Subgroups — #14543943

Order 2176.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763741	C₂	1	2	yes	maximal
2	C₄×#63214	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	—	2	2	no	—
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	—	2	1	no	—
11	#63214	D₄	1	1	yes	characteristic
12	#63214	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₇	—	2	1	no	—
14	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₇	C₁₆	1	2	yes	—
16	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₇	M₁₆	1	1	yes	characteristic
18	#1422	—	17	1	no	maximal, Sylow
19	C₂²×C₁₇	M₃₂	1	1	yes	characteristic
20	C₄×C₁₇	—	2	2	no	—
21	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
23	M₆₄	—	17	2	no	—
24	C₄×C₁₆	—	17	1	no	—
25	C₂×C₁₇	—	2	1	no	—
26	C₂×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₆	—	17	1	no	—
28	C₂×C₁₆	—	17	1	no	—
29	C₄×C₈	#595	1	1	yes	characteristic
30	C₃₂	—	34	2	no	—
31	C₁₇	#1422	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	#3624	1	1	yes	characteristic
33	C₂×C₈	C₂×#595	1	1	yes	characteristic
34	C₄²	#3624	1	1	yes	characteristic
35	C₁₆	—	17	1	no	—
36	C₁₆	—	17	1	no	—
37	C₁₆	—	34	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×#3624	1	1	yes	characteristic
40	C₈	#63216	1	2	yes	—
41	C₈	#63243	1	1	yes	characteristic
42	C₈	C₄⋊#595	1	1	yes	characteristic
43	C₂²	#10587538	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₂×#63216	1	1	yes	characteristic
46	C₄	C₄⋊#3624	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#63216	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#595
commutator	C₄×C₁₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂×C₁₇	C₄⋊C₁₆
prime radical	C₂²×C₁₇	M₃₂
cosocle	C₂×#63214	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1422
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
31. C₁₇	#1422	semidirect

Maximal subgroups

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

subgroup	index
#11763741	2
C₄×#63214	2
#1422	17