Subgroups — #14526613

Order 2176.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762862	C₂	1	2	yes	maximal
2	C₁₇×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₁₇	C₄	1	2	yes	—
4	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
5	C₁₇×#95	—	2	2	no	—
6	C₂²⋊#3622	—	2	2	no	—
7	C₄⋊#3622	—	2	2	no	—
8	C₄×#3622	C₄	1	4	yes	complemented
9	C₂²×C₄×C₁₇	—	2	2	no	—
10	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₇	D₄	1	2	yes	—
12	C₄²×C₁₇	—	2	2	no	—
13	C₄²×C₁₇	C₈	1	4	yes	complemented
14	C₄²×C₁₇	C₂×C₄	1	2	yes	—
15	C₄²×C₁₇	D₄	1	1	yes	characteristic
16	C₄²×C₁₇	Q₈	1	1	yes	characteristic
17	C₂×#3622	—	2	4	no	—
18	C₂³×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₇	—	2	4	no	—
20	C₂×C₄×C₁₇	—	4	2	no	—
21	C₂×C₄×C₁₇	—	4	4	no	—
22	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
28	#3622	—	4	4	no	—
29	#1274	—	17	1	no	maximal, Sylow
30	C₂²×C₁₇	—	2	2	no	—
31	C₂²×C₁₇	#95	1	1	yes	characteristic
32	C₂²×C₁₇	C₂²⋊C₈	1	2	yes	—
33	C₄×C₁₇	—	2	2	no	—
34	C₄×C₁₇	—	2	2	no	—
35	C₄×C₁₇	—	4	4	no	—
36	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
37	C₄×C₁₇	#97	1	1	yes	characteristic
38	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
39	#431	—	17	2	no	—
40	#376	D₁₇	1	1	yes	characteristic
41	C₂×C₁₇	—	2	2	no	—
42	C₂×C₁₇	#336	1	1	yes	characteristic
43	C₂×C₁₇	H(3,ℤ/4)	1	2	yes	—
44	C₂×C₄²	Dic₁₇	1	2	yes	—
45	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
46	C₄⋊C₈	—	34	2	no	—
47	C₂²⋊C₈	—	34	2	no	—
48	C₄×C₈	—	17	4	no	—
49	#95	—	2	2	no	—
50	C₁₇	#1274	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	—	2	2	no	—
52	C₂²×C₄	C₂×Dic₁₇	1	1	yes	characteristic
53	C₂²×C₄	C₂²⋊D₁₇	1	2	yes	—
54	C₂×C₈	—	34	4	no	—
55	C₄²	—	2	2	no	—
56	C₄²	#3622	1	4	yes	complemented
57	C₄²	Dic₃₄	1	1	yes	characteristic
58	C₄²	C₄×D₁₇	1	2	yes	—
59	C₄²	D₆₈	1	1	yes	characteristic
60	C₂³	C₂²⋊Dic₁₇	1	1	yes	characteristic
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	C₂×#3622	1	2	yes	—
65	C₂×C₄	#63223	1	2	yes	—
66	C₂×C₄	C₄×Dic₁₇	1	1	yes	characteristic
67	C₂×C₄	#63225	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
69	C₂×C₄	#63227	1	2	yes	—
70	C₈	—	68	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	C₂²⋊#3622	1	2	yes	—
73	C₂²	#10587502	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	4	4	no	—
77	C₄	C₄×#3622	1	1	yes	characteristic
78	C₄	#10587474	1	1	yes	characteristic
79	C₄	C₄⋊#3622	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	#11762564	1	1	yes	characteristic
82	C₂	#11762565	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₁₇
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₂×C₄²	C₂×D₁₇
Fitting	C₁₇×#376	C₂
socle	C₂²×C₁₇	#95
prime radical	C₂³×C₁₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₇	C₂²
hypercenter	#376	D₁₇
hypocenter	C₁₇	#1274
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
8. C₄×#3622	C₄	semidirect
13. C₄²×C₁₇	C₈	semidirect
50. C₁₇	#1274	semidirect
56. C₄²	#3622	semidirect

Maximal subgroups

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

subgroup	index
#11762862	2
C₁₇×#376	2
#1274	17