Subgroups — #18082371

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926949	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	2	yes	maximal
3	#14564436	C₂	1	2	yes	maximal
4	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926949	—	2	2	no	—
8	#11926949	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	2	no	—
10	C₂×#10597267	—	2	4	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926306	—	2	4	no	—
14	#11926265	—	2	2	no	—
15	C₂×C₁₉×#106	—	2	2	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#384	C₂²	1	2	yes	—
18	C₂²×Dic₃₈	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
28	#10597315	—	2	2	no	—
29	#10597315	—	2	2	no	—
30	#10597315	—	2	2	no	—
31	#10597315	C₂×C₄	1	4	yes	—
32	C₁₉×#106	—	4	4	no	—
33	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	#10597275	—	2	8	no	—
36	#10597267	—	4	8	no	—
37	C₄×C₁₉⋊C₈	—	2	1	no	—
38	C₄×C₁₉⋊C₈	—	2	1	no	—
39	C₄×C₁₉⋊C₈	—	2	1	no	—
40	C₄×C₁₉⋊C₈	—	2	1	no	—
41	C₂²×C₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₁₉	—	4	2	no	—
46	C₂×Dic₃₈	—	2	4	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×Dic₃₈	—	4	4	no	—
49	C₂×Dic₃₈	—	4	2	no	—
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
52	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
53	C₄⋊C₄×C₁₉	—	4	4	no	—
54	C₄⋊C₄×C₁₉	—	4	4	no	—
55	C₄⋊C₄×C₁₉	—	4	4	no	—
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	#41	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊Dic₁₉	—	2	4	no	—
61	C₄⋊Dic₁₉	—	2	4	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	4	no	—
67	C₂×C₁₉⋊C₈	—	2	4	no	—
68	#9836	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	#127	1	1	yes	characteristic
70	C₂×C₄×C₁₉	—	8	2	no	—
71	C₂×C₄×C₁₉	—	8	2	no	—
72	C₂×C₄×C₁₉	—	8	2	no	—
73	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
81	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
82	C₂×C₄×C₁₉	#137	1	4	yes	—
83	C₂×Dic₁₉	—	4	4	no	—
84	C₂×Dic₁₉	—	8	2	no	—
85	C₂×Dic₁₉	—	8	2	no	—
86	Dic₃₈	—	4	8	no	—
87	Dic₃₈	—	8	4	no	—
88	C₈×C₁₉	#103	1	8	yes	complemented
89	C₁₉⋊C₈	—	4	2	no	—
90	C₁₉⋊C₈	—	4	2	no	—
91	C₂×#500	—	19	1	no	—
92	#1990	—	19	2	no	—
93	#1956	—	19	2	no	—
94	#1844	D₁₉	1	1	yes	characteristic
95	C₂×#322	—	19	1	no	—
96	C₂²×C₁₉	#390	1	1	yes	characteristic
97	C₂²×C₁₉	#492	1	1	yes	characteristic
98	C₂²×C₁₉	#494	1	1	yes	characteristic
99	C₂²×C₁₉	#496	1	2	yes	—
100	C₂²×C₁₉	#497	1	2	yes	—
101	C₄×C₁₉	—	16	2	no	—
102	C₄×C₁₉	C₂×#103	1	2	yes	—
103	C₄×C₁₉	#441	1	2	yes	—
104	C₄×C₁₉	#442	1	2	yes	—
105	C₄×C₁₉	#469	1	2	yes	—
106	C₄×C₁₉	#470	1	2	yes	—
107	C₄×C₁₉	#487	1	2	yes	—
108	Dic₁₉	—	8	4	no	—
109	C₂×C₄⋊Q₈	—	19	2	no	—
110	#500	—	19	4	no	—
111	#500	—	38	2	no	—
112	C₂×#107	—	38	2	no	—
113	C₂×#106	—	2	2	no	—
114	C₂×#103	—	38	4	no	—
115	C₂×C₄×C₈	—	19	1	no	—
116	C₂×C₄×C₈	—	19	1	no	—
117	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
118	#384	C₂×D₁₉	1	2	yes	—
119	#340	—	38	4	no	—
120	#322	—	38	2	no	—
121	C₂×C₁₉	#1714	1	2	yes	—
122	C₂×C₁₉	#1723	1	2	yes	—
123	C₂×C₁₉	#1956	1	1	yes	characteristic
124	C₂×C₁₉	#1971	1	1	yes	characteristic
125	C₂×C₁₉	#1972	1	1	yes	characteristic
126	C₂²×Q₈	—	38	2	no	—
127	C₂²×C₈	—	19	2	no	—
128	C₂²×C₈	—	19	2	no	—
129	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
130	C₄⋊Q₈	—	19	4	no	—
131	C₄⋊Q₈	—	38	2	no	—
132	C₄⋊Q₈	—	38	2	no	—
133	C₄⋊Q₈	—	38	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄⋊C₄	—	38	2	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	#107	—	38	8	no	—
141	#106	—	4	4	no	—
142	#103	—	76	8	no	—
143	C₄×C₈	—	38	1	no	—
144	C₄×C₈	—	38	1	no	—
145	C₄×C₈	—	38	1	no	—
146	C₄×C₈	—	38	1	no	—
147	C₄×C₈	C₄×D₁₉	1	2	yes	—
148	C₄×C₈	D₇₆	1	2	yes	—
149	C₁₉	#9836	1	1	yes	characteristic, complemented, Sylow
150	C₂×Q₈	—	38	4	no	—
151	C₂×Q₈	—	76	2	no	—
152	C₂×Q₈	—	76	4	no	—
153	C₂×Q₈	—	76	4	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	—	76	2	no	—
156	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
157	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
159	C₂×C₈	—	38	2	no	—
160	C₂×C₈	—	38	2	no	—
161	C₂×C₈	—	38	4	no	—
162	C₂×C₈	—	38	4	no	—
163	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
164	C₂×C₈	#64526	1	4	yes	—
165	C₂×C₈	#64528	1	4	yes	—
166	C₄⋊C₄	—	4	4	no	—
167	C₄⋊C₄	—	4	4	no	—
168	C₄⋊C₄	—	4	4	no	—
169	C₄⋊C₄	—	38	4	no	—
170	C₄⋊C₄	—	38	4	no	—
171	C₄⋊C₄	—	76	2	no	—
172	C₄⋊C₄	—	76	2	no	—
173	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₄²	C₂×D₇₆	1	1	yes	characteristic
175	C₄²	#64545	1	1	yes	characteristic
176	C₄²	#64545	1	1	yes	characteristic
177	C₂³	#10597386	1	1	yes	characteristic
178	Q₈	—	76	8	no	—
179	Q₈	—	152	4	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	76	4	no	—
184	C₂×C₄	—	152	2	no	—
185	C₂×C₄	—	152	2	no	—
186	C₂×C₄	#10597339	1	1	yes	characteristic
187	C₂×C₄	#10597339	1	1	yes	characteristic
188	C₂×C₄	#10597341	1	1	yes	characteristic
189	C₂×C₄	#10597341	1	1	yes	characteristic
190	C₂×C₄	#10597360	1	4	yes	—
191	C₂×C₄	#10597361	1	4	yes	—
192	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
193	C₂×C₄	C₂×#64526	1	2	yes	—
194	C₂×C₄	C₂×#64528	1	2	yes	—
195	C₂×C₄	#10597393	1	1	yes	characteristic
196	C₈	—	76	2	no	—
197	C₈	—	76	2	no	—
198	C₈	#10597267	1	8	yes	complemented
199	C₂²	#11926445	1	1	yes	characteristic
200	C₂²	#11926916	1	1	yes	characteristic
201	C₂²	#11926923	1	1	yes	characteristic
202	C₂²	#11926930	1	2	yes	—
203	C₂²	#11926935	1	2	yes	—
204	C₄	—	16	2	no	—
205	C₄	—	152	4	no	—
206	C₄	C₂×#10597267	1	2	yes	—
207	C₄	#11926650	1	2	yes	—
208	C₄	#11926655	1	2	yes	—
209	C₄	#11926798	1	2	yes	—
210	C₄	#11926803	1	2	yes	—
211	C₄	#11926896	1	2	yes	—
212	C₂	#14563254	1	2	yes	—
213	C₂	#14563309	1	2	yes	—
214	C₂	#14564436	1	1	yes	characteristic
215	C₂	#14564504	1	1	yes	characteristic
216	C₂	#14564509	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#9836
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
8. #11926949	C₄	semidirect
88. C₈×C₁₉	#103	semidirect
149. C₁₉	#9836	semidirect
198. C₈	#10597267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926949	2
#14564595	2
#14564436	2
C₂×#11926265	2
C₁₉×#1844	2
#9836	19