Subgroups — C₄×#11926309 #18087726

Order 4864.

910 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	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	C₄×#64520	—	2	4	no	—
6	C₄×#64520	C₄	1	8	yes	—
7	C₂×#10597260	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926309	C₄	1	16	yes	direct product factor
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	—	2	4	no	—
13	C₂×C₄×C₈×C₁₉	C₄	1	4	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	8	yes	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	4	yes	—
25	C₂×#64520	—	2	4	no	—
26	C₂×#64520	—	2	8	no	—
27	C₂×#64520	C₂×C₄	1	16	yes	—
28	C₂×#64520	C₂×C₄	1	8	yes	—
29	C₂²×C₁₉⋊C₈	—	2	4	no	—
30	C₄×C₈×C₁₉	—	2	8	no	—
31	#10597260	—	2	8	no	—
32	C₄×C₁₉⋊C₈	—	2	8	no	—
33	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	—	2	8	no	—
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
36	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂²×C₄×C₁₉	#41	1	4	yes	—
44	C₂×C₈×C₁₉	—	2	4	no	—
45	C₂×C₈×C₁₉	—	2	4	no	—
46	C₂×C₈×C₁₉	—	2	16	no	—
47	C₂×C₈×C₁₉	C₄²	1	8	yes	—
48	C₄²×C₁₉	C₄²	1	4	yes	—
49	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
52	#64520	—	2	8	no	—
53	#64520	—	2	16	no	—
54	#64520	C₄²	1	16	yes	—
55	C₂×C₁₉⋊C₈	—	2	8	no	—
56	C₂×C₁₉⋊C₈	—	2	16	no	—
57	C₄×#341	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	—	2	4	no	—
59	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
60	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	2	16	no	—
64	C₂×C₄×C₁₉	#95	1	4	yes	—
65	C₂×C₄×C₁₉	#95	1	4	yes	—
66	C₂×C₄×C₁₉	#108	1	8	yes	—
67	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
68	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
72	C₂×C₄×C₁₉	#117	1	4	yes	—
73	C₂×C₄×C₁₉	#117	1	2	yes	—
74	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
75	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
76	C₈×C₁₉	—	2	8	no	—
77	C₁₉⋊C₈	—	2	16	no	—
78	C₂×C₄×M₁₆	—	19	2	no	—
79	C₂²×C₄×C₈	D₁₉	1	1	yes	characteristic
80	C₂×#341	—	19	4	no	—
81	C₂²×C₁₉	—	2	4	no	—
82	C₂²×C₁₉	—	2	8	no	—
83	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
84	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
85	C₂²×C₁₉	C₄×C₄⋊C₄	1	4	yes	—
86	C₂²×C₁₉	C₂×#108	1	4	yes	—
87	C₄×C₁₉	—	2	4	no	—
88	C₄×C₁₉	#341	1	8	yes	complemented
89	C₄×C₁₉	C₄³	1	1	yes	characteristic
90	C₄×C₁₉	#376	1	1	yes	characteristic
91	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
92	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
93	C₂²×M₁₆	—	19	4	no	—
94	C₂³×C₈	C₂×D₁₉	1	2	yes	—
95	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
96	C₄×M₁₆	—	19	8	no	—
97	C₄×M₁₆	—	38	4	no	—
98	C₂×#97	—	38	2	no	—
99	C₂×C₄×C₈	—	2	4	no	—
100	C₂×C₄×C₈	—	38	2	no	—
101	C₂×C₄×C₈	Dic₁₉	1	4	yes	—
102	#341	—	19	16	no	—
103	C₂×C₁₉	—	2	4	no	—
104	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
105	C₂×C₁₉	C₂×#341	1	2	yes	—
106	C₂×C₁₉	C₄×#108	1	4	yes	—
107	C₂³×C₄	Dic₃₈	1	2	yes	—
108	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
109	C₂×M₁₆	—	19	16	no	—
110	C₂×M₁₆	—	19	8	no	—
111	C₂×M₁₆	—	38	8	no	—
112	C₂×M₁₆	—	38	4	no	—
113	C₂²×C₈	—	2	4	no	—
114	C₂²×C₈	—	2	4	no	—
115	C₂²×C₈	—	38	4	no	—
116	C₂²×C₈	C₄×D₁₉	1	8	yes	—
117	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
118	C₂×C₄²	C₄×D₁₉	1	4	yes	—
119	C₂×C₄²	D₇₆	1	1	yes	characteristic
120	C₂×C₄²	D₇₆	1	1	yes	characteristic
121	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
122	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
123	#97	—	38	8	no	—
124	C₄×C₈	—	2	8	no	—
125	C₄×C₈	—	38	8	no	—
126	C₁₉	C₄×#341	1	1	yes	characteristic, complemented, Sylow
127	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
128	C₂²×C₄	—	2	8	no	—
129	C₂²×C₄	Dic₁₉⋊C₄	1	8	yes	—
130	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
131	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
132	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
133	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
134	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
135	C₂²×C₄	#64541	1	4	yes	—
136	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
138	M₁₆	—	19	16	no	—
139	M₁₆	—	38	8	no	—
140	M₁₆	—	38	16	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	16	no	—
144	C₂×C₈	—	38	16	no	—
145	C₂×C₈	—	38	8	no	—
146	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
147	C₄²	C₄×Dic₁₉	1	4	yes	—
148	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
149	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
150	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
151	C₂³	—	2	4	no	—
152	C₂³	C₄×Dic₃₈	1	4	yes	—
153	C₂³	C₂×Dic₁₉⋊C₄	1	2	yes	—
154	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	16	no	—
157	C₂×C₄	#10597276	1	8	yes	—
158	C₂×C₄	C₁₉⋊#95	1	4	yes	—
159	C₂×C₄	C₁₉⋊#95	1	4	yes	—
160	C₂×C₄	C₄²×D₁₉	1	4	yes	—
161	C₂×C₄	#10597318	1	4	yes	—
162	C₂×C₄	C₄×D₇₆	1	4	yes	—
163	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
164	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
165	C₂×C₄	#10597372	1	2	yes	—
166	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
167	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
168	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
169	C₈	—	2	8	no	—
170	C₈	—	38	16	no	—
171	C₂²	—	2	4	no	—
172	C₂²	—	2	8	no	—
173	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
174	C₂²	C₄×C₄⋊Dic₁₉	1	2	yes	—
175	C₂²	C₄×Dic₁₉⋊C₄	1	4	yes	—
176	C₂²	C₂×#10597276	1	4	yes	—
177	C₄	—	2	4	no	—
178	C₄	#11926309	1	8	yes	direct product factor
179	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
180	C₄	#11926390	1	1	yes	characteristic
181	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
182	C₄	C₄×(C₂×D₁₉)⋊C₄	1	4	yes	—
183	C₂	—	2	4	no	—
184	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
185	C₂	C₂×#11926309	1	2	yes	—
186	C₂	C₄×#10597276	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	D₇₆
commutator	C₄×C₁₉	C₄³
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	C₄×#341
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. #11926309	C₄	direct (N × H)
88. C₄×C₁₉	#341	semidirect
126. C₁₉	C₄×#341	semidirect
178. C₄	#11926309	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
C₂×#11926309	2
C₂²×C₄×C₈×C₁₉	2
C₄×#341	19

Subgroups — C4×#11926309 #18087726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926309 #18087726