Subgroups — C₂×#13050095 #14580366

Order 2624.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050095	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	—	2	1	no	—
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₁	—	2	1	no	—
8	C₄⋊C₄×C₄₁	—	2	1	no	—
9	C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
10	C₄⋊Dic₄₁	—	2	1	no	—
11	C₄⋊Dic₄₁	C₂²	1	2	yes	—
12	C₂×#66491	C₄	1	4	yes	complemented
13	C₂×#66491	C₂²	1	2	yes	—
14	C₂³×C₄₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	—	2	2	no	—
16	C₂×C₄×C₄₁	—	4	2	no	—
17	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₁	Q₈	1	2	yes	—
20	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₁	—	2	2	no	—
22	C₂×Dic₄₁	—	4	2	no	—
23	#66491	C₂×C₄	1	4	yes	complemented
24	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
25	C₂²×C₄₁	SD₁₆	1	2	yes	—
26	C₂²×C₄₁	SD₁₆	1	2	yes	—
27	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₁	—	4	2	no	—
29	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₄₁	—	4	2	no	—
33	C₂×C₄₁	#106	1	4	yes	complemented
34	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×#106	—	41	1	no	maximal, Sylow
38	C₄₁	C₂×#106	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₈	—	41	1	no	—
40	C₂×C₄⋊C₄	—	41	1	no	—
41	C₂×C₄⋊C₄	D₄₁	1	1	yes	characteristic
42	#106	—	41	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	82	1	no	—
45	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
46	C₂×C₈	—	41	4	no	—
47	C₂×C₈	—	41	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	41	2	no	—
50	C₄⋊C₄	—	82	1	no	—
51	C₄⋊C₄	C₂×D₄₁	1	2	yes	—
52	C₂³	C₂²⋊D₄₁	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	82	2	no	—
56	C₂×C₄	—	164	2	no	—
57	C₂×C₄	Dic₈₂	1	2	yes	—
58	C₂×C₄	C₄×D₄₁	1	2	yes	—
59	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
61	C₈	—	41	4	no	—
62	C₂²	#10620279	1	2	yes	—
63	C₂²	#10620283	1	2	yes	—
64	C₂²	#10620284	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	164	2	no	—
68	C₄	#10620279	1	2	yes	—
69	C₄	C₂×Dic₈₂	1	1	yes	characteristic
70	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
71	C₂	#13050095	1	4	yes	direct product factor
72	C₂	C₂×#10620279	1	1	yes	characteristic
73	C₂	C₂×#10620284	1	1	yes	characteristic
74	C₂	C₂×#10620283	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #13050095	C₂	direct (N × H)
12. C₂×#66491	C₄	semidirect
23. #66491	C₂×C₄	semidirect
33. C₂×C₄₁	#106	semidirect
38. C₄₁	C₂×#106	semidirect
71. C₂	#13050095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66491	2
C₂×C₄⋊Dic₄₁	2
#13050095	2
C₂×C₄⋊C₄×C₄₁	2
C₂×#106	41

Subgroups — C2×#13050095 #14580366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050095 #14580366