Subgroups — #18075785

Order 4864.

362 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572569	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	#14562326	C₂	1	2	yes	maximal
4	#14561509	C₂	1	2	yes	maximal
5	C₁₉×#1848	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	C₄	1	2	yes	—
9	C₈×Dic₃₈	—	2	1	no	—
10	C₈×Dic₃₈	C₄	1	2	yes	—
11	#11926570	—	2	1	no	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	#11926499	—	2	1	no	—
15	#11926295	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926292	—	2	2	no	—
18	#11926289	—	2	2	no	—
19	C₂×C₁₉×#108	—	2	1	no	—
20	C₂×C₁₉×#108	—	2	1	no	—
21	C₁₉×#423	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597372	—	2	1	no	—
28	#10597370	—	2	1	no	—
29	#10597370	Q₈	1	2	yes	—
30	C₂×#64520	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	#10597316	—	2	1	no	—
33	#10597315	D₄	1	1	yes	characteristic
34	#10597315	D₄	1	1	yes	characteristic
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
37	C₁₉×#108	—	4	2	no	—
38	C₁₉×#108	—	4	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	#10597272	—	2	2	no	—
46	Dic₁₉⋊C₈	—	2	2	no	—
47	Dic₁₉⋊C₈	—	2	2	no	—
48	C₈×Dic₁₉	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×Dic₃₈	—	2	1	no	—
57	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
58	M₁₆×C₁₉	—	4	2	no	—
59	M₁₆×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
68	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
69	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₂²⋊Dic₁₉	—	2	2	no	—
74	C₄⋊Dic₁₉	—	2	1	no	—
75	C₄⋊Dic₁₉	—	2	1	no	—
76	C₄⋊Dic₁₉	—	2	1	no	—
77	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
78	Dic₁₉⋊C₄	—	2	2	no	—
79	Dic₁₉⋊C₄	—	2	2	no	—
80	C₄×Dic₁₉	—	2	2	no	—
81	#64520	—	4	1	no	—
82	#64520	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	C₂×C₁₉⋊C₈	—	8	2	no	—
86	#8683	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	4	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	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	—	2	2	no	—
102	Dic₃₈	—	4	2	no	—
103	Dic₃₈	—	4	2	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	8	2	no	—
107	C₈×C₁₉	#103	1	2	yes	—
108	C₈×C₁₉	#103	1	2	yes	—
109	C₁₉⋊C₈	—	4	2	no	—
110	C₁₉⋊C₈	—	8	2	no	—
111	#2960	—	19	1	no	—
112	#1848	D₁₉	1	1	yes	characteristic
113	C₂×#334	—	19	1	no	—
114	#1550	—	19	2	no	—
115	#1292	—	19	2	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#380	1	1	yes	characteristic
119	C₂²×C₁₉	#475	1	1	yes	characteristic
120	C₂²×C₁₉	#477	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
125	C₄×C₁₉	#417	1	1	yes	characteristic
126	C₄×C₁₉	#460	1	1	yes	characteristic
127	C₄×C₁₉	#462	1	1	yes	characteristic
128	C₄×C₁₉	#471	1	2	yes	—
129	Dic₁₉	—	4	2	no	—
130	Dic₁₉	—	4	2	no	—
131	#533	—	19	1	no	—
132	#446	—	19	2	no	—
133	#446	—	38	1	no	—
134	C₈×Q₈	—	19	2	no	—
135	C₈×Q₈	—	38	1	no	—
136	C₂×#108	—	2	1	no	—
137	C₂×#108	—	2	1	no	—
138	#424	—	38	1	no	—
139	#423	—	19	1	no	—
140	#423	C₂×D₁₉	1	2	yes	—
141	C₂×C₄⋊C₈	—	19	2	no	—
142	#405	—	38	1	no	—
143	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
144	#334	—	38	1	no	—
145	#334	—	38	1	no	—
146	#333	—	38	2	no	—
147	#332	—	38	2	no	—
148	C₂×C₁₉	—	2	1	no	—
149	C₂×C₁₉	—	2	1	no	—
150	C₂×C₁₉	#1803	1	1	yes	characteristic
151	C₂×C₁₉	#1813	1	1	yes	characteristic
152	C₂×C₁₉	#1815	1	1	yes	characteristic
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	38	1	no	—
155	C₂²×C₈	—	38	2	no	—
156	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
158	C₄⋊Q₈	—	19	1	no	—
159	C₄⋊Q₈	—	19	1	no	—
160	#125	—	38	1	no	—
161	C₂²⋊Q₈	—	19	2	no	—
162	C₂²⋊Q₈	—	38	1	no	—
163	C₄×Q₈	—	19	2	no	—
164	C₄×Q₈	—	38	1	no	—
165	#117	—	38	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	#108	—	4	2	no	—
168	#108	—	4	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	19	2	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	—	38	2	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₄⋊C₈	—	38	2	no	—
177	#97	—	38	2	no	—
178	C₄×C₈	—	38	2	no	—
179	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
180	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
181	C₄×C₈	D₇₆	1	1	yes	characteristic
182	C₄×C₈	D₇₆	1	1	yes	characteristic
183	C₁₉	#8683	1	1	yes	characteristic, complemented, Sylow
184	C₂×Q₈	—	19	2	no	—
185	C₂×Q₈	—	38	1	no	—
186	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
187	C₂²×C₄	#64545	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	M₁₆	—	4	2	no	—
190	M₁₆	—	4	2	no	—
191	M₁₆	—	76	1	no	—
192	M₁₆	—	76	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	38	2	no	—
197	C₂×C₈	—	76	2	no	—
198	C₂×C₈	—	152	2	no	—
199	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	#64526	1	2	yes	—
204	C₂×C₈	#64528	1	2	yes	—
205	C₄⋊C₄	—	19	2	no	—
206	C₄⋊C₄	—	38	1	no	—
207	C₄⋊C₄	—	38	1	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₄⋊C₄	—	38	1	no	—
210	C₄⋊C₄	—	38	2	no	—
211	C₂²⋊C₄	—	38	2	no	—
212	C₄²	—	38	2	no	—
213	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
214	C₄²	C₂×D₇₆	1	1	yes	characteristic
215	C₄²	D₄×D₁₉	1	1	yes	characteristic
216	C₄²	#64543	1	1	yes	characteristic
217	C₂³	#10597392	1	1	yes	characteristic
218	Q₈	—	76	2	no	—
219	Q₈	—	76	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	38	2	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
225	C₂×C₄	#10597338	1	1	yes	characteristic
226	C₂×C₄	#10597341	1	1	yes	characteristic
227	C₂×C₄	#10597343	1	1	yes	characteristic
228	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
229	C₂×C₄	#10597378	1	1	yes	characteristic
230	C₂×C₄	C₂×#64526	1	1	yes	characteristic
231	C₂×C₄	#10597384	1	1	yes	characteristic
232	C₂×C₄	#10597388	1	1	yes	characteristic
233	C₂×C₄	C₂×#64528	1	1	yes	characteristic
234	C₈	—	2	1	no	—
235	C₈	—	2	1	no	—
236	C₈	—	8	2	no	—
237	C₈	—	76	2	no	—
238	C₈	—	152	2	no	—
239	C₈	#10597267	1	2	yes	—
240	C₈	#10597267	1	2	yes	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#11926401	1	1	yes	characteristic
244	C₂²	#11926826	1	1	yes	characteristic
245	C₂²	#11926836	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	76	2	no	—
250	C₄	—	76	2	no	—
251	C₄	C₂×#10597267	1	1	yes	characteristic
252	C₄	#11926543	1	1	yes	characteristic
253	C₄	#11926741	1	1	yes	characteristic
254	C₄	#11926751	1	1	yes	characteristic
255	C₄	#11926808	1	2	yes	—
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	#14563637	1	1	yes	characteristic
259	C₂	#14563682	1	1	yes	characteristic
260	C₂	#14563691	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1848	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1848	D₁₉
hypocenter	C₁₉	#8683
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

Complements

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

N	H ≅ G/N	type
183. C₁₉	#8683	semidirect

Maximal subgroups

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

subgroup	index
#14572569	2
C₂×#11926295	2
#14562326	2
#14561509	2
C₁₉×#1848	2
#8683	19