Subgroups — #18088358

Order 4864.

1126 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926414	C₂	1	2	yes	maximal
2	C₂×#11926307	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊Dic₁₉	—	2	4	no	—
5	C₂²×C₄⋊Dic₁₉	C₂²	1	4	yes	—
6	#11926414	—	2	4	no	—
7	#11926414	C₄	1	8	yes	complemented
8	#11926307	—	2	8	no	—
9	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₉	—	2	4	no	—
12	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	complemented
13	C₂³×C₄×C₁₉	D₄	1	2	yes	—
14	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₂³×Dic₁₉	—	2	4	no	—
16	C₂²×C₈×C₁₉	—	2	4	no	—
17	C₂²×C₈×C₁₉	—	2	4	no	—
18	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₉	D₄	1	4	yes	—
20	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₁₉	D₄	1	4	yes	—
24	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	—	2	8	no	—
26	C₂×C₄⋊Dic₁₉	—	2	8	no	—
27	C₂×C₄⋊Dic₁₉	—	2	16	no	—
28	C₂×C₄⋊Dic₁₉	—	2	4	no	—
29	C₂×C₄⋊Dic₁₉	—	4	8	no	—
30	C₂×C₄⋊Dic₁₉	—	4	8	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
32	C₄×C₈×C₁₉	—	2	8	no	—
33	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
36	C₂²×C₄×C₁₉	D₈	1	4	yes	—
37	C₂²×C₄×C₁₉	SD₁₆	1	8	yes	—
38	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
45	C₂²×C₄×C₁₉	#41	1	4	yes	—
46	C₂²×Dic₁₉	—	2	8	no	—
47	C₂²×Dic₁₉	—	4	4	no	—
48	C₂²×Dic₁₉	—	4	4	no	—
49	C₂²×Dic₁₉	—	4	8	no	—
50	C₂²×Dic₁₉	—	4	8	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	—	2	4	no	—
53	C₂×C₈×C₁₉	—	2	8	no	—
54	C₂×C₈×C₁₉	—	2	8	no	—
55	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	complemented
56	C₄²×C₁₉	C₄²	1	4	yes	—
57	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
58	C₄²×C₁₉	C₄⋊C₄	1	8	yes	—
59	C₄⋊Dic₁₉	—	2	16	no	—
60	C₄⋊Dic₁₉	—	4	32	no	—
61	C₄⋊Dic₁₉	—	4	8	no	—
62	#10841	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
64	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂³×C₁₉	#124	1	2	yes	—
66	C₂³×C₁₉	#127	1	1	yes	characteristic
67	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
68	C₂³×C₁₉	C₂×D₈	1	2	yes	—
69	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
70	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
71	C₂×C₄×C₁₉	#95	1	8	yes	—
72	C₂×C₄×C₁₉	#102	1	16	yes	—
73	C₂×C₄×C₁₉	#103	1	16	yes	—
74	C₂×C₄×C₁₉	#106	1	8	yes	—
75	C₂×C₄×C₁₉	#107	1	8	yes	—
76	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
80	C₂×C₄×C₁₉	#117	1	2	yes	—
81	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
82	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
83	C₂×C₄×C₁₉	#121	1	4	yes	—
84	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
85	C₂×C₄×C₁₉	#125	1	2	yes	—
86	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
87	C₂×Dic₁₉	—	4	8	no	—
88	C₂×Dic₁₉	—	4	16	no	—
89	C₂×Dic₁₉	—	8	8	no	—
90	C₂×Dic₁₉	—	8	4	no	—
91	C₂×Dic₁₉	—	8	4	no	—
92	C₈×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₈	D₁₉	1	1	yes	characteristic
94	C₂×#384	—	19	2	no	—
95	C₂×#340	—	19	4	no	—
96	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
97	C₂²×C₁₉	#382	1	1	yes	characteristic
98	C₂²×C₁₉	#384	1	1	yes	characteristic
99	C₂²×C₁₉	#390	1	2	yes	—
100	C₂²×C₁₉	#391	1	2	yes	—
101	C₂²×C₁₉	C₂×#102	1	4	yes	—
102	C₂²×C₁₉	C₂×#103	1	4	yes	—
103	C₂²×C₁₉	C₂×#106	1	2	yes	—
104	C₂²×C₁₉	C₂×#107	1	2	yes	—
105	C₂²×C₁₉	#486	1	4	yes	—
106	C₂²×C₁₉	#487	1	4	yes	—
107	C₂²×C₁₉	#492	1	2	yes	—
108	C₂²×C₁₉	#493	1	1	yes	characteristic
109	C₂²×C₁₉	#494	1	1	yes	characteristic
110	C₂²×C₁₉	#498	1	2	yes	—
111	C₂²×C₁₉	#500	1	2	yes	—
112	C₄×C₁₉	#340	1	16	yes	complemented
113	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
114	C₄×C₁₉	#380	1	2	yes	—
115	C₄×C₁₉	#389	1	4	yes	—
116	Dic₁₉	—	8	8	no	—
117	C₂³×C₈	C₂×D₁₉	1	2	yes	—
118	C₂²×C₄⋊C₄	—	19	4	no	—
119	C₂²×C₄⋊C₄	—	38	4	no	—
120	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₄×C₈	—	2	4	no	—
122	C₂×C₄×C₈	Dic₁₉	1	4	yes	complemented
123	#384	—	19	8	no	—
124	#384	—	38	4	no	—
125	#340	—	38	8	no	—
126	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
127	C₂×C₁₉	C₂×#340	1	2	yes	—
128	C₂×C₁₉	#1834	1	2	yes	—
129	C₂×C₁₉	#1844	1	1	yes	characteristic
130	C₂×C₁₉	#1845	1	1	yes	characteristic
131	C₂×C₁₉	#1956	1	2	yes	—
132	C₂×C₁₉	#1957	1	2	yes	—
133	C₂×C₁₉	#1990	1	4	yes	—
134	C₂³×C₄	—	38	4	no	—
135	C₂³×C₄	D₇₆	1	2	yes	—
136	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
137	C₂²×C₈	—	2	4	no	—
138	C₂²×C₈	—	2	4	no	—
139	C₂²×C₈	Dic₃₈	1	4	yes	—
140	C₂²×C₈	D₇₆	1	4	yes	—
141	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
142	C₂×C₄⋊C₄	—	19	8	no	—
143	C₂×C₄⋊C₄	—	38	8	no	—
144	C₂×C₄⋊C₄	—	38	8	no	—
145	C₂×C₄⋊C₄	—	38	16	no	—
146	C₂×C₄⋊C₄	—	38	4	no	—
147	C₂×C₄⋊C₄	—	76	8	no	—
148	C₂×C₄⋊C₄	—	76	8	no	—
149	C₂×C₄²	Dic₃₈	1	2	yes	—
150	C₂×C₄²	C₄×D₁₉	1	4	yes	—
151	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
153	C₄×C₈	—	2	8	no	—
154	C₁₉	#10841	1	1	yes	characteristic, complemented, Sylow
155	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
156	C₂²×C₄	—	38	8	no	—
157	C₂²×C₄	—	76	4	no	—
158	C₂²×C₄	—	76	4	no	—
159	C₂²×C₄	—	76	8	no	—
160	C₂²×C₄	—	76	8	no	—
161	C₂²×C₄	#64516	1	8	yes	—
162	C₂²×C₄	D₁₅₂	1	4	yes	—
163	C₂²×C₄	Dic₇₆	1	4	yes	—
164	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
165	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	8	yes	—
166	C₂²×C₄	C₂×Dic₃₈	1	2	yes	—
167	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
169	C₂²×C₄	C₂×D₇₆	1	2	yes	—
170	C₂²×C₄	#64541	1	4	yes	—
171	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
173	C₂×C₈	—	2	8	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	2	8	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	complemented
178	C₄⋊C₄	—	38	16	no	—
179	C₄⋊C₄	—	76	8	no	—
180	C₄⋊C₄	—	76	32	no	—
181	C₄²	C₄×Dic₁₉	1	4	yes	—
182	C₄²	Dic₁₉⋊C₄	1	8	yes	—
183	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
184	C₂³	#10597315	1	1	yes	characteristic
185	C₂³	#10597320	1	1	yes	characteristic
186	C₂³	#10597321	1	2	yes	—
187	C₂³	C₂×#64516	1	4	yes	—
188	C₂³	C₂×D₁₅₂	1	2	yes	—
189	C₂³	C₂×Dic₇₆	1	2	yes	—
190	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
191	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
192	C₂×C₄	—	76	16	no	—
193	C₂×C₄	—	76	8	no	—
194	C₂×C₄	—	152	8	no	—
195	C₂×C₄	—	152	4	no	—
196	C₂×C₄	—	152	4	no	—
197	C₂×C₄	#10597273	1	16	yes	—
198	C₂×C₄	#10597274	1	8	yes	—
199	C₂×C₄	#10597275	1	8	yes	—
200	C₂×C₄	#10597278	1	16	yes	—
201	C₂×C₄	C₁₉⋊#95	1	8	yes	—
202	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
203	C₂×C₄	#10597315	1	2	yes	—
204	C₂×C₄	#10597316	1	2	yes	—
205	C₂×C₄	C₄×D₇₆	1	4	yes	—
206	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
207	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
208	C₂×C₄	#10597370	1	4	yes	—
209	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
210	C₂×C₄	#10597372	1	2	yes	—
211	C₂×C₄	#10597376	1	4	yes	—
212	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
213	C₈	—	2	8	no	—
214	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
215	C₂²	#11926410	1	1	yes	characteristic
216	C₂²	#11926414	1	1	yes	characteristic
217	C₂²	#11926446	1	2	yes	—
218	C₂²	#11926450	1	2	yes	—
219	C₂²	C₂×#10597278	1	4	yes	—
220	C₂²	C₂×#10597273	1	4	yes	—
221	C₂²	C₂×#10597274	1	2	yes	—
222	C₂²	C₂×#10597275	1	2	yes	—
223	C₂²	#11926891	1	4	yes	—
224	C₂²	#11926895	1	4	yes	—
225	C₂²	#11926917	1	2	yes	—
226	C₂²	#11926921	1	1	yes	characteristic
227	C₂²	#11926924	1	1	yes	characteristic
228	C₂²	#11926942	1	2	yes	—
229	C₂²	#11926949	1	2	yes	—
230	C₄	—	152	8	no	—
231	C₄	#11926307	1	16	yes	complemented
232	C₄	C₄×C₄⋊Dic₁₉	1	2	yes	—
233	C₄	#11926404	1	2	yes	—
234	C₄	#11926442	1	4	yes	—
235	C₂	#14561865	1	1	yes	characteristic
236	C₂	C₂×#11926307	1	2	yes	—
237	C₂	#14563763	1	2	yes	—
238	C₂	#14563792	1	1	yes	characteristic
239	C₂	#14563795	1	1	yes	characteristic
240	C₂	#14564437	1	2	yes	—
241	C₂	#14564441	1	2	yes	—
242	C₂	#14564596	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄×C₈	D₁₉
hypocenter	C₁₉	#10841
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #11926414	C₄	semidirect
12. C₂×C₄×C₈×C₁₉	C₄	semidirect
55. C₂×C₈×C₁₉	C₄⋊C₄	semidirect
112. C₄×C₁₉	#340	semidirect
122. C₂×C₄×C₈	Dic₁₉	semidirect
154. C₁₉	#10841	semidirect
177. C₂×C₈	C₄⋊Dic₁₉	semidirect
231. C₄	#11926307	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926414	2
C₂×#11926307	2
C₂²×C₄×C₈×C₁₉	2
#10841	19