Subgroups — C₄×#13133153 #20274617

Order 6784.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133153	C₂	1	2	yes	maximal
2	C₄×#11719917	C₂	1	2	yes	maximal
3	#16810388	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11719917	C₂²	1	4	yes	—
6	#13133153	C₄	1	8	yes	direct product factor
7	#13133128	—	2	2	no	—
8	C₄×#88322	—	2	2	no	—
9	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₅₃	C₄	1	4	yes	—
13	C₂²×C₄×C₅₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₅₃	—	2	2	no	—
16	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₅₃	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
19	C₄²×C₅₃	C₂×C₄	1	2	yes	—
20	C₄²×C₅₃	D₄	1	1	yes	characteristic
21	C₄²×C₅₃	D₄	1	1	yes	characteristic
22	#11719917	—	2	4	no	—
23	#11719917	C₂×C₄	1	8	yes	—
24	C₂×#88322	—	2	4	no	—
25	C₂³×C₅₃	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₅₃	—	2	4	no	—
27	C₂×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₅₃	C₂²×C₄	1	2	yes	—
30	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₅₃	#41	1	2	yes	—
33	C₈×C₅₃	—	2	2	no	—
34	C₈×C₅₃	C₄²	1	4	yes	—
35	#88322	—	2	8	no	—
36	C₂²×C₅₃	—	2	2	no	—
37	C₂²×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₅₃	C₄×Q₈	1	2	yes	—
39	C₄×C₅₃	—	2	2	no	—
40	C₄×C₅₃	#108	1	4	yes	complemented
41	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₅₃	#117	1	1	yes	characteristic
43	C₄×C₅₃	C₄×D₄	1	2	yes	—
44	C₄×#108	—	53	1	no	maximal, Sylow
45	C₂×C₅₃	—	2	2	no	—
46	C₂×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₅₃	C₂×#108	1	2	yes	—
48	C₂×#108	—	53	2	no	—
49	C₄×M₁₆	—	53	2	no	—
50	C₂×C₄×C₈	D₅₃	1	1	yes	characteristic
51	#341	—	53	2	no	—
52	C₅₃	C₄×#108	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	53	4	no	—
54	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
57	#108	—	53	8	no	—
58	#97	—	106	2	no	—
59	C₄×C₈	—	106	2	no	—
60	C₄×C₈	Dic₅₃	1	4	yes	—
61	C₂²×C₄	Dic₁₀₆	1	2	yes	—
62	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
63	M₁₆	—	53	8	no	—
64	M₁₆	—	106	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	106	4	no	—
67	C₂×C₈	C₄×D₅₃	1	4	yes	—
68	C₂×C₈	C₂×Dic₅₃	1	2	yes	—
69	C₂×C₈	C₂×Dic₅₃	1	2	yes	—
70	C₄²	D₂₁₂	1	1	yes	characteristic
71	C₄²	D₂₁₂	1	1	yes	characteristic
72	C₄²	C₂×Dic₅₃	1	2	yes	—
73	C₂³	C₂×Dic₁₀₆	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₅₃	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₅₃	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₅₃	1	2	yes	—
78	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
79	C₂×C₄	#11719945	1	2	yes	—
80	C₂×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	106	8	no	—
83	C₈	C₄×Dic₅₃	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
86	C₂²	C₄×Dic₁₀₆	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#13133153	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
90	C₄	#13133176	1	1	yes	characteristic
91	C₄	C₄×D₂₁₂	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₅₃	1	1	yes	characteristic
94	C₂	C₂×#13133153	1	2	yes	—

	subgroup	G/H
center	C₄²	D₂₁₂
commutator	C₄×C₅₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₂×C₄×C₈×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₅₃
hypocenter	C₅₃	C₄×#108
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #13133153	C₄	direct (N × H)
40. C₄×C₅₃	#108	semidirect
52. C₅₃	C₄×#108	semidirect
88. C₄	#13133153	direct (N × H)

Subgroups — C4×#13133153 #20274617

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13133153 #20274617