Subgroups — #14545833

Order 2176.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763904	C₂	1	1	yes	maximal, characteristic
2	#11763898	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×#595	C₂	1	1	yes	maximal, characteristic
4	Q₈×#595	—	2	1	no	—
5	C₄⋊#3633	—	2	1	no	—
6	#10587665	—	2	1	no	—
7	Q₁₆×D₁₇	C₄	1	1	yes	characteristic
8	#10587549	—	2	1	no	—
9	#10587534	C₄	1	1	yes	characteristic
10	C₈×#595	C₂²	1	1	yes	characteristic
11	C₂×#3633	—	4	1	no	—
12	Q₈×D₁₇	—	2	1	no	—
13	C₄⋊#595	—	2	1	no	—
14	C₄⋊#595	—	4	1	no	—
15	C₄×#595	—	4	1	no	—
16	C₄×#595	D₄	1	1	yes	characteristic
17	#63242	D₄	1	1	yes	characteristic
18	#63241	—	2	2	no	—
19	Q₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
20	#63231	—	2	1	no	—
21	Dic₆₈	C₈	1	1	yes	characteristic, complemented
22	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#595	—	4	1	no	—
24	C₂×#595	D₈	1	1	yes	characteristic
25	C₂×#595	SD₁₆	1	1	yes	characteristic
26	#3633	—	8	1	no	—
27	Q₈×C₁₇	—	2	1	no	—
28	C₄×D₁₇	—	4	1	no	—
29	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	Dic₃₄	—	2	1	no	—
31	Dic₃₄	—	4	1	no	—
32	#3624	—	2	1	no	—
33	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#3622	M₁₆	1	1	yes	characteristic
35	#1334	—	17	1	no	maximal, Sylow
36	C₂×D₁₇	#102	1	1	yes	characteristic
37	#595	—	2	1	no	—
38	#595	—	2	1	no	—
39	#595	—	8	1	no	—
40	C₄×C₁₇	—	4	1	no	—
41	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
42	Dic₁₇	—	4	1	no	—
43	Dic₁₇	#104	1	1	yes	characteristic
44	C₄×Q₁₆	—	17	1	no	—
45	#346	—	17	1	no	—
46	#334	—	17	1	no	—
47	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
48	D₁₇	#360	1	1	yes	characteristic
49	D₁₇	#362	1	1	yes	characteristic
50	C₂×Q₁₆	—	17	1	no	—
51	C₄×Q₈	—	34	1	no	—
52	C₂×C₁₆	—	34	1	no	—
53	#107	—	17	1	no	—
54	C₄⋊C₈	—	34	1	no	—
55	#103	—	34	1	no	—
56	C₄×C₈	—	17	1	no	—
57	C₁₇	#1334	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₈	—	34	1	no	—
59	Q₁₆	—	17	1	no	—
60	Q₁₆	—	34	1	no	—
61	Q₁₆	#3633	1	1	yes	characteristic, complemented
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	68	1	no	—
65	C₄⋊C₄	—	34	1	no	—
66	C₄⋊C₄	—	68	1	no	—
67	C₄²	—	17	1	no	—
68	C₄²	—	68	1	no	—
69	C₁₆	—	34	2	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	34	1	no	—
72	Q₈	—	68	1	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	68	1	no	—
77	C₂×C₄	—	68	1	no	—
78	C₈	—	17	1	no	—
79	C₈	—	34	1	no	—
80	C₈	—	136	1	no	—
81	C₈	C₂×#3633	1	1	yes	characteristic
82	C₂²	—	17	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	17	1	no	—
85	C₄	—	34	1	no	—
86	C₄	—	34	1	no	—
87	C₄	—	68	1	no	—
88	C₄	—	136	1	no	—
89	C₄	C₂²⋊#3633	1	1	yes	characteristic
90	C₂	—	17	1	no	—
91	C₂	—	17	1	no	—
92	C₂	D₄⋊#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄⋊#3633
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₈	C₂×#3633
Fitting	Q₁₆×C₁₇	C₈
socle	C₂×C₁₇	D₄⋊C₈
prime radical	C₂×D₁₇	#102
cosocle	C₈×#595	C₂²
hypercenter	Q₁₆	#3633
hypocenter	C₁₇	#1334
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
19. Q₁₆×C₁₇	C₈	semidirect
21. Dic₆₈	C₈	semidirect
57. C₁₇	#1334	semidirect
61. Q₁₆	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763904	2
#11763898	2
Q₁₆×#595	2
#1334	17