Subgroups — #14545125

Order 2176.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587538	C₂	1	2	yes	maximal
2	#11763731	C₂	1	4	yes	maximal, complemented
3	#11762767	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₁₇	C₄	1	1	yes	characteristic
5	#10587612	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	#10587538	—	2	2	no	—
8	#10587538	C₂²	1	4	yes	—
9	C₂×#63216	—	2	2	no	—
10	#10587486	C₄	1	2	yes	—
11	C₈×Dic₁₇	C₂²	1	2	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₁₇	C₈	1	4	yes	—
14	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
15	C₂²⋊Dic₁₇	—	2	1	no	—
16	C₄⋊Dic₁₇	—	2	1	no	—
17	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
18	C₂×#3622	C₂×C₄	1	1	yes	characteristic
19	C₂×#3622	D₄	1	2	yes	—
20	C₂×#3622	Q₈	1	2	yes	—
21	C₂×#3622	C₂³	1	1	yes	characteristic
22	#63216	—	2	4	no	—
23	C₂³×C₁₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	—	2	2	no	—
29	C₈×C₁₇	C₂×C₈	1	4	yes	—
30	#3622	C₄⋊C₄	1	2	yes	—
31	#3622	C₂×D₄	1	1	yes	characteristic
32	#3622	C₂×Q₈	1	1	yes	characteristic
33	#2153	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	—	4	1	no	—
35	C₂²×C₁₇	C₄⋊C₈	1	2	yes	—
36	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
37	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
38	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
40	Dic₁₇	—	4	2	no	—
41	C₂×M₃₂	—	17	2	no	—
42	#405	—	17	1	no	—
43	#364	—	17	4	no	—
44	C₂×C₁₇	—	2	1	no	—
45	C₂×C₁₇	—	2	2	no	—
46	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
47	C₂×M₁₆	#595	1	1	yes	characteristic
48	C₂²×C₈	—	17	1	no	—
49	#117	—	17	1	no	—
50	M₃₂	—	17	4	no	—
51	M₃₂	—	34	2	no	—
52	C₂×C₁₆	—	34	2	no	—
53	#97	—	17	2	no	—
54	C₄×C₈	—	17	2	no	—
55	C₁₇	#2153	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₂×#595	1	1	yes	characteristic
57	M₁₆	#3624	1	4	yes	—
58	C₂×C₈	—	17	2	no	—
59	C₂×C₈	—	17	2	no	—
60	C₂×C₈	—	17	1	no	—
61	C₂×C₈	—	17	1	no	—
62	C₂×C₈	C₂×#595	1	2	yes	—
63	C₄⋊C₄	—	34	1	no	—
64	C₂²⋊C₄	—	34	1	no	—
65	C₄²	—	17	2	no	—
66	C₁₆	—	34	4	no	—
67	C₂³	#63243	1	1	yes	characteristic
68	C₂×C₄	—	34	2	no	—
69	C₂×C₄	#63243	1	1	yes	characteristic
70	C₂×C₄	C₄⋊#595	1	2	yes	—
71	C₂×C₄	C₂×#3624	1	2	yes	—
72	C₂×C₄	C₂²×#595	1	1	yes	characteristic
73	C₈	—	17	1	no	—
74	C₈	—	17	2	no	—
75	C₈	—	17	1	no	—
76	C₈	C₂×#3624	1	4	yes	—
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊#3624	1	2	yes	—
79	C₂²	C₂×#63243	1	1	yes	characteristic
80	C₄	—	68	2	no	—
81	C₄	C₄⋊#3624	1	2	yes	—
82	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
83	C₄	C₂²×#3624	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂×M₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂×C₄⋊C₈
prime radical	C₂³×C₁₇	M₁₆
cosocle	C₂×#3622	C₂³
hypercenter	C₂×M₁₆	#595
hypocenter	C₁₇	#2153
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #11763731	C₂	semidirect
55. C₁₇	#2153	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587538	2
#11763731	2
#11762767	2
#2153	17