Subgroups — #103×C₁₁₆₃ #49151663

Order 37216.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁₆₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₁₁₆₃	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₁₆₃	—	2	1	no	—
5	Q₈×C₁₁₆₃	C₄	1	2	yes	complemented
6	C₂×C₄×C₁₁₆₃	—	2	1	no	—
7	C₂×C₄×C₁₁₆₃	—	2	1	no	—
8	C₂×C₄×C₁₁₆₃	C₂²	1	1	yes	characteristic
9	C₈×C₁₁₆₃	—	2	1	no	—
10	C₂²×C₁₁₆₃	D₄	1	1	yes	characteristic
11	C₄×C₁₁₆₃	—	2	2	no	—
12	C₄×C₁₁₆₃	—	4	1	no	—
13	C₄×C₁₁₆₃	C₂×C₄	1	1	yes	characteristic
14	C₄×C₁₁₆₃	D₄	1	1	yes	characteristic
15	C₂×C₁₁₆₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₁₁₆₃	SD₁₆	1	1	yes	characteristic
17	C₂×C₁₁₆₃	Q₁₆	1	1	yes	characteristic
18	C₁₁₆₃	#103	1	1	yes	characteristic, direct product factor, Sylow
19	#103	C₁₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×Q₈	C₂×C₁₁₆₃	1	1	yes	characteristic
21	C₂×C₈	C₂×C₁₁₆₃	1	1	yes	characteristic
22	C₄⋊C₄	C₂×C₁₁₆₃	1	1	yes	characteristic
23	Q₈	—	2	1	no	—
24	Q₈	C₄×C₁₁₆₃	1	2	yes	complemented
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂²×C₁₁₆₃	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₂²	D₄×C₁₁₆₃	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	4	1	no	—
32	C₄	C₂×C₄×C₁₁₆₃	1	1	yes	characteristic
33	C₄	D₄×C₁₁₆₃	1	1	yes	characteristic
34	C₂	C₂²⋊C₄×C₁₁₆₃	1	1	yes	characteristic
35	C₂	SD₁₆×C₁₁₆₃	1	1	yes	characteristic
36	C₂	Q₁₆×C₁₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁₆₃	D₄
commutator	C₄	C₂×C₄×C₁₁₆₃
Frattini, cosocle	C₂×C₄	C₂²×C₁₁₆₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₆₃ ◁ C₂×C₄×C₁₁₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. Q₈×C₁₁₆₃	C₄	semidirect
18. C₁₁₆₃	#103	direct (N × H)
19. #103	C₁₁₆₃	direct (N × H)
24. Q₈	C₄×C₁₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₁₆₃	2
C₂×C₈×C₁₁₆₃	2
C₄⋊C₄×C₁₁₆₃	2
#103	1163

Subgroups — #103×C1163 #49151663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #103×C₁₁₆₃ #49151663