Subgroups — C₄×#11718053 #15777741

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718053	C₂	1	4	yes	maximal
2	C₂×C₄×#6090	C₂	1	2	yes	maximal
3	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₄³×C₁₃	C₄	1	1	yes	characteristic
9	C₂²×#6090	C₂²	1	4	yes	—
10	#11718053	C₄	1	16	yes	direct product factor
11	C₄×#6090	C₄	1	8	yes	complemented
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	C₈	1	4	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₃	C₈	1	8	yes	—
19	C₄×C₈×C₁₃	C₈	1	4	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
22	C₂×#6090	C₂×C₄	1	8	yes	—
23	C₂×#6090	C₂×C₄	1	16	yes	—
24	C₄×#346	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₄²	1	2	yes	—
29	C₂×C₈×C₁₃	C₄²	1	4	yes	—
30	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
35	C₄²×C₁₃	—	2	8	no	—
36	C₄²×C₁₃	C₄²	1	4	yes	—
37	C₄²×C₁₃	C₄²	1	2	yes	—
38	C₄²×C₁₃	C₂×C₈	1	4	yes	—
39	C₄²×C₁₃	C₂×C₈	1	2	yes	—
40	#6090	C₄²	1	16	yes	complemented
41	C₂×#346	—	13	4	no	—
42	C₂×C₄×C₁₆	—	13	2	no	—
43	C₄²×C₈	D₁₃	1	1	yes	characteristic
44	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	2	8	no	—
46	C₂×C₄×C₁₃	C₄×C₈	1	8	yes	—
47	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
48	C₂×C₄×C₁₃	M₃₂	1	8	yes	—
49	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
51	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
53	C₈×C₁₃	C₄×C₈	1	4	yes	—
54	C₈×C₁₃	C₄×C₈	1	8	yes	—
55	C₈×C₁₃	C₂×C₄²	1	4	yes	—
56	C₂²×C₁₆	—	13	4	no	—
57	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
58	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
59	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
60	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
61	C₄³	Dic₁₃	1	1	yes	characteristic
62	#346	—	13	16	no	—
63	C₄×C₁₆	—	13	8	no	—
64	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
65	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
66	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
67	C₄×C₁₃	—	2	8	no	—
68	C₄×C₁₃	#346	1	8	yes	complemented
69	C₄×C₁₃	C₄³	1	1	yes	characteristic
70	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
71	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
72	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
73	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
74	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
75	C₂×C₄²	#1055	1	4	yes	—
76	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
77	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
78	C₂×C₁₆	—	13	8	no	—
79	C₂×C₁₆	—	13	16	no	—
80	C₄×C₈	#1055	1	8	yes	—
81	C₄×C₈	#1055	1	4	yes	—
82	C₄×C₈	C₄×D₁₃	1	4	yes	—
83	C₄×C₈	C₄×D₁₃	1	8	yes	—
84	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
85	C₂×C₁₃	C₂×#346	1	2	yes	—
86	C₂×C₁₃	C₄×M₃₂	1	4	yes	—
87	C₂²×C₄	C₂×#1055	1	4	yes	—
88	C₂²×C₄	C₂×#1055	1	2	yes	—
89	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
90	C₂×C₈	C₂×#1055	1	4	yes	—
91	C₂×C₈	C₂×#1055	1	4	yes	—
92	C₂×C₈	C₂×#1055	1	4	yes	—
93	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
94	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
95	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
96	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
97	C₄²	—	2	8	no	—
98	C₄²	C₂×#1055	1	4	yes	—
99	C₄²	C₂×#1055	1	2	yes	—
100	C₄²	C₄×Dic₁₃	1	4	yes	—
101	C₄²	C₄×Dic₁₃	1	2	yes	—
102	C₁₆	—	13	16	no	—
103	C₁₃	C₄×#346	1	1	yes	characteristic, complemented, Sylow
104	C₂³	C₂²×#1055	1	1	yes	characteristic
105	C₂×C₄	—	2	8	no	—
106	C₂×C₄	C₄×#1055	1	8	yes	—
107	C₂×C₄	C₄×#1055	1	4	yes	—
108	C₂×C₄	#88052	1	8	yes	—
109	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
110	C₂×C₄	C₂²×#1055	1	2	yes	—
111	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
113	C₈	C₄×#1055	1	8	yes	—
114	C₈	C₄×#1055	1	4	yes	—
115	C₈	C₄²×D₁₃	1	4	yes	—
116	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
117	C₂²	C₂×C₄×#1055	1	2	yes	—
118	C₂²	C₂×#88052	1	4	yes	—
119	C₄	—	2	8	no	—
120	C₄	#11718053	1	8	yes	direct product factor
121	C₄	C₂×C₄×#1055	1	2	yes	—
122	C₄	C₂×C₄×#1055	1	1	yes	characteristic
123	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
124	C₂	C₄²×#1055	1	1	yes	characteristic
125	C₂	C₂×#11718053	1	2	yes	—
126	C₂	C₄×#88052	1	4	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	C₄×#346
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
10. #11718053	C₄	direct (N × H)
11. C₄×#6090	C₄	semidirect
40. #6090	C₄²	semidirect
68. C₄×C₁₃	#346	semidirect
103. C₁₃	C₄×#346	semidirect
120. C₄	#11718053	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×#11718053	2
C₂×C₄×#6090	2
C₄²×C₈×C₁₃	2
C₄×#346	13

Subgroups — C4×#11718053 #15777741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718053 #15777741