Subgroups — #17949089

Order 4352.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587467	C₂	1	2	yes	maximal
2	C₈×#63214	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587467	C₄	1	4	yes	—
4	C₄×#63214	C₄	1	1	yes	characteristic
5	C₄×#63214	C₂²	1	1	yes	characteristic
6	C₈²×C₁₇	C₄	1	1	yes	characteristic
7	C₄×C₈×C₁₇	C₈	1	2	yes	—
8	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×#63214	C₈	1	2	yes	—
10	C₂×#63214	C₂×C₄	1	2	yes	—
11	#10587467	C₈	1	8	yes	complemented
12	C₂×C₈×C₁₇	C₁₆	1	4	yes	—
13	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
16	#63214	C₁₆	1	4	yes	—
17	#63214	C₂×C₈	1	4	yes	—
18	#7329	—	17	1	no	maximal, Sylow
19	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
20	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
21	C₈×C₁₇	—	2	4	no	—
22	C₈×C₁₇	C₄×C₈	1	2	yes	—
23	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
24	C₄×C₃₂	—	17	2	no	—
25	C₈×C₁₆	—	17	1	no	—
26	C₂²×C₁₇	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₁₇	C₈²	1	1	yes	characteristic
28	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₇	M₆₄	1	4	yes	—
30	C₂×C₃₂	—	17	4	no	—
31	C₄×C₁₆	—	17	1	no	—
32	C₄×C₁₆	—	17	1	no	—
33	C₈²	#595	1	1	yes	characteristic
34	C₂×C₁₇	C₈×C₁₆	1	1	yes	characteristic
35	C₂×C₁₇	#1397	1	2	yes	—
36	C₂×C₁₆	—	17	2	no	—
37	C₂×C₁₆	—	17	2	no	—
38	C₄×C₈	#3624	1	2	yes	—
39	C₄×C₈	C₂×#595	1	1	yes	characteristic
40	C₃₂	—	17	8	no	—
41	C₁₇	#7329	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	#63216	1	4	yes	—
43	C₂×C₈	#63242	1	1	yes	characteristic
44	C₂×C₈	C₄×#595	1	1	yes	characteristic
45	C₄²	C₂×#3624	1	1	yes	characteristic
46	C₁₆	—	17	4	no	—
47	C₁₆	—	17	4	no	—
48	C₂×C₄	C₂×#63216	1	2	yes	—
49	C₂×C₄	C₄×#3624	1	1	yes	characteristic
50	C₈	—	2	4	no	—
51	C₈	#10587529	1	2	yes	—
52	C₈	C₈×#595	1	2	yes	—
53	C₂²	C₄×#63216	1	1	yes	characteristic
54	C₄	C₈×#3624	1	1	yes	characteristic
55	C₄	#11763695	1	1	yes	characteristic
56	C₄	#11763741	1	4	yes	—
57	C₂	C₈×#63216	1	1	yes	characteristic
58	C₂	#14543891	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×#595
commutator	C₂×C₁₇	C₈×C₁₆
Fitting	C₈²×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₁₆
cosocle	C₄×#63214	C₂²
hypercenter	C₈²	#595
hypocenter	C₁₇	#7329
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
11. #10587467	C₈	semidirect
41. C₁₇	#7329	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10587467	2
C₈×#63214	2
#7329	17