Subgroups — #18073127

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926675	C₂	1	1	yes	maximal, characteristic
2	#14561959	C₂	1	1	yes	maximal, characteristic
3	#14561922	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#14561486	C₂	1	1	yes	maximal, characteristic
6	#14561486	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
8	#11926675	—	2	1	no	—
9	#11926675	—	2	1	no	—
10	#11926675	—	2	1	no	—
11	#11926675	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926597	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597260	C₄	1	2	yes	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926270	C₄	1	4	yes	—
19	#11926266	—	2	1	no	—
20	#11926266	—	2	1	no	—
21	#11926265	—	2	1	no	—
22	C₈×C₁₉⋊C₈	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#101	C₄	1	2	yes	—
25	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#343	C₄	1	2	yes	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₁₉×#101	—	2	4	no	—
43	C₁₉×#97	—	2	1	no	—
44	C₁₉×#97	—	2	1	no	—
45	C₄×C₈×C₁₉	—	2	1	no	—
46	C₄×C₈×C₁₉	—	2	1	no	—
47	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
48	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
55	#10597260	—	2	2	no	—
56	#10597260	—	2	2	no	—
57	C₄×C₁₉⋊C₈	—	2	1	no	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
61	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
62	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
68	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	M₁₆×C₁₉	—	2	2	no	—
73	M₁₆×C₁₉	—	2	2	no	—
74	M₁₆×C₁₉	—	2	2	no	—
75	M₁₆×C₁₉	M₁₆	1	4	yes	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	—	2	2	no	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₁₉	#41	1	1	yes	characteristic
87	C₄²×C₁₉	#41	1	1	yes	characteristic
88	C₂×C₁₉⋊C₈	—	2	2	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	2	2	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
98	#8167	—	19	1	no	maximal, Sylow
99	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
100	Q₈×C₁₉	—	4	2	no	—
101	Q₈×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
117	C₂×C₄×C₁₉	#131	1	2	yes	—
118	C₈×C₁₉	—	2	4	no	—
119	C₈×C₁₉	—	4	2	no	—
120	C₁₉⋊C₈	—	2	1	no	—
121	C₁₉⋊C₈	—	2	1	no	—
122	C₁₉⋊C₈	—	2	1	no	—
123	C₁₉⋊C₈	—	4	2	no	—
124	C₁₉⋊C₈	—	4	2	no	—
125	C₁₉⋊C₈	—	4	2	no	—
126	C₁₉⋊C₈	#101	1	2	yes	complemented
127	C₂×#446	—	19	1	no	—
128	C₄×#101	D₁₉	1	1	yes	characteristic
129	#1461	—	19	1	no	—
130	#1451	—	19	1	no	—
131	C₈×M₁₆	—	19	1	no	—
132	#1283	—	19	1	no	—
133	#1283	—	19	1	no	—
134	C₂²×C₁₉	—	2	1	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
138	C₂²×C₁₉	#405	1	1	yes	characteristic
139	C₄×C₁₉	—	2	1	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	4	2	no	—
143	C₄×C₁₉	—	4	2	no	—
144	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
145	C₄×C₁₉	#413	1	1	yes	characteristic
146	C₄×C₁₉	#435	1	2	yes	—
147	C₄×C₁₉	#436	1	2	yes	—
148	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
149	#446	—	38	1	no	—
150	#446	—	38	1	no	—
151	#446	—	38	1	no	—
152	#446	—	38	1	no	—
153	#431	—	19	1	no	—
154	#431	—	19	1	no	—
155	C₂×C₄⋊C₈	—	19	2	no	—
156	C₂×C₄⋊C₈	—	19	1	no	—
157	C₂×#101	Dic₁₉	1	2	yes	—
158	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
159	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
160	C₂×#97	—	19	2	no	—
161	C₂×C₄×C₈	—	19	1	no	—
162	#343	Dic₁₉	1	2	yes	—
163	#324	—	19	4	no	—
164	#322	—	38	1	no	—
165	#322	—	38	1	no	—
166	#322	—	38	1	no	—
167	C₈²	—	38	1	no	—
168	C₂×C₁₉	—	2	1	no	—
169	C₂×C₁₉	—	2	1	no	—
170	C₂×C₁₉	#1753	1	1	yes	characteristic
171	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
172	C₂×C₁₉	#1757	1	1	yes	characteristic
173	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
175	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
176	C₂²×C₈	—	19	1	no	—
177	C₂²×C₈	—	19	1	no	—
178	C₂²×C₈	—	19	2	no	—
179	C₄×Q₈	—	2	1	no	—
180	C₄×Q₈	—	2	1	no	—
181	C₄×Q₈	—	2	1	no	—
182	C₄×Q₈	—	2	1	no	—
183	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
184	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
185	C₂×C₄²	C₄×D₁₉	1	2	yes	—
186	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
187	C₄⋊C₈	—	38	2	no	—
188	C₄⋊C₈	—	38	2	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	#101	—	2	4	no	—
194	C₂²⋊C₈	—	19	2	no	—
195	C₂²⋊C₈	—	19	2	no	—
196	#97	—	2	1	no	—
197	#97	—	2	1	no	—
198	#97	—	38	2	no	—
199	#97	—	38	2	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₄×C₈	—	19	1	no	—
203	C₄×C₈	—	19	1	no	—
204	C₄×C₈	—	19	1	no	—
205	C₄×C₈	—	19	1	no	—
206	C₄×C₈	—	38	1	no	—
207	C₄×C₈	—	38	1	no	—
208	C₁₉	#8167	1	1	yes	characteristic, complemented, Sylow
209	C₂×Q₈	—	2	1	no	—
210	C₂×Q₈	—	2	1	no	—
211	C₂×Q₈	—	2	2	no	—
212	C₂×Q₈	—	2	2	no	—
213	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
214	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
215	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
218	M₁₆	—	2	2	no	—
219	M₁₆	—	2	2	no	—
220	M₁₆	—	2	2	no	—
221	M₁₆	#64520	1	4	yes	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	19	1	no	—
225	C₂×C₈	—	19	1	no	—
226	C₂×C₈	—	19	1	no	—
227	C₂×C₈	—	19	1	no	—
228	C₂×C₈	—	38	2	no	—
229	C₂×C₈	—	38	2	no	—
230	C₂×C₈	—	38	2	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	76	1	no	—
233	C₂×C₈	—	76	2	no	—
234	C₄⋊C₄	—	2	1	no	—
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄²	—	2	2	no	—
239	C₄²	—	2	2	no	—
240	C₄²	D₄×D₁₉	1	1	yes	characteristic
241	C₄²	D₄×D₁₉	1	1	yes	characteristic
242	C₄²	#64543	1	1	yes	characteristic
243	C₄²	#64543	1	1	yes	characteristic
244	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
245	Q₈	—	4	2	no	—
246	Q₈	—	4	2	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	#10597323	1	1	yes	characteristic
256	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
257	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
258	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
259	C₂×C₄	C₂×#64520	1	2	yes	—
260	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
261	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
262	C₂×C₄	#10597394	1	2	yes	—
263	C₈	—	2	4	no	—
264	C₈	—	4	2	no	—
265	C₈	—	19	2	no	—
266	C₈	—	38	1	no	—
267	C₈	—	38	1	no	—
268	C₈	—	38	1	no	—
269	C₈	—	76	2	no	—
270	C₈	—	76	2	no	—
271	C₈	—	76	2	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
275	C₂²	C₄×#64520	1	1	yes	characteristic
276	C₂²	#11926500	1	1	yes	characteristic
277	C₄	—	2	1	no	—
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	4	2	no	—
281	C₄	—	4	2	no	—
282	C₄	#101×D₁₉	1	1	yes	characteristic
283	C₄	#11926527	1	1	yes	characteristic
284	C₄	#11926616	1	2	yes	—
285	C₄	#11926622	1	2	yes	—
286	C₂	—	2	1	no	—
287	C₂	—	2	1	no	—
288	C₂	#14563419	1	1	yes	characteristic
289	C₂	#101×Dic₁₉	1	1	yes	characteristic
290	C₂	#14563438	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator, prime radical	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#101	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#101	D₁₉
hypocenter	C₁₉	#8167
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

Complements

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

N	H ≅ G/N	type
126. C₁₉⋊C₈	#101	semidirect
208. C₁₉	#8167	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926675	2
#14561959	2
#14561922	2
M₁₆×C₁₉⋊C₈	2
#14561486	2
C₄×C₁₉×#101	2
#8167	19