Subgroups — C₂×#10587544 #11763811

Order 1088.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3624	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587544	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂×#3624	—	2	4	no	—
8	C₂×#3624	C₂²	1	4	yes	—
9	C₄×Dic₁₇	C₄	1	2	yes	—
10	C₄×Dic₁₇	C₂²	1	2	yes	—
11	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₇	—	2	2	no	—
13	C₂×C₄×C₁₇	C₂×C₄	1	2	yes	—
14	C₂×Dic₁₇	C₈	1	4	yes	complemented
15	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₁₇	D₄	1	2	yes	—
18	C₂×Dic₁₇	Q₈	1	2	yes	—
19	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
20	#3624	—	2	4	no	—
21	C₂²×C₁₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₁₇	C₂×C₈	1	2	yes	—
23	C₂²×C₁₇	M₁₆	1	2	yes	—
24	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₁₇	—	2	2	no	—
26	Dic₁₇	C₄⋊C₄	1	2	yes	—
27	Dic₁₇	C₂×C₈	1	4	yes	complemented
28	Dic₁₇	C₂×D₄	1	1	yes	characteristic
29	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄⋊C₈	—	17	1	no	maximal, Sylow
31	C₂×C₁₇	C₄⋊C₈	1	4	yes	complemented
32	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
34	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
35	C₂²×C₈	—	17	2	no	—
36	C₂×C₄²	—	17	1	no	—
37	C₄⋊C₈	—	17	4	no	—
38	C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄	—	17	1	no	—
40	C₂²×C₄	—	17	1	no	—
41	C₂²×C₄	#595	1	1	yes	characteristic
42	C₂×C₈	—	17	4	no	—
43	C₂×C₈	—	34	4	no	—
44	C₄²	—	17	2	no	—
45	C₄²	—	17	2	no	—
46	C₂³	C₂×#595	1	1	yes	characteristic
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	17	4	no	—
49	C₂×C₄	—	17	2	no	—
50	C₂×C₄	—	17	2	no	—
51	C₂×C₄	—	17	1	no	—
52	C₂×C₄	—	17	2	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	C₂×#595	1	2	yes	—
55	C₈	—	34	4	no	—
56	C₂²	#63242	1	2	yes	—
57	C₂²	C₄⋊#595	1	2	yes	—
58	C₂²	#63247	1	2	yes	—
59	C₂²	C₂²×#595	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	17	4	no	—
62	C₄	—	17	1	no	—
63	C₄	—	17	2	no	—
64	C₄	—	17	1	no	—
65	C₂	#10587544	1	4	yes	direct product factor
66	C₂	C₂×#63242	1	1	yes	characteristic
67	C₂	C₂×C₄⋊#595	1	1	yes	characteristic
68	C₂	C₂×#63247	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #10587544	C₂	direct (N × H)
14. C₂×Dic₁₇	C₈	semidirect
27. Dic₁₇	C₂×C₈	semidirect
31. C₂×C₁₇	C₄⋊C₈	semidirect
38. C₁₇	C₂×C₄⋊C₈	semidirect
65. C₂	#10587544	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×#3624	2
C₂×C₄×Dic₁₇	2
#10587544	2
C₂×C₄⋊C₈	17

Subgroups — C2×#10587544 #11763811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587544 #11763811