Subgroups — #18075599

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 296 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	#14563795	C₂	1	1	yes	maximal, characteristic
3	#14563641	C₂	1	2	yes	maximal
4	#14561519	C₂	1	2	yes	maximal
5	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₃₈	—	2	2	no	—
8	C₈×Dic₃₈	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	1	no	—
10	C₂×#10597275	—	2	1	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	C₂×#10597273	—	2	2	no	—
14	C₂×C₈×Dic₁₉	—	2	1	no	—
15	#11926414	C₂²	1	2	yes	—
16	#11926307	—	2	2	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#335	—	2	2	no	—
20	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
29	C₂×Dic₁₉⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₁₉	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
35	C₄×Dic₃₈	Q₈	1	2	yes	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	#10597275	—	4	2	no	—
41	#10597275	—	4	2	no	—
42	#10597273	—	4	4	no	—
43	Dic₁₉⋊C₈	—	2	4	no	—
44	C₈×Dic₁₉	—	2	4	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	1	no	—
51	C₂²×Dic₁₉	—	2	1	no	—
52	C₂²×Dic₁₉	—	4	2	no	—
53	C₂×Dic₃₈	—	2	1	no	—
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	—	2	1	no	—
56	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
57	C₂×Dic₃₈	D₈	1	2	yes	—
58	C₂×Dic₃₈	Q₁₆	1	2	yes	—
59	C₂×C₈×C₁₉	—	2	1	no	—
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
67	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
68	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	8	2	no	—
78	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
79	Dic₁₉⋊C₄	—	2	2	no	—
80	Dic₁₉⋊C₄	—	2	2	no	—
81	C₄×Dic₁₉	—	2	2	no	—
82	C₄×Dic₁₉	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	#8645	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#117	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	C₂²⋊Q₈	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×Q₁₆	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×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
104	C₂×Dic₁₉	—	2	2	no	—
105	C₂×Dic₁₉	—	2	2	no	—
106	C₂×Dic₁₉	—	2	2	no	—
107	C₂×Dic₁₉	—	2	2	no	—
108	C₂×Dic₁₉	—	4	1	no	—
109	C₂×Dic₁₉	—	4	1	no	—
110	C₂×Dic₁₉	—	8	2	no	—
111	C₂×Dic₁₉	—	8	2	no	—
112	C₂×Dic₁₉	—	8	2	no	—
113	Dic₃₈	—	2	2	no	—
114	Dic₃₈	—	2	2	no	—
115	Dic₃₈	—	2	2	no	—
116	Dic₃₈	#107	1	4	yes	complemented
117	C₈×C₁₉	—	2	2	no	—
118	C₈×C₁₉	—	8	2	no	—
119	C₈×C₁₉	#103	1	4	yes	complemented
120	C₁₉⋊C₈	—	4	2	no	—
121	C₂×C₈×Q₈	—	19	1	no	—
122	#1845	—	19	1	no	—
123	#1803	—	19	2	no	—
124	C₂×#335	D₁₉	1	1	yes	characteristic
125	#1296	—	19	2	no	—
126	C₂²×C₁₉	#380	1	1	yes	characteristic
127	C₂²×C₁₉	#460	1	1	yes	characteristic
128	C₂²×C₁₉	#462	1	1	yes	characteristic
129	C₂²×C₁₉	#466	1	1	yes	characteristic
130	C₂²×C₁₉	#467	1	1	yes	characteristic
131	C₂²×C₁₉	#472	1	1	yes	characteristic
132	C₂²×C₁₉	#473	1	1	yes	characteristic
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
136	C₄×C₁₉	#417	1	1	yes	characteristic
137	C₄×C₁₉	C₂×#107	1	1	yes	characteristic
138	C₄×C₁₉	#427	1	1	yes	characteristic
139	C₄×C₁₉	#466	1	1	yes	characteristic
140	C₄×C₁₉	#467	1	1	yes	characteristic
141	C₄×C₁₉	#475	1	1	yes	characteristic
142	C₄×C₁₉	#477	1	1	yes	characteristic
143	Dic₁₉	—	2	4	no	—
144	Dic₁₉	—	4	2	no	—
145	Dic₁₉	—	16	2	no	—
146	C₂×C₄×Q₈	—	19	1	no	—
147	C₈×Q₈	—	19	4	no	—
148	C₈×Q₈	—	38	2	no	—
149	C₂×#107	—	38	1	no	—
150	C₂×#107	—	38	1	no	—
151	C₂×C₄⋊C₈	—	19	1	no	—
152	C₂×C₄⋊C₈	—	38	1	no	—
153	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
154	C₂×#103	—	38	2	no	—
155	C₂×C₄×C₈	—	38	1	no	—
156	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
157	#384	—	19	2	no	—
158	#340	—	38	2	no	—
159	#335	—	2	2	no	—
160	C₂×C₁₉	#1668	1	1	yes	characteristic
161	C₂×C₁₉	#1670	1	1	yes	characteristic
162	C₂×C₁₉	#1674	1	1	yes	characteristic
163	C₂×C₁₉	#1676	1	1	yes	characteristic
164	C₂×C₁₉	#1803	1	1	yes	characteristic
165	C₂×C₁₉	#1808	1	1	yes	characteristic
166	C₂×C₁₉	#1816	1	1	yes	characteristic
167	C₂²×Q₈	—	19	1	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	38	1	no	—
170	C₂²×C₈	D₇₆	1	1	yes	characteristic
171	C₂²×C₈	D₇₆	1	1	yes	characteristic
172	C₄×Q₈	—	19	2	no	—
173	C₄×Q₈	—	19	2	no	—
174	C₄×Q₈	—	38	1	no	—
175	C₄×Q₈	—	38	1	no	—
176	C₂×C₄⋊C₄	—	19	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	—	38	2	no	—
179	C₂×C₄⋊C₄	—	38	2	no	—
180	C₂×C₄⋊C₄	—	38	2	no	—
181	C₂×C₄²	—	38	1	no	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	#107	—	76	2	no	—
184	#107	—	76	2	no	—
185	C₄⋊C₈	—	2	2	no	—
186	C₄⋊C₈	—	2	2	no	—
187	C₄⋊C₈	—	19	2	no	—
188	C₄⋊C₈	—	38	4	no	—
189	C₄⋊C₈	—	38	1	no	—
190	#103	—	76	4	no	—
191	C₄×C₈	—	38	4	no	—
192	C₄×C₈	C₄×D₁₉	1	2	yes	—
193	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
194	C₁₉	#8645	1	1	yes	characteristic, complemented, Sylow
195	C₂×Q₈	—	19	2	no	—
196	C₂×Q₈	—	19	2	no	—
197	C₂×Q₈	—	19	2	no	—
198	C₂×Q₈	—	38	1	no	—
199	C₂×Q₈	—	38	1	no	—
200	C₂×Q₈	—	38	1	no	—
201	C₂²×C₄	—	38	1	no	—
202	C₂²×C₄	—	38	1	no	—
203	C₂²×C₄	—	76	2	no	—
204	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
205	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
206	C₂²×C₄	#64545	1	1	yes	characteristic
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	—	4	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	—	76	1	no	—
214	C₂×C₈	—	76	1	no	—
215	C₂×C₈	#64516	1	2	yes	—
216	C₂×C₈	Dic₇₆	1	2	yes	—
217	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
218	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
219	C₄⋊C₄	—	19	2	no	—
220	C₄⋊C₄	—	38	1	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	38	2	no	—
223	C₄⋊C₄	—	76	2	no	—
224	C₄⋊C₄	—	76	2	no	—
225	C₄⋊C₄	—	76	2	no	—
226	C₄⋊C₄	—	76	2	no	—
227	C₄⋊C₄	—	152	2	no	—
228	C₄²	—	38	2	no	—
229	C₄²	—	38	2	no	—
230	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
231	C₄²	#64543	1	1	yes	characteristic
232	C₄²	Q₈×D₁₉	1	1	yes	characteristic
233	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂³	#10597341	1	1	yes	characteristic
235	Q₈	—	19	4	no	—
236	Q₈	—	38	2	no	—
237	Q₈	—	38	2	no	—
238	Q₈	—	38	2	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	38	2	no	—
242	C₂×C₄	—	38	2	no	—
243	C₂×C₄	—	38	2	no	—
244	C₂×C₄	—	38	2	no	—
245	C₂×C₄	—	76	1	no	—
246	C₂×C₄	—	76	1	no	—
247	C₂×C₄	—	152	2	no	—
248	C₂×C₄	—	152	2	no	—
249	C₂×C₄	—	152	2	no	—
250	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
251	C₂×C₄	#10597338	1	1	yes	characteristic
252	C₂×C₄	#10597343	1	1	yes	characteristic
253	C₂×C₄	C₂×#64516	1	1	yes	characteristic
254	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
255	C₂×C₄	#10597354	1	1	yes	characteristic
256	C₂×C₄	#10597355	1	1	yes	characteristic
257	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
258	C₂×C₄	#10597358	1	1	yes	characteristic
259	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
260	C₂×C₄	#10597365	1	1	yes	characteristic
261	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
262	C₂×C₄	#10597384	1	1	yes	characteristic
263	C₂×C₄	#10597392	1	1	yes	characteristic
264	C₈	—	2	2	no	—
265	C₈	—	8	2	no	—
266	C₈	—	76	2	no	—
267	C₈	#10597273	1	4	yes	complemented
268	C₂²	#11926401	1	1	yes	characteristic
269	C₂²	#11926745	1	1	yes	characteristic
270	C₂²	#11926755	1	1	yes	characteristic
271	C₂²	#11926781	1	1	yes	characteristic
272	C₂²	#11926786	1	1	yes	characteristic
273	C₂²	#11926815	1	1	yes	characteristic
274	C₂²	#11926820	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	38	4	no	—
278	C₄	—	304	2	no	—
279	C₄	—	76	2	no	—
280	C₄	C₂×#10597273	1	1	yes	characteristic
281	C₄	#11926546	1	1	yes	characteristic
282	C₄	#107×D₁₉	1	1	yes	characteristic
283	C₄	#11926581	1	1	yes	characteristic
284	C₄	#11926777	1	1	yes	characteristic
285	C₄	#11926782	1	1	yes	characteristic
286	C₄	#11926830	1	1	yes	characteristic
287	C₄	#11926840	1	1	yes	characteristic
288	C₂	#14562996	1	1	yes	characteristic
289	C₂	#14563006	1	1	yes	characteristic
290	C₂	#14563030	1	1	yes	characteristic
291	C₂	#14563040	1	1	yes	characteristic
292	C₂	#14563641	1	1	yes	characteristic
293	C₂	#14563661	1	1	yes	characteristic
294	C₂	#14563696	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#335	C₂
socle, prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#8645
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
8. C₈×Dic₃₈	C₄	semidirect
116. Dic₃₈	#107	semidirect
119. C₈×C₁₉	#103	semidirect
194. C₁₉	#8645	semidirect
267. C₈	#10597273	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
#14563795	2
#14563641	2
#14561519	2
C₂×C₁₉×#335	2
#8645	19