2	2	no	—
330	C₂	—	2	2	no	—
331	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
332	C₂	D₁₉×#338	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#338	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#338	D₁₉
hypocenter	C₁₉	C₄⋊#338
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#338

Complements

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

N	H ≅ G/N	type
165. Dic₁₉	#338	semidirect
225. C₁₉	C₄⋊#338	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926567	2
C₂×M₁₆×Dic₁₉	2
C₂×C₁₉⋊#338	2
C₂×C₁₉×#338	2
C₄⋊#338	19

Subgroups — Dic19⋊#338 #18088345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₉⋊#338 #18088345