Subgroups — #18075653

Order 4864.

494 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563763	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563635	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561519	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597289	—	2	2	no	—
8	#11926414	C₂²	1	2	yes	—
9	#11926307	—	2	1	no	—
10	#11926307	—	2	1	no	—
11	#11926306	—	2	2	no	—
12	#11926295	—	2	2	no	—
13	C₂²×M₁₆×C₁₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#436	—	2	2	no	—
16	C₁₉×#436	C₄	1	4	yes	complemented
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	4	no	—
23	C₂×M₁₆×C₁₉	—	4	4	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×D₄×C₁₉	—	2	1	no	—
28	C₄×D₄×C₁₉	—	2	1	no	—
29	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₄×D₄×C₁₉	Q₈	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
40	C₁₉×C₂²⋊C₈	—	2	4	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₉	D₄	1	2	yes	—
43	#10597289	—	4	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂⁴×C₁₉	—	2	1	no	—
47	C₂×D₄×C₁₉	—	2	1	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×Dic₁₉	—	4	2	no	—
60	M₁₆×C₁₉	—	4	8	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
69	C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄⋊Dic₁₉	—	8	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#8656	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	2	no	—
85	C₂³×C₁₉	—	4	2	no	—
86	C₂³×C₁₉	—	4	1	no	—
87	C₂³×C₁₉	—	4	1	no	—
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	#121	1	1	yes	characteristic
90	D₄×C₁₉	—	2	4	no	—
91	D₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	4	no	—
98	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#135	1	2	yes	—
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
106	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₉	#137	1	2	yes	—
108	C₂×Dic₁₉	—	8	2	no	—
109	C₂×Dic₁₉	—	8	2	no	—
110	C₂×Dic₁₉	—	8	2	no	—
111	C₈×C₁₉	—	2	2	no	—
112	C₈×C₁₉	—	2	2	no	—
113	C₈×C₁₉	—	4	2	no	—
114	C₁₉⋊C₈	—	8	2	no	—
115	C₂×#436	D₁₉	1	1	yes	characteristic
116	#1834	—	19	1	no	—
117	#1802	—	19	2	no	—
118	C₂×#334	—	19	1	no	—
119	#1296	—	19	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	2	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	#380	1	1	yes	characteristic
126	C₂²×C₁₉	#463	1	2	yes	—
127	C₂²×C₁₉	#469	1	1	yes	characteristic
128	C₂²×C₁₉	#470	1	1	yes	characteristic
129	C₂²×C₁₉	#471	1	2	yes	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	#416	1	1	yes	characteristic
134	C₄×C₁₉	#418	1	1	yes	characteristic
135	C₄×C₁₉	#428	1	2	yes	—
136	C₄×C₁₉	#468	1	2	yes	—
137	C₄×C₁₉	#478	1	2	yes	—
138	Dic₁₉	—	16	2	no	—
139	C₂²×M₁₆	—	2	1	no	—
140	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
141	#436	—	2	2	no	—
142	#436	Dic₁₉	1	4	yes	complemented
143	C₂×C₄⋊C₈	—	19	2	no	—
144	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
145	C₂×#102	—	38	2	no	—
146	C₂×C₂²⋊C₈	—	2	1	no	—
147	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
148	#384	—	19	2	no	—
149	#340	—	38	1	no	—
150	#340	—	38	1	no	—
151	#340	—	38	2	no	—
152	#334	—	38	2	no	—
153	C₂×C₁₉	—	8	2	no	—
154	C₂×C₁₉	#1701	1	2	yes	—
155	C₂×C₁₉	#1703	1	2	yes	—
156	C₂×C₁₉	#1804	1	1	yes	characteristic
157	C₂×C₁₉	#1809	1	1	yes	characteristic
158	C₂×C₁₉	#1815	1	1	yes	characteristic
159	C₂²×D₄	D₇₆	1	1	yes	characteristic
160	C₂³×C₄	—	2	1	no	—
161	C₂×M₁₆	—	2	4	no	—
162	C₂×M₁₆	—	4	4	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	38	2	no	—
165	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
166	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₄×D₄	—	2	1	no	—
168	C₄×D₄	—	2	1	no	—
169	C₄×D₄	Dic₃₈	1	2	yes	—
170	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
171	C₂×C₄⋊C₄	—	38	2	no	—
172	C₂×C₄⋊C₄	—	38	2	no	—
173	C₂×C₄⋊C₄	—	38	2	no	—
174	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
175	C₂×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	38	2	no	—
179	C₄⋊C₈	—	38	2	no	—
180	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
181	#102	—	76	4	no	—
182	C₂²⋊C₈	—	2	4	no	—
183	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
184	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
185	C₁₉	#8656	1	1	yes	characteristic, complemented, Sylow
186	C₂⁴	—	2	1	no	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	2	no	—
195	C₂²×C₄	—	4	2	no	—
196	C₂²×C₄	—	76	2	no	—
197	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
198	C₂²×C₄	#64541	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	M₁₆	—	4	8	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	2	no	—
205	C₂×C₈	—	76	2	no	—
206	C₂×C₈	—	76	2	no	—
207	C₂×C₈	—	76	2	no	—
208	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
209	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₄⋊C₄	—	76	2	no	—
213	C₄⋊C₄	—	76	2	no	—
214	C₄⋊C₄	—	76	2	no	—
215	C₄⋊C₄	—	152	2	no	—
216	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
217	C₂²⋊C₄	—	2	2	no	—
218	C₂²⋊C₄	—	2	2	no	—
219	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
220	C₄²	#64541	1	1	yes	characteristic
221	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
222	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂³	—	2	2	no	—
224	C₂³	—	4	1	no	—
225	C₂³	—	4	1	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	2	no	—
228	C₂³	#10597376	1	1	yes	characteristic
229	D₄	—	2	4	no	—
230	D₄	—	4	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	152	2	no	—
238	C₂×C₄	—	152	2	no	—
239	C₂×C₄	—	152	2	no	—
240	C₂×C₄	#10597354	1	2	yes	—
241	C₂×C₄	#10597355	1	2	yes	—
242	C₂×C₄	#10597370	1	1	yes	characteristic
243	C₂×C₄	#10597370	1	1	yes	characteristic
244	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
245	C₂×C₄	#10597372	1	1	yes	characteristic
246	C₂×C₄	#10597376	1	1	yes	characteristic
247	C₂×C₄	#10597378	1	2	yes	—
248	C₂×C₄	#10597396	1	2	yes	—
249	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
250	C₈	—	2	2	no	—
251	C₈	—	2	2	no	—
252	C₈	—	4	2	no	—
253	C₈	—	152	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	—	4	2	no	—
256	C₂²	—	4	2	no	—
257	C₂²	—	8	2	no	—
258	C₂²	—	8	2	no	—
259	C₂²	#11926404	1	1	yes	characteristic
260	C₂²	#11926759	1	2	yes	—
261	C₂²	#11926797	1	1	yes	characteristic
262	C₂²	#11926802	1	1	yes	characteristic
263	C₂²	#11926807	1	2	yes	—
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	4	2	no	—
267	C₄	—	304	2	no	—
268	C₄	#11926540	1	1	yes	characteristic
269	C₄	#11926549	1	1	yes	characteristic
270	C₄	#11926586	1	2	yes	—
271	C₄	#11926790	1	2	yes	—
272	C₄	#11926844	1	2	yes	—
273	C₂	—	8	2	no	—
274	C₂	#14563196	1	2	yes	—
275	C₂	#14563210	1	2	yes	—
276	C₂	#14563645	1	1	yes	characteristic
277	C₂	#14563668	1	1	yes	characteristic
278	C₂	#14563694	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#436	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#436	D₁₉
hypocenter	C₁₉	#8656
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. #14563763	C₂	semidirect
3. C₂×#11926295	C₂	semidirect
4. #14561519	C₂	semidirect
16. C₁₉×#436	C₄	semidirect
142. #436	Dic₁₉	semidirect
185. C₁₉	#8656	semidirect

Maximal subgroups

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

subgroup	index
#14563763	2
#14563635	2
C₂×#11926295	2
#14561519	2
C₂×C₁₉×#436	2
#8656	19