Subgroups — #14580691

Order 2624.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	1	yes	maximal, characteristic, complemented
2	#13050152	C₂	1	1	yes	maximal, characteristic
3	#13050089	C₂	1	2	yes	maximal, complemented
4	#13050086	C₂	1	2	yes	maximal
5	C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₆₄	C₂²	1	1	yes	characteristic
7	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁	C₂²	1	2	yes	—
9	C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	#10620281	—	2	2	no	—
11	C₄⋊Dic₄₁	C₂²	1	2	yes	—
12	#10620279	—	2	2	no	—
13	C₂²×D₄₁	—	2	1	no	—
14	C₂×C₄×C₄₁	D₄	1	2	yes	—
15	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₁	—	2	2	no	—
17	C₂×Dic₄₁	—	2	1	no	—
18	D₁₆₄	—	2	2	no	—
19	Dic₈₂	—	2	2	no	—
20	C₈×C₄₁	—	2	2	no	—
21	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
22	C₂×D₄₁	—	4	1	no	—
23	C₂×D₄₁	—	4	2	no	—
24	C₄×C₄₁	—	2	2	no	—
25	C₄×C₄₁	#41	1	2	yes	—
26	Dic₄₁	—	4	1	no	—
27	Dic₄₁	—	4	2	no	—
28	C₂×C₄₁	#124	1	1	yes	characteristic
29	C₂×C₄₁	#135	1	2	yes	—
30	D₄₁	—	8	1	no	—
31	#488	—	41	1	no	maximal, Sylow
32	C₄₁	#488	1	1	yes	characteristic, complemented, Sylow
33	#125	—	41	1	no	—
34	#124	—	41	1	no	—
35	#103	—	41	2	no	—
36	#102	—	41	2	no	—
37	C₄×C₈	D₄₁	1	1	yes	characteristic, complemented
38	C₂×Q₈	—	41	1	no	—
39	C₂×D₄	—	41	1	no	—
40	C₂×C₈	C₂×D₄₁	1	2	yes	—
41	C₄⋊C₄	—	41	2	no	—
42	C₄⋊C₄	—	82	2	no	—
43	C₂²⋊C₄	—	82	2	no	—
44	C₄²	C₂×D₄₁	1	1	yes	characteristic
45	C₂³	—	82	1	no	—
46	Q₈	—	82	2	no	—
47	D₄	—	82	2	no	—
48	C₂×C₄	—	82	1	no	—
49	C₂×C₄	—	82	2	no	—
50	C₂×C₄	D₁₆₄	1	2	yes	—
51	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₂²	—	164	1	no	—
54	C₂²	—	164	2	no	—
55	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	164	1	no	—
58	C₄	—	164	2	no	—
59	C₄	#10620306	1	2	yes	—
60	C₂	—	328	1	no	—
61	C₂	#13050152	1	1	yes	characteristic
62	C₂	#13050186	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₆₄
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₄×C₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	C₂×D₁₆₄	C₂²
hypercenter	C₄×C₈	D₄₁
hypocenter	C₄₁	#488
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #13050156	C₂	semidirect
3. #13050089	C₂	semidirect
5. C₄×C₈×C₄₁	C₂	semidirect
32. C₄₁	#488	semidirect
37. C₄×C₈	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050156	2
#13050152	2
#13050089	2
#13050086	2
C₄×C₈×C₄₁	2
#488	41