Subgroups — #14581250

Order 2624.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050237	C₂	1	1	yes	maximal, characteristic, complemented
2	#13050235	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050183	C₂	1	1	yes	maximal, characteristic
4	#10620308	—	2	1	no	—
5	#10620297	—	2	1	no	—
6	D₈×C₄₁	C₄	1	1	yes	characteristic
7	#10620283	—	2	1	no	—
8	Dic₁₆₄	C₄	1	1	yes	characteristic
9	C₈×D₄₁	C₂²	1	1	yes	characteristic
10	#10620270	—	2	1	no	—
11	D₄×C₄₁	—	2	1	no	—
12	C₂²⋊D₄₁	—	4	1	no	—
13	C₂×Dic₄₁	—	4	1	no	—
14	C₄×D₄₁	D₄	1	1	yes	characteristic
15	Dic₈₂	—	2	1	no	—
16	#66493	—	4	1	no	—
17	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
18	#66491	D₄	1	1	yes	characteristic
19	C₂²×C₄₁	—	4	1	no	—
20	C₂×D₄₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₄₁	—	4	1	no	—
23	Dic₄₁	D₈	1	1	yes	characteristic
24	C₂×C₄₁	—	8	1	no	—
25	C₂×C₄₁	#102	1	1	yes	characteristic
26	D₄₁	—	2	1	no	—
27	#359	—	41	1	no	maximal, Sylow
28	C₄₁	#359	1	1	yes	characteristic, complemented, Sylow
29	#135	—	41	1	no	—
30	C₂×C₁₆	—	41	1	no	—
31	#108	—	41	1	no	—
32	#41	—	82	1	no	—
33	Q₁₆	—	41	1	no	—
34	SD₁₆	—	82	1	no	—
35	D₈	#4223	1	1	yes	characteristic
36	M₁₆	—	82	1	no	—
37	C₂×C₈	—	41	1	no	—
38	C₁₆	—	82	1	no	—
39	Q₈	—	82	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	164	1	no	—
42	C₂×C₄	—	41	1	no	—
43	C₂×C₄	—	164	1	no	—
44	C₈	—	41	1	no	—
45	C₈	—	164	1	no	—
46	C₈	C₂×#4223	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	—	41	1	no	—
49	C₄	—	41	1	no	—
50	C₄	—	164	1	no	—
51	C₄	C₂²⋊#4223	1	1	yes	characteristic
52	C₂	—	8	1	no	—
53	C₂	—	82	1	no	—
54	C₂	#13050226	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13050226
commutator	C₈×C₄₁	C₂×C₄
Frattini	C₈	C₂×#4223
Fitting	D₈×C₄₁	C₄
socle	C₂×C₄₁	#102
prime radical	#13050183	C₂
cosocle	C₈×D₄₁	C₂²
hypercenter	D₈	#4223
hypocenter	C₄₁	#359
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #13050237	C₂	semidirect
2. #13050235	C₂	semidirect
28. C₄₁	#359	semidirect

Maximal subgroups

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

subgroup	index
#13050237	2
#13050235	2
#13050183	2
#359	41