Subgroups — #18087792

Order 4864.

1518 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926404	C₂	1	2	yes	maximal
2	C₂×#11926307	C₂	1	4	yes	maximal, complemented
3	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊Dic₁₉	C₂²	1	4	yes	—
5	C₂²×C₂²⋊Dic₁₉	—	2	2	no	—
6	#11926404	—	2	4	no	—
7	#11926404	C₄	1	8	yes	complemented
8	C₂×C₁₉⋊#95	—	2	2	no	—
9	#11926307	—	2	8	no	—
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	—	2	4	no	—
12	C₂²×M₁₆×C₁₉	—	2	8	no	—
13	C₂²×M₁₆×C₁₉	C₄	1	4	yes	complemented
14	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
15	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	—	2	4	no	—
17	C₂³×C₄×C₁₉	—	2	4	no	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	4	yes	—
22	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₉	—	2	4	no	—
25	C₂×M₁₆×C₁₉	—	2	32	no	—
26	C₂×M₁₆×C₁₉	—	2	8	no	—
27	C₂×M₁₆×C₁₉	—	2	16	no	—
28	C₂²×C₈×C₁₉	—	2	4	no	—
29	C₂²×C₈×C₁₉	—	2	4	no	—
30	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₉	D₄	1	8	yes	—
32	C₂×C₂²⋊Dic₁₉	—	2	8	no	—
33	C₂×C₂²⋊Dic₁₉	—	4	8	no	—
34	C₂×C₄⋊Dic₁₉	—	2	8	no	—
35	C₂×C₄⋊Dic₁₉	—	2	8	no	—
36	C₂×C₄⋊Dic₁₉	—	2	4	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
38	C₁₉⋊#95	—	2	8	no	—
39	C₂⁴×C₁₉	—	2	4	no	—
40	C₂⁴×C₁₉	—	2	4	no	—
41	C₂⁴×C₁₉	—	2	4	no	—
42	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
43	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	4	no	—
46	C₂²×C₄×C₁₉	—	2	4	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	—	2	16	no	—
49	C₂²×C₄×C₁₉	—	2	8	no	—
50	C₂²×C₄×C₁₉	—	2	8	no	—
51	C₂²×C₄×C₁₉	—	2	8	no	—
52	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
56	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
61	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	#41	1	4	yes	—
63	C₂²×Dic₁₉	—	2	8	no	—
64	C₂²×Dic₁₉	—	4	8	no	—
65	C₂²×Dic₁₉	—	4	8	no	—
66	C₂²×Dic₁₉	—	4	4	no	—
67	C₂²×Dic₁₉	—	4	4	no	—
68	M₁₆×C₁₉	—	2	32	no	—
69	C₂×C₈×C₁₉	—	2	4	no	—
70	C₂×C₈×C₁₉	—	2	4	no	—
71	C₂×C₈×C₁₉	—	2	16	no	—
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
73	C₂²⋊Dic₁₉	—	4	16	no	—
74	C₄⋊Dic₁₉	—	2	16	no	—
75	C₄⋊Dic₁₉	—	4	4	no	—
76	C₄⋊Dic₁₉	—	4	4	no	—
77	#10722	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	4	no	—
79	C₂³×C₁₉	—	2	8	no	—
80	C₂³×C₁₉	—	2	8	no	—
81	C₂³×C₁₉	—	2	4	no	—
82	C₂³×C₁₉	—	2	4	no	—
83	C₂³×C₁₉	—	2	8	no	—
84	C₂³×C₁₉	—	4	8	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	—	4	4	no	—
87	C₂³×C₁₉	#95	1	4	yes	—
88	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
89	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂³×C₁₉	#121	1	4	yes	—
91	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
92	C₂³×C₁₉	#137	1	4	yes	—
93	C₂×C₄×C₁₉	—	2	4	no	—
94	C₂×C₄×C₁₉	—	2	8	no	—
95	C₂×C₄×C₁₉	—	2	8	no	—
96	C₂×C₄×C₁₉	—	2	4	no	—
97	C₂×C₄×C₁₉	—	2	4	no	—
98	C₂×C₄×C₁₉	—	2	16	no	—
99	C₂×C₄×C₁₉	#95	1	4	yes	—
100	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
104	C₂×C₄×C₁₉	#117	1	2	yes	—
105	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
106	C₂×C₄×C₁₉	#120	1	4	yes	—
107	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
108	C₂×C₄×C₁₉	#123	1	4	yes	—
109	C₂×Dic₁₉	—	4	8	no	—
110	C₂×Dic₁₉	—	4	8	no	—
111	C₂×Dic₁₉	—	4	8	no	—
112	C₂×Dic₁₉	—	8	8	no	—
113	C₂×Dic₁₉	—	8	8	no	—
114	C₈×C₁₉	—	2	8	no	—
115	C₂³×M₁₆	D₁₉	1	1	yes	characteristic
116	C₂×#380	—	19	2	no	—
117	C₂×#340	—	19	4	no	—
118	C₂²×C₁₉	—	2	4	no	—
119	C₂²×C₁₉	—	2	8	no	—
120	C₂²×C₁₉	—	4	8	no	—
121	C₂²×C₁₉	—	4	8	no	—
122	C₂²×C₁₉	—	4	8	no	—
123	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
124	C₂²×C₁₉	#380	1	2	yes	—
125	C₂²×C₁₉	#386	1	4	yes	—
126	C₂²×C₁₉	#417	1	4	yes	—
127	C₂²×C₁₉	#418	1	2	yes	—
128	C₂²×C₁₉	#419	1	2	yes	—
129	C₂²×C₁₉	#428	1	4	yes	—
130	C₂²×C₁₉	#468	1	8	yes	—
131	C₂²×C₁₉	#469	1	4	yes	—
132	C₂²×C₁₉	#470	1	4	yes	—
133	C₄×C₁₉	—	2	4	no	—
134	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
135	C₄×C₁₉	#379	1	1	yes	characteristic
136	C₄×C₁₉	#381	1	1	yes	characteristic
137	C₄×C₁₉	#385	1	4	yes	—
138	Dic₁₉	—	8	8	no	—
139	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
140	C₂²×M₁₆	—	2	4	no	—
141	C₂²×M₁₆	—	2	8	no	—
142	C₂²×M₁₆	Dic₁₉	1	4	yes	complemented
143	C₂³×C₈	C₂×D₁₉	1	2	yes	—
144	C₂²×C₄⋊C₄	—	19	4	no	—
145	C₂²×C₂²⋊C₄	—	38	2	no	—
146	#380	—	19	8	no	—
147	#380	—	38	4	no	—
148	C₂×#95	—	38	2	no	—
149	#340	—	38	8	no	—
150	C₂×C₁₉	—	4	4	no	—
151	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
152	C₂×C₁₉	#1736	1	2	yes	—
153	C₂×C₁₉	#1809	1	4	yes	—
154	C₂×C₁₉	#1894	1	4	yes	—
155	C₂×C₁₉	#1895	1	4	yes	—
156	C₂⁵	D₇₆	1	1	yes	characteristic
157	C₂³×C₄	—	2	4	no	—
158	C₂³×C₄	—	2	4	no	—
159	C₂³×C₄	—	38	4	no	—
160	C₂³×C₄	Dic₃₈	1	2	yes	—
161	C₂³×C₄	C₄×D₁₉	1	4	yes	—
162	C₂³×C₄	D₇₆	1	1	yes	characteristic
163	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
164	C₂³×C₄	C₂²⋊D₁₉	1	4	yes	—
165	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
166	C₂×M₁₆	—	2	32	no	—
167	C₂×M₁₆	—	2	8	no	—
168	C₂×M₁₆	—	2	16	no	—
169	C₂²×C₈	—	2	4	no	—
170	C₂²×C₈	—	2	4	no	—
171	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
172	C₂²×C₈	C₂²⋊D₁₉	1	8	yes	—
173	C₂×C₄⋊C₄	—	19	8	no	—
174	C₂×C₄⋊C₄	—	38	8	no	—
175	C₂×C₄⋊C₄	—	38	8	no	—
176	C₂×C₄⋊C₄	—	38	4	no	—
177	C₂×C₂²⋊C₄	—	38	8	no	—
178	C₂×C₂²⋊C₄	—	76	8	no	—
179	#95	—	38	8	no	—
180	C₁₉	#10722	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	—	2	4	no	—
182	C₂⁴	—	2	4	no	—
183	C₂⁴	—	2	4	no	—
184	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
185	C₂⁴	(C₂×D₁₉)⋊C₄	1	4	yes	—
186	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
187	C₂²×C₄	—	2	4	no	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	8	no	—
190	C₂²×C₄	—	2	8	no	—
191	C₂²×C₄	—	2	4	no	—
192	C₂²×C₄	—	2	16	no	—
193	C₂²×C₄	—	2	8	no	—
194	C₂²×C₄	—	38	8	no	—
195	C₂²×C₄	—	76	8	no	—
196	C₂²×C₄	—	76	8	no	—
197	C₂²×C₄	—	76	4	no	—
198	C₂²×C₄	—	76	4	no	—
199	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
200	C₂²×C₄	Dic₁₉⋊C₄	1	8	yes	—
201	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
202	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
203	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
204	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
205	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
206	C₂²×C₄	#64541	1	4	yes	—
207	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
208	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
209	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
210	M₁₆	—	2	32	no	—
211	C₂×C₈	—	2	4	no	—
212	C₂×C₈	—	2	4	no	—
213	C₂×C₈	—	2	16	no	—
214	C₂×C₈	C₂²⋊Dic₁₉	1	8	yes	complemented
215	C₄⋊C₄	—	38	16	no	—
216	C₄⋊C₄	—	76	4	no	—
217	C₄⋊C₄	—	76	4	no	—
218	C₂²⋊C₄	—	76	16	no	—
219	C₂³	—	2	8	no	—
220	C₂³	—	2	4	no	—
221	C₂³	—	2	4	no	—
222	C₂³	—	2	8	no	—
223	C₂³	—	2	4	no	—
224	C₂³	—	2	8	no	—
225	C₂³	—	4	8	no	—
226	C₂³	—	4	4	no	—
227	C₂³	—	4	4	no	—
228	C₂³	C₁₉⋊#95	1	4	yes	—
229	C₂³	#10597354	1	4	yes	—
230	C₂³	#10597355	1	4	yes	—
231	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
232	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
233	C₂³	#10597376	1	4	yes	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	8	no	—
236	C₂×C₄	—	2	8	no	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	2	16	no	—
240	C₂×C₄	—	76	8	no	—
241	C₂×C₄	—	76	8	no	—
242	C₂×C₄	—	76	8	no	—
243	C₂×C₄	—	152	8	no	—
244	C₂×C₄	—	152	8	no	—
245	C₂×C₄	C₁₉⋊#95	1	4	yes	—
246	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
248	C₂×C₄	#10597370	1	4	yes	—
249	C₂×C₄	#10597372	1	2	yes	—
250	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
251	C₂×C₄	#10597375	1	4	yes	—
252	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
253	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
254	C₂×C₄	#10597399	1	4	yes	—
255	C₈	—	2	8	no	—
256	C₂²	—	2	8	no	—
257	C₂²	—	2	4	no	—
258	C₂²	—	4	8	no	—
259	C₂²	—	4	8	no	—
260	C₂²	—	4	8	no	—
261	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
262	C₂²	#11926404	1	2	yes	—
263	C₂²	#11926423	1	4	yes	—
264	C₂²	#11926546	1	4	yes	—
265	C₂²	#11926550	1	2	yes	—
266	C₂²	#11926554	1	2	yes	—
267	C₂²	#11926586	1	4	yes	—
268	C₂²	#11926790	1	8	yes	—
269	C₂²	#11926797	1	4	yes	—
270	C₂²	#11926802	1	4	yes	—
271	C₄	—	2	4	no	—
272	C₄	—	152	8	no	—
273	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
274	C₄	#11926400	1	1	yes	characteristic
275	C₄	#11926407	1	1	yes	characteristic
276	C₄	#11926417	1	4	yes	—
277	C₂	—	4	4	no	—
278	C₂	#14561858	1	1	yes	characteristic
279	C₂	#14563355	1	2	yes	—
280	C₂	#14563668	1	4	yes	—
281	C₂	#14564068	1	4	yes	—
282	C₂	#14564073	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂³×M₁₆×C₁₉	C₂
socle	C₂⁴×C₁₉	C₂×D₄
prime radical	C₂⁵×C₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂³×M₁₆	D₁₉
hypocenter	C₁₉	#10722
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#11926307	C₂	semidirect
7. #11926404	C₄	semidirect
13. C₂²×M₁₆×C₁₉	C₄	semidirect
72. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
142. C₂²×M₁₆	Dic₁₉	semidirect
180. C₁₉	#10722	semidirect
214. C₂×C₈	C₂²⋊Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926404	2
C₂×#11926307	2
C₂³×M₁₆×C₁₉	2
#10722	19