Subgroups — #18088368

Order 4864.

814 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926568	C₂	1	2	yes	maximal
2	C₂×#11926309	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₂²	1	4	yes	—
5	#11926568	—	2	4	no	—
6	#11926568	C₄	1	8	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
8	#11926309	—	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	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
14	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
15	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	4	yes	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	4	yes	—
26	C₂×#64520	—	2	4	no	—
27	C₂×#64520	—	2	8	no	—
28	C₂×#64520	—	2	8	no	—
29	C₂×#64520	C₂×C₄	1	8	yes	—
30	C₂²×C₁₉⋊C₈	—	2	4	no	—
31	C₄×C₈×C₁₉	—	2	4	no	—
32	C₄×C₈×C₁₉	—	2	4	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	16	no	—
34	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	2	8	no	—
36	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
37	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	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	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
45	C₂²×C₄×C₁₉	#41	1	4	yes	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	—	2	4	no	—
48	C₂×C₈×C₁₉	—	2	8	no	—
49	C₂×C₈×C₁₉	—	2	8	no	—
50	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
51	C₄²×C₁₉	C₄²	1	2	yes	—
52	C₄²×C₁₉	C₄²	1	2	yes	—
53	C₄²×C₁₉	C₂²⋊C₄	1	8	yes	—
54	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
56	#64520	—	2	16	no	—
57	#64520	—	4	8	no	—
58	C₂×C₁₉⋊C₈	—	2	8	no	—
59	C₂×C₁₉⋊C₈	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	#10844	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	—	2	4	no	—
63	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
64	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂³×C₁₉	#125	1	2	yes	—
66	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	16	no	—
69	C₂×C₄×C₁₉	#95	1	4	yes	—
70	C₂×C₄×C₁₉	#95	1	4	yes	—
71	C₂×C₄×C₁₉	#108	1	8	yes	—
72	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
75	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
76	C₂×C₄×C₁₉	#117	1	2	yes	—
77	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
78	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
79	C₂×C₄×C₁₉	#121	1	4	yes	—
80	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
81	C₂×C₄×C₁₉	#124	1	2	yes	—
82	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
84	C₈×C₁₉	—	2	8	no	—
85	C₁₉⋊C₈	—	4	8	no	—
86	C₂×#423	—	19	2	no	—
87	C₂²×C₄×C₈	D₁₉	1	1	yes	characteristic
88	C₂×#341	—	19	4	no	—
89	C₂²×C₁₉	—	2	4	no	—
90	C₂²×C₁₉	—	2	4	no	—
91	C₂²×C₁₉	—	2	4	no	—
92	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
93	C₂²×C₁₉	#382	1	1	yes	characteristic
94	C₂²×C₁₉	#384	1	1	yes	characteristic
95	C₂²×C₁₉	#389	1	4	yes	—
96	C₂²×C₁₉	C₂×#108	1	4	yes	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	#341	1	8	yes	complemented
99	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
100	C₄×C₁₉	#380	1	2	yes	—
101	C₄×C₁₉	#390	1	2	yes	—
102	C₄×C₁₉	#391	1	2	yes	—
103	C₂²×M₁₆	—	19	4	no	—
104	C₂³×C₈	C₂×D₁₉	1	2	yes	—
105	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
106	#423	—	19	8	no	—
107	#423	—	38	4	no	—
108	C₂×C₄⋊C₈	—	38	4	no	—
109	C₂×C₄×C₈	—	2	4	no	—
110	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
111	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
112	#341	—	38	8	no	—
113	C₂×C₁₉	—	2	4	no	—
114	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
115	C₂×C₁₉	C₂×#341	1	2	yes	—
116	C₂×C₁₉	#1837	1	2	yes	—
117	C₂×C₁₉	#1848	1	2	yes	—
118	C₂³×C₄	Dic₃₈	1	2	yes	—
119	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂×M₁₆	—	19	8	no	—
121	C₂×M₁₆	—	38	4	no	—
122	C₂×M₁₆	—	38	8	no	—
123	C₂×M₁₆	—	38	8	no	—
124	C₂²×C₈	—	2	4	no	—
125	C₂²×C₈	—	2	4	no	—
126	C₂²×C₈	—	38	4	no	—
127	C₂²×C₈	Dic₃₈	1	4	yes	—
128	C₂²×C₈	D₇₆	1	4	yes	—
129	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
130	C₂×C₄²	C₄×D₁₉	1	4	yes	—
131	C₂×C₄²	D₇₆	1	2	yes	—
132	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
135	C₄⋊C₈	—	38	16	no	—
136	C₄×C₈	—	2	4	no	—
137	C₄×C₈	—	2	4	no	—
138	C₁₉	#10844	1	1	yes	characteristic, complemented, Sylow
139	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
140	C₂²×C₄	—	2	8	no	—
141	C₂²×C₄	Dic₁₉⋊C₄	1	8	yes	—
142	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
143	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
144	C₂²×C₄	C₂×Dic₃₈	1	2	yes	—
145	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
146	C₂²×C₄	C₂×D₇₆	1	2	yes	—
147	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
148	C₂²×C₄	#64541	1	4	yes	—
149	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
151	M₁₆	—	38	16	no	—
152	M₁₆	—	76	8	no	—
153	C₂×C₈	—	2	8	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	—	2	8	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	38	8	no	—
158	C₂×C₈	—	76	4	no	—
159	C₂×C₈	—	76	4	no	—
160	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
161	C₄²	C₄×Dic₁₉	1	2	yes	—
162	C₄²	C₄×Dic₁₉	1	2	yes	—
163	C₄²	(C₂×D₁₉)⋊C₄	1	8	yes	—
164	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
165	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
166	C₂³	—	2	4	no	—
167	C₂³	#10597315	1	2	yes	—
168	C₂³	#10597316	1	2	yes	—
169	C₂³	C₂×Dic₁₉⋊C₄	1	2	yes	—
170	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	16	no	—
173	C₂×C₄	#10597276	1	8	yes	—
174	C₂×C₄	C₁₉⋊#95	1	4	yes	—
175	C₂×C₄	C₁₉⋊#95	1	4	yes	—
176	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
177	C₂×C₄	#10597315	1	1	yes	characteristic
178	C₂×C₄	C₄×D₇₆	1	4	yes	—
179	C₂×C₄	#10597320	1	1	yes	characteristic
180	C₂×C₄	#10597321	1	2	yes	—
181	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
182	C₂×C₄	#10597370	1	4	yes	—
183	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
184	C₂×C₄	#10597372	1	2	yes	—
185	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
186	C₂×C₄	#10597376	1	4	yes	—
187	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
188	C₈	—	2	8	no	—
189	C₈	—	76	8	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
194	C₂²	#11926410	1	1	yes	characteristic
195	C₂²	#11926414	1	1	yes	characteristic
196	C₂²	#11926442	1	4	yes	—
197	C₂²	C₂×#10597276	1	4	yes	—
198	C₄	—	2	4	no	—
199	C₄	#11926309	1	8	yes	complemented
200	C₄	C₄×C₄⋊Dic₁₉	1	2	yes	—
201	C₄	#11926404	1	2	yes	—
202	C₄	#11926446	1	2	yes	—
203	C₄	#11926450	1	2	yes	—
204	C₂	—	2	4	no	—
205	C₂	#14561865	1	1	yes	characteristic
206	C₂	C₂×#11926309	1	2	yes	—
207	C₂	#14563773	1	2	yes	—
208	C₂	#14563807	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₄×C₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄×C₈	D₁₉
hypocenter	C₁₉	#10844
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
98. C₄×C₁₉	#341	semidirect
138. C₁₉	#10844	semidirect
199. C₄	#11926309	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926568	2
C₂×#11926309	2
C₂²×C₄×C₈×C₁₉	2
#10844	19