Subgroups — #18075481

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926674	C₂	1	1	yes	maximal, characteristic
2	#14563628	C₂	1	2	yes	maximal
3	#14562391	C₂	1	1	yes	maximal, characteristic
4	#14561509	C₂	1	2	yes	maximal
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	—	2	1	no	—
9	#11926674	—	2	1	no	—
10	#11926674	—	2	1	no	—
11	#11926568	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
14	C₂×#10597281	—	2	2	no	—
15	C₂×#10597272	C₄	1	2	yes	—
16	#11926312	—	2	2	no	—
17	#11926295	—	2	1	no	—
18	#11926295	—	2	1	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#335	—	2	1	no	—
22	C₁₉×#335	—	2	1	no	—
23	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
29	C₂×Dic₁₉⋊C₄	Q₈	1	2	yes	—
30	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
31	C₂×#64520	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₄×Dic₃₈	—	2	1	no	—
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	#10597281	—	4	4	no	—
44	#10597272	—	2	2	no	—
45	#10597272	—	2	2	no	—
46	Dic₁₉⋊C₈	—	2	2	no	—
47	Dic₁₉⋊C₈	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
56	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
57	C₂×Dic₃₈	—	2	1	no	—
58	C₂×Dic₃₈	—	2	1	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	C₂×Dic₃₈	—	2	2	no	—
61	M₁₆×C₁₉	—	4	2	no	—
62	M₁₆×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×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	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄⋊Dic₁₉	—	2	1	no	—
75	C₄⋊Dic₁₉	—	2	1	no	—
76	Dic₁₉⋊C₄	—	2	2	no	—
77	Dic₁₉⋊C₄	—	2	2	no	—
78	C₄×Dic₁₉	—	2	2	no	—
79	C₄×Dic₁₉	—	2	2	no	—
80	#64520	—	4	2	no	—
81	#64520	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	#8619	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	C₂×C₂²⋊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	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
96	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₂×Dic₁₉	—	2	2	no	—
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	2	4	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	Dic₃₈	—	4	2	no	—
103	Dic₃₈	—	4	1	no	—
104	Dic₃₈	—	4	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	8	2	no	—
109	C₈×C₁₉	#101	1	2	yes	complemented
110	C₁₉⋊C₈	—	4	2	no	—
111	C₁₉⋊C₈	—	8	2	no	—
112	C₂×#446	—	19	1	no	—
113	#1801	—	19	2	no	—
114	#1567	D₁₉	1	1	yes	characteristic
115	#1566	—	19	1	no	—
116	#1292	—	19	2	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	#380	1	1	yes	characteristic
120	C₂²×C₁₉	#428	1	2	yes	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
125	C₄×C₁₉	#413	1	1	yes	characteristic
126	C₄×C₁₉	#468	1	2	yes	—
127	C₄×C₁₉	#469	1	1	yes	characteristic
128	C₄×C₁₉	#470	1	1	yes	characteristic
129	Dic₁₉	—	4	2	no	—
130	Dic₁₉	—	4	2	no	—
131	C₂×C₄×Q₈	—	19	1	no	—
132	#446	—	38	1	no	—
133	#446	—	38	1	no	—
134	#446	—	38	1	no	—
135	#446	—	38	1	no	—
136	#423	—	19	2	no	—
137	#423	C₂×D₁₉	1	2	yes	—
138	C₂×C₄⋊C₈	—	19	2	no	—
139	C₂×C₄⋊C₈	—	19	1	no	—
140	C₂×#101	—	38	2	no	—
141	C₂×#97	—	19	2	no	—
142	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
143	#343	—	38	2	no	—
144	#335	—	2	1	no	—
145	#335	—	2	1	no	—
146	#334	—	38	1	no	—
147	#334	—	38	1	no	—
148	C₂×C₁₉	—	2	2	no	—
149	C₂×C₁₉	#1801	1	1	yes	characteristic
150	C₂×C₁₉	#1809	1	1	yes	characteristic
151	C₂×C₁₉	#1813	1	1	yes	characteristic
152	C₂²×Q₈	—	19	1	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	38	2	no	—
155	C₂²×C₈	—	19	2	no	—
156	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
157	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
158	C₄×Q₈	—	38	1	no	—
159	C₄×Q₈	—	38	1	no	—
160	C₄×Q₈	—	38	1	no	—
161	C₄×Q₈	—	38	1	no	—
162	C₂×C₄⋊C₄	—	19	1	no	—
163	C₂×C₄⋊C₄	—	19	2	no	—
164	C₂×C₄²	—	19	2	no	—
165	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	2	no	—
170	C₄⋊C₈	—	38	1	no	—
171	C₄⋊C₈	—	38	2	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₄⋊C₈	—	38	1	no	—
174	#101	—	76	4	no	—
175	#97	—	38	2	no	—
176	#97	—	38	2	no	—
177	C₄×C₈	D₇₆	1	1	yes	characteristic
178	C₄×C₈	D₇₆	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₁₉	#8619	1	1	yes	characteristic, complemented, Sylow
182	C₂×Q₈	—	38	1	no	—
183	C₂×Q₈	—	38	1	no	—
184	C₂×Q₈	—	38	2	no	—
185	C₂×Q₈	—	38	2	no	—
186	C₂²×C₄	—	19	2	no	—
187	C₂²×C₄	—	19	2	no	—
188	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
189	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
190	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
191	M₁₆	—	4	2	no	—
192	M₁₆	—	4	2	no	—
193	M₁₆	—	76	2	no	—
194	M₁₆	—	76	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	4	2	no	—
198	C₂×C₈	—	38	2	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	—	76	2	no	—
201	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
204	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
205	C₄⋊C₄	—	38	1	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	1	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₄²	—	38	2	no	—
210	C₄²	—	38	2	no	—
211	C₄²	C₂×D₇₆	1	1	yes	characteristic
212	C₄²	#64543	1	1	yes	characteristic
213	C₄²	#64545	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
215	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
216	Q₈	—	76	2	no	—
217	Q₈	—	76	1	no	—
218	Q₈	—	76	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	38	4	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	38	2	no	—
225	C₂×C₄	—	76	2	no	—
226	C₂×C₄	#10597338	1	1	yes	characteristic
227	C₂×C₄	#10597341	1	1	yes	characteristic
228	C₂×C₄	#10597343	1	1	yes	characteristic
229	C₂×C₄	#10597357	1	2	yes	—
230	C₂×C₄	#10597364	1	2	yes	—
231	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
232	C₂×C₄	#10597384	1	1	yes	characteristic
233	C₂×C₄	#10597392	1	1	yes	characteristic
234	C₈	—	2	1	no	—
235	C₈	—	2	1	no	—
236	C₈	—	2	1	no	—
237	C₈	—	8	2	no	—
238	C₈	—	76	2	no	—
239	C₈	—	152	2	no	—
240	C₈	#10597281	1	2	yes	complemented
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#11926401	1	1	yes	characteristic
244	C₂²	#11926585	1	2	yes	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	76	2	no	—
249	C₄	—	76	2	no	—
250	C₄	C₂×#10597281	1	1	yes	characteristic
251	C₄	#11926526	1	1	yes	characteristic
252	C₄	#11926791	1	2	yes	—
253	C₄	#11926794	1	1	yes	characteristic
254	C₄	#11926799	1	1	yes	characteristic
255	C₂	—	2	2	no	—
256	C₂	#14563628	1	1	yes	characteristic
257	C₂	#14563669	1	1	yes	characteristic
258	C₂	#14563682	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#8619
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
109. C₈×C₁₉	#101	semidirect
181. C₁₉	#8619	semidirect
240. C₈	#10597281	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926674	2
#14563628	2
#14562391	2
#14561509	2
C₁₉×#1567	2
#8619	19