Subgroups — #14543799

Order 2176.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763730	C₂	1	1	yes	maximal, characteristic
2	#11763673	C₂	1	1	yes	maximal, characteristic
3	#11763187	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₇	C₄	1	1	yes	characteristic
5	#10587630	—	2	1	no	—
6	C₂×#63231	—	2	1	no	—
7	C₂×Dic₆₈	C₄	1	1	yes	characteristic
8	C₄⋊#3624	—	2	1	no	—
9	C₂×#63216	—	2	1	no	—
10	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₇	—	2	1	no	—
12	C₂×Dic₃₄	—	2	1	no	—
13	C₂×#3624	—	4	1	no	—
14	Q₁₆×C₁₇	—	4	1	no	—
15	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#63231	—	4	1	no	—
17	#63231	—	4	1	no	—
18	#63225	—	4	1	no	—
19	#63225	—	4	1	no	—
20	C₄×Dic₁₇	D₄	1	1	yes	characteristic
21	C₂×#3622	D₄	1	1	yes	characteristic
22	Dic₆₈	—	4	1	no	—
23	#63216	—	4	1	no	—
24	Q₈×C₁₇	—	4	1	no	—
25	Q₈×C₁₇	—	4	1	no	—
26	C₂×C₄×C₁₇	—	4	1	no	—
27	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	—	4	1	no	—
29	C₂×Dic₁₇	D₈	1	1	yes	characteristic
30	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
31	Dic₃₄	—	4	1	no	—
32	Dic₃₄	—	4	1	no	—
33	#3624	—	8	1	no	—
34	C₈×C₁₇	—	2	1	no	—
35	#3622	D₈	1	1	yes	characteristic
36	#3622	SD₁₆	1	1	yes	characteristic
37	#1362	—	17	1	no	maximal, Sylow
38	C₂²×C₁₇	#102	1	1	yes	characteristic
39	C₄×C₁₇	—	8	1	no	—
40	C₄×C₁₇	#100	1	1	yes	characteristic
41	C₄×C₁₇	#102	1	1	yes	characteristic
42	Dic₁₇	—	2	1	no	—
43	Dic₁₇	—	8	1	no	—
44	Dic₁₇	SD₃₂	1	1	yes	characteristic
45	Dic₁₇	Q₃₂	1	1	yes	characteristic
46	#494	—	17	1	no	—
47	C₄⋊C₁₆	—	17	1	no	—
48	#335	—	17	1	no	—
49	C₂×C₁₇	#331	1	1	yes	characteristic
50	C₂×C₁₇	#358	1	1	yes	characteristic
51	C₂×C₁₇	#362	1	1	yes	characteristic
52	C₂×Q₁₆	—	17	1	no	—
53	C₂×Q₁₆	—	34	1	no	—
54	C₂×Q₁₆	#595	1	1	yes	characteristic
55	C₄⋊Q₈	—	34	1	no	—
56	C₂×C₁₆	—	34	1	no	—
57	C₄⋊C₈	—	34	1	no	—
58	C₄×C₈	—	17	1	no	—
59	C₁₇	#1362	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	34	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	68	1	no	—
64	Q₁₆	—	68	1	no	—
65	Q₁₆	—	68	1	no	—
66	C₂×C₈	—	17	1	no	—
67	C₂×C₈	—	68	1	no	—
68	C₂×C₈	C₂×#595	1	1	yes	characteristic
69	C₄⋊C₄	—	68	1	no	—
70	C₄⋊C₄	—	68	1	no	—
71	C₄²	—	17	1	no	—
72	C₁₆	—	68	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	68	1	no	—
76	Q₈	—	68	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	17	1	no	—
79	C₂×C₄	—	17	1	no	—
80	C₂×C₄	—	68	1	no	—
81	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	17	1	no	—
84	C₈	—	17	1	no	—
85	C₈	—	136	1	no	—
86	C₂²	#10587547	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	17	1	no	—
89	C₄	—	17	1	no	—
90	C₄	—	34	1	no	—
91	C₄	—	136	1	no	—
92	C₄	#10587547	1	1	yes	characteristic
93	C₄	#10587553	1	1	yes	characteristic
94	C₂	#11763667	1	1	yes	characteristic
95	C₂	#11763722	1	1	yes	characteristic
96	C₂	#11763728	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587547
commutator	C₂×C₈×C₁₇	C₂×C₄
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×Q₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#102
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×Q₁₆	#595
hypocenter	C₁₇	#1362
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
59. C₁₇	#1362	semidirect

Maximal subgroups

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

subgroup	index
#11763730	2
#11763673	2
#11763187	2
#1362	17