Subgroups — #18075468

Order 4864.

398 conjugacy classes of subgroups.

The subgroup lattice has 278 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	#14563628	C₂	1	2	yes	maximal
3	#14562394	C₂	1	1	yes	maximal, characteristic
4	#14561509	C₂	1	2	yes	maximal
5	C₁₉×#1567	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	—	2	1	no	—
10	C₈×Dic₃₈	—	2	1	no	—
11	#11926568	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
14	C₂×#10597281	—	2	2	no	—
15	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
16	#11926312	—	2	2	no	—
17	#11926297	—	2	1	no	—
18	#11926297	—	2	1	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#335	—	2	1	no	—
22	C₁₉×#335	—	2	1	no	—
23	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
29	C₂×Dic₁₉⋊C₄	Q₈	1	2	yes	—
30	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
31	C₂×#64520	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₄×Dic₃₈	—	2	1	no	—
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	#10597281	—	4	4	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	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
56	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
57	C₂×Dic₃₈	—	2	1	no	—
58	C₂×Dic₃₈	—	2	1	no	—
59	C₂×Dic₃₈	—	2	1	no	—
60	C₂×Dic₃₈	—	2	1	no	—
61	C₂×Dic₃₈	D₈	1	2	yes	—
62	C₂×Dic₃₈	Q₁₆	1	2	yes	—
63	M₁₆×C₁₉	—	4	2	no	—
64	M₁₆×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×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	C₄²×C₁₉	#41	1	1	yes	characteristic
76	C₄⋊Dic₁₉	—	2	1	no	—
77	C₄⋊Dic₁₉	—	2	1	no	—
78	Dic₁₉⋊C₄	—	2	2	no	—
79	Dic₁₉⋊C₄	—	2	2	no	—
80	C₄×Dic₁₉	—	2	2	no	—
81	C₄×Dic₁₉	—	2	2	no	—
82	#64520	—	4	2	no	—
83	#64520	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	#8617	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
102	C₂×Dic₁₉	—	2	2	no	—
103	C₂×Dic₁₉	—	2	2	no	—
104	C₂×Dic₁₉	—	2	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	#107	1	4	yes	—
107	Dic₃₈	—	2	2	no	—
108	Dic₃₈	—	2	2	no	—
109	Dic₃₈	—	2	2	no	—
110	Dic₃₈	—	2	2	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	1	no	—
113	C₈×C₁₉	—	2	1	no	—
114	C₈×C₁₉	—	8	2	no	—
115	C₈×C₁₉	#101	1	2	yes	complemented
116	C₁₉⋊C₈	—	4	2	no	—
117	C₁₉⋊C₈	—	8	2	no	—
118	C₂×C₈×Q₈	—	19	1	no	—
119	#1801	—	19	2	no	—
120	#1567	—	19	1	no	—
121	#1567	D₁₉	1	1	yes	characteristic
122	#1292	—	19	2	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	#380	1	1	yes	characteristic
126	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
127	C₂²×C₁₉	#427	1	1	yes	characteristic
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
132	C₄×C₁₉	#413	1	1	yes	characteristic
133	C₄×C₁₉	#466	1	1	yes	characteristic
134	C₄×C₁₉	#466	1	1	yes	characteristic
135	C₄×C₁₉	#467	1	1	yes	characteristic
136	C₄×C₁₉	#467	1	1	yes	characteristic
137	Dic₁₉	—	2	4	no	—
138	Dic₁₉	—	4	2	no	—
139	C₂×C₄×Q₈	—	19	1	no	—
140	C₈×Q₈	—	38	1	no	—
141	C₈×Q₈	—	38	1	no	—
142	C₈×Q₈	—	38	1	no	—
143	C₈×Q₈	—	38	1	no	—
144	#423	—	19	2	no	—
145	#423	C₂×D₁₉	1	2	yes	—
146	C₂×C₄⋊C₈	—	19	2	no	—
147	C₂×C₄⋊C₈	—	19	1	no	—
148	C₂×#101	—	38	2	no	—
149	C₂×C₄×C₈	—	19	2	no	—
150	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
151	#343	—	38	2	no	—
152	#335	—	2	1	no	—
153	#335	—	2	1	no	—
154	#335	—	38	1	no	—
155	#335	—	38	1	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	#1801	1	1	yes	characteristic
159	C₂×C₁₉	#1808	1	1	yes	characteristic
160	C₂×C₁₉	#1813	1	1	yes	characteristic
161	C₂²×Q₈	—	19	1	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	38	2	no	—
164	C₂²×C₈	—	19	2	no	—
165	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
166	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
167	C₄×Q₈	—	38	1	no	—
168	C₄×Q₈	—	38	1	no	—
169	C₄×Q₈	—	38	1	no	—
170	C₄×Q₈	—	38	1	no	—
171	C₂×C₄⋊C₄	—	19	1	no	—
172	C₂×C₄⋊C₄	—	19	2	no	—
173	C₂×C₄²	—	19	2	no	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	38	2	no	—
178	C₄⋊C₈	—	38	2	no	—
179	C₄⋊C₈	—	38	1	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₄⋊C₈	—	38	2	no	—
182	C₄⋊C₈	—	38	1	no	—
183	#101	—	76	4	no	—
184	C₄×C₈	—	38	2	no	—
185	C₄×C₈	—	38	2	no	—
186	C₄×C₈	D₇₆	1	1	yes	characteristic
187	C₄×C₈	D₇₆	1	1	yes	characteristic
188	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
190	C₁₉	#8617	1	1	yes	characteristic, complemented, Sylow
191	C₂×Q₈	—	19	2	no	—
192	C₂×Q₈	—	19	2	no	—
193	C₂×Q₈	—	38	1	no	—
194	C₂×Q₈	—	38	1	no	—
195	C₂×Q₈	—	38	1	no	—
196	C₂×Q₈	—	38	1	no	—
197	C₂²×C₄	—	19	2	no	—
198	C₂²×C₄	—	19	2	no	—
199	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
200	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
201	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
202	M₁₆	—	4	2	no	—
203	M₁₆	—	4	2	no	—
204	M₁₆	—	76	2	no	—
205	M₁₆	—	76	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	4	1	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	38	2	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	2	no	—
212	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
214	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
215	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	C₄⋊C₄	—	38	1	no	—
217	C₄⋊C₄	—	38	2	no	—
218	C₄⋊C₄	—	38	1	no	—
219	C₄⋊C₄	—	38	2	no	—
220	C₄²	—	38	2	no	—
221	C₄²	—	38	2	no	—
222	C₄²	C₂×D₇₆	1	1	yes	characteristic
223	C₄²	#64543	1	1	yes	characteristic
224	C₄²	#64545	1	1	yes	characteristic
225	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
226	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
227	Q₈	—	38	2	no	—
228	Q₈	—	38	2	no	—
229	Q₈	—	38	2	no	—
230	Q₈	—	38	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	19	4	no	—
235	C₂×C₄	—	38	2	no	—
236	C₂×C₄	—	38	2	no	—
237	C₂×C₄	—	38	2	no	—
238	C₂×C₄	—	76	2	no	—
239	C₂×C₄	#10597338	1	1	yes	characteristic
240	C₂×C₄	#10597341	1	1	yes	characteristic
241	C₂×C₄	#10597343	1	1	yes	characteristic
242	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
243	C₂×C₄	#10597358	1	1	yes	characteristic
244	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
245	C₂×C₄	#10597365	1	1	yes	characteristic
246	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#10597384	1	1	yes	characteristic
248	C₂×C₄	#10597392	1	1	yes	characteristic
249	C₈	—	2	1	no	—
250	C₈	—	2	1	no	—
251	C₈	—	2	1	no	—
252	C₈	—	8	2	no	—
253	C₈	—	76	2	no	—
254	C₈	—	152	2	no	—
255	C₈	#10597281	1	2	yes	complemented
256	C₂²	—	2	1	no	—
257	C₂²	—	2	1	no	—
258	C₂²	#11926401	1	1	yes	characteristic
259	C₂²	#107×D₁₉	1	1	yes	characteristic
260	C₂²	#11926581	1	1	yes	characteristic
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	38	4	no	—
265	C₄	—	76	2	no	—
266	C₄	C₂×#10597281	1	1	yes	characteristic
267	C₄	#11926526	1	1	yes	characteristic
268	C₄	#11926777	1	1	yes	characteristic
269	C₄	#11926781	1	1	yes	characteristic
270	C₄	#11926782	1	1	yes	characteristic
271	C₄	#11926786	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	2	1	no	—
274	C₂	#14563628	1	1	yes	characteristic
275	C₂	#14563661	1	1	yes	characteristic
276	C₂	#14563682	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#8617
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
115. C₈×C₁₉	#101	semidirect
190. C₁₉	#8617	semidirect
255. C₈	#10597281	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
#14563628	2
#14562394	2
#14561509	2
C₁₉×#1567	2
#8617	19