Subgroups — #11763861

Order 1088.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587573	C₂	1	1	yes	maximal, characteristic
2	#10587544	C₂	1	1	yes	maximal, characteristic
3	#10587544	C₂	1	1	yes	maximal, characteristic
4	#10587542	C₂	1	1	yes	maximal, characteristic
5	#10587542	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic
7	C₄×#3624	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₄	C₄	1	1	yes	characteristic
9	C₂×#3624	C₂²	1	1	yes	characteristic
10	C₂×#3624	C₂²	1	1	yes	characteristic
11	C₂×#3624	C₂²	1	1	yes	characteristic
12	C₂×#3624	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
14	#63225	C₄	1	1	yes	characteristic
15	#63225	C₄	1	1	yes	characteristic
16	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
18	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
26	Dic₃₄	—	2	2	no	—
27	#3624	—	2	1	no	—
28	#3624	—	2	1	no	—
29	#3624	—	2	1	no	—
30	#3624	Q₈	1	2	yes	complemented
31	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₁₇	—	2	1	no	—
33	C₄×C₁₇	—	2	1	no	—
34	C₄×C₁₇	—	2	1	no	—
35	Dic₁₇	—	2	1	no	—
36	Dic₁₇	—	2	1	no	—
37	Dic₁₇	M₁₆	1	2	yes	—
38	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
39	Dic₁₇	#41	1	1	yes	characteristic
40	#446	—	17	1	no	maximal, Sylow
41	C₂×C₁₇	C₄×Q₈	1	1	yes	characteristic
42	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
43	C₂×C₁₇	#131	1	1	yes	characteristic
44	C₄×Q₈	—	17	1	no	—
45	C₄⋊C₈	—	17	1	no	—
46	C₄⋊C₈	—	17	1	no	—
47	C₄⋊C₈	—	17	1	no	—
48	#97	—	17	1	no	—
49	#97	—	17	1	no	—
50	C₄×C₈	—	17	1	no	—
51	C₁₇	#446	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	17	1	no	—
53	C₂×C₈	—	17	1	no	—
54	C₂×C₈	—	17	1	no	—
55	C₂×C₈	—	17	1	no	—
56	C₂×C₈	—	17	1	no	—
57	C₄⋊C₄	—	17	1	no	—
58	C₄⋊C₄	—	17	1	no	—
59	C₄⋊C₄	#595	1	1	yes	characteristic
60	C₄²	—	17	1	no	—
61	C₄²	—	17	1	no	—
62	C₄²	—	17	1	no	—
63	Q₈	—	34	2	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	—	17	1	no	—
66	C₂×C₄	—	17	1	no	—
67	C₂×C₄	—	17	1	no	—
68	C₂×C₄	C₂×#595	1	1	yes	characteristic
69	C₂×C₄	C₂×#595	1	1	yes	characteristic
70	C₂×C₄	C₂×#595	1	1	yes	characteristic
71	C₈	—	17	2	no	—
72	C₈	—	34	1	no	—
73	C₈	—	34	1	no	—
74	C₈	—	34	1	no	—
75	C₂²	C₂²×#595	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	2	1	no	—
79	C₄	—	17	2	no	—
80	C₄	—	17	1	no	—
81	C₄	—	17	1	no	—
82	C₄	—	34	1	no	—
83	C₄	—	34	1	no	—
84	C₂	D₁₇⋊M₁₆	1	1	yes	characteristic
85	C₂	#10587678	1	1	yes	characteristic
86	C₂	Q₈×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₄
Fitting	C₄⋊C₄×C₁₇	C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₄⋊C₄	#595
hypocenter	C₁₇	#446
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
30. #3624	Q₈	semidirect
51. C₁₇	#446	semidirect

Maximal subgroups

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

subgroup	index
#10587573	2
#10587544	2
#10587542	2
C₄⋊#3624	2
C₄×#3624	2
#446	17