Subgroups — #11763661

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587581	C₂	1	1	yes	maximal, characteristic
2	(C₂×#595)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587543	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#595	—	2	1	no	—
5	C₂×D₆₈	—	2	1	no	—
6	C₂×D₆₈	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
8	C₂×#3624	—	2	1	no	—
9	C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic, complemented
10	#63227	—	2	1	no	—
11	C₂²×D₁₇	—	2	1	no	—
12	C₂²×D₁₇	D₄	1	1	yes	characteristic
13	C₂×#595	—	2	2	no	—
14	C₂×#595	—	4	1	no	—
15	C₂×#595	—	4	1	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	D₄	1	1	yes	characteristic
19	D₆₈	—	4	1	no	—
20	D₆₈	—	4	1	no	—
21	D₆₈	—	4	1	no	—
22	C₄×D₁₇	—	4	1	no	—
23	#3624	—	4	1	no	—
24	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₁₇	—	2	1	no	—
26	C₂×D₁₇	—	2	1	no	—
27	C₂×D₁₇	—	4	1	no	—
28	C₂×D₁₇	—	4	1	no	—
29	C₂×D₁₇	—	4	1	no	—
30	C₂×D₁₇	D₈	1	1	yes	characteristic
31	C₂×D₁₇	SD₁₆	1	1	yes	characteristic
32	#595	—	4	2	no	—
33	C₄×C₁₇	—	2	1	no	—
34	C₄×C₁₇	—	4	1	no	—
35	Dic₁₇	—	2	1	no	—
36	#327	—	17	1	no	maximal, Sylow
37	C₂×C₁₇	#99	1	1	yes	characteristic
38	C₂×C₁₇	#102	1	1	yes	characteristic
39	C₂×C₁₇	#104	1	1	yes	characteristic
40	D₁₇	—	2	1	no	—
41	D₁₇	—	2	1	no	—
42	D₁₇	—	8	1	no	—
43	#121	—	17	1	no	—
44	C₂²⋊C₈	—	17	1	no	—
45	#95	—	17	1	no	—
46	C₁₇	#327	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₄	—	17	1	no	—
48	C₂×D₄	—	34	1	no	—
49	C₂²×C₄	—	17	1	no	—
50	C₂²×C₄	—	34	1	no	—
51	C₂×C₈	—	34	1	no	—
52	C₄⋊C₄	#595	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	34	1	no	—
54	C₂³	—	17	1	no	—
55	C₂³	—	34	1	no	—
56	D₄	—	68	1	no	—
57	D₄	—	68	1	no	—
58	D₄	—	68	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	34	2	no	—
62	C₂×C₄	—	68	1	no	—
63	C₂×C₄	—	68	1	no	—
64	C₂×C₄	—	68	1	no	—
65	C₂×C₄	C₂×#595	1	1	yes	characteristic
66	C₈	—	68	1	no	—
67	C₂²	—	17	1	no	—
68	C₂²	—	17	1	no	—
69	C₂²	—	34	1	no	—
70	C₂²	—	34	1	no	—
71	C₂²	—	68	1	no	—
72	C₂²	—	68	1	no	—
73	C₂²	—	68	1	no	—
74	C₂²	C₂²⋊#595	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	34	1	no	—
78	C₄	—	68	2	no	—
79	C₂	—	34	1	no	—
80	C₂	—	34	1	no	—
81	C₂	—	136	1	no	—
82	C₂	#10587539	1	1	yes	characteristic
83	C₂	#10587547	1	1	yes	characteristic
84	C₂	#10587550	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₄
Frattini	C₂×C₄	C₂×#595
Fitting	C₄⋊C₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
prime radical	#10587581	C₂
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₄⋊C₄	#595
hypocenter	C₁₇	#327
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. (C₂×#595)⋊C₄	C₂	semidirect
3. #10587543	C₂	semidirect
6. C₂×D₆₈	C₄	semidirect
9. C₄⋊C₄×C₁₇	C₄	semidirect
46. C₁₇	#327	semidirect
52. C₄⋊C₄	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587581	2
(C₂×#595)⋊C₄	2
#10587543	2
#327	17