Subgroups — #14580668

Order 2624.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050144	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050095	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050089	C₂	1	1	yes	maximal, characteristic, complemented
5	#13050087	C₂	1	1	yes	maximal, characteristic, complemented
6	#13050076	C₂	1	1	yes	maximal, characteristic
7	#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₁	—	2	1	no	—
9	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
14	#10620281	—	2	1	no	—
15	C₄⋊Dic₄₁	—	2	1	no	—
16	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
17	#10620279	—	2	1	no	—
18	C₂×#66491	C₂²	1	1	yes	characteristic
19	C₂²×D₄₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	—	2	1	no	—
21	C₂×C₄×C₄₁	—	2	1	no	—
22	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₁	—	2	1	no	—
24	C₂×Dic₄₁	—	2	1	no	—
25	C₂×Dic₄₁	D₄	1	1	yes	characteristic
26	C₄×D₄₁	—	2	1	no	—
27	C₄×D₄₁	—	2	1	no	—
28	C₄×D₄₁	—	4	2	no	—
29	Dic₈₂	—	2	1	no	—
30	Dic₈₂	—	2	1	no	—
31	C₈×C₄₁	—	2	1	no	—
32	#66491	—	2	1	no	—
33	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
34	C₂×D₄₁	—	2	1	no	—
35	C₂×D₄₁	—	2	1	no	—
36	C₂×D₄₁	SD₁₆	1	2	yes	—
37	C₄×C₄₁	—	4	1	no	—
38	C₄×C₄₁	—	4	1	no	—
39	C₄×C₄₁	#41	1	1	yes	characteristic
40	C₄×C₄₁	#41	1	1	yes	characteristic
41	Dic₄₁	—	2	1	no	—
42	Dic₄₁	—	4	1	no	—
43	Dic₄₁	—	4	1	no	—
44	C₂×C₄₁	#123	1	1	yes	characteristic
45	C₂×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₄₁	#137	1	1	yes	characteristic
47	D₄₁	—	2	2	no	—
48	#483	—	41	1	no	maximal, Sylow
49	C₄₁	#483	1	1	yes	characteristic, complemented, Sylow
50	C₂²⋊Q₈	—	41	1	no	—
51	C₂×C₄⋊C₄	—	41	1	no	—
52	#106	—	41	1	no	—
53	#106	D₄₁	1	1	yes	characteristic, complemented
54	#103	—	41	1	no	—
55	#103	—	41	1	no	—
56	C₂²⋊C₈	—	41	1	no	—
57	C₂×Q₈	—	41	1	no	—
58	C₂²×C₄	—	41	1	no	—
59	C₂²×C₄	—	82	1	no	—
60	C₂×C₈	—	41	1	no	—
61	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
62	C₄⋊C₄	—	41	1	no	—
63	C₄⋊C₄	—	82	1	no	—
64	C₄⋊C₄	—	82	1	no	—
65	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
66	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
67	C₂²⋊C₄	—	82	1	no	—
68	C₂³	—	41	1	no	—
69	Q₈	—	82	1	no	—
70	Q₈	—	82	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	41	1	no	—
74	C₂×C₄	—	82	1	no	—
75	C₂×C₄	—	82	1	no	—
76	C₂×C₄	—	82	1	no	—
77	C₂×C₄	—	82	1	no	—
78	C₂×C₄	—	164	2	no	—
79	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	82	1	no	—
82	C₂²	—	41	2	no	—
83	C₂²	—	82	1	no	—
84	C₂²	—	82	1	no	—
85	C₂²	D₄×D₄₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	82	1	no	—
89	C₄	—	164	1	no	—
90	C₄	—	164	1	no	—
91	C₄	#10620306	1	1	yes	characteristic
92	C₄	#10620310	1	1	yes	characteristic
93	C₂	—	82	2	no	—
94	C₂	#13050149	1	1	yes	characteristic
95	C₂	SD₁₆×D₄₁	1	1	yes	characteristic
96	C₂	#13050193	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#106×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	C₂²×D₄₁	D₄
hypercenter	#106	D₄₁
hypocenter	C₄₁	#483
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #13050095	C₂	semidirect
4. #13050089	C₂	semidirect
5. #13050087	C₂	semidirect
7. #106×C₄₁	C₂	semidirect
49. C₄₁	#483	semidirect
53. #106	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050144	2
C₄⋊C₄×D₄₁	2
#13050095	2
#13050089	2
#13050087	2
#13050076	2
#106×C₄₁	2
#483	41