Subgroups — C₄×C₁₆×#261 #16789009

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×#261	C₂	1	4	yes	maximal
3	C₄×C₈×#261	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×#261	C₄	1	2	yes	—
6	C₂×C₈×#261	C₂²	1	2	yes	—
7	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
8	C₄²×#261	C₄	1	1	yes	characteristic
9	C₄×D₁₃⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
11	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11718257	C₄	1	2	yes	complemented
13	C₄×#6092	C₄	1	2	yes	complemented
14	C₁₆×#261	C₄	1	16	yes	direct product factor
15	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic, complemented
16	C₁₆×Dic₁₃	C₄	1	2	yes	complemented
17	C₄×#6090	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×#261	C₈	1	4	yes	—
19	C₂×C₄×#261	C₂×C₄	1	2	yes	—
20	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
23	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×#1057	C₈	1	4	yes	—
25	C₂×#6092	C₂×C₄	1	4	yes	—
26	C₈×#261	C₈	1	8	yes	—
27	C₈×#261	C₂×C₄	1	8	yes	—
28	D₁₃⋊C₁₆	C₂×C₄	1	8	yes	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	C₄×#1055	C₂×C₄	1	1	yes	characteristic
35	C₁₆×D₁₃	C₂×C₄	1	8	yes	—
36	C₄²×C₁₆	—	13	1	no	maximal, Sylow
37	C₂²×#261	C₂×C₈	1	4	yes	—
38	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
39	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×#1057	C₂×C₈	1	4	yes	—
41	C₄×#261	C₁₆	1	16	yes	direct product factor
42	C₄×#261	C₄²	1	4	yes	—
43	C₄×#261	C₂×C₈	1	4	yes	—
44	D₁₃⋊C₈	C₄²	1	4	yes	—
45	D₁₃⋊C₈	C₂×C₈	1	4	yes	—
46	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₄²×C₁₃	C₄²	1	1	yes	characteristic
49	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
50	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
51	C₂×#1055	C₄²	1	1	yes	characteristic
52	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
53	C₈×D₁₃	C₂×C₈	1	4	yes	—
54	C₈×D₁₃	C₂²×C₄	1	4	yes	—
55	#6092	C₄²	1	8	yes	complemented
56	C₁₃×C₁₆	C₄²	1	4	yes	complemented
57	#6090	C₄²	1	4	yes	complemented
58	C₂×C₄×C₁₆	—	13	4	no	—
59	C₂×C₄×C₁₆	—	13	1	no	—
60	C₂×C₄×C₁₆	—	13	1	no	—
61	C₄²×C₈	—	13	1	no	—
62	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
63	C₂×#261	C₄×C₈	1	8	yes	—
64	C₂×#261	C₂×C₁₆	1	16	yes	—
65	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
66	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
68	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
69	C₄×D₁₃	C₂×C₁₆	1	8	yes	—
70	C₄×D₁₃	C₂×C₄²	1	2	yes	—
71	C₄×D₁₃	C₂²×C₈	1	2	yes	—
72	#1057	C₄×C₈	1	8	yes	—
73	C₈×C₁₃	C₄×C₈	1	2	yes	—
74	C₈×C₁₃	C₂×C₄²	1	2	yes	—
75	#1055	C₄×C₈	1	2	yes	—
76	#1055	C₂×C₄²	1	2	yes	—
77	C₂²×C₁₆	—	13	2	no	—
78	C₂²×C₁₆	—	13	2	no	—
79	C₂×C₄×C₈	—	13	2	no	—
80	C₂×C₄×C₈	—	13	1	no	—
81	C₂×C₄×C₈	—	13	2	no	—
82	C₂×C₄×C₈	—	13	1	no	—
83	C₄³	—	13	1	no	—
84	C₄×C₁₆	—	13	16	no	—
85	C₄×C₁₆	—	13	2	no	—
86	C₄×C₁₆	—	13	2	no	—
87	C₄×C₁₆	—	13	2	no	—
88	C₄×C₁₆	—	13	1	no	—
89	C₄×C₁₆	#261	1	1	yes	characteristic, direct product factor
90	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
92	C₂×D₁₃	C₂²×C₁₆	1	4	yes	—
93	#261	C₄×C₁₆	1	16	yes	direct product factor
94	C₄×C₁₃	C₄×C₁₆	1	4	yes	complemented
95	C₄×C₁₃	C₄³	1	1	yes	characteristic
96	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
97	Dic₁₃	C₄×C₁₆	1	4	yes	complemented
98	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
99	C₂²×C₈	—	13	2	no	—
100	C₂²×C₈	—	13	1	no	—
101	C₂²×C₈	—	13	1	no	—
102	C₂×C₄²	—	13	2	no	—
103	C₂×C₄²	—	13	4	no	—
104	C₂×C₄²	—	13	1	no	—
105	C₂×C₁₆	—	13	8	no	—
106	C₂×C₁₆	—	13	4	no	—
107	C₂×C₁₆	—	13	2	no	—
108	C₂×C₁₆	—	13	8	no	—
109	C₂×C₁₆	C₂×#261	1	2	yes	—
110	C₄×C₈	—	13	8	no	—
111	C₄×C₈	—	13	8	no	—
112	C₄×C₈	—	13	4	no	—
113	C₄×C₈	—	13	1	no	—
114	C₄×C₈	—	13	1	no	—
115	C₄×C₈	—	13	1	no	—
116	C₄×C₈	C₂×#261	1	1	yes	characteristic
117	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
118	C₂×C₁₃	C₂×C₄×C₁₆	1	2	yes	—
119	D₁₃	C₂×C₄×C₁₆	1	4	yes	—
120	C₂²×C₄	—	13	4	no	—
121	C₂²×C₄	—	13	2	no	—
122	C₂²×C₄	—	13	1	no	—
123	C₂×C₈	—	13	4	no	—
124	C₂×C₈	—	13	4	no	—
125	C₂×C₈	—	13	4	no	—
126	C₂×C₈	—	13	1	no	—
127	C₂×C₈	—	13	1	no	—
128	C₂×C₈	—	13	4	no	—
129	C₂×C₈	—	13	4	no	—
130	C₂×C₈	C₄×#261	1	1	yes	characteristic
131	C₂×C₈	C₂²×#261	1	1	yes	characteristic
132	C₄²	—	13	4	no	—
133	C₄²	—	13	4	no	—
134	C₄²	—	13	16	no	—
135	C₄²	—	13	2	no	—
136	C₄²	—	13	1	no	—
137	C₄²	C₄×#261	1	1	yes	characteristic
138	C₁₆	—	13	8	no	—
139	C₁₆	—	13	4	no	—
140	C₁₆	C₄×#261	1	4	yes	direct product factor
141	C₁₃	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
142	C₂³	—	13	1	no	—
143	C₂×C₄	—	13	8	no	—
144	C₂×C₄	—	13	16	no	—
145	C₂×C₄	—	13	1	no	—
146	C₂×C₄	—	13	2	no	—
147	C₂×C₄	—	13	8	no	—
148	C₂×C₄	—	13	2	no	—
149	C₂×C₄	—	13	2	no	—
150	C₂×C₄	C₈×#261	1	2	yes	—
151	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
152	C₈	—	13	8	no	—
153	C₈	—	13	2	no	—
154	C₈	—	13	2	no	—
155	C₈	C₈×#261	1	2	yes	—
156	C₈	C₂×C₄×#261	1	2	yes	—
157	C₂²	—	13	4	no	—
158	C₂²	—	13	2	no	—
159	C₂²	C₂×C₈×#261	1	1	yes	characteristic
160	C₄	—	13	16	no	—
161	C₄	—	13	4	no	—
162	C₄	—	13	2	no	—
163	C₄	C₁₆×#261	1	4	yes	direct product factor
164	C₄	C₄²×#261	1	1	yes	characteristic
165	C₄	C₂×C₈×#261	1	1	yes	characteristic
166	C₂	—	13	4	no	—
167	C₂	C₄×C₈×#261	1	1	yes	characteristic
168	C₂	C₂×C₁₆×#261	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	#261
commutator, hypocenter	C₁₃	C₄²×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₂²×C₈
cosocle	C₂×C₈×D₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. #11718257	C₄	semidirect
13. C₄×#6092	C₄	semidirect
14. C₁₆×#261	C₄	direct (N × H)
15. C₄×C₁₃×C₁₆	C₄	semidirect
16. C₁₆×Dic₁₃	C₄	semidirect
17. C₄×#6090	C₄	semidirect
41. C₄×#261	C₁₆	direct (N × H)
55. #6092	C₄²	semidirect
56. C₁₃×C₁₆	C₄²	semidirect
57. #6090	C₄²	semidirect
89. C₄×C₁₆	#261	direct (N × H)
93. #261	C₄×C₁₆	direct (N × H)
94. C₄×C₁₃	C₄×C₁₆	semidirect
97. Dic₁₃	C₄×C₁₆	semidirect
140. C₁₆	C₄×#261	direct (N × H)
141. C₁₃	C₄²×C₁₆	semidirect
163. C₄	C₁₆×#261	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×D₁₃⋊C₁₆	2
C₂×C₁₆×#261	2
C₄×C₈×#261	2
C₄×C₁₆×D₁₃	2
C₄²×C₁₆	13

Subgroups — C4×C16×#261 #16789009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₆×#261 #16789009