Subgroups — #14580459

Order 2624.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050186	C₂	1	1	yes	maximal, characteristic
2	#13050170	C₂	1	2	yes	maximal, complemented
3	#13050100	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050092	C₂	1	2	yes	maximal, complemented
5	#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10620306	C₂²	1	2	yes	—
7	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	#10620277	C₂²	1	2	yes	—
11	Dic₁₆₄	C₄	1	1	yes	characteristic, complemented
12	D₃₂₈	C₄	1	1	yes	characteristic, complemented
13	#10620273	C₄	1	2	yes	complemented
14	#10620272	—	2	2	no	—
15	C₈×D₄₁	—	2	2	no	—
16	C₂×C₄×C₄₁	—	2	1	no	—
17	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
18	C₂²⋊D₄₁	—	2	2	no	—
19	D₁₆₄	C₂×C₄	1	2	yes	—
20	C₄×D₄₁	—	2	2	no	—
21	Dic₈₂	C₂×C₄	1	2	yes	—
22	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₁	D₄	1	2	yes	—
25	#66491	—	2	2	no	—
26	C₂²×C₄₁	#41	1	1	yes	characteristic
27	C₂×D₄₁	—	2	2	no	—
28	C₄×C₄₁	—	4	1	no	—
29	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
31	Dic₄₁	—	2	2	no	—
32	C₂×C₄₁	—	2	1	no	—
33	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
34	D₄₁	—	4	2	no	—
35	#444	—	41	1	no	maximal, Sylow
36	C₄₁	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	—	41	1	no	—
38	#131	—	41	2	no	—
39	#108	—	41	1	no	—
40	#104	—	41	2	no	—
41	#97	D₄₁	1	1	yes	characteristic, complemented
42	#41	—	41	2	no	—
43	Q₁₆	—	41	1	no	—
44	SD₁₆	—	41	2	no	—
45	D₈	—	41	1	no	—
46	M₁₆	—	41	2	no	—
47	M₁₆	—	82	2	no	—
48	C₂×C₈	—	82	2	no	—
49	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
50	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
51	C₄²	C₂×D₄₁	1	1	yes	characteristic
52	Q₈	—	41	2	no	—
53	D₄	—	41	2	no	—
54	D₄	—	82	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	82	2	no	—
57	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
58	C₈	—	82	2	no	—
59	C₈	C₄×D₄₁	1	1	yes	characteristic
60	C₈	C₄×D₄₁	1	1	yes	characteristic
61	C₈	D₁₆₄	1	2	yes	—
62	C₂²	—	82	2	no	—
63	C₂²	#10620306	1	1	yes	characteristic
64	C₄	—	4	1	no	—
65	C₄	—	82	2	no	—
66	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
67	C₄	C₂×D₁₆₄	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	164	2	no	—
70	C₂	C₄×D₁₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₆₄
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#97×C₄₁	C₂
socle	C₂×C₄₁	C₄×D₄
prime radical	#13050186	C₂
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	#97	D₄₁
hypocenter	C₄₁	#444
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #13050170	C₂	semidirect
3. #13050100	C₂	semidirect
4. #13050092	C₂	semidirect
5. #97×C₄₁	C₂	semidirect
11. Dic₁₆₄	C₄	semidirect
12. D₃₂₈	C₄	semidirect
13. #10620273	C₄	semidirect
36. C₄₁	#444	semidirect
41. #97	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050186	2
#13050170	2
#13050100	2
#13050092	2
#97×C₄₁	2
#444	41