Subgroups — #18075665

Order 4864.

394 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14562063	C₂	1	2	yes	maximal
4	#14561530	C₂	1	2	yes	maximal
5	C₁₉×#1848	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₃₈	—	2	1	no	—
8	C₈×Dic₃₈	—	2	1	no	—
9	C₈×Dic₃₈	C₄	1	2	yes	—
10	C₈×Dic₃₈	C₄	1	2	yes	—
11	#11926597	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×C₈×Dic₁₉	—	2	1	no	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926274	—	2	4	no	—
18	C₂×C₁₉×#108	—	2	1	no	—
19	C₂×C₁₉×#108	—	2	1	no	—
20	C₁₉×#423	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×Dic₃₈	Q₈	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
28	C₂×Dic₁₉⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₁₉	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
34	C₄×Dic₃₈	D₄	1	2	yes	—
35	C₁₉×#108	—	4	2	no	—
36	C₁₉×#108	—	4	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	Dic₁₉⋊C₈	—	2	2	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	C₈×Dic₁₉	—	2	2	no	—
47	C₈×Dic₁₉	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
51	C₄×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	2	1	no	—
56	C₂²×Dic₁₉	—	2	1	no	—
57	C₂×Dic₃₈	—	2	1	no	—
58	C₂×Dic₃₈	—	2	4	no	—
59	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
60	M₁₆×C₁₉	—	4	2	no	—
61	M₁₆×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	2	1	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
70	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
71	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄⋊Dic₁₉	—	2	1	no	—
76	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
77	Dic₁₉⋊C₄	—	2	2	no	—
78	Dic₁₉⋊C₄	—	2	2	no	—
79	C₄×Dic₁₉	—	2	2	no	—
80	C₄×Dic₁₉	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	#8659	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
99	C₂×Dic₁₉	—	2	4	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	—	2	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	Dic₃₈	—	2	4	no	—
104	Dic₃₈	—	2	2	no	—
105	Dic₃₈	#108	1	4	yes	complemented
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	8	2	no	—
109	C₈×C₁₉	#103	1	2	yes	—
110	C₈×C₁₉	#103	1	2	yes	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₁₉⋊C₈	—	8	2	no	—
113	C₂×C₈×Q₈	—	19	1	no	—
114	#1848	D₁₉	1	1	yes	characteristic
115	#1564	—	19	1	no	—
116	#1487	—	19	2	no	—
117	#1301	—	19	2	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	#380	1	1	yes	characteristic
121	C₂²×C₁₉	#475	1	1	yes	characteristic
122	C₂²×C₁₉	#477	1	1	yes	characteristic
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
127	C₄×C₁₉	#417	1	1	yes	characteristic
128	C₄×C₁₉	C₂×#108	1	2	yes	—
129	C₄×C₁₉	#460	1	1	yes	characteristic
130	C₄×C₁₉	#462	1	1	yes	characteristic
131	Dic₁₉	—	2	4	no	—
132	Dic₁₉	—	4	2	no	—
133	C₂×C₄×Q₈	—	19	1	no	—
134	C₈×Q₈	—	19	2	no	—
135	C₈×Q₈	—	19	2	no	—
136	C₈×Q₈	—	38	1	no	—
137	C₈×Q₈	—	38	1	no	—
138	#431	—	19	2	no	—
139	C₂×#108	—	2	1	no	—
140	C₂×#108	—	2	1	no	—
141	#423	C₂×D₁₉	1	2	yes	—
142	C₂×C₄⋊C₈	—	19	1	no	—
143	C₂×C₄⋊C₈	—	38	1	no	—
144	C₂×C₄×C₈	—	38	1	no	—
145	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
146	#335	—	38	1	no	—
147	#334	—	38	1	no	—
148	Q₈⋊C₈	—	38	4	no	—
149	C₂×C₁₉	—	2	1	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	#1803	1	1	yes	characteristic
152	C₂×C₁₉	#1810	1	1	yes	characteristic
153	C₂×C₁₉	#1814	1	1	yes	characteristic
154	C₂²×Q₈	—	19	1	no	—
155	C₂×M₁₆	—	2	2	no	—
156	C₂²×C₈	—	38	1	no	—
157	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
158	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
159	C₄×Q₈	—	19	2	no	—
160	C₄×Q₈	—	19	2	no	—
161	C₄×Q₈	—	38	1	no	—
162	C₄×Q₈	—	38	1	no	—
163	C₂×C₄⋊C₄	—	19	1	no	—
164	C₂×C₄⋊C₄	—	38	1	no	—
165	C₂×C₄²	—	38	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	#108	—	4	2	no	—
168	#108	—	4	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	19	2	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	—	38	2	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₂²⋊C₈	—	38	2	no	—
177	C₄×C₈	—	38	2	no	—
178	C₄×C₈	—	38	2	no	—
179	C₄×C₈	—	38	2	no	—
180	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
181	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
182	C₄×C₈	D₇₆	1	1	yes	characteristic
183	C₄×C₈	D₇₆	1	1	yes	characteristic
184	C₁₉	#8659	1	1	yes	characteristic, complemented, Sylow
185	C₂×Q₈	—	19	2	no	—
186	C₂×Q₈	—	38	4	no	—
187	C₂×Q₈	—	38	1	no	—
188	C₂²×C₄	—	38	1	no	—
189	C₂²×C₄	—	38	1	no	—
190	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
191	C₂²×C₄	#64545	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	4	2	no	—
198	C₂×C₈	—	38	2	no	—
199	C₂×C₈	—	76	1	no	—
200	C₂×C₈	—	76	1	no	—
201	C₂×C₈	—	76	2	no	—
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
204	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₈	#64526	1	2	yes	—
207	C₂×C₈	#64528	1	2	yes	—
208	C₄⋊C₄	—	19	2	no	—
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	38	2	no	—
211	C₄⋊C₄	—	38	1	no	—
212	C₄²	—	38	2	no	—
213	C₄²	—	38	2	no	—
214	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
215	C₄²	C₂×D₇₆	1	1	yes	characteristic
216	C₄²	D₄×D₁₉	1	1	yes	characteristic
217	C₄²	#64543	1	1	yes	characteristic
218	C₂³	#10597392	1	1	yes	characteristic
219	Q₈	—	19	4	no	—
220	Q₈	—	38	4	no	—
221	Q₈	—	38	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	38	4	no	—
225	C₂×C₄	—	38	2	no	—
226	C₂×C₄	—	38	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
229	C₂×C₄	#10597338	1	1	yes	characteristic
230	C₂×C₄	#10597341	1	1	yes	characteristic
231	C₂×C₄	#10597343	1	1	yes	characteristic
232	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
233	C₂×C₄	#10597378	1	1	yes	characteristic
234	C₂×C₄	C₂×#64526	1	1	yes	characteristic
235	C₂×C₄	#10597384	1	1	yes	characteristic
236	C₂×C₄	#10597388	1	1	yes	characteristic
237	C₂×C₄	C₂×#64528	1	1	yes	characteristic
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	8	2	no	—
241	C₈	—	76	2	no	—
242	C₈	—	152	2	no	—
243	C₈	#10597267	1	2	yes	—
244	C₈	#10597267	1	2	yes	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	#11926401	1	1	yes	characteristic
248	C₂²	#11926826	1	1	yes	characteristic
249	C₂²	#11926836	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	38	4	no	—
254	C₄	—	76	2	no	—
255	C₄	C₂×#10597267	1	1	yes	characteristic
256	C₄	#11926543	1	1	yes	characteristic
257	C₄	#108×D₁₉	1	2	yes	—
258	C₄	#11926741	1	1	yes	characteristic
259	C₄	#11926751	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	#14563637	1	1	yes	characteristic
263	C₂	#14563670	1	1	yes	characteristic
264	C₂	#14563690	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1848	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1848	D₁₉
hypocenter	C₁₉	#8659
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

Complements

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

N	H ≅ G/N	type
105. Dic₃₈	#108	semidirect
184. C₁₉	#8659	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₃₈	2
#14562383	2
#14562063	2
#14561530	2
C₁₉×#1848	2
#8659	19