Subgroups — #46830549

Order 34624.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575823	C₂	1	4	yes	maximal, complemented
2	#31772625	C₂	1	1	yes	maximal, characteristic
3	C₄×#16864513	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₁₆₄	—	2	2	no	—
6	C₂×D₂₁₆₄	C₂²	1	2	yes	—
7	#22575823	—	2	8	no	—
8	C₂×#16864513	C₂²	1	2	yes	—
9	C₂×Q₈×C₅₄₁	C₂²	1	2	yes	—
10	C₄⋊C₄×C₅₄₁	—	2	2	no	—
11	C₄²×C₅₄₁	C₂²	1	1	yes	characteristic
12	C₂²×D₅₄₁	—	2	2	no	—
13	D₂₁₆₄	—	2	4	no	—
14	D₂₁₆₄	—	4	4	no	—
15	#16864513	D₄	1	4	yes	complemented
16	Q₈×C₅₄₁	—	2	4	no	—
17	C₂×C₄×C₅₄₁	—	2	2	no	—
18	C₂×C₄×C₅₄₁	D₄	1	2	yes	—
19	C₂×C₄×C₅₄₁	C₂³	1	1	yes	characteristic
20	C₂²×C₅₄₁	C₂×D₄	1	1	yes	characteristic
21	C₂×D₅₄₁	—	4	2	no	—
22	C₂×D₅₄₁	—	4	4	no	—
23	C₄×C₅₄₁	—	4	2	no	—
24	C₄×C₅₄₁	SD₁₆	1	4	yes	complemented
25	C₄×C₅₄₁	C₂×D₄	1	2	yes	—
26	C₂×C₅₄₁	#127	1	1	yes	characteristic
27	C₂×C₅₄₁	C₂×SD₁₆	1	2	yes	—
28	D₅₄₁	—	8	2	no	—
29	C₅₄₁	#492	1	1	yes	characteristic, complemented, Sylow
30	#492	—	541	1	no	maximal, Sylow
31	C₂×SD₁₆	—	541	4	no	—
32	C₄⋊Q₈	D₅₄₁	1	1	yes	characteristic, complemented
33	#127	—	541	1	no	—
34	C₄×C₈	—	541	1	no	—
35	C₂×Q₈	C₂×D₅₄₁	1	2	yes	—
36	C₂×D₄	—	541	2	no	—
37	C₂×D₄	—	1082	2	no	—
38	SD₁₆	—	1082	8	no	—
39	C₂×C₈	—	541	2	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂×D₅₄₁	1	1	yes	characteristic
42	C₂³	—	1082	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	1082	4	no	—
45	D₄	—	2164	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂²⋊D₅₄₁	1	2	yes	—
48	C₂×C₄	C₂²×D₅₄₁	1	1	yes	characteristic
49	C₈	—	541	4	no	—
50	C₂²	—	2164	2	no	—
51	C₂²	—	2164	4	no	—
52	C₂²	C₂×C₂²⋊D₅₄₁	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#22575823	1	4	yes	complemented
55	C₄	D₄×D₅₄₁	1	2	yes	—
56	C₂	—	4328	2	no	—
57	C₂	#31772624	1	1	yes	characteristic
58	C₂	C₂×#22575823	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₄₁
commutator, cosocle	C₂×C₄×C₅₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₅₄₁
Fitting	C₄⋊Q₈×C₅₄₁	C₂
socle	C₂²×C₅₄₁	C₂×D₄
prime radical	#31772625	C₂
hypercenter	C₄⋊Q₈	D₅₄₁
hypocenter	C₅₄₁	#492
LCS	G ▷ C₂×C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#22575823	C₂	semidirect
3. C₄×#16864513	C₂	semidirect
4. C₄⋊Q₈×C₅₄₁	C₂	semidirect
15. #16864513	D₄	semidirect
24. C₄×C₅₄₁	SD₁₆	semidirect
29. C₅₄₁	#492	semidirect
32. C₄⋊Q₈	D₅₄₁	semidirect
54. C₄	#22575823	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575823	2
#31772625	2
C₄×#16864513	2
C₄⋊Q₈×C₅₄₁	2
#492	541