Subgroups — C₂×#31772559 #46830205

Order 34624.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864513	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅₄₁	C₂	1	1	yes	maximal, characteristic
3	#31772559	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₅₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₅₄₁	—	2	1	no	—
6	C₂×#16864513	C₄	1	4	yes	complemented
7	C₂×#16864513	C₂²	1	2	yes	—
8	C₄⋊Dic₅₄₁	—	2	1	no	—
9	C₄⋊Dic₅₄₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₅₄₁	—	2	1	no	—
11	C₂²×C₄×C₅₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₅₄₁	—	2	1	no	—
13	C₄⋊C₄×C₅₄₁	C₂²	1	2	yes	—
14	C₂×Dic₅₄₁	—	2	2	no	—
15	C₂×Dic₅₄₁	—	4	2	no	—
16	#16864513	C₂×C₄	1	4	yes	complemented
17	C₂³×C₅₄₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₅₄₁	—	2	2	no	—
19	C₂×C₄×C₅₄₁	—	4	2	no	—
20	C₂×C₄×C₅₄₁	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅₄₁	Q₈	1	2	yes	—
23	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
24	C₂²×C₅₄₁	C₄⋊C₄	1	2	yes	—
25	C₂²×C₅₄₁	SD₁₆	1	2	yes	—
26	C₂²×C₅₄₁	SD₁₆	1	2	yes	—
27	C₂²×C₅₄₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₅₄₁	—	4	2	no	—
29	C₄×C₅₄₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₅₄₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₅₄₁	—	4	2	no	—
33	C₂×C₅₄₁	#106	1	4	yes	complemented
34	C₂×C₅₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅₄₁	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₅₄₁	C₂×SD₁₆	1	1	yes	characteristic
37	C₅₄₁	C₂×#106	1	1	yes	characteristic, complemented, Sylow
38	C₂×#106	—	541	1	no	maximal, Sylow
39	C₂²×C₈	—	541	1	no	—
40	C₂×C₄⋊C₄	—	541	1	no	—
41	C₂×C₄⋊C₄	D₅₄₁	1	1	yes	characteristic
42	#106	—	541	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	1082	1	no	—
45	C₂²×C₄	C₂×D₅₄₁	1	1	yes	characteristic
46	C₂×C₈	—	541	4	no	—
47	C₂×C₈	—	541	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	541	2	no	—
50	C₄⋊C₄	—	1082	1	no	—
51	C₄⋊C₄	C₂×D₅₄₁	1	2	yes	—
52	C₂³	C₂²⋊D₅₄₁	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	1082	2	no	—
56	C₂×C₄	—	2164	2	no	—
57	C₂×C₄	C₄×D₅₄₁	1	2	yes	—
58	C₂×C₄	C₂²⋊D₅₄₁	1	1	yes	characteristic
59	C₂×C₄	Dic₁₀₈₂	1	2	yes	—
60	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
61	C₈	—	541	4	no	—
62	C₂²	#22575815	1	2	yes	—
63	C₂²	#22575823	1	2	yes	—
64	C₂²	#22575824	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₅₄₁	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	2164	2	no	—
68	C₄	#22575815	1	2	yes	—
69	C₄	C₂×C₄×D₅₄₁	1	1	yes	characteristic
70	C₄	C₂×Dic₁₀₈₂	1	1	yes	characteristic
71	C₂	#31772559	1	4	yes	direct product factor
72	C₂	C₂×#22575815	1	1	yes	characteristic
73	C₂	C₂×#22575823	1	1	yes	characteristic
74	C₂	C₂×#22575824	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₅₄₁
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₄₁
Fitting	C₂×C₄⋊C₄×C₅₄₁	C₂
socle, prime radical	C₂³×C₅₄₁	D₄
cosocle	C₂×C₄×C₅₄₁	C₂³
hypercenter	C₂×C₄⋊C₄	D₅₄₁
hypocenter	C₅₄₁	C₂×#106
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
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. #31772559	C₂	direct (N × H)
6. C₂×#16864513	C₄	semidirect
16. #16864513	C₂×C₄	semidirect
33. C₂×C₅₄₁	#106	semidirect
37. C₅₄₁	C₂×#106	semidirect
71. C₂	#31772559	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×#16864513	2
C₂×C₄⋊Dic₅₄₁	2
#31772559	2
C₂×C₄⋊C₄×C₅₄₁	2
C₂×#106	541

Subgroups — C2×#31772559 #46830205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31772559 #46830205