Subgroups — #14528959

Order 2176.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587490	C₂	1	4	yes	maximal
2	#11762833	C₂	1	2	yes	maximal
3	C₂×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
5	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×#63223	C₂²	1	4	yes	—
7	C₁₇×#97	C₄	1	4	yes	—
8	#10587490	—	2	8	no	—
9	C₄⋊#3622	—	2	4	no	—
10	C₂²×C₄×C₁₇	Q₈	1	2	yes	—
11	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
13	C₂×C₈×C₁₇	D₄	1	4	yes	—
14	C₂×C₈×C₁₇	Q₈	1	4	yes	—
15	C₄²×C₁₇	C₂×C₄	1	2	yes	—
16	C₄²×C₁₇	D₄	1	2	yes	—
17	#63223	—	2	8	no	—
18	C₂×#3622	—	2	4	no	—
19	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₁₇	—	4	2	no	—
21	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₂×Q₈	1	2	yes	—
26	C₈×C₁₇	C₄⋊C₄	1	8	yes	—
27	#3622	—	4	4	no	—
28	#1849	—	17	1	no	maximal, Sylow
29	C₂²×C₁₇	—	2	2	no	—
30	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₁₇	C₄⋊Q₈	1	2	yes	—
32	C₄×C₁₇	—	2	4	no	—
33	C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
34	C₄×C₁₇	#127	1	1	yes	characteristic
35	C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
36	C₂×#108	—	17	4	no	—
37	#423	—	17	2	no	—
38	C₂×#97	D₁₇	1	1	yes	characteristic
39	C₂×C₁₇	—	2	2	no	—
40	C₂×C₁₇	#384	1	1	yes	characteristic
41	C₂×C₁₇	#430	1	2	yes	—
42	C₂×M₁₆	—	17	4	no	—
43	C₂²×C₈	C₂×D₁₇	1	2	yes	—
44	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
45	#108	—	34	8	no	—
46	C₄⋊C₈	—	34	4	no	—
47	#97	Dic₁₇	1	4	yes	—
48	C₁₇	#1849	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	Dic₃₄	1	2	yes	—
50	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
51	M₁₆	—	34	8	no	—
52	C₂×C₈	—	34	4	no	—
53	C₂×C₈	Dic₃₄	1	4	yes	—
54	C₂×C₈	D₆₈	1	4	yes	—
55	C₂×C₈	C₂×Dic₁₇	1	4	yes	—
56	C₄²	D₆₈	1	2	yes	—
57	C₄²	C₂×Dic₁₇	1	2	yes	—
58	C₂³	C₂×Dic₃₄	1	1	yes	characteristic
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₄⋊Dic₁₇	1	4	yes	—
61	C₂×C₄	C₂×Dic₃₄	1	2	yes	—
62	C₂×C₄	C₂×D₆₈	1	2	yes	—
63	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
64	C₂×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
65	C₈	—	68	4	no	—
66	C₈	C₄⋊Dic₁₇	1	8	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	#10587555	1	2	yes	—
69	C₂²	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
70	C₄	—	2	4	no	—
71	C₄	#10587555	1	1	yes	characteristic
72	C₄	#10587560	1	1	yes	characteristic
73	C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#11762679	1	1	yes	characteristic
76	C₂	#11762858	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₆₈
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₇
Fitting	C₂×C₁₇×#97	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#1849
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
48. C₁₇	#1849	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587490	2
#11762833	2
C₂×C₁₇×#97	2
#1849	17