Subgroups — C₂×#31772553 #46830167

Order 34624.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₈₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅₄₁	C₂	1	1	yes	maximal, characteristic
3	#31772553	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₀₈₂	—	2	2	no	—
6	C₂×Dic₁₀₈₂	—	2	1	no	—
7	C₂×Dic₁₀₈₂	C₄	1	4	yes	complemented
8	C₂×Dic₁₀₈₂	C₂²	1	2	yes	—
9	C₂²×Dic₅₄₁	—	2	1	no	—
10	C₂²×Dic₅₄₁	—	2	1	no	—
11	C₄⋊Dic₅₄₁	—	2	1	no	—
12	C₄⋊Dic₅₄₁	C₂²	1	2	yes	—
13	C₂²×C₄×C₅₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₅₄₁	—	2	2	no	—
15	C₂×C₈×C₅₄₁	C₂²	1	2	yes	—
16	Dic₁₀₈₂	—	2	4	no	—
17	Dic₁₀₈₂	—	2	2	no	—
18	Dic₁₀₈₂	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₅₄₁	—	2	4	no	—
20	C₂×Dic₅₄₁	—	2	2	no	—
21	C₂×Dic₅₄₁	—	2	2	no	—
22	C₂×Dic₅₄₁	—	4	2	no	—
23	C₂³×C₅₄₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅₄₁	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₅₄₁	D₄	1	2	yes	—
26	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
27	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
28	C₈×C₅₄₁	—	2	2	no	—
29	C₂²×C₅₄₁	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₅₄₁	SD₁₆	1	2	yes	—
31	C₂²×C₅₄₁	Q₁₆	1	2	yes	—
32	C₂²×C₅₄₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅₄₁	C₂²⋊C₄	1	2	yes	—
34	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₅₄₁	C₂×D₄	1	1	yes	characteristic
36	Dic₅₄₁	—	2	4	no	—
37	Dic₅₄₁	—	4	2	no	—
38	C₂×C₅₄₁	#103	1	4	yes	complemented
39	C₂×C₅₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₅₄₁	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₅₄₁	C₂×Q₁₆	1	1	yes	characteristic
42	C₅₄₁	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	541	1	no	maximal, Sylow
44	C₂²×Q₈	—	541	1	no	—
45	C₂²×C₈	D₅₄₁	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	541	1	no	—
47	#103	—	541	4	no	—
48	C₂×Q₈	—	541	4	no	—
49	C₂×Q₈	—	541	2	no	—
50	C₂×Q₈	—	1082	2	no	—
51	C₂×Q₈	—	1082	1	no	—
52	C₂²×C₄	—	1082	1	no	—
53	C₂²×C₄	—	1082	1	no	—
54	C₂²×C₄	C₂×D₅₄₁	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₅₄₁	1	2	yes	—
57	C₄⋊C₄	—	541	2	no	—
58	C₄⋊C₄	—	1082	1	no	—
59	C₂³	D₂₁₆₄	1	1	yes	characteristic
60	Q₈	—	541	4	no	—
61	Q₈	—	1082	4	no	—
62	Q₈	—	1082	2	no	—
63	C₂×C₄	—	1082	4	no	—
64	C₂×C₄	—	1082	2	no	—
65	C₂×C₄	—	1082	2	no	—
66	C₂×C₄	—	2164	2	no	—
67	C₂×C₄	C₄×D₅₄₁	1	2	yes	—
68	C₂×C₄	C₂²⋊D₅₄₁	1	2	yes	—
69	C₂×C₄	D₂₁₆₄	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	#22575813	1	2	yes	—
73	C₂²	#22575825	1	2	yes	—
74	C₂²	Dic₂₁₆₄	1	2	yes	—
75	C₂²	C₂×D₂₁₆₄	1	1	yes	characteristic
76	C₄	—	1082	4	no	—
77	C₄	—	2164	2	no	—
78	C₄	#22575813	1	2	yes	—
79	C₄	C₂×C₄×D₅₄₁	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₅₄₁	1	1	yes	characteristic
81	C₂	#31772553	1	4	yes	direct product factor
82	C₂	C₂×#22575813	1	1	yes	characteristic
83	C₂	C₂×#22575825	1	1	yes	characteristic
84	C₂	C₂×Dic₂₁₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₁₆₄
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₄₁
Fitting	C₂²×C₈×C₅₄₁	C₂
socle, prime radical	C₂³×C₅₄₁	D₄
cosocle	C₂×C₄×C₅₄₁	C₂³
hypercenter	C₂²×C₈	D₅₄₁
hypocenter	C₅₄₁	C₂×#103
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #31772553	C₂	direct (N × H)
7. C₂×Dic₁₀₈₂	C₄	semidirect
18. Dic₁₀₈₂	C₂×C₄	semidirect
38. C₂×C₅₄₁	#103	semidirect
42. C₅₄₁	C₂×#103	semidirect
81. C₂	#31772553	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×Dic₁₀₈₂	2
C₂×C₄⋊Dic₅₄₁	2
#31772553	2
C₂²×C₈×C₅₄₁	2
C₂×#103	541

Subgroups — C2×#31772553 #46830167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31772553 #46830167