Subgroups — #14545836

Order 2176.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763913	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763893	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763851	C₂	1	1	yes	maximal, characteristic
4	#10587678	—	2	1	no	—
5	C₄×#3633	—	2	1	no	—
6	#10587666	—	2	1	no	—
7	#10587598	C₄	1	1	yes	characteristic
8	#10587548	—	2	1	no	—
9	#10587536	C₄	1	1	yes	characteristic
10	C₈×#595	C₂²	1	1	yes	characteristic
11	C₂×#3633	—	2	2	no	—
12	#63254	—	2	1	no	—
13	#63247	—	4	1	no	—
14	C₂×#3624	—	4	1	no	—
15	C₄×#595	D₄	1	1	yes	characteristic
16	#63243	—	2	1	no	—
17	#63242	D₄	1	1	yes	characteristic
18	#63241	—	4	1	no	—
19	D₈×C₁₇	C₈	1	1	yes	characteristic, complemented
20	#63229	—	2	1	no	—
21	Dic₆₈	C₈	1	1	yes	characteristic, complemented
22	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#595	—	2	1	no	—
24	#3633	—	4	2	no	—
25	D₄×C₁₇	—	2	1	no	—
26	C₂²⋊D₁₇	—	4	1	no	—
27	C₂×Dic₁₇	—	4	1	no	—
28	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	Dic₃₄	—	2	1	no	—
30	#3624	—	4	1	no	—
31	#3624	D₈	1	1	yes	characteristic
32	#3624	SD₁₆	1	1	yes	characteristic
33	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#3622	M₁₆	1	1	yes	characteristic
35	#1336	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	—	4	1	no	—
37	C₂×D₁₇	#104	1	1	yes	characteristic
38	#595	—	2	2	no	—
39	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
40	Dic₁₇	—	4	1	no	—
41	Dic₁₇	#102	1	1	yes	characteristic
42	#443	—	17	1	no	—
43	#364	—	17	1	no	—
44	#322	—	17	1	no	—
45	C₂×C₁₇	—	8	1	no	—
46	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
47	D₁₇	—	2	1	no	—
48	#135	—	17	1	no	—
49	#131	—	34	1	no	—
50	M₃₂	—	34	1	no	—
51	#108	—	17	1	no	—
52	#104	—	34	1	no	—
53	C₄×C₈	—	17	1	no	—
54	C₄×C₈	—	34	1	no	—
55	C₁₇	#1336	1	1	yes	characteristic, complemented, Sylow
56	#41	—	34	1	no	—
57	Q₁₆	—	17	1	no	—
58	SD₁₆	—	34	1	no	—
59	D₈	#3633	1	1	yes	characteristic, complemented
60	M₁₆	—	34	1	no	—
61	M₁₆	—	68	1	no	—
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	34	2	no	—
65	C₂×C₈	—	68	1	no	—
66	C₄²	—	17	1	no	—
67	C₁₆	—	68	1	no	—
68	Q₈	—	34	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	68	1	no	—
71	C₂×C₄	—	17	1	no	—
72	C₂×C₄	—	34	1	no	—
73	C₂×C₄	—	68	1	no	—
74	C₈	—	17	1	no	—
75	C₈	—	17	1	no	—
76	C₈	—	17	1	no	—
77	C₈	—	68	1	no	—
78	C₈	—	68	2	no	—
79	C₈	C₂×#3633	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	—	17	1	no	—
82	C₄	—	17	1	no	—
83	C₄	—	34	2	no	—
84	C₄	—	68	1	no	—
85	C₄	C₂²⋊#3633	1	1	yes	characteristic
86	C₂	—	8	1	no	—
87	C₂	—	34	1	no	—
88	C₂	D₄⋊#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄⋊#3633
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₈	C₂×#3633
Fitting	D₈×C₁₇	C₈
socle	C₂×C₁₇	D₄⋊C₈
prime radical	#10587598	C₄
cosocle	C₈×#595	C₂²
hypercenter	D₈	#3633
hypocenter	C₁₇	#1336
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #11763913	C₂	semidirect
2. #11763893	C₂	semidirect
19. D₈×C₁₇	C₈	semidirect
21. Dic₆₈	C₈	semidirect
55. C₁₇	#1336	semidirect
59. D₈	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763913	2
#11763893	2
#11763851	2
#1336	17