Subgroups — #21434620

Order 7552.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837959	C₂	1	2	yes	maximal
2	#16837811	C₂	1	8	yes	maximal, complemented
3	#16837440	C₂	1	4	yes	maximal
4	C₂×#97×C₅₉	C₂	1	1	yes	maximal, characteristic
5	#14273727	C₂²	1	4	yes	—
6	#14273719	C₂²	1	4	yes	—
7	#14273706	—	2	4	no	—
8	C₄×Dic₁₁₈	—	2	4	no	—
9	#14273686	C₂²	1	4	yes	—
10	#14273661	C₂²	1	8	yes	—
11	#14273659	C₂²	1	8	yes	—
12	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	#97×C₅₉	C₂²	1	4	yes	—
15	C₂²×C₄×C₅₉	D₄	1	2	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₁₈	—	2	4	no	—
18	C₂×C₈×C₅₉	Q₈	1	8	yes	complemented
19	C₂×C₈×C₅₉	C₂³	1	4	yes	—
20	C₄²×C₅₉	D₄	1	2	yes	—
21	C₄²×C₅₉	C₂³	1	2	yes	—
22	C₂²⋊Dic₅₉	—	2	4	no	—
23	C₄⋊Dic₅₉	—	2	4	no	—
24	C₄⋊Dic₅₉	C₂³	1	8	yes	—
25	Dic₅₉⋊C₄	—	2	8	no	—
26	C₄×Dic₅₉	—	2	4	no	—
27	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	—	4	2	no	—
29	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
32	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
33	C₂×Dic₅₉	—	2	8	no	—
34	Dic₁₁₈	—	4	8	no	—
35	C₈×C₅₉	C₂×Q₈	1	8	yes	—
36	C₂²×C₅₉	—	2	2	no	—
37	C₂²×C₅₉	C₄⋊Q₈	1	2	yes	—
38	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₅₉	—	2	4	no	—
40	C₄×C₅₉	C₄⋊Q₈	1	2	yes	—
41	C₄×C₅₉	C₂²×Q₈	1	2	yes	—
42	Dic₅₉	—	4	8	no	—
43	#3162	—	59	1	no	maximal, Sylow
44	C₂×C₅₉	—	2	2	no	—
45	C₂×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₅₉	#575	1	2	yes	—
47	#533	—	59	2	no	—
48	#501	—	59	8	no	—
49	#427	—	59	4	no	—
50	C₂×#97	D₅₉	1	1	yes	characteristic
51	C₅₉	#3162	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₈	C₂×D₅₉	1	2	yes	—
53	C₄⋊Q₈	—	59	4	no	—
54	#125	—	59	4	no	—
55	C₂²⋊Q₈	—	118	4	no	—
56	C₄×Q₈	—	118	4	no	—
57	#117	—	59	4	no	—
58	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
59	#107	—	59	8	no	—
60	#106	—	59	8	no	—
61	#97	C₂×D₅₉	1	4	yes	—
62	C₂×Q₈	—	118	4	no	—
63	C₂²×C₄	D₂₃₆	1	2	yes	—
64	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
65	C₂×C₈	Dic₁₁₈	1	8	yes	complemented
66	C₂×C₈	C₂²×D₅₉	1	4	yes	—
67	C₄⋊C₄	—	59	8	no	—
68	C₄⋊C₄	—	118	8	no	—
69	C₄⋊C₄	—	118	4	no	—
70	C₂²⋊C₄	—	118	4	no	—
71	C₄²	—	118	4	no	—
72	C₄²	D₂₃₆	1	2	yes	—
73	C₄²	C₂²×D₅₉	1	2	yes	—
74	C₂³	C₂×D₂₃₆	1	1	yes	characteristic
75	Q₈	—	236	8	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	118	8	no	—
78	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
79	C₂×C₄	C₂×D₂₃₆	1	4	yes	—
80	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
81	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
82	C₈	C₂×Dic₁₁₈	1	8	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	#14273727	1	2	yes	—
85	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	236	8	no	—
88	C₄	#14273727	1	2	yes	—
89	C₄	C₂²×Dic₁₁₈	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	C₂×#14273727	1	1	yes	characteristic
92	C₂	#16838202	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₂×#97×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	C₂×#97	D₅₉
hypocenter	C₅₉	#3162
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #16837811	C₂	semidirect
18. C₂×C₈×C₅₉	Q₈	semidirect
51. C₅₉	#3162	semidirect
65. C₂×C₈	Dic₁₁₈	semidirect