Subgroups — #20242690

Order 6016.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689489	C₂	1	3	yes	maximal
2	#15688865	C₂	1	3	yes	maximal, complemented
3	C₄₇×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094021	C₂²	1	1	yes	characteristic
5	#13093944	—	2	6	no	—
6	#13093935	C₂²	1	3	yes	—
7	#125×C₄₇	—	2	6	no	—
8	#125×C₄₇	C₂²	1	3	yes	—
9	C₂×D₁₈₈	—	2	3	no	—
10	C₄⋊C₄×C₄₇	—	2	6	no	—
11	C₄⋊C₄×C₄₇	—	2	6	no	—
12	C₄⋊C₄×C₄₇	D₄	1	6	yes	—
13	C₄²×C₄₇	—	2	2	no	—
14	C₄²×C₄₇	C₂³	1	1	yes	characteristic
15	C₂×C₄₇⋊C₈	—	2	3	no	—
16	C₂²×D₄₇	—	4	1	no	—
17	C₂×C₄×C₄₇	—	2	6	no	—
18	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
19	D₁₈₈	—	4	6	no	—
20	C₄₇⋊C₈	—	4	3	no	—
21	C₂²×C₄₇	#120	1	1	yes	characteristic
22	C₂×D₄₇	—	8	3	no	—
23	C₄×C₄₇	—	2	3	no	—
24	C₄×C₄₇	—	4	6	no	—
25	#1658	—	47	1	no	maximal, Sylow
26	C₂×C₄₇	#454	1	3	yes	—
27	D₄₇	—	16	1	no	—
28	#564	D₄₇	1	1	yes	characteristic, complemented
29	#490	—	47	3	no	—
30	#330	—	47	3	no	—
31	C₄₇	#1658	1	1	yes	characteristic, complemented, Sylow
32	#127	—	47	1	no	—
33	#125	—	2	6	no	—
34	#125	C₂×D₄₇	1	3	yes	—
35	#102	—	94	6	no	—
36	#97	—	47	3	no	—
37	C₂×D₄	—	94	3	no	—
38	C₂×C₈	—	94	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₄₇	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₄₇	1	1	yes	characteristic
44	C₂³	—	188	1	no	—
45	D₄	—	188	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
48	C₈	—	188	3	no	—
49	C₂²	—	376	3	no	—
50	C₂²	#13093993	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	752	1	no	—
54	C₂	#15689296	1	3	yes	—

	subgroup	G/H
center	C₂²	#13093993
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#564	C₂
socle	C₂²×C₄₇	#120
hypercenter	#564	D₄₇
hypocenter	C₄₇	#1658
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #15688865	C₂	semidirect
3. C₄₇×#564	C₂	semidirect
28. #564	D₄₇	semidirect
31. C₄₇	#1658	semidirect