Subgroups — #14543697

Order 2176.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#63216	C₂	1	2	yes	maximal
2	C₈×#3622	C₂	1	1	yes	maximal, characteristic
3	C₂×#63216	C₄	1	4	yes	—
4	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
5	C₄×#3622	C₄	1	1	yes	characteristic
6	C₄×#3622	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₈	1	2	yes	—
8	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×#3622	C₈	1	2	yes	—
10	C₂×#3622	C₂×C₄	1	2	yes	—
11	#63216	—	2	4	no	—
12	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₇	C₁₆	1	4	yes	complemented
16	#3622	—	2	2	no	—
17	#3622	M₁₆	1	4	yes	—
18	#1312	—	17	1	no	maximal, Sylow
19	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₁₇	#97	1	2	yes	—
21	C₄×C₁₇	C₂×C₁₆	1	2	yes	—
22	C₄×C₁₇	M₃₂	1	2	yes	—
23	C₄×C₁₆	—	17	2	no	—
24	C₈²	—	17	1	no	—
25	C₂×C₁₇	#322	1	1	yes	characteristic
26	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
27	C₂×C₁₇	#346	1	1	yes	characteristic
28	C₂×C₁₆	—	17	4	no	—
29	C₄×C₈	—	17	1	no	—
30	C₄×C₈	—	17	1	no	—
31	C₄×C₈	#595	1	1	yes	characteristic
32	C₁₇	#1312	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	—	17	2	no	—
34	C₂×C₈	—	17	2	no	—
35	C₂×C₈	#3624	1	2	yes	—
36	C₄²	C₂×#595	1	1	yes	characteristic
37	C₁₆	—	34	4	no	—
38	C₂×C₄	#63242	1	1	yes	characteristic
39	C₂×C₄	C₄×#595	1	1	yes	characteristic
40	C₂×C₄	C₂×#3624	1	1	yes	characteristic
41	C₈	—	17	4	no	—
42	C₈	—	34	2	no	—
43	C₈	#63216	1	4	yes	complemented
44	C₂²	C₄×#3624	1	1	yes	characteristic
45	C₄	#10587530	1	2	yes	—
46	C₄	#10587532	1	2	yes	—
47	C₄	C₂×#63216	1	2	yes	—
48	C₂	#11763650	1	1	yes	characteristic
49	C₂	C₄×#63216	1	1	yes	characteristic
50	C₂	#11763698	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#595
commutator	C₂×C₁₇	C₄×C₁₆
Fitting	C₄×C₈×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₈
cosocle	C₄×#3622	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1312
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₈×C₁₇	C₁₆	semidirect
32. C₁₇	#1312	semidirect
43. C₈	#63216	semidirect

Maximal subgroups

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

subgroup	index
C₄×#63216	2
C₈×#3622	2
#1312	17