Subgroups — C₂³×#10587467 #17978834

Order 4352.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587467	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#63214	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587467	C₂²	1	28	yes	direct product factor
4	C₂²×#63214	C₄	1	7	yes	—
5	C₂²×#63214	C₂²	1	7	yes	—
6	C₂³×C₈×C₁₇	C₄	1	1	yes	characteristic
7	C₂³×C₄×C₁₇	C₈	1	1	yes	characteristic
8	C₂²×C₈×C₁₇	C₈	1	7	yes	—
9	C₂²×C₈×C₁₇	C₂×C₄	1	7	yes	—
10	C₂×#63214	C₂×C₄	1	21	yes	—
11	C₂×#63214	C₂³	1	7	yes	—
12	#10587467	C₂³	1	8	yes	direct product factor
13	C₂⁴×C₁₇	C₁₆	1	1	yes	characteristic
14	C₂²×C₄×C₁₇	C₁₆	1	7	yes	—
15	C₂²×C₄×C₁₇	C₂×C₈	1	7	yes	—
16	C₂×C₈×C₁₇	C₂×C₈	1	21	yes	—
17	C₂×C₈×C₁₇	C₂²×C₄	1	7	yes	—
18	#63214	C₂²×C₄	1	7	yes	—
19	#63214	C₂⁴	1	1	yes	characteristic
20	C₂³×C₃₂	—	17	1	no	maximal, Sylow
21	C₂³×C₁₇	C₃₂	1	8	yes	complemented
22	C₂³×C₁₇	C₂×C₁₆	1	7	yes	—
23	C₂×C₄×C₁₇	C₂×C₁₆	1	21	yes	—
24	C₂×C₄×C₁₇	C₂²×C₈	1	7	yes	—
25	C₈×C₁₇	C₂²×C₈	1	7	yes	—
26	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
27	C₂³×C₁₆	—	17	1	no	—
28	C₂²×C₃₂	—	17	14	no	—
29	C₂²×C₁₇	C₂×C₃₂	1	28	yes	complemented
30	C₂²×C₁₇	C₂²×C₁₆	1	7	yes	—
31	C₄×C₁₇	C₂²×C₁₆	1	7	yes	—
32	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
33	C₂³×C₈	#595	1	1	yes	characteristic
34	C₂²×C₁₆	—	17	7	no	—
35	C₂²×C₁₆	—	17	7	no	—
36	C₂×C₃₂	—	17	28	no	—
37	C₂×C₁₇	C₂²×C₃₂	1	14	yes	complemented
38	C₂×C₁₇	C₂³×C₁₆	1	1	yes	characteristic
39	C₂³×C₄	#3624	1	1	yes	characteristic
40	C₂²×C₈	#3624	1	7	yes	—
41	C₂²×C₈	C₂×#595	1	7	yes	—
42	C₂×C₁₆	—	17	21	no	—
43	C₂×C₁₆	—	17	7	no	—
44	C₃₂	—	17	8	no	—
45	C₁₇	C₂³×C₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂⁴	#63216	1	1	yes	characteristic
47	C₂²×C₄	#63216	1	7	yes	—
48	C₂²×C₄	C₂×#3624	1	7	yes	—
49	C₂×C₈	C₂×#3624	1	21	yes	—
50	C₂×C₈	C₂²×#595	1	7	yes	—
51	C₁₆	—	17	1	no	—
52	C₁₆	—	17	7	no	—
53	C₂³	#10587467	1	8	yes	direct product factor
54	C₂³	C₂×#63216	1	7	yes	—
55	C₂×C₄	C₂×#63216	1	21	yes	—
56	C₂×C₄	C₂²×#3624	1	7	yes	—
57	C₈	C₂²×#3624	1	7	yes	—
58	C₈	C₂³×#595	1	1	yes	characteristic
59	C₂²	C₂×#10587467	1	28	yes	direct product factor
60	C₂²	C₂²×#63216	1	7	yes	—
61	C₄	C₂²×#63216	1	7	yes	—
62	C₄	C₂³×#3624	1	1	yes	characteristic
63	C₂	C₂²×#10587467	1	14	yes	direct product factor
64	C₂	C₂³×#63216	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	#595
commutator, hypocenter	C₁₇	C₂³×C₃₂
Frattini	C₈	C₂³×#595
Fitting	C₂³×C₈×C₁₇	C₄
socle, prime radical	C₂⁴×C₁₇	C₁₆
cosocle	#63214	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#10587467	C₂	direct (N × H)
3. C₂×#10587467	C₂²	direct (N × H)
12. #10587467	C₂³	direct (N × H)
21. C₂³×C₁₇	C₃₂	semidirect
29. C₂²×C₁₇	C₂×C₃₂	semidirect
37. C₂×C₁₇	C₂²×C₃₂	semidirect
45. C₁₇	C₂³×C₃₂	semidirect
53. C₂³	#10587467	direct (N × H)
59. C₂²	C₂×#10587467	direct (N × H)
63. C₂	C₂²×#10587467	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#10587467	2
C₂³×#63214	2
C₂³×C₃₂	17

Subgroups — C23×#10587467 #17978834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#10587467 #17978834