Subgroups — #16840766

Order 3904.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758213	C₂	1	2	yes	maximal
2	C₄⋊#92420	C₂	1	4	yes	maximal, complemented
3	C₄²×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₆₁	C₄	1	2	yes	—
5	C₂×C₄×D₆₁	C₂²	1	1	yes	characteristic
6	C₂×#92420	C₂²	1	4	yes	—
7	#11758213	—	2	4	no	—
8	C₄²×C₆₁	C₄	1	1	yes	characteristic
9	C₄×Dic₆₁	C₄	1	1	yes	characteristic
10	C₄×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×D₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₆₁	C₂×C₄	1	2	yes	—
14	C₂×Dic₆₁	C₂×C₄	1	2	yes	—
15	C₂×Dic₆₁	C₂³	1	1	yes	characteristic
16	C₄×D₆₁	—	2	4	no	—
17	C₄×D₆₁	D₄	1	2	yes	—
18	C₄×D₆₁	Q₈	1	2	yes	—
19	#92420	—	2	4	no	—
20	C₂²×C₆₁	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₆₁	—	2	2	no	—
22	C₂×D₆₁	C₄⋊C₄	1	2	yes	—
23	C₄×C₆₁	C₄⋊C₄	1	2	yes	—
24	C₄×C₆₁	M₁₆	1	4	yes	complemented
25	Dic₆₁	—	2	2	no	—
26	Dic₆₁	C₂×D₄	1	1	yes	characteristic
27	Dic₆₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₆₁	C₂×M₁₆	1	2	yes	—
30	D₆₁	—	2	2	no	—
31	#423	—	61	1	no	maximal, Sylow
32	C₆₁	#423	1	1	yes	characteristic, complemented, Sylow
33	C₂×M₁₆	—	61	2	no	—
34	C₂×C₄²	—	61	1	no	—
35	C₄⋊C₈	—	61	4	no	—
36	C₂²×C₄	—	61	1	no	—
37	C₂²×C₄	—	61	2	no	—
38	M₁₆	—	122	4	no	—
39	C₂×C₈	—	61	4	no	—
40	C₄²	—	61	2	no	—
41	C₄²	—	61	1	no	—
42	C₄²	#6923	1	1	yes	characteristic
43	C₂³	—	61	1	no	—
44	C₂×C₄	—	61	1	no	—
45	C₂×C₄	—	61	2	no	—
46	C₂×C₄	—	61	2	no	—
47	C₂×C₄	—	61	2	no	—
48	C₂×C₄	—	122	4	no	—
49	C₂×C₄	C₂×#6923	1	2	yes	—
50	C₂×C₄	C₂×#6923	1	1	yes	characteristic
51	C₈	—	122	4	no	—
52	C₂²	—	61	2	no	—
53	C₂²	—	122	2	no	—
54	C₂²	C₂²×#6923	1	1	yes	characteristic
55	C₄	—	61	1	no	—
56	C₄	—	61	1	no	—
57	C₄	—	122	2	no	—
58	C₄	#11758213	1	4	yes	complemented
59	C₄	C₄⋊#6923	1	2	yes	—
60	C₂	—	122	2	no	—
61	C₂	C₂×C₄⋊#6923	1	1	yes	characteristic
62	C₂	C₂×#11758213	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₄
Fitting	C₄²×C₆₁	C₄
prime radical	C₂²×D₆₁	C₂×C₄
cosocle	C₂×Dic₆₁	C₂³
hypercenter	C₄²	#6923
hypocenter	C₆₁	#423
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#92420	C₂	semidirect
24. C₄×C₆₁	M₁₆	semidirect
32. C₆₁	#423	semidirect
58. C₄	#11758213	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758213	2
C₄⋊#92420	2
C₄²×D₆₁	2
#423	61