Subgroups — #11763675

Order 1088.

118 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	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×Dic₁₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₂×#3624	—	2	2	no	—
7	C₂×#3624	—	2	2	no	—
8	C₂×#3624	C₄	1	4	yes	complemented
9	C₄×Dic₁₇	—	2	2	no	—
10	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₇	—	2	1	no	—
12	C₂×C₄×C₁₇	—	2	1	no	—
13	C₂×C₄×C₁₇	C₈	1	2	yes	complemented
14	C₂×Dic₁₇	—	2	1	no	—
15	C₂×Dic₁₇	—	2	1	no	—
16	C₂×Dic₁₇	C₈	1	2	yes	complemented
17	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₇	D₄	1	1	yes	characteristic
19	C₂×Dic₁₇	D₄	1	2	yes	—
20	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
21	#3624	—	2	4	no	—
22	C₂²×C₁₇	C₄²	1	1	yes	characteristic
23	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
28	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
29	C₄×C₁₇	—	2	2	no	—
30	Dic₁₇	—	2	2	no	—
31	Dic₁₇	C₂²⋊C₄	1	2	yes	—
32	Dic₁₇	C₄⋊C₄	1	2	yes	—
33	#336	—	17	1	no	maximal, Sylow
34	C₂×C₁₇	#95	1	1	yes	characteristic
35	C₂×C₁₇	C₄×C₈	1	1	yes	characteristic
36	C₂×C₁₇	#97	1	1	yes	characteristic
37	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×C₁₇	C₄⋊C₈	1	1	yes	characteristic
40	C₂×C₁₇	C₄⋊C₈	1	1	yes	characteristic
41	C₂²×C₈	—	17	2	no	—
42	C₂×C₄²	—	17	1	no	—
43	C₁₇	#336	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	17	1	no	—
45	C₂²×C₄	—	17	1	no	—
46	C₂²×C₄	#595	1	1	yes	characteristic
47	C₂×C₈	—	17	4	no	—
48	C₂×C₈	—	34	2	no	—
49	C₂×C₈	—	34	2	no	—
50	C₄²	—	34	2	no	—
51	C₂³	C₂×#595	1	1	yes	characteristic
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	17	2	no	—
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	17	1	no	—
57	C₂×C₄	—	17	2	no	—
58	C₂×C₄	—	17	2	no	—
59	C₂×C₄	—	34	1	no	—
60	C₂×C₄	—	34	1	no	—
61	C₂×C₄	#3624	1	2	yes	complemented
62	C₈	—	34	4	no	—
63	C₂²	#63242	1	1	yes	characteristic
64	C₂²	#63243	1	1	yes	characteristic
65	C₂²	C₄×#595	1	1	yes	characteristic
66	C₂²	C₄⋊#595	1	1	yes	characteristic
67	C₂²	C₂×#3624	1	1	yes	characteristic
68	C₂²	#63247	1	1	yes	characteristic
69	C₂²	C₂²⋊#595	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	17	2	no	—
72	C₄	—	17	2	no	—
73	C₄	—	34	2	no	—
74	C₂	C₄×#3624	1	1	yes	characteristic
75	C₂	C₄⋊#3624	1	1	yes	characteristic
76	C₂	#10587542	1	1	yes	characteristic
77	C₂	#10587543	1	1	yes	characteristic
78	C₂	#10587544	1	1	yes	characteristic
79	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic
80	C₂	C₂²⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×#595
commutator	C₂×C₁₇	C₄×C₈
Fitting	C₂²×C₄×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂²×Dic₁₇	C₂²
hypercenter	C₂²×C₄	#595
hypocenter	C₁₇	#336
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
8. C₂×#3624	C₄	semidirect
13. C₂×C₄×C₁₇	C₈	semidirect
16. C₂×Dic₁₇	C₈	semidirect
43. C₁₇	#336	semidirect
61. C₂×C₄	#3624	semidirect

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
#336	17