Subgroups — #18091310

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926414	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926312	C₂	1	4	yes	maximal
3	#14563329	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₁₉	C₄	1	4	yes	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	#11926414	—	2	2	no	—
9	#11926414	—	2	1	no	—
10	#11926414	—	2	1	no	—
11	#11926312	—	2	8	no	—
12	#11926299	—	2	2	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#336	—	2	1	no	—
16	C₁₉×#336	—	2	1	no	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂³×Dic₁₉	C₂×C₄	1	4	yes	—
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	4	no	—
22	C₂×M₁₆×C₁₉	—	2	4	no	—
23	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	—	2	4	no	—
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	4	no	—
30	C₂×C₄⋊Dic₁₉	—	2	4	no	—
31	C₂×C₄⋊Dic₁₉	—	2	4	no	—
32	C₂×C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₄⋊Dic₁₉	—	2	2	no	—
34	C₂×C₄⋊Dic₁₉	—	2	4	no	—
35	C₂×C₄⋊Dic₁₉	—	4	8	no	—
36	C₂×#64520	—	2	2	no	—
37	C₂×#64520	—	2	4	no	—
38	C₂×#64520	—	2	4	no	—
39	C₂×#64520	Q₈	1	4	yes	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	—	2	4	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
51	C₂²×C₄×C₁₉	#41	1	2	yes	—
52	C₂²×C₄×C₁₉	#41	1	4	yes	—
53	C₂²×C₄×C₁₉	#41	1	2	yes	—
54	C₂²×Dic₁₉	—	2	4	no	—
55	C₂²×Dic₁₉	—	2	8	no	—
56	C₂²×Dic₁₉	—	4	8	no	—
57	M₁₆×C₁₉	—	2	8	no	—
58	M₁₆×C₁₉	—	4	4	no	—
59	C₂×C₈×C₁₉	—	2	4	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	4	no	—
65	C₄⋊Dic₁₉	—	4	8	no	—
66	C₄⋊Dic₁₉	—	4	8	no	—
67	C₄⋊Dic₁₉	—	4	4	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	2	no	—
70	#64520	—	2	8	no	—
71	#64520	—	4	4	no	—
72	C₂×C₁₉⋊C₈	—	2	4	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	#11354	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	—	2	2	no	—
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂³×C₁₉	#117	1	2	yes	—
80	C₂³×C₁₉	C₄×D₄	1	2	yes	—
81	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
82	C₂×C₄×C₁₉	—	2	16	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	#100	1	4	yes	—
88	C₂×C₄×C₁₉	#101	1	4	yes	—
89	C₂×C₄×C₁₉	#121	1	2	yes	—
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
92	C₂×C₄×C₁₉	#123	1	2	yes	—
93	C₂×C₄×C₁₉	#123	1	4	yes	—
94	C₂×C₄×C₁₉	#123	1	2	yes	—
95	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#125	1	4	yes	—
98	C₂×C₄×C₁₉	#126	1	4	yes	—
99	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
101	C₂×Dic₁₉	—	4	4	no	—
102	C₂×Dic₁₉	—	4	8	no	—
103	C₂×Dic₁₉	—	8	8	no	—
104	C₈×C₁₉	—	4	4	no	—
105	C₁₉⋊C₈	—	4	4	no	—
106	C₂×#384	—	19	1	no	—
107	C₂×#343	—	19	4	no	—
108	#1728	—	19	1	no	—
109	#1728	D₁₉	1	1	yes	characteristic
110	C₂²×C₁₉	—	2	4	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	—	2	2	no	—
113	C₂²×C₁₉	—	2	4	no	—
114	C₂²×C₁₉	#381	1	1	yes	characteristic
115	C₂²×C₁₉	#387	1	4	yes	—
116	C₂²×C₁₉	#390	1	1	yes	characteristic
117	C₂²×C₁₉	#391	1	1	yes	characteristic
118	C₂²×C₁₉	C₂×#100	1	2	yes	—
119	C₂²×C₁₉	C₂×#101	1	2	yes	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	#397	1	2	yes	—
123	C₄×C₁₉	#398	1	2	yes	—
124	C₄×C₁₉	#399	1	2	yes	—
125	C₄×C₁₉	#400	1	2	yes	—
126	Dic₁₉	—	8	4	no	—
127	C₂²×M₁₆	—	19	2	no	—
128	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
129	C₂²×C₄⋊C₄	—	19	2	no	—
130	C₂²×C₄⋊C₄	—	19	4	no	—
131	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
132	#384	—	38	2	no	—
133	#384	—	38	1	no	—
134	#384	—	38	1	no	—
135	#343	—	38	8	no	—
136	#336	—	2	1	no	—
137	#336	—	2	1	no	—
138	#336	—	38	2	no	—
139	C₂×C₁₉	—	2	4	no	—
140	C₂×C₁₉	#1445	1	1	yes	characteristic
141	C₂×C₁₉	#1821	1	2	yes	—
142	C₂×C₁₉	#1965	1	1	yes	characteristic
143	C₂×C₁₉	#1966	1	1	yes	characteristic
144	C₂×C₁₉	#1997	1	2	yes	—
145	C₂³×C₄	—	19	4	no	—
146	C₂³×C₄	C₄×D₁₉	1	2	yes	—
147	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	4	no	—
150	C₂×M₁₆	—	2	4	no	—
151	C₂×M₁₆	—	19	4	no	—
152	C₂×M₁₆	—	38	2	no	—
153	C₂×M₁₆	—	38	4	no	—
154	C₂×M₁₆	—	38	4	no	—
155	C₂×M₁₆	D₇₆	1	4	yes	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	38	2	no	—
158	C₂×C₄⋊C₄	—	38	4	no	—
159	C₂×C₄⋊C₄	—	38	4	no	—
160	C₂×C₄⋊C₄	—	38	4	no	—
161	C₂×C₄⋊C₄	—	38	2	no	—
162	C₂×C₄⋊C₄	—	38	4	no	—
163	C₂×C₄⋊C₄	—	38	2	no	—
164	C₂×C₄⋊C₄	—	76	8	no	—
165	C₂×C₄²	—	2	4	no	—
166	C₂×C₄²	D₇₆	1	2	yes	—
167	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₁₉	#11354	1	1	yes	characteristic, complemented, Sylow
170	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	4	no	—
174	C₂²×C₄	—	38	4	no	—
175	C₂²×C₄	—	38	8	no	—
176	C₂²×C₄	—	76	8	no	—
177	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
178	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
179	C₂²×C₄	C₂×D₇₆	1	2	yes	—
180	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
181	C₂²×C₄	#64541	1	2	yes	—
182	C₂²×C₄	#64543	1	4	yes	—
183	C₂²×C₄	#64543	1	2	yes	—
184	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
185	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	M₁₆	—	2	8	no	—
187	M₁₆	—	4	4	no	—
188	M₁₆	—	38	8	no	—
189	M₁₆	—	76	4	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	38	4	no	—
194	C₂×C₈	—	76	2	no	—
195	C₂×C₈	—	76	2	no	—
196	C₄⋊C₄	—	76	8	no	—
197	C₄⋊C₄	—	76	4	no	—
198	C₄⋊C₄	—	76	8	no	—
199	C₄⋊C₄	—	76	2	no	—
200	C₄⋊C₄	—	76	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	4	no	—
204	C₂³	—	2	2	no	—
205	C₂³	—	2	2	no	—
206	C₂³	C₄×D₇₆	1	2	yes	—
207	C₂³	#10597323	1	2	yes	—
208	C₂³	#10597333	1	2	yes	—
209	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂×C₄	—	2	16	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	76	4	no	—
216	C₂×C₄	—	76	8	no	—
217	C₂×C₄	—	152	8	no	—
218	C₂×C₄	#10597280	1	4	yes	—
219	C₂×C₄	#10597281	1	4	yes	—
220	C₂×C₄	#10597320	1	1	yes	characteristic
221	C₂×C₄	#10597321	1	1	yes	characteristic
222	C₂×C₄	#10597325	1	4	yes	—
223	C₂×C₄	#10597332	1	4	yes	—
224	C₂×C₄	#10597332	1	2	yes	—
225	C₂×C₄	#10597335	1	4	yes	—
226	C₂×C₄	#10597343	1	4	yes	—
227	C₂×C₄	#10597343	1	2	yes	—
228	C₂×C₄	#10597376	1	2	yes	—
229	C₂×C₄	#10597381	1	2	yes	—
230	C₂×C₄	#10597382	1	1	yes	characteristic
231	C₂×C₄	#10597390	1	1	yes	characteristic
232	C₈	—	4	4	no	—
233	C₈	—	76	4	no	—
234	C₂²	—	2	4	no	—
235	C₂²	—	2	2	no	—
236	C₂²	—	2	2	no	—
237	C₂²	—	2	4	no	—
238	C₂²	#11926405	1	1	yes	characteristic
239	C₂²	#11926429	1	4	yes	—
240	C₂²	#11926446	1	1	yes	characteristic
241	C₂²	#11926449	1	1	yes	characteristic
242	C₂²	C₂×#10597280	1	2	yes	—
243	C₂²	C₂×#10597281	1	2	yes	—
244	C₄	—	2	4	no	—
245	C₄	—	2	4	no	—
246	C₄	—	152	4	no	—
247	C₄	#11926469	1	2	yes	—
248	C₄	#11926474	1	2	yes	—
249	C₄	#11926481	1	2	yes	—
250	C₄	#11926484	1	2	yes	—
251	C₂	—	2	4	no	—
252	C₂	#14561902	1	1	yes	characteristic
253	C₂	#14563713	1	2	yes	—
254	C₂	#14564475	1	1	yes	characteristic
255	C₂	#14564479	1	1	yes	characteristic
256	C₂	#14564623	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1728	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1728	D₁₉
hypocenter	C₁₉	#11354
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1728

Complements

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

N	H ≅ G/N	type
169. C₁₉	#11354	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926414	2
C₂×#11926312	2
#14563329	2
C₁₉×#1728	2
#11354	19