Subgroups — #11763537

Order 1088.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic
2	#10587630	C₂	1	2	yes	maximal
3	#10587575	C₂	1	4	yes	maximal
4	#10587573	C₂	1	2	yes	maximal
5	#10587556	C₂	1	2	yes	maximal
6	#10587555	C₂	1	1	yes	maximal, characteristic
7	C₄×Dic₃₄	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₃₄	C₂	1	2	yes	maximal
9	C₂×Q₈×C₁₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₄	C₂²	1	2	yes	—
11	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
14	C₄²×C₁₇	C₂²	1	1	yes	characteristic
15	C₄²×C₁₇	C₂²	1	2	yes	—
16	C₄⋊Dic₁₇	C₂²	1	2	yes	—
17	C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
18	C₄⋊Dic₁₇	C₂²	1	2	yes	—
19	#63225	C₂²	1	2	yes	—
20	#63225	C₂²	1	4	yes	—
21	#63225	C₂²	1	4	yes	—
22	#63225	C₂²	1	4	yes	—
23	C₄×Dic₁₇	C₂²	1	4	yes	—
24	C₄×Dic₁₇	C₂²	1	2	yes	—
25	Q₈×C₁₇	—	2	2	no	—
26	C₂×C₄×C₁₇	C₂³	1	2	yes	—
27	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂³	1	2	yes	—
29	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
31	C₂×Dic₁₇	C₂³	1	4	yes	—
32	C₂×Dic₁₇	C₂³	1	2	yes	—
33	C₂×Dic₁₇	C₂³	1	2	yes	—
34	Dic₃₄	—	2	4	no	—
35	Dic₃₄	Q₈	1	4	yes	complemented
36	C₂²×C₁₇	C₂⁴	1	1	yes	characteristic
37	C₄×C₁₇	—	2	2	no	—
38	C₄×C₁₇	—	2	2	no	—
39	C₄×C₁₇	—	2	1	no	—
40	C₄×C₁₇	C₂×Q₈	1	2	yes	—
41	C₄×C₁₇	#41	1	2	yes	—
42	Dic₁₇	—	2	4	no	—
43	Dic₁₇	—	2	2	no	—
44	Dic₁₇	C₂×Q₈	1	4	yes	—
45	#557	—	17	1	no	maximal, Sylow
46	C₂×C₁₇	C₂²×Q₈	1	1	yes	characteristic
47	C₂×C₁₇	C₂×#41	1	1	yes	characteristic
48	C₂×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
49	C₄⋊Q₈	—	17	2	no	—
50	C₄⋊Q₈	—	17	1	no	—
51	#125	—	17	4	no	—
52	#125	—	17	2	no	—
53	C₄×Q₈	—	17	2	no	—
54	C₄×Q₈	—	17	2	no	—
55	C₄×Q₈	—	17	1	no	—
56	C₄×Q₈	D₁₇	1	1	yes	characteristic
57	C₁₇	#557	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₈	—	17	1	no	—
59	C₂×Q₈	—	17	2	no	—
60	C₂×Q₈	C₂×D₁₇	1	1	yes	characteristic
61	C₄⋊C₄	—	17	2	no	—
62	C₄⋊C₄	—	17	4	no	—
63	C₄⋊C₄	—	17	1	no	—
64	C₄⋊C₄	—	17	4	no	—
65	C₄⋊C₄	—	17	2	no	—
66	C₄⋊C₄	—	17	4	no	—
67	C₄⋊C₄	—	17	2	no	—
68	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
69	C₄⋊C₄	C₂×D₁₇	1	2	yes	—
70	C₄²	—	17	4	no	—
71	C₄²	—	17	2	no	—
72	C₄²	C₂×D₁₇	1	2	yes	—
73	C₄²	C₂×D₁₇	1	1	yes	characteristic
74	Q₈	—	2	2	no	—
75	Q₈	—	17	4	no	—
76	Q₈	—	34	4	no	—
77	C₂×C₄	—	17	2	no	—
78	C₂×C₄	—	17	2	no	—
79	C₂×C₄	—	17	4	no	—
80	C₂×C₄	C₂²×D₁₇	1	2	yes	—
81	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
82	C₂×C₄	C₂²×D₁₇	1	2	yes	—
83	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
84	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
85	C₂²	C₂³×D₁₇	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	1	no	—
89	C₄	—	17	4	no	—
90	C₄	—	34	4	no	—
91	C₄	—	34	2	no	—
92	C₄	#63252	1	2	yes	—
93	C₄	Q₈×D₁₇	1	2	yes	—
94	C₂	C₂×#63252	1	1	yes	characteristic
95	C₂	C₂×Q₈×D₁₇	1	1	yes	characteristic
96	C₂	#10587697	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₇
commutator, socle, prime radical, cosocle	C₂²×C₁₇	C₂⁴
Fitting	C₄×Q₈×C₁₇	C₂
hypercenter	C₄×Q₈	D₁₇
hypocenter	C₁₇	#557
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
35. Dic₃₄	Q₈	semidirect
57. C₁₇	#557	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₁₇	2
#10587630	2
#10587575	2
#10587573	2
#10587556	2
#10587555	2
C₄×Dic₃₄	2
#557	17