Subgroups — #14580650

Order 2624.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050138	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050098	C₂	1	2	yes	maximal, complemented
4	#13050086	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₄₁	—	2	1	no	—
8	C₂²×Dic₄₁	—	2	1	no	—
9	C₂×D₁₆₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	2	yes	—
11	#10620281	—	2	1	no	—
12	C₄⋊Dic₄₁	—	2	1	no	—
13	C₄⋊Dic₄₁	C₂²	1	2	yes	—
14	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₄₁	D₄	1	1	yes	characteristic
16	C₂²×D₄₁	—	2	1	no	—
17	C₂×C₄×C₄₁	—	2	2	no	—
18	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
20	C₂²⋊D₄₁	—	4	2	no	—
21	C₂×Dic₄₁	—	2	2	no	—
22	C₂×Dic₄₁	—	2	1	no	—
23	C₂×Dic₄₁	—	4	2	no	—
24	D₁₆₄	—	2	2	no	—
25	C₈×C₄₁	—	2	2	no	—
26	C₂²×C₄₁	—	2	1	no	—
27	C₂²×C₄₁	—	2	1	no	—
28	C₂²×C₄₁	D₈	1	2	yes	—
29	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
30	C₂×D₄₁	—	4	1	no	—
31	C₂×D₄₁	—	4	1	no	—
32	C₂×D₄₁	—	4	1	no	—
33	C₄×C₄₁	—	2	1	no	—
34	C₄×C₄₁	#41	1	2	yes	—
35	Dic₄₁	—	4	2	no	—
36	Dic₄₁	—	4	1	no	—
37	C₂×C₄₁	—	2	2	no	—
38	C₂×C₄₁	#123	1	1	yes	characteristic
39	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
40	C₂×C₄₁	#137	1	1	yes	characteristic
41	D₄₁	—	8	1	no	—
42	#480	—	41	1	no	maximal, Sylow
43	C₄₁	#480	1	1	yes	characteristic, complemented, Sylow
44	#121	—	41	1	no	—
45	C₂×C₄⋊C₄	—	41	1	no	—
46	#107	—	41	2	no	—
47	#102	—	41	2	no	—
48	C₂²⋊C₈	D₄₁	1	1	yes	characteristic, complemented
49	C₂×D₄	—	41	1	no	—
50	C₂×D₄	—	82	1	no	—
51	C₂²×C₄	—	82	1	no	—
52	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
53	C₂×C₈	C₂×D₄₁	1	2	yes	—
54	C₄⋊C₄	—	41	2	no	—
55	C₄⋊C₄	—	41	1	no	—
56	C₄⋊C₄	—	82	1	no	—
57	C₂²⋊C₄	—	82	1	no	—
58	C₂³	—	82	1	no	—
59	C₂³	D₁₆₄	1	1	yes	characteristic
60	D₄	—	82	2	no	—
61	D₄	—	164	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	82	1	no	—
64	C₂×C₄	—	82	2	no	—
65	C₂×C₄	—	164	2	no	—
66	C₂×C₄	D₁₆₄	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	164	1	no	—
72	C₂²	—	164	1	no	—
73	C₂²	—	164	1	no	—
74	C₂²	D₃₂₈	1	2	yes	—
75	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	164	2	no	—
78	C₄	—	164	1	no	—
79	C₄	#10620308	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	328	1	no	—
82	C₂	#13050148	1	1	yes	characteristic
83	C₂	C₂×D₃₂₈	1	1	yes	characteristic
84	C₂	#13050197	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₆₄
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂²⋊C₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	#13050138	C₂
hypercenter	C₂²⋊C₈	D₄₁
hypocenter	C₄₁	#480
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₄₁	C₂	semidirect
3. #13050098	C₂	semidirect
4. #13050086	C₂	semidirect
5. C₂²⋊C₈×C₄₁	C₂	semidirect
43. C₄₁	#480	semidirect
48. C₂²⋊C₈	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050138	2
C₂×C₄⋊Dic₄₁	2
#13050098	2
#13050086	2
C₂²⋊C₈×C₄₁	2
#480	41