Subgroups — #11763812

Order 1088.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63247	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587544	C₂	1	2	yes	maximal, complemented
4	C₄⋊#3624	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
8	#63247	—	2	4	no	—
9	C₂×#3624	C₂²	1	4	yes	—
10	C₄×Dic₁₇	C₄	1	1	yes	characteristic
11	C₄×Dic₁₇	C₄	1	1	yes	characteristic
12	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₇	—	2	2	no	—
16	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	—	2	2	no	—
19	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₇	D₄	1	2	yes	—
23	C₂×Dic₁₇	Q₈	1	2	yes	—
24	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
25	#3624	—	2	4	no	—
26	C₂²×C₁₇	—	2	1	no	—
27	C₂²×C₁₇	—	2	1	no	—
28	C₂²×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₁₇	—	2	1	no	—
31	C₄×C₁₇	M₁₆	1	2	yes	complemented
32	Dic₁₇	—	2	1	no	—
33	Dic₁₇	C₄⋊C₄	1	2	yes	—
34	Dic₁₇	M₁₆	1	2	yes	complemented
35	Dic₁₇	C₂×D₄	1	1	yes	characteristic
36	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
37	#423	—	17	1	no	maximal, Sylow
38	C₂×C₁₇	—	2	2	no	—
39	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
42	C₂×M₁₆	—	17	2	no	—
43	C₂×C₄²	—	17	1	no	—
44	C₄⋊C₈	—	17	2	no	—
45	C₄⋊C₈	—	17	2	no	—
46	C₁₇	#423	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	17	1	no	—
48	C₂²×C₄	—	17	1	no	—
49	C₂²×C₄	#595	1	1	yes	characteristic
50	M₁₆	—	34	4	no	—
51	C₂×C₈	—	17	4	no	—
52	C₄²	—	17	1	no	—
53	C₄²	—	17	1	no	—
54	C₄²	—	17	1	no	—
55	C₄²	—	17	1	no	—
56	C₂³	C₂×#595	1	1	yes	characteristic
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	17	2	no	—
59	C₂×C₄	—	17	2	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	34	2	no	—
65	C₂×C₄	C₂×#595	1	1	yes	characteristic
66	C₂×C₄	C₂×#595	1	1	yes	characteristic
67	C₈	—	34	4	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	2	1	no	—
70	C₂²	C₄⋊#595	1	2	yes	—
71	C₂²	C₂²×#595	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	17	2	no	—
74	C₄	—	17	1	no	—
75	C₄	—	17	2	no	—
76	C₄	—	17	1	no	—
77	C₄	—	34	1	no	—
78	C₄	#63247	1	2	yes	complemented
79	C₂	—	2	2	no	—
80	C₂	D₁₇⋊M₁₆	1	1	yes	characteristic
81	C₂	C₂×C₄⋊#595	1	1	yes	characteristic
82	C₂	C₂×#63247	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #10587544	C₂	semidirect
4. C₄⋊#3624	C₂	semidirect
31. C₄×C₁₇	M₁₆	semidirect
34. Dic₁₇	M₁₆	semidirect
46. C₁₇	#423	semidirect
78. C₄	#63247	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63247	2
C₂×C₄×Dic₁₇	2
#10587544	2
C₄⋊#3624	2
#423	17