Subgroups — #29601067

Order 15616.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21448128	C₂	1	2	yes	maximal, complemented
2	Dic₁₉₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#21444035	C₂	1	2	yes	maximal, complemented
4	D₃₉₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840194	—	2	2	no	—
7	Dic₉₇₆	C₂²	1	2	yes	—
8	#16839601	—	2	2	no	—
9	D₁₉₅₂	C₂²	1	2	yes	—
10	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
11	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
12	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
13	#14519799	—	4	2	no	—
14	Dic₄₈₈	—	2	2	no	—
15	#14519722	—	4	2	no	—
16	D₉₇₆	—	2	2	no	—
17	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
18	C₃₂×C₆₁	D₄	1	1	yes	characteristic
19	C₃₂×C₆₁	C₂³	1	1	yes	characteristic
20	#11758222	—	8	2	no	—
21	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
22	Dic₂₄₄	—	4	2	no	—
23	D₄₈₈	—	4	2	no	—
24	#11758190	—	8	2	no	—
25	C₁₆×C₆₁	D₈	1	1	yes	characteristic
26	C₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	D₁₆	1	1	yes	characteristic
28	C₂²⋊D₆₁	—	16	2	no	—
29	D₂₄₄	—	8	2	no	—
30	C₄×D₆₁	—	16	2	no	—
31	Dic₁₂₂	—	8	2	no	—
32	C₈×C₆₁	D₁₆	1	1	yes	characteristic
33	C₈×C₆₁	C₂×D₈	1	1	yes	characteristic
34	#13741	—	61	1	no	maximal, Sylow
35	C₂²×C₆₁	D₃₂	1	1	yes	characteristic
36	C₂×D₆₁	—	16	2	no	—
37	C₄×C₆₁	D₃₂	1	1	yes	characteristic
38	C₄×C₆₁	C₂×D₁₆	1	1	yes	characteristic
39	Dic₆₁	—	16	2	no	—
40	#2262	—	61	2	no	—
41	Q₁₂₈	—	61	1	no	—
42	SD₁₂₈	—	61	2	no	—
43	D₆₄	—	61	1	no	—
44	C₂×C₆₄	D₆₁	1	1	yes	characteristic, complemented
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	C₂×D₃₂	1	1	yes	characteristic
47	D₆₁	—	32	2	no	—
48	#508	—	122	2	no	—
49	Q₆₄	—	61	2	no	—
50	SD₆₄	—	122	2	no	—
51	D₃₂	—	61	2	no	—
52	C₂×C₃₂	C₂×D₆₁	1	1	yes	characteristic
53	C₆₄	C₂×D₆₁	1	1	yes	characteristic
54	C₆₄	C₂×D₆₁	1	1	yes	characteristic
55	C₆₁	#13741	1	1	yes	characteristic, complemented, Sylow
56	#135	—	244	2	no	—
57	Q₃₂	—	122	2	no	—
58	SD₃₂	—	244	2	no	—
59	D₁₆	—	122	2	no	—
60	C₂×C₁₆	D₂₄₄	1	1	yes	characteristic
61	C₃₂	D₂₄₄	1	1	yes	characteristic
62	C₃₂	C₂²×D₆₁	1	1	yes	characteristic
63	#41	—	488	2	no	—
64	Q₁₆	—	244	2	no	—
65	SD₁₆	—	488	2	no	—
66	D₈	—	244	2	no	—
67	C₂×C₈	D₄₈₈	1	1	yes	characteristic
68	C₁₆	D₄₈₈	1	1	yes	characteristic
69	C₁₆	C₂×D₂₄₄	1	1	yes	characteristic
70	Q₈	—	488	2	no	—
71	D₄	—	976	2	no	—
72	D₄	—	488	2	no	—
73	C₂×C₄	—	976	2	no	—
74	C₂×C₄	D₉₇₆	1	1	yes	characteristic
75	C₈	D₉₇₆	1	1	yes	characteristic
76	C₈	C₂×D₄₈₈	1	1	yes	characteristic
77	C₂²	—	976	2	no	—
78	C₂²	D₁₉₅₂	1	1	yes	characteristic
79	C₄	—	976	2	no	—
80	C₄	D₁₉₅₂	1	1	yes	characteristic
81	C₄	C₂×D₉₇₆	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	1952	2	no	—
84	C₂	C₂×D₁₉₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₉₅₂
commutator, cosocle	C₃₂×C₆₁	C₂³
Frattini	C₃₂	C₂²×D₆₁
Fitting	C₂×C₆₁×C₆₄	C₂
socle	C₂×C₆₁	C₂×D₃₂
hypercenter	C₂×C₆₄	D₆₁
hypocenter	C₆₁	#13741
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. #21448128	C₂	semidirect
2. Dic₁₉₅₂	C₂	semidirect
3. #21444035	C₂	semidirect
4. D₃₉₀₄	C₂	semidirect
5. C₂×C₆₁×C₆₄	C₂	semidirect
44. C₂×C₆₄	D₆₁	semidirect
55. C₆₁	#13741	semidirect

Maximal subgroups

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

subgroup	index
#21448128	2
Dic₁₉₅₂	2
#21444035	2
D₃₉₀₄	2
C₂×C₆₁×C₆₄	2
#13741	61