Subgroups — C₂²×#11763891 #17982818

Order 4352.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₈	#3633
commutator, hypocenter	C₁₇	C₂²×C₆₄
Frattini	C₈	C₂²×#3633
Fitting	C₂²×C₈×C₁₇	C₈
socle, prime radical	C₂³×C₁₇	C₃₂
cosocle	#10587467	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11763891	C₂	direct (N × H)
3. #11763891	C₂²	direct (N × H)
25. C₂²×C₁₇	C₆₄	semidirect
33. C₂×C₁₇	C₂×C₆₄	semidirect
40. C₁₇	C₂²×C₆₄	semidirect
51. C₂²	#11763891	direct (N × H)
55. C₂	C₂×#11763891	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×#11763891	2
C₂²×#10587467	2
C₂²×C₆₄	17

Subgroups — C22×#11763891 #17982818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11763891 #17982818