Subgroups — #14543895

Order 2176.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763741	C₂	1	2	yes	maximal
2	#11762585	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂×#63214	C₄	1	1	yes	characteristic
5	C₂×#63214	C₂²	1	1	yes	characteristic
6	#10587467	C₄	1	4	yes	complemented
7	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₇	C₈	1	1	yes	characteristic
10	#63214	C₈	1	2	yes	—
11	#63214	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₇	—	2	1	no	—
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₁₇	—	2	1	no	—
15	C₈×C₁₇	C₄²	1	1	yes	characteristic
16	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	#1398	—	17	1	no	maximal, Sylow
18	C₂²×C₁₇	M₃₂	1	1	yes	characteristic
19	C₄×C₁₇	—	4	1	no	—
20	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
21	C₄×C₁₇	M₃₂	1	1	yes	characteristic
22	M₆₄	—	17	2	no	—
23	#346	—	17	1	no	—
24	C₂×C₁₇	—	2	1	no	—
25	C₂×C₁₇	#346	1	1	yes	characteristic
26	C₂×C₁₆	—	17	1	no	—
27	C₂×C₁₆	—	17	1	no	—
28	C₄×C₈	#595	1	1	yes	characteristic
29	C₃₂	—	17	4	no	—
30	C₁₇	#1398	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	#3624	1	1	yes	characteristic
32	C₂×C₈	C₂×#595	1	1	yes	characteristic
33	C₄²	#3624	1	1	yes	characteristic
34	C₁₆	—	17	2	no	—
35	C₁₆	—	17	2	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×#3624	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	#63242	1	1	yes	characteristic
40	C₈	C₄×#595	1	1	yes	characteristic
41	C₂²	#10587538	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	#10587538	1	1	yes	characteristic
44	C₄	C₄×#3624	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#11763697	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#595
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₂×C₈	C₂×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂×C₁₇	#346
prime radical	C₂²×C₁₇	M₃₂
cosocle	C₂×#63214	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1398
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10587467	C₄	semidirect
30. C₁₇	#1398	semidirect

Maximal subgroups

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

subgroup	index
#11763741	2
#11762585	2
#1398	17