Subgroups — C₂×#22576759 #31776006

Order 17504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₄₇	C₂	1	1	yes	maximal, characteristic
2	#22576759	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₅₄₇	C₄	1	1	yes	characteristic
6	C₂×Dic₅₄₇	C₄	1	1	yes	characteristic
7	C₄×D₅₄₇	C₄	1	2	yes	—
8	C₄×D₅₄₇	C₂²	1	2	yes	—
9	C₅₄₇⋊C₈	C₂²	1	2	yes	complemented
10	C₂×C₄×C₅₄₇	C₂²	1	1	yes	characteristic
11	C₈×C₅₄₇	C₂²	1	2	yes	complemented
12	C₂²×C₅₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×D₅₄₇	—	2	2	no	—
14	C₂×D₅₄₇	C₂×C₄	1	2	yes	—
15	C₄×C₅₄₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₅₄₇	C₂³	1	1	yes	characteristic
17	Dic₅₄₇	C₂×C₄	1	2	yes	—
18	C₂×C₅₄₇	M₁₆	1	2	yes	complemented
19	C₂×C₅₄₇	C₂²×C₄	1	1	yes	characteristic
20	D₅₄₇	—	2	2	no	—
21	C₅₄₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×M₁₆	—	547	1	no	maximal, Sylow
23	C₂²×C₄	—	547	1	no	—
24	M₁₆	—	547	4	no	—
25	C₂×C₈	—	547	1	no	—
26	C₂×C₈	D₅₄₇	1	1	yes	characteristic, complemented
27	C₂³	—	547	1	no	—
28	C₂×C₄	—	547	1	no	—
29	C₂×C₄	—	547	2	no	—
30	C₂×C₄	—	547	2	no	—
31	C₂×C₄	C₂×D₅₄₇	1	1	yes	characteristic
32	C₈	—	547	2	no	—
33	C₈	C₂×D₅₄₇	1	2	yes	complemented
34	C₂²	—	547	2	no	—
35	C₂²	—	1094	2	no	—
36	C₂²	C₄×D₅₄₇	1	1	yes	characteristic
37	C₄	—	547	2	no	—
38	C₄	C₄×D₅₄₇	1	1	yes	characteristic
39	C₄	C₂²×D₅₄₇	1	1	yes	characteristic
40	C₂	—	1094	2	no	—
41	C₂	#22576759	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₅₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₅₄₇
commutator	C₂×C₅₄₇	C₂²×C₄
Frattini	C₄	C₂²×D₅₄₇
Fitting	C₂×C₈×C₅₄₇	C₂
socle	C₂²×C₅₄₇	C₂×C₄
prime radical	C₂²×D₅₄₇	C₄
cosocle	C₄×C₅₄₇	C₂³
hypercenter	C₂×C₈	D₅₄₇
hypocenter	C₅₄₇	C₂×M₁₆
LCS	G ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #22576759	C₂	direct (N × H)
3. C₂×C₅₄₇⋊C₈	C₂	semidirect
4. C₂×C₈×C₅₄₇	C₂	semidirect
9. C₅₄₇⋊C₈	C₂²	semidirect
11. C₈×C₅₄₇	C₂²	semidirect
18. C₂×C₅₄₇	M₁₆	semidirect
21. C₅₄₇	C₂×M₁₆	semidirect
26. C₂×C₈	D₅₄₇	semidirect
33. C₈	C₂×D₅₄₇	semidirect
41. C₂	#22576759	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅₄₇	2
#22576759	2
C₂×C₅₄₇⋊C₈	2
C₂×C₈×C₅₄₇	2
C₂×M₁₆	547

Subgroups — C2×#22576759 #31776006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22576759 #31776006