Subgroups — #18075658

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563763	C₂	1	1	yes	maximal, characteristic
2	#14563640	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
4	#14561519	C₂	1	2	yes	maximal
5	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597292	—	2	2	no	—
8	#11926414	C₂²	1	2	yes	—
9	#11926307	—	2	1	no	—
10	#11926307	—	2	1	no	—
11	#11926306	—	2	2	no	—
12	#11926295	—	2	2	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#446	—	2	2	no	—
15	C₁₉×#446	C₄	1	4	yes	complemented
16	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	—	2	1	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄×Q₈×C₁₉	—	2	1	no	—
25	C₄×Q₈×C₁₉	—	2	1	no	—
26	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₄×Q₈×C₁₉	Q₈	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₄⋊Dic₁₉	—	2	2	no	—
34	C₂×C₄⋊Dic₁₉	—	2	2	no	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	4	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
39	C₁₉×#97	—	2	4	no	—
40	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	#10597292	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×Dic₁₉	—	4	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	8	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	#8657	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	#121	1	1	yes	characteristic
81	Q₈×C₁₉	—	2	4	no	—
82	Q₈×C₁₉	—	4	2	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	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	2	yes	—
96	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	2	yes	—
99	C₂×Dic₁₉	—	8	2	no	—
100	C₂×Dic₁₉	—	8	2	no	—
101	C₂×Dic₁₉	—	8	2	no	—
102	C₈×C₁₉	—	2	2	no	—
103	C₈×C₁₉	—	2	2	no	—
104	C₈×C₁₉	—	4	2	no	—
105	C₁₉⋊C₈	—	8	2	no	—
106	C₂×#446	D₁₉	1	1	yes	characteristic
107	#1834	—	19	1	no	—
108	#1803	—	19	2	no	—
109	C₂×#334	—	19	1	no	—
110	#1296	—	19	2	no	—
111	C₂²×C₁₉	#380	1	1	yes	characteristic
112	C₂²×C₁₉	#464	1	2	yes	—
113	C₂²×C₁₉	#469	1	1	yes	characteristic
114	C₂²×C₁₉	#470	1	1	yes	characteristic
115	C₂²×C₁₉	#471	1	2	yes	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	4	2	no	—
120	C₄×C₁₉	#416	1	1	yes	characteristic
121	C₄×C₁₉	#419	1	1	yes	characteristic
122	C₄×C₁₉	#428	1	2	yes	—
123	C₄×C₁₉	#468	1	2	yes	—
124	C₄×C₁₉	#479	1	2	yes	—
125	Dic₁₉	—	16	2	no	—
126	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
127	#446	—	2	2	no	—
128	#446	Dic₁₉	1	4	yes	complemented
129	C₂×C₄⋊C₈	—	2	1	no	—
130	C₂×C₄⋊C₈	—	19	2	no	—
131	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
132	C₂×#103	—	38	2	no	—
133	C₂×#97	—	2	1	no	—
134	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
135	#384	—	19	2	no	—
136	#340	—	38	1	no	—
137	#340	—	38	1	no	—
138	#340	—	38	2	no	—
139	#334	—	38	2	no	—
140	C₂×C₁₉	#1702	1	2	yes	—
141	C₂×C₁₉	#1704	1	2	yes	—
142	C₂×C₁₉	#1805	1	1	yes	characteristic
143	C₂×C₁₉	#1809	1	1	yes	characteristic
144	C₂×C₁₉	#1815	1	1	yes	characteristic
145	C₂²×Q₈	D₇₆	1	1	yes	characteristic
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	38	2	no	—
148	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
150	C₄×Q₈	—	2	1	no	—
151	C₄×Q₈	—	2	1	no	—
152	C₄×Q₈	Dic₃₈	1	2	yes	—
153	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
154	C₂×C₄⋊C₄	—	2	1	no	—
155	C₂×C₄⋊C₄	—	38	2	no	—
156	C₂×C₄⋊C₄	—	38	2	no	—
157	C₂×C₄⋊C₄	—	38	2	no	—
158	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
159	C₂×C₄²	—	2	1	no	—
160	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
161	C₄⋊C₈	—	2	4	no	—
162	C₄⋊C₈	—	2	1	no	—
163	C₄⋊C₈	—	38	2	no	—
164	C₄⋊C₈	—	38	2	no	—
165	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
166	#103	—	76	4	no	—
167	#97	—	2	4	no	—
168	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
169	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
170	C₁₉	#8657	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	76	2	no	—
178	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
179	C₂²×C₄	#64541	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	—	76	2	no	—
187	C₂×C₈	—	76	2	no	—
188	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
189	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₄⋊C₄	—	76	2	no	—
195	C₄⋊C₄	—	76	2	no	—
196	C₄⋊C₄	—	76	2	no	—
197	C₄⋊C₄	—	152	2	no	—
198	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
202	C₄²	#64541	1	1	yes	characteristic
203	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
204	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂³	#10597376	1	1	yes	characteristic
206	Q₈	—	2	4	no	—
207	Q₈	—	4	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	152	2	no	—
215	C₂×C₄	—	152	2	no	—
216	C₂×C₄	—	152	2	no	—
217	C₂×C₄	#10597354	1	2	yes	—
218	C₂×C₄	#10597355	1	2	yes	—
219	C₂×C₄	#10597370	1	1	yes	characteristic
220	C₂×C₄	#10597370	1	1	yes	characteristic
221	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
222	C₂×C₄	#10597372	1	1	yes	characteristic
223	C₂×C₄	#10597376	1	1	yes	characteristic
224	C₂×C₄	#10597388	1	2	yes	—
225	C₂×C₄	#10597396	1	2	yes	—
226	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	2	2	no	—
229	C₈	—	4	2	no	—
230	C₈	—	152	2	no	—
231	C₂²	#11926404	1	1	yes	characteristic
232	C₂²	#11926766	1	2	yes	—
233	C₂²	#11926797	1	1	yes	characteristic
234	C₂²	#11926802	1	1	yes	characteristic
235	C₂²	#11926807	1	2	yes	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	304	2	no	—
241	C₄	#11926540	1	1	yes	characteristic
242	C₄	#11926553	1	1	yes	characteristic
243	C₄	#11926586	1	2	yes	—
244	C₄	#11926790	1	2	yes	—
245	C₄	#11926851	1	2	yes	—
246	C₂	#14563203	1	2	yes	—
247	C₂	#14563217	1	2	yes	—
248	C₂	#14563650	1	1	yes	characteristic
249	C₂	#14563668	1	1	yes	characteristic
250	C₂	#14563694	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#446	C₂
socle, prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#446	D₁₉
hypocenter	C₁₉	#8657
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
15. C₁₉×#446	C₄	semidirect
128. #446	Dic₁₉	semidirect
170. C₁₉	#8657	semidirect

Maximal subgroups

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

subgroup	index
#14563763	2
#14563640	2
C₂×#11926295	2
#14561519	2
C₂×C₁₉×#446	2
#8657	19