Subgroups — C₈×#10597293 #18073102

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597293	C₂	1	1	yes	maximal, characteristic
2	#14561959	C₂	1	1	yes	maximal, characteristic
3	C₈×#64520	C₂	1	2	yes	maximal
4	#14561485	C₂	1	2	yes	maximal
5	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597293	C₄	1	2	yes	—
8	C₄×#64520	C₂²	1	2	yes	—
9	#11926313	C₄	1	2	yes	—
10	#11926270	C₄	1	4	yes	—
11	#11926266	—	2	2	no	—
12	C₈×C₁₉⋊C₈	—	2	2	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₈×Q₈×C₁₉	—	2	2	no	—
15	C₈×Q₈×C₁₉	—	2	2	no	—
16	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64520	C₂×C₄	1	4	yes	—
31	C₁₉×C₄⋊C₈	—	2	4	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₄×C₈×C₁₉	—	2	2	no	—
34	C₄×C₈×C₁₉	—	2	2	no	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	C₄×C₈×C₁₉	D₄	1	2	yes	—
37	#10597293	C₈	1	8	yes	direct product factor
38	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	#10597260	—	2	2	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	C₂×C₈	1	4	yes	—
46	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	#64520	—	2	4	no	—
65	#64520	C₂×C₈	1	8	yes	—
66	C₂×C₁₉⋊C₈	—	2	4	no	—
67	C₂×C₁₉⋊C₈	—	2	4	no	—
68	C₈×#101	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	Q₈×C₁₉	—	2	8	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
84	C₂×C₄×C₁₉	#131	1	2	yes	—
85	C₈×C₁₉	—	2	1	no	—
86	C₈×C₁₉	—	2	2	no	—
87	C₈×C₁₉	—	4	2	no	—
88	C₈×C₁₉	#101	1	2	yes	complemented
89	C₁₉⋊C₈	—	2	8	no	—
90	C₁₉⋊C₈	—	4	4	no	—
91	C₂×C₈×Q₈	D₁₉	1	1	yes	characteristic
92	C₄×#101	—	19	1	no	—
93	#1461	—	19	1	no	—
94	C₈×M₁₆	—	19	2	no	—
95	#1283	—	19	2	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
100	C₂²×C₁₉	#405	1	1	yes	characteristic
101	C₄×C₁₉	—	2	4	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
106	C₄×C₁₉	#413	1	1	yes	characteristic
107	C₄×C₁₉	C₈×D₄	1	4	yes	—
108	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
109	C₈×Q₈	—	2	2	no	—
110	C₈×Q₈	—	2	2	no	—
111	#431	—	19	2	no	—
112	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
113	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
114	C₂×#101	—	19	2	no	—
115	C₄×M₁₆	—	19	2	no	—
116	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
117	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
118	#343	—	19	2	no	—
119	#324	—	19	4	no	—
120	#322	—	38	2	no	—
121	C₈²	—	38	2	no	—
122	C₂×C₁₉	—	2	1	no	—
123	C₂×C₁₉	—	2	1	no	—
124	C₂×C₁₉	C₈×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
126	C₂×C₁₉	#1757	1	1	yes	characteristic
127	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
128	C₂×M₁₆	—	19	4	no	—
129	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
130	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
131	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
132	C₄×Q₈	—	2	2	no	—
133	C₄×Q₈	—	2	2	no	—
134	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
135	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
137	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₈	—	2	4	no	—
139	C₄⋊C₈	—	2	2	no	—
140	C₄⋊C₈	—	38	2	no	—
141	#101	—	19	8	no	—
142	C₂²⋊C₈	—	19	4	no	—
143	#97	—	38	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	—	2	2	no	—
146	C₄×C₈	—	38	2	no	—
147	C₄×C₈	—	38	2	no	—
148	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
149	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
150	C₁₉	C₈×#101	1	1	yes	characteristic, complemented, Sylow
151	C₂×Q₈	—	2	2	no	—
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	C₈×D₁₉	1	4	yes	—
154	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
155	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
156	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
159	M₁₆	—	19	8	no	—
160	M₁₆	—	38	4	no	—
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	4	1	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	38	4	no	—
166	C₂×C₈	—	38	4	no	—
167	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
168	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
169	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	#64541	1	2	yes	—
175	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
176	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
177	Q₈	—	2	8	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	1	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	C₈×Dic₁₉	1	4	yes	—
186	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
187	C₂×C₄	#10597347	1	2	yes	—
188	C₂×C₄	#10597372	1	1	yes	characteristic
189	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
190	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
192	C₈	—	2	2	no	—
193	C₈	—	2	1	no	—
194	C₈	—	4	2	no	—
195	C₈	—	38	8	no	—
196	C₈	—	76	4	no	—
197	C₈	#10597293	1	2	yes	direct product factor
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
201	C₂²	C₂×C₈×Dic₁₉	1	1	yes	characteristic
202	C₂²	#11926499	1	1	yes	characteristic
203	C₄	—	2	4	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	2	no	—
207	C₄	C₂×#10597293	1	1	yes	characteristic
208	C₄	#11926528	1	1	yes	characteristic
209	C₄	C₈×C₂²⋊D₁₉	1	4	yes	—
210	C₂	—	2	1	no	—
211	C₂	—	2	1	no	—
212	C₂	C₈×C₂²⋊Dic₁₉	1	1	yes	characteristic
213	C₂	C₄×#10597293	1	1	yes	characteristic
214	C₂	#14563435	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈×Q₈	D₁₉
hypocenter	C₁₉	C₈×#101
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
37. #10597293	C₈	direct (N × H)
88. C₈×C₁₉	#101	semidirect
150. C₁₉	C₈×#101	semidirect
197. C₈	#10597293	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10597293	2
#14561959	2
C₈×#64520	2
#14561485	2
C₂×C₈×Q₈×C₁₉	2
C₈×#101	19

Subgroups — C8×#10597293 #18073102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#10597293 #18073102