Subgroups — #14580644

Order 2624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₈₂	C₂	1	1	yes	maximal, characteristic
3	#13050098	C₂	1	1	yes	maximal, characteristic
4	#13050096	C₂	1	1	yes	maximal, characteristic
5	#13050089	C₂	1	1	yes	maximal, characteristic
6	#13050089	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
15	#10620279	—	2	1	no	—
16	#10620279	—	2	1	no	—
17	#10620279	—	2	1	no	—
18	C₄×Dic₄₁	—	2	1	no	—
19	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₁	—	2	1	no	—
23	C₂×Dic₄₁	—	2	1	no	—
24	C₂×Dic₄₁	—	2	1	no	—
25	C₂×Dic₄₁	—	2	1	no	—
26	Dic₈₂	—	2	1	no	—
27	Dic₈₂	Q₈	1	2	yes	—
28	C₈×C₄₁	—	2	1	no	—
29	C₈×C₄₁	—	2	1	no	—
30	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₁	—	2	1	no	—
32	C₄×C₄₁	—	2	1	no	—
33	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₄₁	#41	1	1	yes	characteristic
35	Dic₄₁	—	2	2	no	—
36	Dic₄₁	—	4	1	no	—
37	Dic₄₁	—	4	1	no	—
38	Dic₄₁	—	4	1	no	—
39	C₂×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₄₁	#135	1	1	yes	characteristic
41	C₂×C₄₁	#137	1	1	yes	characteristic
42	#479	—	41	1	no	maximal, Sylow
43	C₄₁	#479	1	1	yes	characteristic, complemented, Sylow
44	#125	—	41	1	no	—
45	C₄×Q₈	—	41	1	no	—
46	#107	—	41	1	no	—
47	#106	—	41	1	no	—
48	C₄⋊C₈	D₄₁	1	1	yes	characteristic
49	#103	—	41	1	no	—
50	#103	—	41	1	no	—
51	C₂×Q₈	—	41	1	no	—
52	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
53	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
54	C₄⋊C₄	—	41	1	no	—
55	C₄⋊C₄	—	41	1	no	—
56	C₄⋊C₄	—	41	1	no	—
57	C₄⋊C₄	—	82	1	no	—
58	C₄⋊C₄	—	82	1	no	—
59	C₄⋊C₄	—	82	1	no	—
60	C₄²	—	82	1	no	—
61	C₄²	C₂×D₄₁	1	1	yes	characteristic
62	Q₈	—	41	2	no	—
63	Q₈	—	82	1	no	—
64	C₂×C₄	—	82	1	no	—
65	C₂×C₄	—	82	1	no	—
66	C₂×C₄	—	82	1	no	—
67	C₂×C₄	—	82	1	no	—
68	C₂×C₄	D₁₆₄	1	1	yes	characteristic
69	C₂×C₄	D₁₆₄	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	82	2	no	—
77	C₄	—	164	1	no	—
78	C₄	—	164	1	no	—
79	C₄	—	164	1	no	—
80	C₄	#10620308	1	1	yes	characteristic
81	C₄	Q₈×D₄₁	1	1	yes	characteristic
82	C₂	#13050144	1	1	yes	characteristic
83	C₂	#13050186	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	C₄⋊C₈×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
hypercenter	C₄⋊C₈	D₄₁
hypocenter	C₄₁	#479
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
43. C₄₁	#479	semidirect

Maximal subgroups

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

subgroup	index
#13050156	2
C₄×Dic₈₂	2
#13050098	2
#13050096	2
#13050089	2
C₄⋊C₈×C₄₁	2
#479	41