Subgroups — #11763707

Order 1088.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587634	C₂	1	1	yes	maximal, characteristic
2	#10587538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63216	C₂	1	1	yes	maximal, characteristic, complemented
4	#41×C₁₇	C₄	1	1	yes	characteristic
5	#63223	—	2	1	no	—
6	#63223	C₄	1	1	yes	characteristic
7	C₂×#3622	—	2	1	no	—
8	C₂×#3622	C₂²	1	1	yes	characteristic
9	#63216	—	2	1	no	—
10	#63216	—	2	1	no	—
11	Q₈×C₁₇	C₈	1	1	yes	characteristic
12	D₄×C₁₇	—	2	1	no	—
13	D₄×C₁₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₇	—	2	1	no	—
15	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#3622	—	2	1	no	—
17	#3622	D₄	1	1	yes	characteristic
18	#3622	D₄	1	1	yes	characteristic
19	C₂²×C₁₇	—	2	1	no	—
20	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
21	C₄×C₁₇	—	2	1	no	—
22	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
24	#350	—	17	1	no	maximal, Sylow
25	C₂×C₁₇	—	2	1	no	—
26	C₂×C₁₇	—	4	1	no	—
27	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
28	#131	—	17	1	no	—
29	M₃₂	—	17	1	no	—
30	C₂×C₁₆	—	17	1	no	—
31	C₁₇	#350	1	1	yes	characteristic, complemented, Sylow
32	#41	#595	1	1	yes	characteristic
33	M₁₆	—	17	1	no	—
34	M₁₆	—	34	1	no	—
35	C₂×C₈	—	17	1	no	—
36	C₂×C₈	—	34	1	no	—
37	C₁₆	—	34	1	no	—
38	C₁₆	—	34	1	no	—
39	Q₈	#3624	1	1	yes	characteristic
40	D₄	—	2	1	no	—
41	D₄	#3624	1	1	yes	characteristic
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	C₂×#595	1	1	yes	characteristic
44	C₈	—	17	1	no	—
45	C₈	—	17	1	no	—
46	C₈	—	34	1	no	—
47	C₂²	—	2	1	no	—
48	C₂²	#63247	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	C₂×#3624	1	1	yes	characteristic
51	C₄	C₂²⋊#595	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	4	1	no	—
54	C₂	C₂²⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₈
Frattini	C₂×C₄	C₂×#595
Fitting, prime radical	#41×C₁₇	C₄
socle	C₂×C₁₇	C₂²⋊C₈
cosocle	C₂×#3622	C₂²
hypercenter	#41	#595
hypocenter	C₁₇	#350
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. #10587538	C₂	semidirect
3. C₂×#63216	C₂	semidirect
31. C₁₇	#350	semidirect

Maximal subgroups

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

subgroup	index
#10587634	2
#10587538	2
C₂×#63216	2
#350	17