Subgroups — C₂²×#63242 #11763880

Order 1088.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3624	C₂	1	2	yes	maximal, complemented
3	C₂×#63242	C₂	1	12	yes	maximal, direct product factor
4	C₂³×D₁₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₇	C₄	1	6	yes	—
8	C₂×C₄×D₁₇	C₂²	1	6	yes	—
9	C₂×#3624	C₂²	1	12	yes	complemented
10	#63242	C₂²	1	16	yes	direct product factor
11	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₁₇	C₈	1	8	yes	complemented
13	C₂²×D₁₇	C₂×C₄	1	6	yes	—
14	C₂×C₄×C₁₇	C₂×C₄	1	6	yes	—
15	C₂×Dic₁₇	C₂×C₄	1	3	yes	—
16	C₂×Dic₁₇	C₂³	1	3	yes	—
17	C₄×D₁₇	C₂×C₄	1	12	yes	—
18	C₄×D₁₇	C₂³	1	4	yes	—
19	#3624	C₂³	1	8	yes	complemented
20	C₂²×C₁₇	C₂×C₈	1	4	yes	complemented
21	C₂²×C₁₇	C₂²×C₄	1	3	yes	—
22	C₂×D₁₇	C₂×C₈	1	24	yes	complemented
23	C₂×D₁₇	C₂²×C₄	1	4	yes	—
24	C₄×C₁₇	C₂²×C₄	1	4	yes	—
25	Dic₁₇	C₂²×C₄	1	3	yes	—
26	Dic₁₇	C₂⁴	1	1	yes	characteristic
27	C₂³×C₈	—	17	1	no	maximal, Sylow
28	C₂×C₁₇	C₂²×C₈	1	6	yes	complemented
29	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
30	D₁₇	C₂²×C₈	1	8	yes	complemented
31	C₂³×C₄	—	17	1	no	—
32	C₂²×C₈	—	17	12	no	—
33	C₂²×C₈	—	17	2	no	—
34	C₁₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	17	1	no	—
36	C₂²×C₄	—	17	1	no	—
37	C₂²×C₄	—	17	6	no	—
38	C₂²×C₄	—	17	6	no	—
39	C₂²×C₄	#595	1	1	yes	characteristic
40	C₂×C₈	—	17	16	no	—
41	C₂×C₈	—	17	12	no	—
42	C₂³	—	17	8	no	—
43	C₂³	—	17	6	no	—
44	C₂³	C₂×#595	1	1	yes	characteristic
45	C₂×C₄	—	17	3	no	—
46	C₂×C₄	—	17	3	no	—
47	C₂×C₄	—	17	4	no	—
48	C₂×C₄	—	17	12	no	—
49	C₂×C₄	C₂×#595	1	6	yes	—
50	C₈	—	17	8	no	—
51	C₂²	—	17	24	no	—
52	C₂²	—	17	4	no	—
53	C₂²	#63242	1	4	yes	direct product factor
54	C₂²	C₂²×#595	1	3	yes	—
55	C₄	—	17	1	no	—
56	C₄	—	17	3	no	—
57	C₄	C₂²×#595	1	4	yes	—
58	C₂	—	17	8	no	—
59	C₂	C₂×#63242	1	6	yes	direct product factor
60	C₂	C₂³×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#595
commutator, hypocenter	C₁₇	C₂³×C₈
Frattini	C₂	C₂³×#595
Fitting	C₂²×C₄×C₁₇	C₄
socle	C₂³×C₁₇	C₂×C₄
prime radical	C₂³×D₁₇	C₄
cosocle	Dic₁₇	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#3624	C₂	semidirect
3. C₂×#63242	C₂	direct (N × H)
9. C₂×#3624	C₂²	semidirect
10. #63242	C₂²	direct (N × H)
12. C₂²×D₁₇	C₈	semidirect
19. #3624	C₂³	semidirect
20. C₂²×C₁₇	C₂×C₈	semidirect
22. C₂×D₁₇	C₂×C₈	semidirect
28. C₂×C₁₇	C₂²×C₈	semidirect
30. D₁₇	C₂²×C₈	semidirect
34. C₁₇	C₂³×C₈	semidirect
53. C₂²	#63242	direct (N × H)
59. C₂	C₂×#63242	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×C₄×D₁₇	2
C₂²×#3624	2
C₂×#63242	2
C₂³×C₈	17

Subgroups — C22×#63242 #11763880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#63242 #11763880