Subgroups — #14545878

Order 2176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763917	C₂	1	2	yes	maximal, complemented
2	C₂×#10587538	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3622	C₄	1	1	yes	characteristic
4	#10587538	—	2	2	no	—
5	C₂×#63216	C₄	1	1	yes	characteristic
6	C₂×#63216	C₂²	1	1	yes	characteristic
7	#10587528	—	2	2	no	—
8	C₂²×C₄×C₁₇	C₈	1	1	yes	characteristic
9	C₂×#3622	—	2	1	no	—
10	C₂×#3622	—	2	1	no	—
11	C₂×#3622	C₈	1	1	yes	characteristic
12	C₂×#3622	C₂×C₄	1	1	yes	characteristic
13	#63216	—	2	1	no	—
14	#63216	D₄	1	2	yes	—
15	C₂³×C₁₇	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
20	#3622	—	2	1	no	—
21	#3622	C₂²⋊C₄	1	1	yes	characteristic
22	#3622	M₁₆	1	1	yes	characteristic
23	#1400	—	17	1	no	maximal, Sylow
24	C₂²×C₁₇	—	2	1	no	—
25	C₂²×C₁₇	—	4	1	no	—
26	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₁₇	—	2	1	no	—
28	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₁₇	M₃₂	1	1	yes	characteristic
30	C₂×M₃₂	—	17	1	no	—
31	M₆₄	—	17	2	no	—
32	C₂×C₁₇	—	2	1	no	—
33	C₂×C₁₇	—	4	1	no	—
34	C₂×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₂²×C₈	—	17	1	no	—
36	M₃₂	—	34	2	no	—
37	C₂×C₁₆	—	17	1	no	—
38	C₂×C₁₆	—	17	1	no	—
39	C₃₂	—	34	2	no	—
40	C₁₇	#1400	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	#3633	1	1	yes	characteristic
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	—	17	1	no	—
44	C₂×C₈	—	34	1	no	—
45	C₂×C₈	—	34	1	no	—
46	C₁₆	—	17	2	no	—
47	C₁₆	—	34	1	no	—
48	C₂³	#63241	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	#63241	1	1	yes	characteristic
52	C₂×C₄	C₂×#3633	1	1	yes	characteristic
53	C₈	—	17	1	no	—
54	C₈	—	17	1	no	—
55	C₈	—	34	1	no	—
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×#63241	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#10587670	1	1	yes	characteristic
61	C₄	C₂²⋊#3633	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊#63241	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#3633
commutator	C₂²×C₁₇	C₂×C₁₆
Frattini	C₂×C₄	C₂×#3633
Fitting	C₂²×C₄×C₁₇	C₈
socle	C₂×C₁₇	C₂²⋊C₁₆
prime radical	C₂³×C₁₇	C₁₆
cosocle	C₂×#63216	C₂²
hypercenter	C₂²×C₄	#3633
hypocenter	C₁₇	#1400
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #11763917	C₂	semidirect
40. C₁₇	#1400	semidirect

Maximal subgroups

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

subgroup	index
#11763917	2
C₂×#10587538	2
#1400	17