Subgroups — C₂²×#10587528 #14546012

Order 2176.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587528	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#63216	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3622	C₄	1	1	yes	characteristic
4	C₂×#63216	C₄	1	3	yes	—
5	C₂×#63216	C₂²	1	3	yes	—
6	#10587528	C₂²	1	4	yes	direct product factor
7	C₂²×C₄×C₁₇	C₈	1	1	yes	characteristic
8	C₂×#3622	C₈	1	3	yes	—
9	C₂×#3622	C₂×C₄	1	3	yes	—
10	#63216	C₂×C₄	1	3	yes	—
11	#63216	C₂³	1	1	yes	characteristic
12	C₂³×C₁₇	C₁₆	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₁₆	1	3	yes	—
14	C₂×C₄×C₁₇	C₂×C₈	1	3	yes	—
15	#3622	C₂×C₈	1	3	yes	—
16	#3622	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₃₂	—	17	1	no	maximal, Sylow
18	C₂²×C₁₇	C₃₂	1	4	yes	complemented
19	C₂²×C₁₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₇	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
22	C₂²×C₁₆	—	17	1	no	—
23	C₂×C₃₂	—	17	6	no	—
24	C₂×C₁₇	C₂×C₃₂	1	6	yes	complemented
25	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
26	C₂²×C₈	—	17	1	no	—
27	C₂×C₁₆	—	17	3	no	—
28	C₂×C₁₆	—	17	3	no	—
29	C₃₂	—	17	4	no	—
30	C₁₇	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	#3633	1	1	yes	characteristic
32	C₂×C₈	—	17	3	no	—
33	C₂×C₈	—	17	3	no	—
34	C₁₆	—	17	1	no	—
35	C₁₆	—	17	3	no	—
36	C₂³	#63241	1	1	yes	characteristic
37	C₂×C₄	#63241	1	3	yes	—
38	C₂×C₄	C₂×#3633	1	3	yes	—
39	C₈	—	17	1	no	—
40	C₈	—	17	3	no	—
41	C₂²	#10587528	1	4	yes	direct product factor
42	C₂²	C₂×#63241	1	3	yes	—
43	C₄	C₂×#63241	1	3	yes	—
44	C₄	C₂²×#3633	1	1	yes	characteristic
45	C₂	C₂×#10587528	1	6	yes	direct product factor
46	C₂	C₂²×#63241	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#3633
commutator, hypocenter	C₁₇	C₂²×C₃₂
Frattini	C₄	C₂²×#3633
Fitting	C₂²×C₄×C₁₇	C₈
socle, prime radical	C₂³×C₁₇	C₁₆
cosocle	#63216	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#10587528	C₂	direct (N × H)
6. #10587528	C₂²	direct (N × H)
18. C₂²×C₁₇	C₃₂	semidirect
24. C₂×C₁₇	C₂×C₃₂	semidirect
30. C₁₇	C₂²×C₃₂	semidirect
41. C₂²	#10587528	direct (N × H)
45. C₂	C₂×#10587528	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10587528	2
C₂²×#63216	2
C₂²×C₃₂	17

Subgroups — C22×#10587528 #14546012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10587528 #14546012