Subgroups — #18075788

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	#14563807	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
3	#14562325	C₂	1	2	yes	maximal
4	#14561509	C₂	1	2	yes	maximal
5	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597276	—	2	1	no	—
7	C₂×#10597276	—	2	1	no	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926295	—	2	1	no	—
11	#11926295	—	2	1	no	—
12	#11926293	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₁₉×#446	—	2	1	no	—
16	C₁₉×#446	C₄	1	2	yes	—
17	C₈×Q₈×C₁₉	—	2	1	no	—
18	C₈×Q₈×C₁₉	C₄	1	2	yes	—
19	C₁₉×#424	—	2	1	no	—
20	C₁₉×#423	C₂²	1	1	yes	characteristic
21	C₁₉×#405	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
27	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
28	C₁₉×#125	—	2	1	no	—
29	C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₁₉×C₂²⋊Q₈	Q₈	1	2	yes	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₁₉×#117	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×#64520	—	2	2	no	—
36	C₂²×C₁₉⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
41	C₁₉×#97	—	2	2	no	—
42	C₄×C₈×C₁₉	—	2	2	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	#10597276	—	4	2	no	—
48	#10597276	—	4	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	1	no	—
54	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
58	M₁₆×C₁₉	—	4	1	no	—
59	M₁₆×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	—	2	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	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
75	C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₄²×C₁₉	—	2	2	no	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	#64520	—	4	2	no	—
82	#64520	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	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	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×Q₁₆	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	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	4	2	no	—
107	C₈×C₁₉	#103	1	2	yes	—
108	C₈×C₁₉	#103	1	2	yes	—
109	C₁₉⋊C₈	—	8	2	no	—
110	C₁₉⋊C₈	—	8	2	no	—
111	#2960	D₁₉	1	1	yes	characteristic
112	#1848	—	19	1	no	—
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	—	4	2	no	—
125	C₄×C₁₉	—	4	2	no	—
126	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
127	C₄×C₁₉	#417	1	1	yes	characteristic
128	C₄×C₁₉	#460	1	1	yes	characteristic
129	C₄×C₁₉	#462	1	1	yes	characteristic
130	C₄×C₁₉	#471	1	2	yes	—
131	#533	C₂×D₁₉	1	1	yes	characteristic
132	#446	—	2	1	no	—
133	#446	Dic₁₉	1	2	yes	—
134	C₈×Q₈	—	2	1	no	—
135	C₈×Q₈	Dic₁₉	1	2	yes	—
136	C₂×#108	—	38	1	no	—
137	C₂×#108	—	38	1	no	—
138	#424	—	2	1	no	—
139	#423	—	19	2	no	—
140	#423	C₂×D₁₉	1	1	yes	characteristic
141	C₂×C₄⋊C₈	—	19	2	no	—
142	#405	—	2	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	1	no	—
154	C₂×M₁₆	—	38	2	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	D₇₆	1	1	yes	characteristic
159	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
160	#125	—	2	1	no	—
161	C₂²⋊Q₈	—	2	1	no	—
162	C₂²⋊Q₈	Dic₃₈	1	2	yes	—
163	C₄×Q₈	—	2	1	no	—
164	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
165	#117	—	2	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	#108	—	76	2	no	—
168	#108	—	76	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	—	38	2	no	—
174	C₄⋊C₈	—	38	2	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
177	#97	—	2	2	no	—
178	C₄×C₈	—	2	2	no	—
179	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
180	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
181	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₁₉	#8683	1	1	yes	characteristic, complemented, Sylow
184	C₂×Q₈	—	2	1	no	—
185	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
186	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
187	C₂²×C₄	#64541	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	M₁₆	—	4	1	no	—
190	M₁₆	—	4	1	no	—
191	M₁₆	—	76	2	no	—
192	M₁₆	—	76	2	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	76	2	no	—
197	C₂×C₈	—	76	2	no	—
198	C₂×C₈	—	152	2	no	—
199	C₂×C₈	#64527	1	2	yes	—
200	C₂×C₈	#64528	1	2	yes	—
201	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
204	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
205	C₄⋊C₄	—	2	1	no	—
206	C₄⋊C₄	—	2	1	no	—
207	C₄⋊C₄	—	2	1	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
211	C₂²⋊C₄	—	2	2	no	—
212	C₄²	—	2	2	no	—
213	C₄²	C₂×D₇₆	1	1	yes	characteristic
214	C₄²	#64541	1	1	yes	characteristic
215	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
216	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂³	#10597370	1	1	yes	characteristic
218	Q₈	—	4	2	no	—
219	Q₈	—	4	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	#10597370	1	1	yes	characteristic
225	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
226	C₂×C₄	#10597372	1	1	yes	characteristic
227	C₂×C₄	#10597376	1	1	yes	characteristic
228	C₂×C₄	#10597376	1	1	yes	characteristic
229	C₂×C₄	C₂×#64527	1	1	yes	characteristic
230	C₂×C₄	C₂×#64528	1	1	yes	characteristic
231	C₂×C₄	#10597395	1	1	yes	characteristic
232	C₂×C₄	#10597397	1	1	yes	characteristic
233	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
234	C₈	—	2	1	no	—
235	C₈	—	2	1	no	—
236	C₈	—	4	2	no	—
237	C₈	—	152	2	no	—
238	C₈	—	152	2	no	—
239	C₈	#10597292	1	2	yes	—
240	C₈	#10597292	1	2	yes	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#11926404	1	1	yes	characteristic
244	C₂²	#11926829	1	1	yes	characteristic
245	C₂²	#11926839	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	2	no	—
251	C₄	C₂×#10597292	1	1	yes	characteristic
252	C₄	#11926545	1	1	yes	characteristic
253	C₄	#11926744	1	1	yes	characteristic
254	C₄	#11926754	1	1	yes	characteristic
255	C₄	#11926807	1	2	yes	—
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	#14563640	1	1	yes	characteristic
259	C₂	#14563685	1	1	yes	characteristic
260	C₂	#14563694	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2960	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2960	D₁₉
hypocenter	C₁₉	#8683
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

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
#14563807	2
C₂×#11926295	2
#14562325	2
#14561509	2
C₁₉×#2960	2
#8683	19