Subgroups — C₄⋊#11762528 #16922220

Order 4352.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762528	C₂	1	2	yes	maximal
2	C₄×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#11762528	—	2	2	no	—
4	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
10	C₁₇×C₃₂	—	2	1	no	—
11	C₁₇×C₃₂	D₄	1	1	yes	characteristic
12	C₁₇×C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₇	C₁₆	1	1	yes	characteristic
16	C₁₆×C₁₇	—	2	1	no	—
17	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
19	C₄⋊C₆₄	—	17	1	no	maximal, Sylow
20	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
22	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₁₇	—	2	1	no	—
24	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₇	M₃₂	1	1	yes	characteristic
26	C₂×C₆₄	—	17	2	no	—
27	C₄×C₃₂	D₁₇	1	1	yes	characteristic
28	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
29	C₄×C₁₇	—	2	1	no	—
30	C₄×C₁₇	C₆₄	1	2	yes	complemented
31	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
32	C₄×C₁₇	M₆₄	1	1	yes	characteristic
33	C₂×C₃₂	Dic₁₇	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
35	C₄×C₁₆	Dic₁₇	1	1	yes	characteristic
36	C₆₄	—	34	2	no	—
37	C₂×C₁₇	C₄⋊C₃₂	1	1	yes	characteristic
38	C₂×C₁₇	C₂×C₆₄	1	1	yes	characteristic
39	C₂×C₁₇	M₁₂₈	1	1	yes	characteristic
40	C₂×C₁₆	#3622	1	1	yes	characteristic
41	C₂×C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
42	C₄×C₈	#3622	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	Dic₃₄	1	1	yes	characteristic
45	C₃₂	D₆₈	1	1	yes	characteristic
46	C₁₇	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₈	#63214	1	1	yes	characteristic
48	C₂×C₈	C₂×#3622	1	1	yes	characteristic
49	C₄²	#63214	1	1	yes	characteristic
50	C₁₆	—	2	1	no	—
51	C₁₆	#63223	1	1	yes	characteristic
52	C₁₆	C₄⋊Dic₁₇	1	1	yes	characteristic
53	C₂×C₄	#10587465	1	1	yes	characteristic
54	C₂×C₄	#10587465	1	1	yes	characteristic
55	C₂×C₄	C₂×#63214	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₄⋊#3622	1	1	yes	characteristic
58	C₈	#10587483	1	1	yes	characteristic
59	C₂²	C₂×#10587465	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	#11762528	1	2	yes	complemented
62	C₄	C₄⋊#63214	1	1	yes	characteristic
63	C₄	#11762643	1	1	yes	characteristic
64	C₂	C₄⋊#10587465	1	1	yes	characteristic
65	C₂	C₂×#11762528	1	1	yes	characteristic
66	C₂	#14526995	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₁₇
commutator	C₂×C₁₇	C₂×C₆₄
Fitting	C₄×C₁₇×C₃₂	C₂
socle, prime radical	C₂²×C₁₇	C₂×C₃₂
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	C₄×C₃₂	D₁₇
hypocenter	C₁₇	C₄⋊C₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
30. C₄×C₁₇	C₆₄	semidirect
46. C₁₇	C₄⋊C₆₄	semidirect
61. C₄	#11762528	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762528	2
C₄×C₁₇×C₃₂	2
C₄⋊C₆₄	17

Subgroups — C4⋊#11762528 #16922220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#11762528 #16922220