Subgroups — #14580458

Order 2624.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050171	C₂	1	2	yes	maximal, complemented
2	#13050100	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050091	C₂	1	2	yes	maximal, complemented
4	#13050074	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₄₁	C₂	1	1	yes	maximal, characteristic
6	#41×C₄₁	C₂²	1	2	yes	—
7	Q₁₆×C₄₁	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₄₁	C₄	1	2	yes	complemented
9	D₈×C₄₁	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
12	#10620277	—	2	2	no	—
13	#10620277	C₂²	1	2	yes	—
14	C₂×#66491	—	2	2	no	—
15	C₂×#66491	C₂²	1	1	yes	characteristic
16	Q₈×C₄₁	C₂×C₄	1	2	yes	—
17	D₄×C₄₁	—	2	2	no	—
18	D₄×C₄₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₁	—	2	2	no	—
20	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₁	—	2	1	no	—
22	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
24	#66491	—	2	2	no	—
25	#66491	D₄	1	2	yes	—
26	C₂²×C₄₁	—	2	2	no	—
27	C₂²×C₄₁	#41	1	1	yes	characteristic
28	C₄×C₄₁	—	2	2	no	—
29	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
31	Dic₄₁	—	4	1	no	—
32	C₂×C₄₁	—	2	1	no	—
33	C₂×C₄₁	—	4	2	no	—
34	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
35	#444	—	41	1	no	maximal, Sylow
36	C₄₁	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	D₄₁	1	1	yes	characteristic
38	#131	—	41	2	no	—
39	#108	—	41	1	no	—
40	#104	—	41	2	no	—
41	#97	—	41	1	no	—
42	#41	C₂×D₄₁	1	2	yes	—
43	Q₁₆	Dic₄₁	1	1	yes	characteristic, complemented
44	SD₁₆	Dic₄₁	1	2	yes	complemented
45	D₈	Dic₄₁	1	1	yes	characteristic, complemented
46	M₁₆	—	41	2	no	—
47	M₁₆	—	82	2	no	—
48	C₂×C₈	—	41	1	no	—
49	C₂×C₈	—	82	2	no	—
50	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
51	C₄²	—	41	1	no	—
52	Q₈	C₂×Dic₄₁	1	2	yes	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₄₁	1	2	yes	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	82	1	no	—
57	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
58	C₈	—	41	2	no	—
59	C₈	—	82	2	no	—
60	C₈	C₂×Dic₄₁	1	1	yes	characteristic
61	C₈	C₂×Dic₄₁	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	#10620308	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	164	1	no	—
66	C₄	D₄×D₄₁	1	1	yes	characteristic
67	C₄	C₂²×Dic₄₁	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	2	no	—
70	C₂	D₄×Dic₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₁
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting, prime radical	#135×C₄₁	C₂
socle	C₂×C₄₁	C₄×D₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	#135	D₄₁
hypocenter	C₄₁	#444
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #13050171	C₂	semidirect
2. #13050100	C₂	semidirect
3. #13050091	C₂	semidirect
4. #13050074	C₂	semidirect
7. Q₁₆×C₄₁	C₄	semidirect
8. SD₁₆×C₄₁	C₄	semidirect
9. D₈×C₄₁	C₄	semidirect
36. C₄₁	#444	semidirect
43. Q₁₆	Dic₄₁	semidirect
44. SD₁₆	Dic₄₁	semidirect
45. D₈	Dic₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050171	2
#13050100	2
#13050091	2
#13050074	2
#135×C₄₁	2
#444	41