Subgroups — C₂×C₁₆×#1057 #16786570

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718257	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1057	C₂	1	1	yes	maximal, characteristic
3	C₁₆×#1057	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#1057	C₄	1	2	yes	—
6	C₂²×#6092	C₄	1	2	yes	—
7	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
8	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6090	C₄	1	1	yes	characteristic
10	#11718257	C₄	1	2	yes	—
11	#11718257	C₂²	1	2	yes	—
12	C₈×#1057	C₄	1	2	yes	—
13	C₈×#1057	C₂²	1	2	yes	—
14	C₁₆×Dic₁₃	C₄	1	2	yes	—
15	C₁₆×Dic₁₃	C₂²	1	2	yes	—
16	C₂²×#1057	C₈	1	4	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
20	C₄×#1057	C₈	1	4	yes	—
21	C₄×#1057	C₂×C₄	1	4	yes	—
22	C₂×#6092	C₈	1	8	yes	complemented
23	C₂×#6092	C₂×C₄	1	4	yes	—
24	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
25	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
26	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
30	C₂×#6090	C₈	1	4	yes	complemented
31	C₂×#6090	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₁₆	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
34	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
35	C₂×#1057	C₁₆	1	16	yes	direct product factor
36	C₂×#1057	C₂×C₈	1	8	yes	—
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
39	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
42	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
43	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×#1055	C₄²	1	1	yes	characteristic
45	C₂×#1055	C₂×C₈	1	4	yes	—
46	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
47	#6092	C₂×C₈	1	8	yes	complemented
48	C₁₃×C₁₆	C₂×C₈	1	4	yes	complemented
49	#6090	C₂×C₈	1	4	yes	complemented
50	C₂×C₄×C₁₆	—	13	1	no	—
51	C₂×C₄×C₁₆	—	13	1	no	—
52	C₂×C₈²	—	13	1	no	—
53	C₈×C₁₆	—	13	4	no	—
54	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
57	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
60	C₂×Dic₁₃	C₂×C₁₆	1	8	yes	—
61	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
62	#1057	C₂×C₁₆	1	16	yes	direct product factor
63	C₈×C₁₃	C₄×C₈	1	2	yes	—
64	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
65	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
66	#1055	C₄×C₈	1	2	yes	—
67	#1055	C₂²×C₈	1	2	yes	—
68	C₂²×C₁₆	—	13	2	no	—
69	C₂²×C₁₆	—	13	1	no	—
70	C₂²×C₁₆	#261	1	1	yes	characteristic
71	C₂×C₄×C₈	—	13	2	no	—
72	C₂×C₄×C₈	—	13	1	no	—
73	C₄×C₁₆	—	13	2	no	—
74	C₄×C₁₆	—	13	2	no	—
75	C₄×C₁₆	—	13	2	no	—
76	C₄×C₁₆	—	13	2	no	—
77	C₈²	—	13	2	no	—
78	C₈²	—	13	2	no	—
79	C₂²×C₁₃	C₈²	1	2	yes	—
80	C₂²×C₁₃	C₄×C₁₆	1	4	yes	—
81	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
82	C₄×C₁₃	C₈²	1	2	yes	—
83	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
84	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
85	Dic₁₃	C₄×C₁₆	1	4	yes	—
86	Dic₁₃	C₂²×C₁₆	1	4	yes	—
87	C₂²×C₈	—	13	4	no	—
88	C₂²×C₈	—	13	1	no	—
89	C₂²×C₈	C₂×#261	1	1	yes	characteristic
90	C₂×C₄²	—	13	1	no	—
91	C₂×C₁₆	—	13	8	no	—
92	C₂×C₁₆	—	13	4	no	—
93	C₂×C₁₆	—	13	4	no	—
94	C₂×C₁₆	—	13	2	no	—
95	C₂×C₁₆	#1057	1	4	yes	direct product factor
96	C₂×C₁₆	C₂×#261	1	2	yes	—
97	C₄×C₈	—	13	4	no	—
98	C₄×C₈	—	13	4	no	—
99	C₄×C₈	—	13	1	no	—
100	C₄×C₈	—	13	1	no	—
101	C₄×C₈	—	13	1	no	—
102	C₄×C₈	—	13	1	no	—
103	C₂×C₁₃	C₈×C₁₆	1	4	yes	complemented
104	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
105	C₂×C₁₃	C₂×C₄×C₁₆	1	2	yes	—
106	C₂²×C₄	—	13	2	no	—
107	C₂²×C₄	C₄×#261	1	1	yes	characteristic
108	C₂×C₈	—	13	8	no	—
109	C₂×C₈	—	13	16	no	—
110	C₂×C₈	—	13	4	no	—
111	C₂×C₈	—	13	1	no	—
112	C₂×C₈	—	13	1	no	—
113	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
114	C₂×C₈	C₄×#261	1	1	yes	characteristic
115	C₂×C₈	C₂×#1057	1	2	yes	—
116	C₂×C₈	C₂²×#261	1	1	yes	characteristic
117	C₄²	—	13	2	no	—
118	C₄²	—	13	1	no	—
119	C₄²	—	13	1	no	—
120	C₁₆	—	13	8	no	—
121	C₁₆	—	13	4	no	—
122	C₁₆	C₂×#1057	1	4	yes	direct product factor
123	C₁₃	C₂×C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
124	C₂³	C₈×#261	1	1	yes	characteristic
125	C₂×C₄	—	13	8	no	—
126	C₂×C₄	—	13	2	no	—
127	C₂×C₄	—	13	2	no	—
128	C₂×C₄	C₈×#261	1	1	yes	characteristic
129	C₂×C₄	C₈×#261	1	2	yes	—
130	C₂×C₄	C₄×#1057	1	2	yes	—
131	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
132	C₈	—	13	16	no	—
133	C₈	—	13	2	no	—
134	C₈	—	13	2	no	—
135	C₈	C₄×#1057	1	2	yes	—
136	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
137	C₈	C₂²×#1057	1	1	yes	characteristic
138	C₂²	C₁₆×#261	1	4	yes	—
139	C₂²	C₈×#1057	1	2	yes	—
140	C₂²	C₂×C₈×#261	1	1	yes	characteristic
141	C₄	—	13	4	no	—
142	C₄	—	13	4	no	—
143	C₄	C₈×#1057	1	2	yes	—
144	C₄	C₂×C₈×#261	1	1	yes	characteristic
145	C₄	C₂×C₄×#1057	1	1	yes	characteristic
146	C₂	C₁₆×#1057	1	4	yes	direct product factor
147	C₂	C₂×C₈×#1057	1	1	yes	characteristic
148	C₂	C₂×C₁₆×#261	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	#261
commutator, hypocenter	C₁₃	C₂×C₈×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle, prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₈×Dic₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₁₆×#1057	C₂	direct (N × H)
22. C₂×#6092	C₈	semidirect
24. C₂×C₁₃×C₁₆	C₈	semidirect
30. C₂×#6090	C₈	semidirect
35. C₂×#1057	C₁₆	direct (N × H)
47. #6092	C₂×C₈	semidirect
48. C₁₃×C₁₆	C₂×C₈	semidirect
49. #6090	C₂×C₈	semidirect
62. #1057	C₂×C₁₆	direct (N × H)
95. C₂×C₁₆	#1057	direct (N × H)
103. C₂×C₁₃	C₈×C₁₆	semidirect
122. C₁₆	C₂×#1057	direct (N × H)
123. C₁₃	C₂×C₈×C₁₆	semidirect
146. C₂	C₁₆×#1057	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×#11718257	2
C₂×C₈×#1057	2
C₁₆×#1057	2
C₂×C₁₆×Dic₁₃	2
C₂×C₈×C₁₆	13

Subgroups — C2×C16×#1057 #16786570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×#1057 #16786570