Subgroups — #14545187

Order 2176.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763853	C₂	1	2	yes	maximal, complemented
2	#11763738	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763724	C₂	1	2	yes	maximal, complemented
4	#11763696	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763242	C₂	1	1	yes	maximal, characteristic
6	#10587680	—	2	2	no	—
7	#10587605	C₂²	1	2	yes	—
8	#10587550	—	2	2	no	—
9	#10587536	C₂²	1	2	yes	—
10	C₈×#595	C₂²	1	1	yes	characteristic
11	#10587529	C₂²	1	1	yes	characteristic
12	C₁₇×Q₃₂	C₄	1	1	yes	characteristic, complemented
13	#10587499	C₄	1	2	yes	complemented
14	D₂₇₂	C₄	1	1	yes	characteristic, complemented
15	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
16	#63256	—	2	2	no	—
17	C₄×#595	D₄	1	1	yes	characteristic
18	#63243	—	2	2	no	—
19	#63243	—	4	2	no	—
20	#63242	—	4	2	no	—
21	#63242	D₄	1	1	yes	characteristic
22	Q₁₆×C₁₇	C₂×C₄	1	2	yes	—
23	#63230	—	2	2	no	—
24	D₁₃₆	C₂×C₄	1	2	yes	—
25	C₈×D₁₇	C₂³	1	1	yes	characteristic
26	#63216	—	2	1	no	—
27	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
28	#63214	C₂×C₄	1	1	yes	characteristic
29	C₂×#595	—	2	1	no	—
30	Q₈×C₁₇	—	2	2	no	—
31	D₆₈	—	2	2	no	—
32	D₆₈	—	4	2	no	—
33	C₄×D₁₇	—	4	2	no	—
34	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
35	#3624	—	4	2	no	—
36	#3624	D₈	1	2	yes	—
37	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
38	#3622	#41	1	1	yes	characteristic
39	#2179	—	17	1	no	maximal, Sylow
40	C₂×D₁₇	—	4	2	no	—
41	C₂×D₁₇	#135	1	1	yes	characteristic
42	#595	—	4	1	no	—
43	C₄×C₁₇	—	4	2	no	—
44	C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
45	Dic₁₇	C₂×D₈	1	1	yes	characteristic
46	#508	—	17	1	no	—
47	#443	—	17	2	no	—
48	#368	—	17	1	no	—
49	#359	—	17	2	no	—
50	#346	—	17	1	no	—
51	C₂×C₁₇	C₄×D₈	1	1	yes	characteristic
52	D₁₇	—	2	1	no	—
53	D₁₇	—	8	2	no	—
54	#135	—	17	2	no	—
55	#131	—	34	2	no	—
56	Q₃₂	#595	1	1	yes	characteristic, complemented
57	SD₃₂	—	17	2	no	—
58	D₁₆	—	17	1	no	—
59	C₂×C₁₆	—	17	1	no	—
60	C₂×C₁₆	—	17	1	no	—
61	#108	—	17	2	no	—
62	#104	—	34	2	no	—
63	C₄×C₈	—	17	1	no	—
64	C₁₇	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	34	2	no	—
66	Q₁₆	C₂×#595	1	2	yes	—
67	SD₁₆	—	34	2	no	—
68	D₈	—	17	2	no	—
69	M₁₆	—	34	2	no	—
70	M₁₆	—	68	2	no	—
71	C₂×C₈	—	17	1	no	—
72	C₂×C₈	—	17	1	no	—
73	C₂×C₈	—	68	2	no	—
74	C₄²	—	17	1	no	—
75	C₁₆	—	17	1	no	—
76	C₁₆	—	34	1	no	—
77	C₁₆	C₂×#595	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	34	2	no	—
80	D₄	—	68	2	no	—
81	C₂×C₄	—	17	1	no	—
82	C₂×C₄	—	34	1	no	—
83	C₂×C₄	—	68	2	no	—
84	C₈	—	17	2	no	—
85	C₈	—	17	1	no	—
86	C₈	—	68	2	no	—
87	C₈	C₂²×#595	1	1	yes	characteristic
88	C₂²	—	17	1	no	—
89	C₂²	—	68	2	no	—
90	C₄	—	4	2	no	—
91	C₄	—	17	1	no	—
92	C₄	—	68	1	no	—
93	C₄	D₄×#595	1	1	yes	characteristic
94	C₂	—	34	1	no	—
95	C₂	—	136	2	no	—
96	C₂	D₈×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#595
commutator	C₈×C₁₇	C₂²×C₄
Frattini	C₈	C₂²×#595
Fitting	C₁₇×Q₃₂	C₄
socle	C₂×C₁₇	C₄×D₈
prime radical	#11763242	C₂
cosocle	C₈×D₁₇	C₂³
hypercenter	Q₃₂	#595
hypocenter	C₁₇	#2179
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #11763853	C₂	semidirect
2. #11763738	C₂	semidirect
3. #11763724	C₂	semidirect
4. #11763696	C₂	semidirect
12. C₁₇×Q₃₂	C₄	semidirect
13. #10587499	C₄	semidirect
14. D₂₇₂	C₄	semidirect
56. Q₃₂	#595	semidirect
64. C₁₇	#2179	semidirect

Maximal subgroups

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

subgroup	index
#11763853	2
#11763738	2
#11763724	2
#11763696	2
#11763242	2
#2179	17