Subgroups — C₄×#11718047 #15752267

Order 3328.

654 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×#1055	C₂	1	2	yes	maximal
2	C₂×#11718047	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
6	C₄³×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×#1055	C₄	1	8	yes	—
8	C₂×C₄×#1055	C₂²	1	4	yes	—
9	#11718047	C₄	1	16	yes	direct product factor
10	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
14	C₂²×#1055	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₃	C₈	1	16	yes	complemented
16	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
17	C₄×#1055	—	2	16	no	—
18	C₄×#1055	C₂×C₄	1	16	yes	—
19	C₄×#322	—	13	1	no	maximal, Sylow
20	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
21	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
22	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₃	C₄²	1	8	yes	—
24	C₂×C₈×C₁₃	C₂×C₈	1	16	yes	—
25	C₄²×C₁₃	C₂×C₈	1	8	yes	—
26	C₄²×C₁₃	M₁₆	1	16	yes	—
27	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
28	C₂×#1055	—	2	16	no	—
29	C₂×#1055	C₄²	1	16	yes	—
30	C₄²×C₈	—	13	2	no	—
31	C₄²×C₈	D₁₃	1	1	yes	characteristic
32	C₂×#322	—	13	4	no	—
33	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₄×C₈	1	8	yes	—
35	C₂×C₄×C₁₃	#97	1	16	yes	—
36	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
37	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
38	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
39	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
40	C₈×C₁₃	C₄×C₈	1	16	yes	complemented
41	#1055	—	2	16	no	—
42	C₂×C₄×C₈	—	13	4	no	—
43	C₂×C₄×C₈	—	13	8	no	—
44	C₂×C₄×C₈	Dic₁₃	1	4	yes	—
45	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
46	C₄³	C₂×D₁₃	1	1	yes	characteristic
47	#322	—	13	16	no	—
48	C₂²×C₁₃	C₄³	1	1	yes	characteristic
49	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
50	C₂²×C₁₃	C₂×#97	1	4	yes	—
51	C₄×C₁₃	#322	1	16	yes	complemented
52	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
53	C₄×C₁₃	C₄×M₁₆	1	8	yes	—
54	C₂²×C₈	—	13	8	no	—
55	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
56	C₂×C₄²	C₄×D₁₃	1	4	yes	—
57	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
58	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
59	C₄×C₈	—	13	16	no	—
60	C₄×C₈	—	26	16	no	—
61	C₄×C₈	#1055	1	16	yes	complemented
62	C₄×C₈	C₄×D₁₃	1	8	yes	—
63	C₂×C₁₃	C₂×#322	1	4	yes	—
64	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
65	C₂×C₁₃	C₄×#97	1	2	yes	—
66	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
67	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
68	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
69	C₂×C₈	—	13	16	no	—
70	C₂×C₈	—	26	16	no	—
71	C₂×C₈	C₂×#1055	1	16	yes	—
72	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
73	C₄²	#6094	1	16	yes	—
74	C₄²	C₂×#1055	1	8	yes	—
75	C₄²	C₂×C₄×D₁₃	1	4	yes	—
76	C₁₃	C₄×#322	1	1	yes	characteristic, complemented, Sylow
77	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
78	C₂×C₄	C₄×#1055	1	8	yes	—
79	C₂×C₄	#88055	1	16	yes	—
80	C₂×C₄	C₄²×D₁₃	1	4	yes	—
81	C₂×C₄	C₂×#6094	1	8	yes	—
82	C₂×C₄	C₂²×#1055	1	4	yes	—
83	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
84	C₈	—	26	16	no	—
85	C₈	C₄×#1055	1	16	yes	complemented
86	C₂²	C₂×C₄×#1055	1	2	yes	—
87	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
88	C₂²	C₂×#88055	1	4	yes	—
89	C₄	#11718047	1	16	yes	direct product factor
90	C₄	C₄×#6094	1	8	yes	—
91	C₄	C₂×C₄×#1055	1	4	yes	—
92	C₂	C₂×#11718047	1	4	yes	—
93	C₂	C₄²×#1055	1	1	yes	characteristic
94	C₂	C₄×#88055	1	2	yes	—

	subgroup	G/H
center	C₄³	C₂×D₁₃
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	C₄×#322
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
9. #11718047	C₄	direct (N × H)
15. C₄×C₈×C₁₃	C₈	semidirect
40. C₈×C₁₃	C₄×C₈	semidirect
51. C₄×C₁₃	#322	semidirect
61. C₄×C₈	#1055	semidirect
76. C₁₃	C₄×#322	semidirect
85. C₈	C₄×#1055	semidirect
89. C₄	#11718047	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×#1055	2
C₂×#11718047	2
C₄²×C₈×C₁₃	2
C₄×#322	13

Subgroups — C4×#11718047 #15752267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718047 #15752267