Subgroups — #46855124

Order 35008.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31776024	C₂	1	1	yes	maximal, characteristic
2	#31776008	C₂	1	2	yes	maximal, complemented
3	#31775938	C₂	1	1	yes	maximal, characteristic, complemented
4	#31775930	C₂	1	2	yes	maximal, complemented
5	#97×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#22576776	C₂²	1	2	yes	—
7	Dic₂₁₈₈	C₄	1	1	yes	characteristic, complemented
8	#22576765	C₄	1	2	yes	complemented
9	D₄₃₇₆	C₄	1	1	yes	characteristic, complemented
10	#22576760	C₂²	1	2	yes	—
11	#22576759	—	2	2	no	—
12	C₈×D₅₄₇	—	2	2	no	—
13	C₂×C₈×C₅₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₅₄₇	C₂²	1	1	yes	characteristic
15	C₄²×C₅₄₇	C₂²	1	1	yes	characteristic
16	Dic₁₀₉₄	C₂×C₄	1	2	yes	—
17	D₂₁₈₈	C₂×C₄	1	2	yes	—
18	C₂²⋊D₅₄₇	—	2	2	no	—
19	C₄×D₅₄₇	—	2	2	no	—
20	C₅₄₇⋊C₈	—	2	2	no	—
21	C₂×C₄×C₅₄₇	—	2	1	no	—
22	C₂×C₄×C₅₄₇	C₂³	1	1	yes	characteristic
23	C₈×C₅₄₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₅₄₇	C₂×C₄	1	1	yes	characteristic
25	C₈×C₅₄₇	D₄	1	2	yes	—
26	C₂²×C₅₄₇	#41	1	1	yes	characteristic
27	C₂×D₅₄₇	—	2	2	no	—
28	C₄×C₅₄₇	—	4	1	no	—
29	C₄×C₅₄₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₅₄₇	C₂×D₄	1	1	yes	characteristic
31	Dic₅₄₇	—	2	2	no	—
32	C₂×C₅₄₇	—	2	1	no	—
33	C₂×C₅₄₇	C₄×D₄	1	1	yes	characteristic
34	D₅₄₇	—	4	2	no	—
35	C₅₄₇	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	547	1	no	maximal, Sylow
37	#135	—	547	1	no	—
38	#131	—	547	2	no	—
39	#108	—	547	1	no	—
40	#104	—	547	2	no	—
41	#97	D₅₄₇	1	1	yes	characteristic, complemented
42	#41	—	547	2	no	—
43	Q₁₆	—	547	1	no	—
44	SD₁₆	—	547	2	no	—
45	D₈	—	547	1	no	—
46	M₁₆	—	547	2	no	—
47	M₁₆	—	1094	2	no	—
48	C₂×C₈	—	1094	2	no	—
49	C₂×C₈	C₂×D₅₄₇	1	1	yes	characteristic
50	C₂×C₈	C₂×D₅₄₇	1	1	yes	characteristic
51	C₄²	C₂×D₅₄₇	1	1	yes	characteristic
52	Q₈	—	547	2	no	—
53	D₄	—	547	2	no	—
54	D₄	—	1094	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	1094	2	no	—
57	C₂×C₄	C₂²×D₅₄₇	1	1	yes	characteristic
58	C₈	—	1094	2	no	—
59	C₈	C₄×D₅₄₇	1	1	yes	characteristic
60	C₈	C₄×D₅₄₇	1	1	yes	characteristic
61	C₈	D₂₁₈₈	1	2	yes	—
62	C₂²	—	1094	2	no	—
63	C₂²	#22576776	1	1	yes	characteristic
64	C₄	—	4	1	no	—
65	C₄	—	1094	2	no	—
66	C₄	C₂×C₄×D₅₄₇	1	1	yes	characteristic
67	C₄	C₂×D₂₁₈₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	2188	2	no	—
70	C₂	C₄×D₂₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₁₈₈
commutator	C₄×C₅₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₄₇
Fitting	#97×C₅₄₇	C₂
socle	C₂×C₅₄₇	C₄×D₄
prime radical	#31776024	C₂
cosocle	C₂×C₄×C₅₄₇	C₂³
hypercenter	#97	D₅₄₇
hypocenter	C₅₄₇	#444
LCS	G ▷ C₄×C₅₄₇ ▷ C₂×C₅₄₇ ▷ C₅₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #31776008	C₂	semidirect
3. #31775938	C₂	semidirect
4. #31775930	C₂	semidirect
5. #97×C₅₄₇	C₂	semidirect
7. Dic₂₁₈₈	C₄	semidirect
8. #22576765	C₄	semidirect
9. D₄₃₇₆	C₄	semidirect
35. C₅₄₇	#444	semidirect
41. #97	D₅₄₇	semidirect

Maximal subgroups

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

subgroup	index
#31776024	2
#31776008	2
#31775938	2
#31775930	2
#97×C₅₄₇	2
#444	547