Subgroups — #18087657

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564596	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	1	yes	maximal, characteristic
3	#14564436	C₂	1	1	yes	maximal, characteristic
4	#14563791	C₂	1	1	yes	maximal, characteristic
5	#14563791	C₂	1	1	yes	maximal, characteristic
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597265	—	2	2	no	—
10	C₂×#10597265	—	2	2	no	—
11	C₂×#10597267	—	2	2	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926414	C₂²	1	1	yes	characteristic
15	#11926307	—	2	2	no	—
16	#11926306	—	2	2	no	—
17	C₂×C₁₉×#106	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₁₉×#384	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
36	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
37	#10597315	—	2	1	no	—
38	#10597315	—	2	1	no	—
39	#10597315	—	2	1	no	—
40	#10597315	Q₈	1	2	yes	—
41	C₁₉×#106	—	4	4	no	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	#10597267	—	4	4	no	—
45	#10597265	—	4	4	no	—
46	#10597265	—	4	4	no	—
47	C₄×C₁₉⋊C₈	—	2	1	no	—
48	C₄×C₁₉⋊C₈	—	2	1	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	4	1	no	—
57	C₂²×Dic₁₉	—	4	1	no	—
58	C₂×Dic₃₈	—	2	2	no	—
59	C₂×Dic₃₈	—	4	2	no	—
60	C₂×Dic₃₈	—	4	2	no	—
61	C₂×Dic₃₈	—	4	1	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	4	1	no	—
78	C₄⋊Dic₁₉	—	4	1	no	—
79	C₄⋊Dic₁₉	—	4	2	no	—
80	C₄⋊Dic₁₉	—	4	2	no	—
81	C₄⋊Dic₁₉	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
87	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
88	#10685	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₉	—	8	1	no	—
91	C₂×C₄×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	—	8	1	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
103	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
106	C₂×C₄×C₁₉	#137	1	2	yes	—
107	C₂×C₄×C₁₉	#137	1	2	yes	—
108	C₂×Dic₁₉	—	4	2	no	—
109	C₂×Dic₁₉	—	8	1	no	—
110	C₂×Dic₁₉	—	8	1	no	—
111	C₂×Dic₁₉	—	8	1	no	—
112	C₂×Dic₁₉	—	8	1	no	—
113	C₂×Dic₁₉	—	8	1	no	—
114	Dic₃₈	—	4	4	no	—
115	Dic₃₈	—	8	2	no	—
116	C₈×C₁₉	—	2	4	no	—
117	C₁₉⋊C₈	—	2	4	no	—
118	C₁₉⋊C₈	—	2	4	no	—
119	#1990	—	19	1	no	—
120	#1990	—	19	1	no	—
121	#1956	—	19	1	no	—
122	#1844	—	19	1	no	—
123	#1844	—	19	1	no	—
124	#1844	D₁₉	1	1	yes	characteristic
125	#1273	—	19	1	no	—
126	C₂²×C₁₉	#399	1	1	yes	characteristic
127	C₂²×C₁₉	#492	1	1	yes	characteristic
128	C₂²×C₁₉	#492	1	1	yes	characteristic
129	C₂²×C₁₉	#492	1	1	yes	characteristic
130	C₂²×C₁₉	#496	1	1	yes	characteristic
131	C₂²×C₁₉	#497	1	1	yes	characteristic
132	C₂²×C₁₉	#497	1	1	yes	characteristic
133	C₄×C₁₉	—	16	1	no	—
134	C₄×C₁₉	—	16	1	no	—
135	C₄×C₁₉	#475	1	2	yes	—
136	C₄×C₁₉	#475	1	2	yes	—
137	C₄×C₁₉	#476	1	2	yes	—
138	C₄×C₁₉	#481	1	2	yes	—
139	C₄×C₁₉	#483	1	2	yes	—
140	C₄×C₁₉	#483	1	2	yes	—
141	Dic₁₉	—	8	2	no	—
142	Dic₁₉	—	16	1	no	—
143	C₂×C₄⋊Q₈	—	19	1	no	—
144	C₂×#106	—	2	2	no	—
145	C₂×#106	—	38	2	no	—
146	C₂×#106	—	38	2	no	—
147	C₂×#103	—	38	2	no	—
148	C₂×C₄×C₈	—	19	1	no	—
149	C₂×C₄×C₈	—	19	1	no	—
150	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
151	#384	—	19	1	no	—
152	#384	C₂×D₁₉	1	1	yes	characteristic
153	#384	C₂×D₁₉	1	1	yes	characteristic
154	#340	—	38	2	no	—
155	#340	—	38	2	no	—
156	C₂×C₁₉	#1705	1	1	yes	characteristic
157	C₂×C₁₉	#1714	1	1	yes	characteristic
158	C₂×C₁₉	#1714	1	1	yes	characteristic
159	C₂×C₁₉	#1716	1	1	yes	characteristic
160	C₂×C₁₉	#2094	1	1	yes	characteristic
161	C₂×C₁₉	#2096	1	1	yes	characteristic
162	C₂×C₁₉	#2096	1	1	yes	characteristic
163	C₂²×Q₈	—	38	1	no	—
164	C₂²×C₈	—	19	2	no	—
165	C₂²×C₈	—	19	2	no	—
166	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
167	C₄⋊Q₈	—	19	2	no	—
168	C₄⋊Q₈	—	38	1	no	—
169	C₄⋊Q₈	—	38	1	no	—
170	C₄⋊Q₈	—	38	1	no	—
171	C₂×C₄⋊C₄	—	2	1	no	—
172	C₂×C₄⋊C₄	—	2	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	—	38	1	no	—
179	C₂×C₄⋊C₄	—	38	1	no	—
180	C₂×C₄⋊C₄	—	38	1	no	—
181	C₂×C₄⋊C₄	—	38	1	no	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	#106	—	4	4	no	—
184	#106	—	76	4	no	—
185	#106	—	76	4	no	—
186	#103	—	76	4	no	—
187	C₄×C₈	—	2	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	38	1	no	—
190	C₄×C₈	—	38	1	no	—
191	C₄×C₈	—	38	1	no	—
192	C₄×C₈	—	38	1	no	—
193	C₁₉	#10685	1	1	yes	characteristic, complemented, Sylow
194	C₂×Q₈	—	38	2	no	—
195	C₂×Q₈	—	76	1	no	—
196	C₂×Q₈	—	76	2	no	—
197	C₂×Q₈	—	76	2	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	76	1	no	—
201	C₂²×C₄	—	76	1	no	—
202	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
203	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	19	4	no	—
208	C₂×C₈	—	19	4	no	—
209	C₂×C₈	—	38	2	no	—
210	C₂×C₈	—	38	2	no	—
211	C₂×C₈	—	38	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	#64526	1	4	yes	—
214	C₄⋊C₄	—	4	2	no	—
215	C₄⋊C₄	—	4	2	no	—
216	C₄⋊C₄	—	4	2	no	—
217	C₄⋊C₄	—	4	2	no	—
218	C₄⋊C₄	—	4	2	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₄⋊C₄	—	38	2	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	76	1	no	—
223	C₄⋊C₄	—	76	1	no	—
224	C₄⋊C₄	—	76	2	no	—
225	C₄⋊C₄	—	76	2	no	—
226	C₄⋊C₄	—	76	2	no	—
227	C₄²	#64541	1	1	yes	characteristic
228	C₄²	#64541	1	1	yes	characteristic
229	C₄²	Q₈×D₁₉	1	1	yes	characteristic
230	C₄²	#64545	1	1	yes	characteristic
231	C₂³	#10597386	1	1	yes	characteristic
232	Q₈	—	76	4	no	—
233	Q₈	—	152	2	no	—
234	C₂×C₄	—	8	1	no	—
235	C₂×C₄	—	8	1	no	—
236	C₂×C₄	—	8	1	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	76	2	no	—
241	C₂×C₄	—	152	1	no	—
242	C₂×C₄	—	152	1	no	—
243	C₂×C₄	—	152	1	no	—
244	C₂×C₄	—	152	1	no	—
245	C₂×C₄	—	152	1	no	—
246	C₂×C₄	#10597340	1	1	yes	characteristic
247	C₂×C₄	#10597340	1	1	yes	characteristic
248	C₂×C₄	#10597342	1	1	yes	characteristic
249	C₂×C₄	#10597342	1	1	yes	characteristic
250	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
251	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
252	C₂×C₄	#10597360	1	2	yes	—
253	C₂×C₄	#10597361	1	2	yes	—
254	C₂×C₄	#10597375	1	1	yes	characteristic
255	C₂×C₄	C₂×#64526	1	2	yes	—
256	C₂×C₄	#10597388	1	2	yes	—
257	C₂×C₄	#10597392	1	1	yes	characteristic
258	C₈	—	2	4	no	—
259	C₈	—	38	4	no	—
260	C₈	—	38	4	no	—
261	C₂²	#11926479	1	1	yes	characteristic
262	C₂²	#11926915	1	1	yes	characteristic
263	C₂²	#11926915	1	1	yes	characteristic
264	C₂²	#11926916	1	1	yes	characteristic
265	C₂²	#11926930	1	1	yes	characteristic
266	C₂²	#11926935	1	1	yes	characteristic
267	C₂²	#11926936	1	1	yes	characteristic
268	C₄	—	16	1	no	—
269	C₄	—	16	1	no	—
270	C₄	—	304	1	no	—
271	C₄	—	152	2	no	—
272	C₄	#11926826	1	2	yes	—
273	C₄	#11926828	1	2	yes	—
274	C₄	#11926833	1	2	yes	—
275	C₄	#11926864	1	2	yes	—
276	C₄	#11926874	1	2	yes	—
277	C₄	#11926876	1	2	yes	—
278	C₂	#14563221	1	1	yes	characteristic
279	C₂	#14563254	1	1	yes	characteristic
280	C₂	#14563260	1	1	yes	characteristic
281	C₂	#14563267	1	1	yes	characteristic
282	C₂	#14565165	1	1	yes	characteristic
283	C₂	#14565175	1	1	yes	characteristic
284	C₂	#14565179	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#10685
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
193. C₁₉	#10685	semidirect

Maximal subgroups

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

subgroup	index
#14564596	2
#14564595	2
#14564436	2
#14563791	2
C₁₉⋊#1273	2
C₁₉×#1844	2
#10685	19