Subgroups — #18073200

Order 4864.

498 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566109	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14563380	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926276	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926274	C₂	1	1	yes	maximal, characteristic
6	#14561476	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₉	—	2	1	no	—
12	#11926449	C₄	1	2	yes	—
13	#11926440	C₄	1	2	yes	—
14	#11926426	—	2	2	no	—
15	C₄×Dic₁₉⋊C₄	—	2	1	no	—
16	#11926390	—	2	1	no	—
17	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
18	#11926298	—	2	2	no	—
19	#11926298	—	2	1	no	—
20	#11926276	C₄	1	4	yes	complemented
21	#11926274	C₄	1	4	yes	complemented
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×Dic₁₉⋊C₄	—	2	1	no	—
33	C₂×Dic₁₉⋊C₄	—	2	2	no	—
34	C₂×C₄×Dic₁₉	—	2	1	no	—
35	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
38	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
39	C₂²×C₁₉⋊C₈	—	2	1	no	—
40	C₂²×C₁₉⋊C₈	—	2	1	no	—
41	C₄×Dic₃₈	—	2	1	no	—
42	C₄×Dic₃₈	—	2	1	no	—
43	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
44	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
47	C₄×C₈×C₁₉	—	2	1	no	—
48	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉⋊#95	—	2	2	no	—
51	C₁₉⋊#95	—	2	2	no	—
52	C₁₉⋊#95	—	2	2	no	—
53	C₈×Dic₁₉	—	4	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄×C₁₉⋊C₈	—	2	1	no	—
57	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×Dic₁₉	—	2	1	no	—
63	C₂²×Dic₁₉	—	2	1	no	—
64	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂×Dic₃₈	—	2	2	no	—
67	C₂×Dic₃₈	—	2	2	no	—
68	C₂×Dic₃₈	—	2	1	no	—
69	C₂×Dic₃₈	C₄²	1	2	yes	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	4	2	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄²×C₁₉	—	4	1	no	—
78	C₄²×C₁₉	—	4	1	no	—
79	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₁₉	#41	1	1	yes	characteristic
82	C₄²×C₁₉	#41	1	1	yes	characteristic
83	C₄⋊Dic₁₉	—	2	1	no	—
84	C₄⋊Dic₁₉	C₄²	1	2	yes	—
85	Dic₁₉⋊C₄	—	2	2	no	—
86	Dic₁₉⋊C₄	—	2	2	no	—
87	Dic₁₉⋊C₄	—	4	4	no	—
88	C₄×Dic₁₉	—	2	2	no	—
89	C₄×Dic₁₉	—	2	2	no	—
90	C₄×Dic₁₉	—	2	2	no	—
91	C₄×Dic₁₉	—	2	2	no	—
92	C₄×Dic₁₉	—	2	1	no	—
93	C₄×Dic₁₉	—	2	1	no	—
94	C₄×Dic₁₉	—	4	2	no	—
95	C₄×Dic₁₉	SD₁₆	1	2	yes	—
96	C₄×Dic₁₉	Q₁₆	1	2	yes	—
97	C₂×C₁₉⋊C₈	—	2	2	no	—
98	C₂×C₁₉⋊C₈	—	2	2	no	—
99	C₂×C₁₉⋊C₈	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	4	1	no	—
101	C₂×C₁₉⋊C₈	—	4	1	no	—
102	#8182	—	19	1	no	maximal, Sylow
103	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#131	1	2	yes	—
115	C₂×C₄×C₁₉	#131	1	2	yes	—
116	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
120	C₂×Dic₁₉	—	2	2	no	—
121	C₂×Dic₁₉	—	2	2	no	—
122	C₂×Dic₁₉	—	2	2	no	—
123	C₂×Dic₁₉	—	2	2	no	—
124	C₂×Dic₁₉	—	2	2	no	—
125	C₂×Dic₁₉	—	2	2	no	—
126	C₂×Dic₁₉	—	2	2	no	—
127	C₂×Dic₁₉	—	4	2	no	—
128	C₂×Dic₁₉	—	4	2	no	—
129	C₂×Dic₁₉	#103	1	4	yes	—
130	Dic₃₈	—	2	2	no	—
131	Dic₃₈	—	2	2	no	—
132	Dic₃₈	—	4	2	no	—
133	C₈×C₁₉	—	4	2	no	—
134	C₈×C₁₉	—	4	2	no	—
135	C₁₉⋊C₈	—	4	2	no	—
136	C₁₉⋊C₈	—	4	2	no	—
137	#2295	—	19	1	no	—
138	C₄×C₄⋊C₈	—	19	1	no	—
139	#1744	—	19	1	no	—
140	C₂×Q₈⋊C₈	—	19	1	no	—
141	C₂×Q₈⋊C₈	—	19	1	no	—
142	#1279	—	19	1	no	—
143	#1279	D₁₉	1	1	yes	characteristic
144	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₁₉	#408	1	2	yes	—
146	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
147	C₂²×C₁₉	#416	1	1	yes	characteristic
148	C₂²×C₁₉	#421	1	2	yes	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	8	2	no	—
152	C₄×C₁₉	#405	1	1	yes	characteristic
153	C₄×C₁₉	#405	1	1	yes	characteristic
154	C₄×C₁₉	#433	1	2	yes	—
155	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
156	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
157	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
158	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
159	Dic₁₉	—	2	4	no	—
160	Dic₁₉	—	4	2	no	—
161	Dic₁₉	—	4	2	no	—
162	Dic₁₉	—	4	2	no	—
163	C₂×C₄×Q₈	—	19	1	no	—
164	C₂×C₄⋊C₈	—	19	1	no	—
165	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
166	C₂×C₄×C₈	—	19	1	no	—
167	C₂×C₄×C₈	—	38	1	no	—
168	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
169	#391	—	19	2	no	—
170	#389	—	19	2	no	—
171	#387	—	38	2	no	—
172	C₄×C₄⋊C₄	—	38	1	no	—
173	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
174	#376	—	38	1	no	—
175	C₄³	—	19	1	no	—
176	#336	—	38	2	no	—
177	#336	—	38	1	no	—
178	Q₈⋊C₈	—	19	4	no	—
179	Q₈⋊C₈	—	19	4	no	—
180	C₂×C₁₉	#1481	1	2	yes	—
181	C₂×C₁₉	#1482	1	2	yes	—
182	C₂×C₁₉	#1750	1	1	yes	characteristic
183	C₂×C₁₉	#1759	1	1	yes	characteristic
184	C₂×C₁₉	C₄×#103	1	1	yes	characteristic
185	C₂²×Q₈	—	19	1	no	—
186	C₂²×C₈	—	2	1	no	—
187	C₂²×C₈	—	2	1	no	—
188	C₂²×C₈	—	38	1	no	—
189	C₂²×C₈	—	38	1	no	—
190	C₄×Q₈	—	19	2	no	—
191	C₄×Q₈	—	19	2	no	—
192	C₄×Q₈	—	38	1	no	—
193	C₄×Q₈	—	38	1	no	—
194	C₂×C₄⋊C₄	—	19	1	no	—
195	C₂×C₄⋊C₄	—	38	1	no	—
196	C₂×C₄⋊C₄	—	38	2	no	—
197	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
198	C₂×C₄²	—	2	1	no	—
199	C₂×C₄²	—	19	1	no	—
200	C₂×C₄²	—	19	2	no	—
201	C₂×C₄²	—	19	1	no	—
202	C₂×C₄²	—	19	2	no	—
203	C₂×C₄²	—	38	1	no	—
204	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
205	C₄⋊C₈	—	2	1	no	—
206	C₄⋊C₈	—	19	2	no	—
207	C₄⋊C₈	—	38	1	no	—
208	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	19	2	no	—
211	C₄×C₈	—	38	1	no	—
212	C₄×C₈	—	76	2	no	—
213	C₄×C₈	C₄×D₁₉	1	2	yes	—
214	#95	—	2	1	no	—
215	#95	—	38	2	no	—
216	#95	—	38	2	no	—
217	#95	—	38	2	no	—
218	C₁₉	#8182	1	1	yes	characteristic, complemented, Sylow
219	C₂×Q₈	—	19	2	no	—
220	C₂×Q₈	—	38	1	no	—
221	C₂×Q₈	—	38	2	no	—
222	C₂×Q₈	—	38	2	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	19	2	no	—
225	C₂²×C₄	—	19	2	no	—
226	C₂²×C₄	—	38	1	no	—
227	C₂²×C₄	—	38	1	no	—
228	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
229	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
230	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	4	2	no	—
234	C₂×C₈	—	4	1	no	—
235	C₂×C₈	—	4	1	no	—
236	C₂×C₈	—	38	2	no	—
237	C₂×C₈	—	38	2	no	—
238	C₂×C₈	—	76	2	no	—
239	C₂×C₈	—	76	1	no	—
240	C₂×C₈	—	76	1	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	2	2	no	—
243	C₄⋊C₄	—	19	2	no	—
244	C₄⋊C₄	—	38	2	no	—
245	C₄⋊C₄	—	38	1	no	—
246	C₄⋊C₄	—	38	2	no	—
247	C₄⋊C₄	—	76	4	no	—
248	C₄²	—	4	1	no	—
249	C₄²	—	4	1	no	—
250	C₄²	—	19	2	no	—
251	C₄²	—	19	2	no	—
252	C₄²	—	38	2	no	—
253	C₄²	—	38	2	no	—
254	C₄²	—	38	2	no	—
255	C₄²	—	38	2	no	—
256	C₄²	—	38	1	no	—
257	C₄²	—	38	1	no	—
258	C₄²	—	76	2	no	—
259	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
260	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
261	C₄²	#64543	1	1	yes	characteristic
262	C₄²	#64545	1	1	yes	characteristic
263	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
264	Q₈	—	38	2	no	—
265	Q₈	—	38	2	no	—
266	Q₈	—	76	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	19	4	no	—
272	C₂×C₄	—	38	2	no	—
273	C₂×C₄	—	38	2	no	—
274	C₂×C₄	—	38	2	no	—
275	C₂×C₄	—	38	2	no	—
276	C₂×C₄	—	38	2	no	—
277	C₂×C₄	—	38	2	no	—
278	C₂×C₄	—	38	2	no	—
279	C₂×C₄	—	76	2	no	—
280	C₂×C₄	—	76	2	no	—
281	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
282	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
283	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
284	C₂×C₄	#10597338	1	1	yes	characteristic
285	C₂×C₄	#10597339	1	1	yes	characteristic
286	C₂×C₄	#10597339	1	1	yes	characteristic
287	C₂×C₄	#10597347	1	2	yes	—
288	C₂×C₄	#10597353	1	2	yes	—
289	C₂×C₄	#10597358	1	1	yes	characteristic
290	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
291	C₂×C₄	#10597362	1	1	yes	characteristic
292	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
293	C₈	—	4	2	no	—
294	C₈	—	4	2	no	—
295	C₈	—	76	2	no	—
296	C₈	—	76	2	no	—
297	C₂²	#11926391	1	1	yes	characteristic
298	C₂²	#11926509	1	2	yes	—
299	C₂²	#103×D₁₉	1	1	yes	characteristic
300	C₂²	#11926537	1	1	yes	characteristic
301	C₂²	#11926559	1	2	yes	—
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	8	2	no	—
305	C₄	—	38	4	no	—
306	C₄	—	76	2	no	—
307	C₄	—	76	2	no	—
308	C₄	—	76	2	no	—
309	C₄	#11926498	1	1	yes	characteristic
310	C₄	#11926501	1	1	yes	characteristic
311	C₄	#11926604	1	2	yes	—
312	C₄	#11926631	1	1	yes	characteristic
313	C₄	#11926635	1	1	yes	characteristic
314	C₄	#11926636	1	1	yes	characteristic
315	C₄	#11926638	1	1	yes	characteristic
316	C₂	#14562036	1	2	yes	—
317	C₂	#14562040	1	2	yes	—
318	C₂	#14563400	1	1	yes	characteristic
319	C₂	#14563444	1	1	yes	characteristic
320	C₂	#14563454	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8182
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
20. #11926276	C₄	semidirect
21. #11926274	C₄	semidirect
218. C₁₉	#8182	semidirect

Maximal subgroups

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

subgroup	index
#14566109	2
C₄⋊C₈×Dic₁₉	2
#14563380	2
C₂×#11926276	2
C₂×#11926274	2
#14561476	2
C₁₉×#1279	2
#8182	19