Subgroups — #11719096

Order 832.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#88161	C₂	1	1	yes	maximal, characteristic
2	#88106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#6092	C₂	1	1	yes	maximal, characteristic, complemented
4	#88098	C₂	1	2	yes	maximal, complemented
5	D₁₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	#6127	C₄	1	1	yes	characteristic
7	C₁₃×M₁₆	C₄	1	1	yes	characteristic
8	C₂×#1055	C₂²	1	1	yes	characteristic
9	#6094	C₄	1	2	yes	—
10	C₈×D₁₃	C₂²	1	2	yes	—
11	#6092	C₂²	1	1	yes	characteristic
12	#6092	C₂²	1	2	yes	—
13	#6092	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₁₃	C₈	1	2	yes	—
16	D₅₂	C₈	1	1	yes	characteristic
17	C₄×D₁₃	C₂×C₄	1	2	yes	—
18	Dic₂₆	C₈	1	1	yes	characteristic
19	C₈×C₁₃	C₂×C₄	1	2	yes	—
20	#1055	C₂×C₄	1	1	yes	characteristic
21	#1055	C₂³	1	1	yes	characteristic
22	#504	—	13	1	no	maximal, Sylow
23	C₂²×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂×D₁₃	C₂×C₈	1	2	yes	—
25	C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	Dic₁₃	C₂×C₈	1	2	yes	—
28	#131	—	13	1	no	—
29	M₃₂	—	13	2	no	—
30	M₃₂	—	13	1	no	—
31	C₂×C₁₆	—	13	2	no	—
32	C₂×C₁₆	—	13	1	no	—
33	C₂×C₁₃	—	2	1	no	—
34	C₂×C₁₃	C₂²×C₈	1	1	yes	characteristic
35	D₁₃	—	2	2	no	—
36	#41	—	13	1	no	—
37	M₁₆	—	13	2	no	—
38	M₁₆	#261	1	1	yes	characteristic
39	C₂×C₈	—	13	1	no	—
40	C₂×C₈	—	13	2	no	—
41	C₁₆	—	13	1	no	—
42	C₁₆	—	13	2	no	—
43	C₁₆	—	13	1	no	—
44	C₁₃	#504	1	1	yes	characteristic, complemented, Sylow
45	Q₈	—	13	1	no	—
46	D₄	—	13	2	no	—
47	D₄	—	13	1	no	—
48	C₂×C₄	—	13	2	no	—
49	C₂×C₄	C₂×#261	1	1	yes	characteristic
50	C₈	—	13	1	no	—
51	C₈	—	13	1	no	—
52	C₈	C₂×#261	1	2	yes	—
53	C₂²	—	13	2	no	—
54	C₂²	D₁₃⋊C₈	1	1	yes	characteristic
55	C₄	—	13	2	no	—
56	C₄	D₁₃⋊C₈	1	1	yes	characteristic
57	C₄	C₂²×#261	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	26	2	no	—
60	C₂	C₂×D₁₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#261
commutator, socle	C₂×C₁₃	C₂²×C₈
Fitting	C₁₃×M₁₆	C₄
prime radical	#6127	C₄
cosocle	#1055	C₂³
hypercenter	M₁₆	#261
hypocenter	C₁₃	#504
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #88106	C₂	semidirect
3. C₂×#6092	C₂	semidirect
4. #88098	C₂	semidirect
5. D₁₃⋊C₁₆	C₂	semidirect
44. C₁₃	#504	semidirect

Maximal subgroups

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

subgroup	index
#88161	2
#88106	2
C₂×#6092	2
#88098	2
D₁₃⋊C₁₆	2
#504	13