Subgroups — #11763868

Order 1088.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587593	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	#10587530	C₂	1	2	yes	maximal, complemented
5	#10587529	C₂	1	2	yes	maximal, complemented
6	#63252	C₄	1	1	yes	characteristic
7	M₁₆×C₁₇	C₄	1	1	yes	characteristic
8	C₂×#3622	C₂²	1	1	yes	characteristic
9	#63218	C₄	1	2	yes	—
10	C₈×D₁₇	C₂²	1	2	yes	—
11	#63216	C₂²	1	1	yes	characteristic
12	#63216	C₂²	1	2	yes	—
13	#63216	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₁₇	C₈	1	2	yes	—
16	D₆₈	C₈	1	1	yes	characteristic
17	C₄×D₁₇	C₂×C₄	1	2	yes	—
18	Dic₃₄	C₈	1	1	yes	characteristic
19	C₈×C₁₇	C₂×C₄	1	2	yes	—
20	#3622	C₂×C₄	1	1	yes	characteristic
21	#3622	C₂³	1	1	yes	characteristic
22	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₇	C₂×C₈	1	2	yes	—
24	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₇	C₂×C₈	1	2	yes	—
27	#504	—	17	1	no	maximal, Sylow
28	C₂×C₁₇	—	2	1	no	—
29	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
30	D₁₇	—	2	2	no	—
31	#131	—	17	1	no	—
32	M₃₂	—	17	2	no	—
33	M₃₂	—	17	1	no	—
34	C₂×C₁₆	—	17	2	no	—
35	C₂×C₁₆	—	17	1	no	—
36	C₁₇	#504	1	1	yes	characteristic, complemented, Sylow
37	#41	—	17	1	no	—
38	M₁₆	—	17	2	no	—
39	M₁₆	#595	1	1	yes	characteristic
40	C₂×C₈	—	17	1	no	—
41	C₂×C₈	—	17	2	no	—
42	C₁₆	—	17	1	no	—
43	C₁₆	—	17	2	no	—
44	C₁₆	—	17	1	no	—
45	Q₈	—	17	1	no	—
46	D₄	—	17	2	no	—
47	D₄	—	17	1	no	—
48	C₂×C₄	—	17	2	no	—
49	C₂×C₄	C₂×#595	1	1	yes	characteristic
50	C₈	—	17	1	no	—
51	C₈	—	17	1	no	—
52	C₈	C₂×#595	1	2	yes	—
53	C₂²	—	17	2	no	—
54	C₂²	#63242	1	1	yes	characteristic
55	C₄	—	17	2	no	—
56	C₄	#63242	1	1	yes	characteristic
57	C₄	C₂²×#595	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	34	2	no	—
60	C₂	C₂×#63242	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#595
commutator, socle	C₂×C₁₇	C₂²×C₈
Fitting	M₁₆×C₁₇	C₄
prime radical	#63252	C₄
cosocle	#3622	C₂³
hypercenter	M₁₆	#595
hypocenter	C₁₇	#504
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ M₁₆

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
4. #10587530	C₂	semidirect
5. #10587529	C₂	semidirect
36. C₁₇	#504	semidirect

Maximal subgroups

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

subgroup	index
#10587593	2
#10587538	2
C₂×#63216	2
#10587530	2
#10587529	2
#504	17