Subgroups — #17949097

Order 4352.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587467	C₂	1	2	yes	maximal
2	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587467	C₄	1	4	yes	—
4	C₄×#63214	C₂²	1	1	yes	characteristic
5	C₈×#3622	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	2	yes	—
8	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×#63214	C₂×C₄	1	2	yes	—
10	C₄×#3622	C₈	1	1	yes	characteristic
11	C₄×#3622	C₈	1	1	yes	characteristic
12	#10587467	—	2	4	no	—
13	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
16	C₂×#3622	C₁₆	1	2	yes	—
17	C₂×#3622	C₁₆	1	2	yes	—
18	C₁₆×C₁₇	—	2	2	no	—
19	#63214	M₁₆	1	4	yes	—
20	#7331	—	17	1	no	maximal, Sylow
21	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
22	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
24	C₈×C₁₇	#97	1	2	yes	—
25	C₈×C₁₇	M₃₂	1	2	yes	—
26	#3622	—	2	2	no	—
27	#3622	C₃₂	1	4	yes	complemented
28	C₄×C₃₂	—	17	2	no	—
29	C₈×C₁₆	—	17	1	no	—
30	C₂²×C₁₇	C₄×C₁₆	1	1	yes	characteristic
31	C₄×C₁₇	#322	1	1	yes	characteristic
32	C₄×C₁₇	#346	1	1	yes	characteristic
33	C₄×C₁₇	C₂×C₃₂	1	2	yes	—
34	C₄×C₁₇	M₆₄	1	2	yes	—
35	C₂×C₃₂	—	17	4	no	—
36	C₄×C₁₆	—	17	1	no	—
37	C₄×C₁₆	#595	1	1	yes	characteristic
38	C₈²	—	17	1	no	—
39	C₂×C₁₇	#1312	1	1	yes	characteristic
40	C₂×C₁₇	C₄×C₃₂	1	1	yes	characteristic
41	C₂×C₁₇	#1397	1	1	yes	characteristic
42	C₂×C₁₆	—	17	2	no	—
43	C₂×C₁₆	#3624	1	2	yes	—
44	C₄×C₈	—	17	1	no	—
45	C₄×C₈	—	17	1	no	—
46	C₄×C₈	C₂×#595	1	1	yes	characteristic
47	C₃₂	—	34	4	no	—
48	C₁₇	#7331	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₈	—	17	2	no	—
50	C₂×C₈	—	17	2	no	—
51	C₂×C₈	C₄×#595	1	1	yes	characteristic
52	C₂×C₈	C₂×#3624	1	1	yes	characteristic
53	C₄²	#63242	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₁₆	—	17	4	no	—
56	C₂×C₄	#10587529	1	1	yes	characteristic
57	C₂×C₄	#10587529	1	1	yes	characteristic
58	C₂×C₄	C₄×#3624	1	1	yes	characteristic
59	C₈	—	17	4	no	—
60	C₈	—	34	2	no	—
61	C₈	#10587532	1	2	yes	—
62	C₈	#10587538	1	2	yes	—
63	C₂²	#11763695	1	1	yes	characteristic
64	C₄	#11763650	1	1	yes	characteristic
65	C₄	#11763697	1	1	yes	characteristic
66	C₄	#11763740	1	2	yes	—
67	C₄	#11763742	1	2	yes	—
68	C₂	#14543699	1	1	yes	characteristic
69	C₂	#14543889	1	1	yes	characteristic
70	C₂	#14543892	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×#595
commutator	C₂×C₁₇	C₄×C₃₂
Fitting	C₄×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₁₆
cosocle	C₄×#63214	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7331
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
27. #3622	C₃₂	semidirect
48. C₁₇	#7331	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10587467	2
C₁₆×#3622	2
#7331	17