Subgroups — #28417985

Order 14944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418744	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#21418733	C₂	1	1	yes	maximal, characteristic, complemented
4	#21418732	C₂	1	1	yes	maximal, characteristic, complemented
5	#21418730	C₂	1	1	yes	maximal, characteristic, complemented
6	#21418726	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₉₃₄	—	2	1	no	—
9	Dic₉₃₄	C₂²	1	1	yes	characteristic
10	D₁₈₆₈	—	2	1	no	—
11	D₁₈₆₈	C₂²	1	1	yes	characteristic
12	C₄×D₄₆₇	—	2	1	no	—
13	C₄×D₄₆₇	—	2	1	no	—
14	C₄×D₄₆₇	C₂²	1	1	yes	characteristic
15	C₄₆₇⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₄₆₇	C₂²	1	1	yes	characteristic
17	Q₈×C₄₆₇	C₂²	1	1	yes	characteristic
18	C₈×C₄₆₇	C₂²	1	1	yes	characteristic
19	C₂×D₄₆₇	—	2	1	no	—
20	C₂×D₄₆₇	D₄	1	1	yes	characteristic
21	C₄×C₄₆₇	—	2	1	no	—
22	C₄×C₄₆₇	—	2	1	no	—
23	C₄×C₄₆₇	C₂³	1	1	yes	characteristic
24	Dic₄₆₇	—	2	1	no	—
25	Dic₄₆₇	D₄	1	1	yes	characteristic
26	C₂×C₄₆₇	C₂×D₄	1	1	yes	characteristic
27	D₄₆₇	—	2	1	no	—
28	D₄₆₇	—	4	1	no	—
29	C₄₆₇	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	467	1	no	maximal, Sylow
31	#41	—	467	1	no	—
32	C₂×Q₈	—	467	1	no	—
33	Q₁₆	—	467	1	no	—
34	Q₁₆	D₄₆₇	1	1	yes	characteristic, complemented
35	SD₁₆	—	467	1	no	—
36	SD₁₆	—	467	1	no	—
37	M₁₆	—	467	1	no	—
38	Q₈	—	934	1	no	—
39	Q₈	—	467	1	no	—
40	Q₈	C₂×D₄₆₇	1	1	yes	characteristic
41	Q₈	C₂×D₄₆₇	1	1	yes	characteristic
42	D₄	—	934	1	no	—
43	D₄	—	467	1	no	—
44	C₂×C₄	—	934	1	no	—
45	C₂×C₄	—	934	1	no	—
46	C₂×C₄	—	467	1	no	—
47	C₈	—	467	1	no	—
48	C₈	C₂×D₄₆₇	1	1	yes	characteristic
49	C₂²	—	934	1	no	—
50	C₂²	—	467	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	934	1	no	—
54	C₄	—	467	1	no	—
55	C₄	C₂²×D₄₆₇	1	1	yes	characteristic
56	C₂	—	1868	1	no	—
57	C₂	—	934	1	no	—
58	C₂	D₄×D₄₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₆₇
commutator, cosocle	C₄×C₄₆₇	C₂³
Frattini	C₄	C₂²×D₄₆₇
Fitting	Q₁₆×C₄₆₇	C₂
socle	C₂×C₄₆₇	C₂×D₄
prime radical	#21418744	C₂
hypercenter	Q₁₆	D₄₆₇
hypocenter	C₄₆₇	#137
LCS	G ▷ C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₄₆₇	C₂	semidirect
3. #21418733	C₂	semidirect
4. #21418732	C₂	semidirect
5. #21418730	C₂	semidirect
6. #21418726	C₂	semidirect
7. Q₁₆×C₄₆₇	C₂	semidirect
29. C₄₆₇	#137	semidirect
34. Q₁₆	D₄₆₇	semidirect

Maximal subgroups

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

subgroup	index
#21418744	2
Q₈×D₄₆₇	2
#21418733	2
#21418732	2
#21418730	2
#21418726	2
Q₁₆×C₄₆₇	2
#137	467