Subgroups — #18075471

Order 4864.

398 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563631	C₂	1	2	yes	maximal
2	#14562394	C₂	1	2	yes	maximal
3	#14561510	C₂	1	2	yes	maximal
4	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	C₂×#10597293	—	2	2	no	—
7	#11926313	—	2	2	no	—
8	#11926297	—	2	2	no	—
9	#11926297	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₈×Q₈×C₁₉	—	2	2	no	—
12	C₈×Q₈×C₁₉	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×#64520	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	2	4	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	C₄×C₈×C₁₉	—	2	2	no	—
32	C₄×C₈×C₁₉	D₄	1	2	yes	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	#10597293	—	4	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂×Q₈×C₁₉	D₈	1	2	yes	—
40	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	—	4	2	no	—
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	#41	1	2	yes	—
59	#64520	—	4	4	no	—
60	#64520	—	4	4	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	#8617	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	Q₈×C₁₉	—	2	4	no	—
65	Q₈×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	4	1	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	#107	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	2	yes	—
77	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#135	1	2	yes	—
81	C₈×C₁₉	—	2	1	no	—
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	—	4	2	no	—
84	C₈×C₁₉	#101	1	2	yes	complemented
85	C₁₉⋊C₈	—	8	4	no	—
86	C₂×C₈×Q₈	D₁₉	1	1	yes	characteristic
87	#1801	—	19	2	no	—
88	#1567	—	19	2	no	—
89	#1292	—	19	2	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	#380	1	1	yes	characteristic
93	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
94	C₂²×C₁₉	#427	1	1	yes	characteristic
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
100	C₄×C₁₉	#413	1	1	yes	characteristic
101	C₄×C₁₉	#466	1	2	yes	—
102	C₄×C₁₉	#467	1	2	yes	—
103	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
104	C₈×Q₈	—	2	2	no	—
105	C₈×Q₈	—	2	2	no	—
106	#423	—	19	4	no	—
107	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
108	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
109	C₂×#101	—	38	2	no	—
110	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
111	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
112	#343	—	38	2	no	—
113	#335	—	38	2	no	—
114	#335	—	38	2	no	—
115	C₂×C₁₉	—	2	1	no	—
116	C₂×C₁₉	—	2	1	no	—
117	C₂×C₁₉	#1801	1	1	yes	characteristic
118	C₂×C₁₉	#1808	1	1	yes	characteristic
119	C₂×C₁₉	#1813	1	1	yes	characteristic
120	C₂²×Q₈	D₇₆	1	1	yes	characteristic
121	C₂×M₁₆	—	38	4	no	—
122	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
123	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
124	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
125	C₄×Q₈	—	2	2	no	—
126	C₄×Q₈	—	2	2	no	—
127	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
128	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
129	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
130	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
131	C₄⋊C₈	—	2	4	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	38	4	no	—
134	C₄⋊C₈	—	38	4	no	—
135	#101	—	76	4	no	—
136	C₄×C₈	—	2	2	no	—
137	C₄×C₈	—	2	2	no	—
138	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
139	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₁₉	#8617	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	—	2	2	no	—
143	C₂×Q₈	D₁₅₂	1	2	yes	—
144	C₂×Q₈	Dic₇₆	1	2	yes	—
145	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
146	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
147	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
148	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
149	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
150	M₁₆	—	76	4	no	—
151	M₁₆	—	76	4	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	4	1	no	—
155	C₂×C₈	—	4	2	no	—
156	C₂×C₈	—	76	4	no	—
157	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
158	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
159	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	2	2	no	—
164	C₄²	#64541	1	2	yes	—
165	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
166	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
167	Q₈	—	2	4	no	—
168	Q₈	—	2	4	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	#10597275	1	4	yes	—
177	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
178	C₂×C₄	#10597350	1	2	yes	—
179	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
180	C₂×C₄	#10597370	1	2	yes	—
181	C₂×C₄	#10597372	1	1	yes	characteristic
182	C₂×C₄	#10597376	1	2	yes	—
183	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
184	C₈	—	2	2	no	—
185	C₈	—	2	1	no	—
186	C₈	—	4	2	no	—
187	C₈	—	152	4	no	—
188	C₈	#10597293	1	2	yes	complemented
189	C₂²	—	2	1	no	—
190	C₂²	—	2	1	no	—
191	C₂²	#11926404	1	1	yes	characteristic
192	C₂²	C₂×#10597275	1	1	yes	characteristic
193	C₂²	#11926582	1	1	yes	characteristic
194	C₄	—	2	1	no	—
195	C₄	—	2	4	no	—
196	C₄	—	2	2	no	—
197	C₄	—	4	2	no	—
198	C₄	C₂×#10597293	1	1	yes	characteristic
199	C₄	#11926528	1	1	yes	characteristic
200	C₄	#11926780	1	2	yes	—
201	C₄	#11926785	1	2	yes	—
202	C₂	—	2	1	no	—
203	C₂	—	2	1	no	—
204	C₂	#14563631	1	1	yes	characteristic
205	C₂	#14563664	1	1	yes	characteristic
206	C₂	#14563685	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈×Q₈	D₁₉
hypocenter	C₁₉	#8617
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
84. C₈×C₁₉	#101	semidirect
140. C₁₉	#8617	semidirect
188. C₈	#10597293	semidirect

Maximal subgroups

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

subgroup	index
#14563631	2
#14562394	2
#14561510	2
C₂×C₈×Q₈×C₁₉	2
#8617	19