Subgroups — #14580701

Order 2624.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050161	C₂	1	1	yes	maximal, characteristic
2	#13050156	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050086	C₂	1	4	yes	maximal, complemented
4	#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆₄	—	2	2	no	—
6	C₂×D₁₆₄	C₂²	1	2	yes	—
7	C₂×C₈×C₄₁	C₂²	1	2	yes	—
8	C₄²×C₄₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₁	C₂²	1	2	yes	—
10	#10620279	—	2	2	no	—
11	C₂²×D₄₁	—	2	2	no	—
12	C₂×C₄×C₄₁	D₄	1	2	yes	—
13	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
14	C₂×Dic₄₁	—	2	2	no	—
15	D₁₆₄	—	2	4	no	—
16	D₁₆₄	—	4	4	no	—
17	C₈×C₄₁	—	2	2	no	—
18	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
19	C₂×D₄₁	—	4	2	no	—
20	C₂×D₄₁	—	4	4	no	—
21	C₄×C₄₁	—	2	2	no	—
22	C₄×C₄₁	#41	1	2	yes	—
23	Dic₄₁	—	4	2	no	—
24	C₂×C₄₁	#124	1	1	yes	characteristic
25	C₂×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
26	D₄₁	—	8	2	no	—
27	#490	—	41	1	no	maximal, Sylow
28	C₄₁	#490	1	1	yes	characteristic, complemented, Sylow
29	#127	—	41	1	no	—
30	#125	—	41	1	no	—
31	#102	—	41	4	no	—
32	#97	D₄₁	1	1	yes	characteristic, complemented
33	C₂×D₄	—	41	2	no	—
34	C₂×D₄	—	82	2	no	—
35	C₂×C₈	C₂×D₄₁	1	2	yes	—
36	C₄⋊C₄	—	41	2	no	—
37	C₄⋊C₄	—	82	2	no	—
38	C₄²	C₂×D₄₁	1	1	yes	characteristic
39	C₂³	—	82	2	no	—
40	D₄	—	82	4	no	—
41	D₄	—	164	4	no	—
42	C₂×C₄	—	82	2	no	—
43	C₂×C₄	D₁₆₄	1	2	yes	—
44	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	164	2	no	—
47	C₂²	—	164	4	no	—
48	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	164	2	no	—
51	C₄	#10620306	1	2	yes	—
52	C₂	—	328	2	no	—
53	C₂	#13050152	1	1	yes	characteristic
54	C₂	#13050192	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₆₄
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#97×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	#13050161	C₂
hypercenter	#97	D₄₁
hypocenter	C₄₁	#490
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #13050156	C₂	semidirect
3. #13050086	C₂	semidirect
4. #97×C₄₁	C₂	semidirect
28. C₄₁	#490	semidirect
32. #97	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050161	2
#13050156	2
#13050086	2
#97×C₄₁	2
#490	41