Subgroups — #14580678

Order 2624.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050143	C₂	1	1	yes	maximal, characteristic
2	#13050123	C₂	1	1	yes	maximal, characteristic
3	#13050098	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050096	C₂	1	1	yes	maximal, characteristic, complemented
5	#13050089	C₂	1	1	yes	maximal, characteristic, complemented
6	#13050089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²⋊Dic₄₁	—	2	1	no	—
13	C₂²⋊Dic₄₁	—	2	1	no	—
14	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
17	#10620279	—	2	1	no	—
18	C₄×Dic₄₁	—	2	1	no	—
19	C₂³×C₄₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	—	2	1	no	—
21	C₂×C₄×C₄₁	—	2	1	no	—
22	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₁	—	2	1	no	—
25	C₂×Dic₄₁	—	2	1	no	—
26	C₂×Dic₄₁	—	2	1	no	—
27	C₂×Dic₄₁	—	2	1	no	—
28	Dic₈₂	—	2	1	no	—
29	Dic₈₂	—	2	1	no	—
30	C₈×C₄₁	—	2	1	no	—
31	C₈×C₄₁	—	2	1	no	—
32	C₂²×C₄₁	—	2	1	no	—
33	C₂²×C₄₁	—	2	1	no	—
34	C₂²×C₄₁	—	2	1	no	—
35	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₁	—	2	1	no	—
37	C₄×C₄₁	#41	1	1	yes	characteristic
38	C₄×C₄₁	#41	1	1	yes	characteristic
39	Dic₄₁	—	4	1	no	—
40	Dic₄₁	—	4	1	no	—
41	Dic₄₁	—	4	1	no	—
42	Dic₄₁	—	4	1	no	—
43	C₂×C₄₁	—	4	1	no	—
44	C₂×C₄₁	#123	1	1	yes	characteristic
45	C₂×C₄₁	#135	1	1	yes	characteristic
46	C₂×C₄₁	#137	1	1	yes	characteristic
47	#485	—	41	1	no	maximal, Sylow
48	C₄₁	#485	1	1	yes	characteristic, complemented, Sylow
49	C₂²⋊Q₈	—	41	1	no	—
50	#117	—	41	1	no	—
51	#107	—	41	1	no	—
52	#106	—	41	1	no	—
53	#103	—	41	1	no	—
54	#103	—	41	1	no	—
55	C₂²⋊C₈	D₄₁	1	1	yes	characteristic
56	C₂×Q₈	—	41	1	no	—
57	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
58	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
59	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
60	C₄⋊C₄	—	41	1	no	—
61	C₄⋊C₄	—	41	1	no	—
62	C₄⋊C₄	—	41	1	no	—
63	C₄⋊C₄	—	82	1	no	—
64	C₂²⋊C₄	—	82	1	no	—
65	C₂²⋊C₄	—	82	1	no	—
66	C₄²	—	82	1	no	—
67	C₂³	D₁₆₄	1	1	yes	characteristic
68	Q₈	—	82	1	no	—
69	Q₈	—	82	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	82	1	no	—
73	C₂×C₄	—	82	1	no	—
74	C₂×C₄	—	82	1	no	—
75	C₂×C₄	—	82	1	no	—
76	C₂×C₄	D₁₆₄	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	164	1	no	—
86	C₄	—	164	1	no	—
87	C₄	—	164	1	no	—
88	C₄	—	164	1	no	—
89	C₄	#10620308	1	1	yes	characteristic
90	C₄	#10620308	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	#13050148	1	1	yes	characteristic
93	C₂	#13050186	1	1	yes	characteristic
94	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	C₂³×C₄₁	D₄
hypercenter	C₂²⋊C₈	D₄₁
hypocenter	C₄₁	#485
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
3. #13050098	C₂	semidirect
4. #13050096	C₂	semidirect
5. #13050089	C₂	semidirect
6. #13050089	C₂	semidirect
48. C₄₁	#485	semidirect

Maximal subgroups

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

subgroup	index
#13050143	2
#13050123	2
#13050098	2
#13050096	2
#13050089	2
C₂²⋊C₈×C₄₁	2
#485	41