Subgroups — #11763813

Order 1088.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63243	C₂	1	2	yes	maximal
2	C₄²×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#3624	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×D₁₇	C₄	1	2	yes	—
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	C₂×#3624	C₂²	1	4	yes	—
7	#63243	—	2	4	no	—
8	C₄²×C₁₇	C₄	1	1	yes	characteristic
9	C₄×Dic₁₇	C₄	1	1	yes	characteristic
10	C₄×Dic₁₇	C₂²	1	2	yes	—
11	C₂²×D₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₄	1	2	yes	—
14	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
15	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
16	C₄×D₁₇	—	2	4	no	—
17	C₄×D₁₇	D₄	1	2	yes	—
18	C₄×D₁₇	Q₈	1	2	yes	—
19	#3624	—	2	4	no	—
20	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₁₇	—	2	2	no	—
22	C₂×D₁₇	C₄⋊C₄	1	2	yes	—
23	C₄×C₁₇	C₄⋊C₄	1	2	yes	—
24	C₄×C₁₇	M₁₆	1	4	yes	complemented
25	Dic₁₇	—	2	2	no	—
26	Dic₁₇	C₂×D₄	1	1	yes	characteristic
27	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
28	#423	—	17	1	no	maximal, Sylow
29	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₁₇	C₂×M₁₆	1	2	yes	—
31	D₁₇	—	2	2	no	—
32	C₂×M₁₆	—	17	2	no	—
33	C₂×C₄²	—	17	1	no	—
34	C₄⋊C₈	—	17	4	no	—
35	C₁₇	#423	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	—	17	1	no	—
37	C₂²×C₄	—	17	2	no	—
38	M₁₆	—	34	4	no	—
39	C₂×C₈	—	17	4	no	—
40	C₄²	—	17	2	no	—
41	C₄²	—	17	1	no	—
42	C₄²	#595	1	1	yes	characteristic
43	C₂³	—	17	1	no	—
44	C₂×C₄	—	17	1	no	—
45	C₂×C₄	—	17	2	no	—
46	C₂×C₄	—	17	2	no	—
47	C₂×C₄	—	17	2	no	—
48	C₂×C₄	—	34	4	no	—
49	C₂×C₄	C₂×#595	1	2	yes	—
50	C₂×C₄	C₂×#595	1	1	yes	characteristic
51	C₈	—	34	4	no	—
52	C₂²	—	17	2	no	—
53	C₂²	—	34	2	no	—
54	C₂²	C₂²×#595	1	1	yes	characteristic
55	C₄	—	17	1	no	—
56	C₄	—	17	1	no	—
57	C₄	—	34	2	no	—
58	C₄	#63243	1	4	yes	complemented
59	C₄	C₄⋊#595	1	2	yes	—
60	C₂	—	34	2	no	—
61	C₂	C₂×#63243	1	2	yes	—
62	C₂	C₂×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄
Fitting	C₄²×C₁₇	C₄
prime radical	C₂²×D₁₇	C₂×C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₄²	#595
hypocenter	C₁₇	#423
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
3. C₄⋊#3624	C₂	semidirect
24. C₄×C₁₇	M₁₆	semidirect
35. C₁₇	#423	semidirect
58. C₄	#63243	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63243	2
C₄²×D₁₇	2
C₄⋊#3624	2
#423	17