Subgroups — #18077201

Order 4864.

558 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572675	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597393	C₂	1	1	yes	maximal, characteristic
3	#14562030	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561955	C₂	1	1	yes	maximal, characteristic
5	#14561467	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597393	C₄	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	#11926623	—	2	2	no	—
11	#11926621	—	2	2	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926506	—	2	2	no	—
15	#11926451	C₄	1	1	yes	characteristic
16	#11926445	C₄	1	1	yes	characteristic
17	#11926434	—	2	2	no	—
18	#11926409	C₄	1	1	yes	characteristic
19	C₄×(C₂×D₁₉)⋊C₄	—	2	2	no	—
20	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	#11926267	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	D₄	1	2	yes	—
30	C₄×Q₈×C₁₉	—	2	1	no	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	#10597393	—	2	2	no	—
39	#10597393	—	2	2	no	—
40	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
41	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
42	C₂×(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
43	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂×C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×#64515	—	2	4	no	—
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	2	1	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
55	C₁₉×C₂²⋊C₈	—	2	1	no	—
56	C₁₉×C₂²⋊C₈	—	2	1	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	C₄×C₈×C₁₉	—	2	1	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
63	(C₂×D₁₉)⋊C₈	—	2	4	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₂³×D₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	M₁₆	1	2	yes	complemented
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	2	no	—
90	C₂×C₄×D₁₉	—	2	2	no	—
91	C₂×C₄×D₁₉	—	4	4	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄²×C₁₉	—	4	1	no	—
99	C₄²×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	(C₂×D₁₉)⋊C₄	—	2	8	no	—
105	(C₂×D₁₉)⋊C₄	—	2	2	no	—
106	(C₂×D₁₉)⋊C₄	—	2	2	no	—
107	(C₂×D₁₉)⋊C₄	—	4	4	no	—
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	C₄×Dic₁₉	—	2	1	no	—
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	—	4	2	no	—
114	C₄×Dic₁₉	—	4	2	no	—
115	C₄×Dic₁₉	M₁₆	1	2	yes	complemented
116	C₂×C₁₉⋊C₈	—	2	2	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	#64515	—	8	4	no	—
119	#8961	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×D₁₉	—	2	2	no	—
122	C₂²×D₁₉	—	2	2	no	—
123	C₂²×D₁₉	—	2	2	no	—
124	C₂²×D₁₉	—	4	2	no	—
125	C₂²×D₁₉	—	4	2	no	—
126	Q₈×C₁₉	—	2	2	no	—
127	Q₈×C₁₉	—	2	2	no	—
128	Q₈×C₁₉	—	4	1	no	—
129	Q₈×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
147	C₂×Dic₁₉	—	2	2	no	—
148	C₂×Dic₁₉	—	2	2	no	—
149	C₂×Dic₁₉	—	2	2	no	—
150	C₂×Dic₁₉	—	4	1	no	—
151	C₂×Dic₁₉	—	4	1	no	—
152	C₂×Dic₁₉	—	4	1	no	—
153	C₂×Dic₁₉	—	4	1	no	—
154	C₂×Dic₁₉	—	4	2	no	—
155	D₇₆	—	4	1	no	—
156	D₇₆	—	4	1	no	—
157	D₇₆	—	4	1	no	—
158	D₇₆	—	4	1	no	—
159	C₄×D₁₉	—	4	4	no	—
160	C₄×D₁₉	—	8	2	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₈×C₁₉	—	8	1	no	—
163	C₁₉⋊C₈	—	4	2	no	—
164	C₁₉⋊C₈	—	8	1	no	—
165	#2975	—	19	1	no	—
166	C₄×#124	—	19	1	no	—
167	#1479	—	19	1	no	—
168	#1479	D₁₉	1	1	yes	characteristic, complemented
169	#1460	—	19	1	no	—
170	#1276	—	19	1	no	—
171	#1276	—	19	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	#386	1	1	yes	characteristic
175	C₂²×C₁₉	#407	1	1	yes	characteristic
176	C₂²×C₁₉	#408	1	1	yes	characteristic
177	C₂×D₁₉	—	4	4	no	—
178	C₂×D₁₉	—	4	2	no	—
179	C₂×D₁₉	—	4	2	no	—
180	C₂×D₁₉	—	4	2	no	—
181	C₂×D₁₉	—	8	2	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	8	1	no	—
187	C₄×C₁₉	#435	1	1	yes	characteristic
188	C₄×C₁₉	#435	1	1	yes	characteristic
189	C₄×C₁₉	#436	1	1	yes	characteristic
190	C₄×C₁₉	#436	1	1	yes	characteristic
191	C₄×C₁₉	#455	1	2	yes	—
192	Dic₁₉	—	4	2	no	—
193	Dic₁₉	—	4	2	no	—
194	Dic₁₉	—	4	2	no	—
195	C₂×#124	—	19	1	no	—
196	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
197	C₂×C₄×D₄	—	19	1	no	—
198	#436	—	38	2	no	—
199	#436	—	38	2	no	—
200	#431	—	19	1	no	—
201	#431	—	19	1	no	—
202	#431	C₂×D₁₉	1	1	yes	characteristic
203	#431	C₂×D₁₉	1	1	yes	characteristic
204	#407	—	38	2	no	—
205	#391	—	19	1	no	—
206	#390	—	19	1	no	—
207	#388	—	38	2	no	—
208	#382	—	19	1	no	—
209	C₄×C₂²⋊C₄	—	38	2	no	—
210	C₄³	—	19	1	no	—
211	Q₈⋊C₈	—	2	2	no	—
212	Q₈⋊C₈	—	38	2	no	—
213	#323	—	38	2	no	—
214	C₂×C₁₉	—	2	1	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	#1870	1	1	yes	characteristic
217	C₂×C₁₉	#1884	1	1	yes	characteristic
218	C₂×C₁₉	#1885	1	1	yes	characteristic
219	D₁₉	—	8	2	no	—
220	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
221	C₂²×D₄	—	19	1	no	—
222	C₂³×C₄	—	19	2	no	—
223	C₂×M₁₆	—	38	4	no	—
224	#124	—	38	2	no	—
225	#124	—	38	2	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×D₄	—	38	1	no	—
231	C₄×D₄	—	38	1	no	—
232	C₄×D₄	—	38	1	no	—
233	C₄×D₄	—	38	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	19	1	no	—
236	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	—	19	2	no	—
238	C₂×C₂²⋊C₄	—	38	2	no	—
239	C₂×C₂²⋊C₄	—	38	2	no	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	19	1	no	—
242	C₂×C₄²	—	19	1	no	—
243	C₂×C₄²	—	38	1	no	—
244	C₂×C₄²	—	38	1	no	—
245	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	19	2	no	—
248	C₄⋊C₈	—	38	1	no	—
249	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
250	C₂²⋊C₈	—	2	1	no	—
251	C₂²⋊C₈	—	2	1	no	—
252	C₂²⋊C₈	—	38	4	no	—
253	C₂²⋊C₈	—	38	1	no	—
254	C₂²⋊C₈	—	38	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	—	38	1	no	—
258	C₄×C₈	—	38	1	no	—
259	#95	—	38	2	no	—
260	#95	—	38	2	no	—
261	C₁₉	#8961	1	1	yes	characteristic, complemented, Sylow
262	C₂⁴	—	19	2	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	#64515	1	2	yes	complemented
269	C₂×D₄	—	38	1	no	—
270	C₂×D₄	—	38	1	no	—
271	C₂×D₄	—	38	1	no	—
272	C₂×D₄	—	38	1	no	—
273	C₂×D₄	—	38	1	no	—
274	C₂×D₄	—	38	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	19	2	no	—
278	C₂²×C₄	—	38	1	no	—
279	C₂²×C₄	—	38	1	no	—
280	C₂²×C₄	—	38	2	no	—
281	C₂²×C₄	—	38	2	no	—
282	C₂²×C₄	—	76	4	no	—
283	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
286	M₁₆	—	152	4	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	38	2	no	—
290	C₂×C₈	—	76	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	38	1	no	—
296	C₄⋊C₄	—	38	1	no	—
297	C₂²⋊C₄	—	38	8	no	—
298	C₂²⋊C₄	—	38	2	no	—
299	C₂²⋊C₄	—	38	2	no	—
300	C₂²⋊C₄	—	76	4	no	—
301	C₄²	—	4	1	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	19	2	no	—
304	C₄²	—	38	1	no	—
305	C₄²	—	38	1	no	—
306	C₄²	—	38	1	no	—
307	C₄²	—	76	2	no	—
308	C₄²	—	76	2	no	—
309	C₄²	#64541	1	1	yes	characteristic
310	C₄²	D₄×D₁₉	1	1	yes	characteristic
311	C₄²	#64543	1	1	yes	characteristic
312	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	C₂³	—	38	2	no	—
314	C₂³	—	38	2	no	—
315	C₂³	—	38	2	no	—
316	C₂³	—	76	2	no	—
317	C₂³	—	76	2	no	—
318	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
319	Q₈	—	2	2	no	—
320	Q₈	—	2	2	no	—
321	Q₈	—	4	1	no	—
322	Q₈	—	4	1	no	—
323	D₄	—	76	1	no	—
324	D₄	—	76	1	no	—
325	D₄	—	76	1	no	—
326	D₄	—	76	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	38	2	no	—
335	C₂×C₄	—	38	2	no	—
336	C₂×C₄	—	38	2	no	—
337	C₂×C₄	—	76	1	no	—
338	C₂×C₄	—	76	1	no	—
339	C₂×C₄	—	76	1	no	—
340	C₂×C₄	—	76	1	no	—
341	C₂×C₄	—	76	4	no	—
342	C₂×C₄	—	76	2	no	—
343	C₂×C₄	—	152	2	no	—
344	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	#10597329	1	1	yes	characteristic
346	C₂×C₄	#10597330	1	1	yes	characteristic
347	C₂×C₄	C₂×#64515	1	1	yes	characteristic
348	C₂×C₄	#10597347	1	1	yes	characteristic
349	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
350	C₂×C₄	#10597353	1	1	yes	characteristic
351	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
352	C₂×C₄	#10597383	1	1	yes	characteristic
353	C₂×C₄	#10597384	1	1	yes	characteristic
354	C₈	—	4	2	no	—
355	C₈	—	8	1	no	—
356	C₈	—	76	2	no	—
357	C₈	—	152	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	76	4	no	—
361	C₂²	—	76	2	no	—
362	C₂²	—	76	2	no	—
363	C₂²	—	76	2	no	—
364	C₂²	—	152	2	no	—
365	C₂²	#11926420	1	1	yes	characteristic
366	C₂²	#11926506	1	1	yes	characteristic
367	C₂²	#11926509	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	8	1	no	—
373	C₄	—	76	2	no	—
374	C₄	—	76	2	no	—
375	C₄	—	76	2	no	—
376	C₄	#11926612	1	1	yes	characteristic
377	C₄	#11926615	1	1	yes	characteristic
378	C₄	#11926619	1	1	yes	characteristic
379	C₄	#11926620	1	1	yes	characteristic
380	C₄	#11926720	1	2	yes	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	152	2	no	—
384	C₂	#14563929	1	1	yes	characteristic
385	C₂	#14564015	1	1	yes	characteristic
386	C₂	#14564020	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1479	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1479	D₁₉
hypocenter	C₁₉	#8961
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1479

Complements

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

N	H ≅ G/N	type
3. #14562030	C₂	semidirect
5. #14561467	C₂	semidirect
6. #14561467	C₂	semidirect
7. C₁₉×#1479	C₂	semidirect
74. C₂×Q₈×C₁₉	M₁₆	semidirect
115. C₄×Dic₁₉	M₁₆	semidirect
168. #1479	D₁₉	semidirect
261. C₁₉	#8961	semidirect
268. C₂×Q₈	#64515	semidirect

Maximal subgroups

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

subgroup	index
#14572675	2
C₄×#10597393	2
#14562030	2
#14561955	2
#14561467	2
C₁₉×#1479	2
#8961	19