Subgroups — #14581237

Order 2624.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050224	C₂	1	1	yes	maximal, characteristic, complemented
2	#13050222	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050134	C₂	1	1	yes	maximal, characteristic
4	C₂³×D₄₁	C₄	1	1	yes	characteristic, complemented
5	C₂×C₂²⋊D₄₁	C₂²	1	1	yes	characteristic
6	C₂×D₁₆₄	—	2	1	no	—
7	C₂²⋊#4223	—	2	1	no	—
8	#10620301	—	2	1	no	—
9	C₂²⋊C₄×C₄₁	C₄	1	1	yes	characteristic, complemented
10	#10620281	—	2	1	no	—
11	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₄₁	—	2	1	no	—
13	C₂²×D₄₁	—	4	2	no	—
14	C₂²×D₄₁	—	4	1	no	—
15	C₂²×D₄₁	D₄	1	1	yes	characteristic
16	C₂×#4223	—	4	1	no	—
17	C₂×C₄×C₄₁	—	2	1	no	—
18	C₂²⋊D₄₁	—	4	1	no	—
19	C₂×Dic₄₁	D₄	1	1	yes	characteristic
20	D₁₆₄	—	4	2	no	—
21	#66493	—	4	1	no	—
22	C₂²×C₄₁	—	2	1	no	—
23	C₂²×C₄₁	—	4	1	no	—
24	C₂²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₄₁	—	2	2	no	—
26	C₂×D₄₁	—	2	1	no	—
27	C₂×D₄₁	—	4	1	no	—
28	C₂×D₄₁	—	4	2	no	—
29	C₂×D₄₁	—	4	1	no	—
30	C₂×D₄₁	—	4	1	no	—
31	C₂×D₄₁	—	4	2	no	—
32	#4223	—	8	1	no	—
33	C₄×C₄₁	—	4	1	no	—
34	Dic₄₁	—	2	1	no	—
35	C₂×C₄₁	—	2	1	no	—
36	C₂×C₄₁	—	4	1	no	—
37	C₂×C₄₁	#99	1	1	yes	characteristic
38	D₄₁	—	4	1	no	—
39	D₄₁	—	4	2	no	—
40	AΣL(1,𝔽₁₆)	—	41	1	no	maximal, Sylow
41	C₄₁	AΣL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
42	#120	—	41	1	no	—
43	#100	—	41	1	no	—
44	#99	—	41	1	no	—
45	C₂⁴	—	41	1	no	—
46	C₂×D₄	—	41	1	no	—
47	C₂×D₄	—	82	1	no	—
48	M₁₆	—	82	1	no	—
49	C₂²⋊C₄	—	82	1	no	—
50	C₂²⋊C₄	—	82	1	no	—
51	C₂²⋊C₄	#4223	1	1	yes	characteristic, complemented
52	C₂³	—	41	1	no	—
53	C₂³	—	82	1	no	—
54	C₂³	—	164	1	no	—
55	C₂³	—	164	2	no	—
56	C₂³	C₂×#4223	1	1	yes	characteristic
57	D₄	—	164	2	no	—
58	D₄	—	164	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	41	1	no	—
61	C₂×C₄	—	164	1	no	—
62	C₈	—	164	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	4	1	no	—
65	C₂²	—	82	2	no	—
66	C₂²	—	82	1	no	—
67	C₂²	—	164	1	no	—
68	C₂²	—	164	1	no	—
69	C₂²	—	164	2	no	—
70	C₂²	—	164	2	no	—
71	C₂²	—	164	1	no	—
72	C₂²	C₂²⋊#4223	1	1	yes	characteristic
73	C₄	—	4	1	no	—
74	C₄	—	328	1	no	—
75	C₄	—	82	1	no	—
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	—	164	1	no	—
79	C₂	—	164	2	no	—
80	C₂	#13050223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13050223
commutator	C₂³×C₄₁	C₂×C₄
Frattini	C₂³	C₂×#4223
Fitting	C₂²⋊C₄×C₄₁	C₄
socle	C₂×C₄₁	#99
prime radical	#13050134	C₂
cosocle	C₂×C₂²⋊D₄₁	C₂²
hypercenter	C₂²⋊C₄	#4223
hypocenter	C₄₁	AΣL(1,𝔽₁₆)
LCS	G ▷ C₂³×C₄₁ ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #13050224	C₂	semidirect
2. #13050222	C₂	semidirect
4. C₂³×D₄₁	C₄	semidirect
9. C₂²⋊C₄×C₄₁	C₄	semidirect
41. C₄₁	AΣL(1,𝔽₁₆)	semidirect
51. C₂²⋊C₄	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050224	2
#13050222	2
#13050134	2
AΣL(1,𝔽₁₆)	41