Subgroups — #18075744

Order 4864.

434 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572348	C₂	1	1	yes	maximal, characteristic
2	#14563799	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562196	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	—	2	1	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	C₄	1	2	yes	complemented
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	C₄	1	2	yes	complemented
12	C₂×#10597275	—	2	1	no	—
13	C₂×#10597274	—	2	1	no	—
14	#11926568	C₂²	1	1	yes	characteristic
15	#11926510	—	2	1	no	—
16	#11926410	C₂²	1	2	yes	—
17	#11926279	—	2	4	no	—
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂×#64541	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597376	—	2	1	no	—
27	#10597376	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×#64520	—	2	1	no	—
30	#10597347	—	4	2	no	—
31	#10597347	—	4	2	no	—
32	C₂×#64515	—	2	2	no	—
33	C₂×C₈×D₁₉	—	2	2	no	—
34	#10597321	—	2	1	no	—
35	#10597320	Q₈	1	1	yes	characteristic
36	C₄×D₇₆	—	2	1	no	—
37	C₄×D₇₆	C₂×C₄	1	2	yes	—
38	#10597315	Q₈	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₄×C₈×C₁₉	—	2	2	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₁₉⋊#95	—	2	2	no	—
47	C₁₉⋊#95	—	2	2	no	—
48	(C₂×D₁₉)⋊C₈	—	2	2	no	—
49	(C₂×D₁₉)⋊C₈	—	2	2	no	—
50	#10597275	—	4	2	no	—
51	#10597274	—	4	2	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂×C₂²⋊D₁₉	—	2	2	no	—
58	C₂²×Dic₁₉	—	4	2	no	—
59	#64541	—	4	1	no	—
60	#64541	—	4	1	no	—
61	#64541	—	4	1	no	—
62	#64541	—	4	1	no	—
63	C₂×D₇₆	—	2	1	no	—
64	C₂×D₇₆	—	2	1	no	—
65	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
66	C₂×C₄×D₁₉	—	2	2	no	—
67	C₂×Dic₃₈	—	2	1	no	—
68	C₂×C₈×C₁₉	—	2	1	no	—
69	C₂×C₈×C₁₉	—	2	1	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₉	D₈	1	2	yes	—
76	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	(C₂×D₁₉)⋊C₄	—	2	2	no	—
82	(C₂×D₁₉)⋊C₄	—	2	2	no	—
83	C₄⋊Dic₁₉	—	2	1	no	—
84	C₄⋊Dic₁₉	—	4	2	no	—
85	C₄⋊Dic₁₉	—	4	2	no	—
86	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
87	#64520	—	4	1	no	—
88	#64520	—	4	1	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	#64515	—	4	4	no	—
91	C₈×D₁₉	—	4	4	no	—
92	#8674	—	19	1	no	maximal, Sylow
93	C₂³×C₁₉	#121	1	1	yes	characteristic
94	C₂²×D₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
107	C₂²⋊D₁₉	—	4	2	no	—
108	C₂²⋊D₁₉	—	4	2	no	—
109	C₂×Dic₁₉	—	2	2	no	—
110	C₂×Dic₁₉	—	8	2	no	—
111	C₂×Dic₁₉	—	8	2	no	—
112	C₂×Dic₁₉	—	8	2	no	—
113	D₇₆	—	4	2	no	—
114	D₇₆	—	4	2	no	—
115	D₇₆	—	4	1	no	—
116	D₇₆	—	4	1	no	—
117	C₄×D₁₉	—	4	2	no	—
118	C₄×D₁₉	—	4	2	no	—
119	Dic₃₈	—	4	1	no	—
120	Dic₃₈	—	4	1	no	—
121	C₈×C₁₉	—	2	1	no	—
122	C₈×C₁₉	—	2	1	no	—
123	C₈×C₁₉	—	8	2	no	—
124	C₈×C₁₉	#102	1	2	yes	—
125	C₈×C₁₉	#102	1	2	yes	—
126	C₁₉⋊C₈	—	4	2	no	—
127	#2931	—	19	1	no	—
128	#1846	—	19	1	no	—
129	#1564	D₁₉	1	1	yes	characteristic, complemented
130	#1517	—	19	2	no	—
131	#1286	—	19	2	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	2	1	no	—
134	C₂²×C₁₉	#380	1	1	yes	characteristic
135	C₂²×C₁₉	#459	1	1	yes	characteristic
136	C₂²×C₁₉	#461	1	1	yes	characteristic
137	C₂×D₁₉	—	4	2	no	—
138	C₂×D₁₉	—	4	2	no	—
139	C₂×D₁₉	—	4	2	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
145	C₄×C₁₉	#417	1	1	yes	characteristic
146	C₄×C₁₉	#474	1	1	yes	characteristic
147	C₄×C₁₉	#476	1	1	yes	characteristic
148	Dic₁₉	—	4	2	no	—
149	Dic₁₉	—	16	2	no	—
150	C₂×#131	—	38	1	no	—
151	#532	—	19	1	no	—
152	#436	—	19	2	no	—
153	#436	—	38	1	no	—
154	C₈×D₄	—	19	2	no	—
155	C₈×D₄	—	38	1	no	—
156	#431	C₂×D₁₉	1	2	yes	—
157	C₂×#107	—	38	1	no	—
158	C₂×#106	—	38	1	no	—
159	#423	—	19	1	no	—
160	#408	—	38	1	no	—
161	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
162	#382	—	19	2	no	—
163	#335	—	2	1	no	—
164	#334	—	2	1	no	—
165	#327	—	38	4	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	2	1	no	—
168	C₂×C₁₉	#1802	1	1	yes	characteristic
169	C₂×C₁₉	#1812	1	1	yes	characteristic
170	C₂×C₁₉	#1814	1	1	yes	characteristic
171	D₁₉	—	8	2	no	—
172	C₂×#41	—	38	1	no	—
173	#131	—	76	2	no	—
174	#131	—	76	2	no	—
175	C₂×M₁₆	—	38	1	no	—
176	C₂×M₁₆	—	38	2	no	—
177	C₂²×C₈	—	38	2	no	—
178	C₂²×C₈	D₇₆	1	1	yes	characteristic
179	C₂²×C₈	D₇₆	1	1	yes	characteristic
180	C₄⋊Q₈	—	19	1	no	—
181	#127	—	19	1	no	—
182	#124	—	38	1	no	—
183	#121	—	19	2	no	—
184	#121	—	38	1	no	—
185	C₄×D₄	—	19	2	no	—
186	C₄×D₄	—	38	1	no	—
187	C₂×C₄⋊C₄	—	38	2	no	—
188	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
189	#107	—	76	2	no	—
190	#106	—	76	2	no	—
191	C₄⋊C₈	—	2	2	no	—
192	C₄⋊C₈	—	19	2	no	—
193	C₄⋊C₈	—	38	1	no	—
194	C₂²⋊C₈	—	2	2	no	—
195	C₂²⋊C₈	—	38	2	no	—
196	C₂²⋊C₈	—	38	2	no	—
197	C₄×C₈	—	2	2	no	—
198	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
199	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
200	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
202	#95	—	38	2	no	—
203	#95	—	38	2	no	—
204	C₁₉	#8674	1	1	yes	characteristic, complemented, Sylow
205	#41	—	76	1	no	—
206	#41	—	76	1	no	—
207	#41	—	76	1	no	—
208	#41	—	76	1	no	—
209	C₂×Q₈	—	38	1	no	—
210	C₂×D₄	—	19	2	no	—
211	C₂×D₄	—	38	2	no	—
212	C₂×D₄	—	38	1	no	—
213	C₂×D₄	—	38	1	no	—
214	C₂²×C₄	—	38	2	no	—
215	C₂²×C₄	—	76	2	no	—
216	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
217	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
218	C₂²×C₄	#64545	1	1	yes	characteristic
219	M₁₆	—	76	1	no	—
220	M₁₆	—	76	1	no	—
221	M₁₆	—	76	4	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	—	4	2	no	—
225	C₂×C₈	—	38	2	no	—
226	C₂×C₈	—	76	4	no	—
227	C₂×C₈	#64516	1	2	yes	—
228	C₂×C₈	D₁₅₂	1	2	yes	—
229	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
230	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
231	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
232	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
233	C₄⋊C₄	—	19	2	no	—
234	C₄⋊C₄	—	38	1	no	—
235	C₄⋊C₄	—	76	2	no	—
236	C₄⋊C₄	—	76	2	no	—
237	C₂²⋊C₄	—	38	2	no	—
238	C₂²⋊C₄	—	38	2	no	—
239	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
240	C₄²	#64543	1	1	yes	characteristic
241	C₄²	Q₈×D₁₉	1	1	yes	characteristic
242	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
243	C₂³	—	38	2	no	—
244	C₂³	#10597341	1	1	yes	characteristic
245	Q₈	—	76	1	no	—
246	Q₈	—	76	1	no	—
247	D₄	—	76	2	no	—
248	D₄	—	76	2	no	—
249	D₄	—	76	2	no	—
250	D₄	—	76	2	no	—
251	D₄	—	76	1	no	—
252	D₄	—	76	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	38	2	no	—
256	C₂×C₄	—	76	2	no	—
257	C₂×C₄	—	76	2	no	—
258	C₂×C₄	—	152	2	no	—
259	C₂×C₄	—	152	2	no	—
260	C₂×C₄	—	152	2	no	—
261	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
262	C₂×C₄	#10597338	1	1	yes	characteristic
263	C₂×C₄	#10597343	1	1	yes	characteristic
264	C₂×C₄	C₂×#64516	1	1	yes	characteristic
265	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
266	C₂×C₄	#10597354	1	1	yes	characteristic
267	C₂×C₄	#10597355	1	1	yes	characteristic
268	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
269	C₂×C₄	#10597384	1	1	yes	characteristic
270	C₂×C₄	#10597392	1	1	yes	characteristic
271	C₈	—	2	1	no	—
272	C₈	—	2	1	no	—
273	C₈	—	8	2	no	—
274	C₈	—	76	2	no	—
275	C₈	#10597278	1	2	yes	—
276	C₈	#10597278	1	2	yes	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	76	2	no	—
280	C₂²	—	76	2	no	—
281	C₂²	—	76	2	no	—
282	C₂²	#11926401	1	1	yes	characteristic
283	C₂²	#11926740	1	1	yes	characteristic
284	C₂²	#11926750	1	1	yes	characteristic
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	—	2	1	no	—
289	C₄	—	304	2	no	—
290	C₄	—	76	2	no	—
291	C₄	C₂×#10597278	1	1	yes	characteristic
292	C₄	#11926546	1	1	yes	characteristic
293	C₄	#11926825	1	1	yes	characteristic
294	C₄	#11926835	1	1	yes	characteristic
295	C₂	—	2	1	no	—
296	C₂	—	2	1	no	—
297	C₂	—	152	2	no	—
298	C₂	#14563636	1	1	yes	characteristic
299	C₂	#14563678	1	1	yes	characteristic
300	C₂	#14563690	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8674
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #14563799	C₂	semidirect
4. #14561494	C₂	semidirect
5. C₁₉×#1564	C₂	semidirect
9. #11926623	C₄	semidirect
11. C₈×D₇₆	C₄	semidirect
129. #1564	D₁₉	semidirect
204. C₁₉	#8674	semidirect

Maximal subgroups

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

subgroup	index
#14572348	2
#14563799	2
#14562196	2
#14561494	2
C₁₉×#1564	2
#8674	19