Subgroups — #14580541

Order 2624.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620283	C₂	1	2	yes	maximal
2	#13050164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#66491	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050087	C₂	1	2	yes	maximal, complemented
5	C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₄₁	—	2	1	no	—
8	C₂×Dic₈₂	C₂²	1	2	yes	—
9	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²⋊C₄×C₄₁	—	2	1	no	—
11	C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	#10620283	—	2	4	no	—
13	C₄⋊Dic₄₁	—	2	1	no	—
14	C₄⋊Dic₄₁	—	2	1	no	—
15	C₂×#66491	C₂²	1	2	yes	—
16	C₂³×C₄₁	—	2	1	no	—
17	D₄×C₄₁	—	2	1	no	—
18	D₄×C₄₁	D₄	1	2	yes	—
19	C₂×C₄×C₄₁	—	2	1	no	—
20	C₂×C₄×C₄₁	—	4	2	no	—
21	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₁	—	2	2	no	—
25	Dic₈₂	—	2	2	no	—
26	Dic₈₂	—	2	2	no	—
27	#66491	—	2	2	no	—
28	C₂²×C₄₁	—	2	2	no	—
29	C₂²×C₄₁	—	4	1	no	—
30	C₂²×C₄₁	—	4	1	no	—
31	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₁	—	2	1	no	—
33	C₄×C₄₁	—	4	1	no	—
34	C₄×C₄₁	SD₁₆	1	2	yes	complemented
35	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₁	#41	1	1	yes	characteristic
37	Dic₄₁	—	4	2	no	—
38	C₂×C₄₁	—	4	2	no	—
39	C₂×C₄₁	#121	1	1	yes	characteristic
40	C₂×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₄₁	#137	1	1	yes	characteristic
42	#461	—	41	1	no	maximal, Sylow
43	C₄₁	#461	1	1	yes	characteristic, complemented, Sylow
44	C₂×SD₁₆	—	41	2	no	—
45	C₄⋊Q₈	—	41	1	no	—
46	C₄×D₄	D₄₁	1	1	yes	characteristic
47	C₄⋊C₈	—	41	1	no	—
48	#103	—	41	2	no	—
49	C₂×Q₈	—	41	2	no	—
50	C₂×D₄	C₂×D₄₁	1	1	yes	characteristic
51	C₂²×C₄	—	2	1	no	—
52	SD₁₆	—	82	4	no	—
53	C₂×C₈	—	41	2	no	—
54	C₄⋊C₄	—	82	1	no	—
55	C₄⋊C₄	—	82	1	no	—
56	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
57	C₂²⋊C₄	—	2	1	no	—
58	C₄²	C₂×D₄₁	1	1	yes	characteristic
59	C₂³	—	2	1	no	—
60	Q₈	—	82	2	no	—
61	Q₈	—	82	2	no	—
62	D₄	—	2	1	no	—
63	D₄	D₁₆₄	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	82	2	no	—
67	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
70	C₈	—	82	2	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	164	2	no	—
78	C₄	#10620283	1	2	yes	complemented
79	C₄	C₂×D₁₆₄	1	1	yes	characteristic
80	C₄	#10620306	1	1	yes	characteristic
81	C₂	—	4	2	no	—
82	C₂	#13050138	1	1	yes	characteristic
83	C₂	C₂×#10620283	1	1	yes	characteristic
84	C₂	#13050194	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₄×D₄×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	C₂×D₄×C₄₁	C₂²
hypercenter	C₄×D₄	D₄₁
hypocenter	C₄₁	#461
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #13050164	C₂	semidirect
3. C₄⋊#66491	C₂	semidirect
4. #13050087	C₂	semidirect
34. C₄×C₄₁	SD₁₆	semidirect
43. C₄₁	#461	semidirect
78. C₄	#10620283	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620283	2
#13050164	2
C₄⋊#66491	2
#13050087	2
C₄×D₄×C₄₁	2
#461	41