Subgroups — #14543891

Order 2176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587467	C₂	1	2	yes	maximal
2	C₄×#63214	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂×#63214	C₄	1	1	yes	characteristic
5	C₂×#63214	C₂²	1	1	yes	characteristic
6	#10587467	C₄	1	4	yes	complemented
7	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₇	C₈	1	1	yes	characteristic
10	#63214	C₈	1	2	yes	—
11	#63214	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₇	C₁₆	1	2	yes	—
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₁₇	C₁₆	1	2	yes	—
15	C₈×C₁₇	C₄²	1	1	yes	characteristic
16	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
17	#1397	—	17	1	no	maximal, Sylow
18	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
19	C₄×C₁₇	—	2	2	no	—
20	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
21	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₃₂	—	17	2	no	—
23	C₄×C₁₆	—	17	1	no	—
24	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₁₇	M₆₄	1	2	yes	—
26	C₂×C₁₆	—	17	1	no	—
27	C₂×C₁₆	—	17	1	no	—
28	C₄×C₈	#595	1	1	yes	characteristic
29	C₃₂	—	17	4	no	—
30	C₁₇	#1397	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	#3624	1	1	yes	characteristic
32	C₂×C₈	C₂×#595	1	1	yes	characteristic
33	C₄²	#3624	1	1	yes	characteristic
34	C₁₆	—	17	2	no	—
35	C₁₆	—	17	2	no	—
36	C₂×C₄	#63216	1	2	yes	—
37	C₂×C₄	C₂×#3624	1	1	yes	characteristic
38	C₈	#63216	1	2	yes	—
39	C₈	#63242	1	1	yes	characteristic
40	C₈	C₄×#595	1	1	yes	characteristic
41	C₂²	C₂×#63216	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₂×#63216	1	1	yes	characteristic
44	C₄	C₄×#3624	1	1	yes	characteristic
45	C₂	C₄×#63216	1	1	yes	characteristic
46	C₂	#11763741	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₄×C₁₆
Fitting	C₄×C₈×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₂×C₁₆
cosocle	C₂×#63214	C₂²
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1397
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10587467	C₄	semidirect
30. C₁₇	#1397	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587467	2
C₄×#63214	2
#1397	17