Subgroups — #17982823

Order 4352.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545888	C₂	1	3	yes	maximal, complemented
2	C₂×#11763891	C₂	1	3	yes	maximal, complemented
3	#14545207	C₂	1	1	yes	maximal, characteristic
4	#11763891	C₂²	1	1	yes	characteristic
5	#11763891	C₂²	1	3	yes	—
6	#11763741	C₄	1	3	yes	—
7	C₂×#10587467	C₂²	1	3	yes	—
8	#11763226	C₄	1	1	yes	characteristic
9	C₁₇×#131	C₈	1	1	yes	characteristic
10	#10587483	C₈	1	3	yes	—
11	C₂×#63214	C₂×C₄	1	3	yes	—
12	#10587467	C₂×C₄	1	3	yes	—
13	#10587467	C₂³	1	1	yes	characteristic
14	#41×C₁₇	C₁₆	1	1	yes	characteristic
15	M₁₆×C₁₇	C₁₆	1	3	yes	—
16	C₂×C₈×C₁₇	C₂×C₈	1	3	yes	—
17	#63214	C₂×C₈	1	3	yes	—
18	#63214	C₂²×C₄	1	1	yes	characteristic
19	#13737	—	17	1	no	maximal, Sylow
20	Q₈×C₁₇	C₃₂	1	1	yes	characteristic
21	D₄×C₁₇	C₃₂	1	3	yes	—
22	C₂×C₄×C₁₇	C₂×C₁₆	1	3	yes	—
23	C₈×C₁₇	C₂×C₁₆	1	3	yes	—
24	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
25	#2258	—	17	1	no	—
26	M₁₂₈	—	17	3	no	—
27	C₂×C₆₄	—	17	3	no	—
28	C₂²×C₁₇	C₂×C₃₂	1	3	yes	—
29	C₄×C₁₇	C₂×C₃₂	1	3	yes	—
30	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
31	#504	—	17	1	no	—
32	M₆₄	—	17	3	no	—
33	C₂×C₃₂	—	17	3	no	—
34	C₆₄	—	17	1	no	—
35	C₆₄	—	17	3	no	—
36	C₂×C₁₇	—	2	3	no	—
37	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
38	#131	#3633	1	1	yes	characteristic
39	M₃₂	—	17	3	no	—
40	C₂×C₁₆	—	17	3	no	—
41	C₃₂	—	17	1	no	—
42	C₃₂	—	17	3	no	—
43	C₁₇	#13737	1	1	yes	characteristic, complemented, Sylow
44	#41	#63241	1	1	yes	characteristic
45	M₁₆	#63241	1	3	yes	—
46	C₂×C₈	C₂×#3633	1	3	yes	—
47	C₁₆	—	17	1	no	—
48	C₁₆	—	17	3	no	—
49	Q₈	#10587528	1	1	yes	characteristic
50	D₄	#10587528	1	3	yes	—
51	C₂×C₄	C₂×#63241	1	3	yes	—
52	C₈	C₂×#63241	1	3	yes	—
53	C₈	C₂²×#3633	1	1	yes	characteristic
54	C₂²	C₂×#10587528	1	3	yes	—
55	C₄	C₂×#10587528	1	3	yes	—
56	C₄	C₂²×#63241	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×#10587528	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#3633
commutator, socle	C₂×C₁₇	C₂²×C₃₂
Fitting	C₁₇×#131	C₈
prime radical	#41×C₁₇	C₁₆
cosocle	#10587467	C₂³
hypercenter	#131	#3633
hypocenter	C₁₇	#13737
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #14545888	C₂	semidirect
2. C₂×#11763891	C₂	semidirect
43. C₁₇	#13737	semidirect

Maximal subgroups

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

subgroup	index
#14545888	2
C₂×#11763891	2
#14545207	2
#13737	17