Subgroups — C₄⋊C₈×D₅₃ #16810642

Order 3392.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅₃	C₂	1	2	yes	maximal
2	C₄²×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#88322	C₂	1	1	yes	maximal, characteristic, complemented
4	#13133146	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₅₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₅₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₅₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₅₃	C₂²	1	2	yes	—
10	C₄²×C₅₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₅₃	C₄	1	1	yes	characteristic
12	C₄×Dic₅₃	C₄	1	1	yes	characteristic
13	C₄×Dic₅₃	C₂²	1	1	yes	characteristic
14	C₂×#88322	C₂²	1	2	yes	—
15	C₈×D₅₃	—	2	4	no	—
16	C₂²×D₅₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₅₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₅₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₅₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₅₃	C₂×C₄	1	1	yes	characteristic
23	C₄×D₅₃	—	2	2	no	—
24	C₄×D₅₃	C₈	1	4	yes	complemented
25	C₄×D₅₃	D₄	1	2	yes	—
26	C₄×D₅₃	Q₈	1	2	yes	—
27	C₈×C₅₃	—	2	2	no	—
28	#88322	—	2	2	no	—
29	C₂²×C₅₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×D₅₃	C₄⋊C₄	1	2	yes	—
31	C₂×D₅₃	C₂×C₈	1	2	yes	—
32	C₂×D₅₃	M₁₆	1	2	yes	—
33	C₄×C₅₃	—	2	1	no	—
34	C₄×C₅₃	C₂×C₈	1	2	yes	complemented
35	C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
37	Dic₅₃	—	2	1	no	—
38	Dic₅₃	C₄⋊C₄	1	2	yes	—
39	Dic₅₃	C₂×C₈	1	2	yes	complemented
40	C₂×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₅₃	C₂²×C₈	1	1	yes	characteristic
42	C₂×C₅₃	C₂×M₁₆	1	1	yes	characteristic
43	D₅₃	C₄⋊C₈	1	4	yes	direct product factor
44	C₂×C₄⋊C₈	—	53	1	no	maximal, Sylow
45	C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₈	—	53	2	no	—
47	C₂×C₄²	—	53	1	no	—
48	C₄⋊C₈	—	53	2	no	—
49	C₄⋊C₈	—	53	1	no	—
50	C₄⋊C₈	D₅₃	1	1	yes	characteristic, direct product factor
51	C₂²×C₄	—	53	1	no	—
52	C₂²×C₄	—	53	1	no	—
53	C₂²×C₄	—	53	1	no	—
54	C₂×C₈	—	53	2	no	—
55	C₂×C₈	—	106	4	no	—
56	C₂×C₈	C₂×D₅₃	1	2	yes	—
57	C₄²	—	53	1	no	—
58	C₄²	—	53	1	no	—
59	C₄²	—	53	1	no	—
60	C₄²	C₂×D₅₃	1	1	yes	characteristic
61	C₂³	—	53	1	no	—
62	C₂×C₄	—	53	1	no	—
63	C₂×C₄	—	53	1	no	—
64	C₂×C₄	—	53	2	no	—
65	C₂×C₄	—	53	2	no	—
66	C₂×C₄	—	53	4	no	—
67	C₂×C₄	—	53	1	no	—
68	C₂×C₄	—	106	2	no	—
69	C₂×C₄	C₄×D₅₃	1	1	yes	characteristic
70	C₂×C₄	C₄×D₅₃	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₅₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	106	2	no	—
74	C₂²	—	53	2	no	—
75	C₂²	—	53	2	no	—
76	C₂²	—	53	2	no	—
77	C₂²	C₂×C₄×D₅₃	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	53	2	no	—
80	C₄	—	53	2	no	—
81	C₄	—	106	1	no	—
82	C₄	C₈×D₅₃	1	2	yes	complemented
83	C₄	D₄×D₅₃	1	1	yes	characteristic
84	C₄	Q₈×D₅₃	1	1	yes	characteristic
85	C₂	—	53	4	no	—
86	C₂	C₄⋊C₄×D₅₃	1	1	yes	characteristic
87	C₂	C₂×C₈×D₅₃	1	1	yes	characteristic
88	C₂	M₁₆×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₅₃
commutator	C₂×C₅₃	C₂²×C₈
Fitting	C₄⋊C₈×C₅₃	C₂
socle	C₂²×C₅₃	C₂²×C₄
prime radical	C₂²×D₅₃	C₂×C₄
cosocle	C₂×C₄×C₅₃	C₂³
hypercenter	C₄⋊C₈	D₅₃
hypocenter	C₅₃	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₄⋊#88322	C₂	semidirect
4. #13133146	C₂	semidirect
5. C₄⋊C₈×C₅₃	C₂	semidirect
24. C₄×D₅₃	C₈	semidirect
34. C₄×C₅₃	C₂×C₈	semidirect
39. Dic₅₃	C₂×C₈	semidirect
43. D₅₃	C₄⋊C₈	direct (N × H)
45. C₅₃	C₂×C₄⋊C₈	semidirect
50. C₄⋊C₈	D₅₃	direct (N × H)
82. C₄	C₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅₃	2
C₄²×D₅₃	2
C₄⋊#88322	2
#13133146	2
C₄⋊C₈×C₅₃	2
C₂×C₄⋊C₈	53

Subgroups — C4⋊C8×D53 #16810642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₈×D₅₃ #16810642