Subgroups — C₂²×#14273673 #21437208

Order 7552.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14273673	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₁₈	—	2	1	no	—
6	C₂×Dic₂₃₆	—	2	3	no	—
7	C₂×Dic₂₃₆	C₂²	1	6	yes	—
8	#14273673	C₂²	1	16	yes	direct product factor
9	C₂×C₅₉⋊C₁₆	C₂²	1	6	yes	—
10	C₂²×Q₈×C₅₉	—	2	1	no	—
11	C₂×Q₁₆×C₅₉	—	2	3	no	—
12	C₂×Q₁₆×C₅₉	C₂²	1	6	yes	—
13	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₅₉	—	2	6	no	—
15	C₂×Q₈×C₅₉	—	4	3	no	—
16	C₂²×C₄×C₅₉	—	4	1	no	—
17	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
18	C₂²×Dic₅₉	—	4	1	no	—
19	C₂×Dic₁₁₈	—	2	6	no	—
20	C₂×Dic₁₁₈	—	4	3	no	—
21	Q₁₆×C₅₉	—	2	6	no	—
22	Q₁₆×C₅₉	C₂³	1	4	yes	—
23	C₂×C₈×C₅₉	D₄	1	3	yes	—
24	C₂×C₈×C₅₉	C₂³	1	3	yes	—
25	Dic₂₃₆	—	2	6	no	—
26	Dic₂₃₆	C₂³	1	4	yes	—
27	C₅₉⋊C₁₆	C₂³	1	4	yes	—
28	C₂³×C₅₉	D₈	1	1	yes	characteristic
29	Q₈×C₅₉	—	2	4	no	—
30	Q₈×C₅₉	—	4	6	no	—
31	C₂×C₄×C₅₉	—	4	6	no	—
32	C₂×C₄×C₅₉	D₈	1	3	yes	—
33	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
34	C₂×Dic₅₉	—	4	6	no	—
35	Dic₁₁₈	—	2	4	no	—
36	Dic₁₁₈	—	4	6	no	—
37	C₈×C₅₉	C₂×D₄	1	3	yes	—
38	C₈×C₅₉	C₂⁴	1	1	yes	characteristic
39	C₂²×C₅₉	Q₃₂	1	4	yes	complemented
40	C₂²×C₅₉	C₂×D₈	1	3	yes	—
41	C₄×C₅₉	—	4	4	no	—
42	C₄×C₅₉	C₂×D₈	1	3	yes	—
43	C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
44	Dic₅₉	—	4	4	no	—
45	C₂²×Q₃₂	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	C₂×Q₃₂	1	6	yes	complemented
47	C₂×C₅₉	C₂²×D₈	1	1	yes	characteristic
48	C₂²×Q₁₆	—	59	1	no	—
49	C₂²×Q₁₆	D₅₉	1	1	yes	characteristic
50	C₂×Q₃₂	—	59	12	no	—
51	C₂²×C₁₆	—	59	1	no	—
52	C₅₉	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
53	C₂²×Q₈	—	2	1	no	—
54	C₂²×Q₈	—	118	1	no	—
55	C₂×Q₁₆	—	2	3	no	—
56	C₂×Q₁₆	—	59	6	no	—
57	C₂×Q₁₆	—	118	3	no	—
58	C₂×Q₁₆	C₂×D₅₉	1	6	yes	—
59	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
60	Q₃₂	—	59	16	no	—
61	C₂×C₁₆	—	59	6	no	—
62	C₂×Q₈	—	2	6	no	—
63	C₂×Q₈	—	4	3	no	—
64	C₂×Q₈	—	118	6	no	—
65	C₂×Q₈	—	236	3	no	—
66	C₂²×C₄	—	4	1	no	—
67	C₂²×C₄	—	236	1	no	—
68	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
69	Q₁₆	—	2	6	no	—
70	Q₁₆	—	59	4	no	—
71	Q₁₆	—	118	6	no	—
72	Q₁₆	C₂²×D₅₉	1	4	yes	—
73	C₂×C₈	C₂²⋊D₅₉	1	3	yes	—
74	C₂×C₈	C₂²×D₅₉	1	3	yes	—
75	C₁₆	—	59	4	no	—
76	C₂³	#11745669	1	1	yes	characteristic
77	Q₈	—	2	4	no	—
78	Q₈	—	4	6	no	—
79	Q₈	—	118	4	no	—
80	Q₈	—	236	6	no	—
81	C₂×C₄	—	4	6	no	—
82	C₂×C₄	—	236	6	no	—
83	C₂×C₄	#11745669	1	3	yes	—
84	C₂×C₄	C₂×C₂²⋊D₅₉	1	3	yes	—
85	C₈	C₂×C₂²⋊D₅₉	1	3	yes	—
86	C₈	C₂³×D₅₉	1	1	yes	characteristic
87	C₂²	#14273673	1	4	yes	direct product factor
88	C₂²	C₂×#11745669	1	3	yes	—
89	C₄	—	4	4	no	—
90	C₄	—	236	4	no	—
91	C₄	C₂×#11745669	1	3	yes	—
92	C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
93	C₂	C₂×#14273673	1	6	yes	direct product factor
94	C₂	C₂²×#11745669	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#11745669
commutator	C₈×C₅₉	C₂⁴
Frattini	C₈	C₂³×D₅₉
Fitting	C₂²×Q₁₆×C₅₉	C₂
socle	C₂³×C₅₉	D₈
hypercenter	C₂²×Q₁₆	D₅₉
hypocenter	C₅₉	C₂²×Q₃₂
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#14273673	C₂	direct (N × H)
8. #14273673	C₂²	direct (N × H)
39. C₂²×C₅₉	Q₃₂	semidirect
46. C₂×C₅₉	C₂×Q₃₂	semidirect
52. C₅₉	C₂²×Q₃₂	semidirect
87. C₂²	#14273673	direct (N × H)
93. C₂	C₂×#14273673	direct (N × H)

Subgroups — C22×#14273673 #21437208

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14273673 #21437208