Subgroups — C₂²⋊#19099577 #35204117

Order 20288.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099577	C₂	1	2	yes	maximal, complemented
2	C₂²×#14579261	C₂	1	1	yes	maximal, characteristic
3	#19099577	—	2	2	no	—
4	C₂×#14579261	—	2	2	no	—
5	C₂×#14579261	C₄	1	1	yes	characteristic
6	C₂×#14579261	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₃₁₇	C₄	1	1	yes	characteristic
8	#14579261	—	2	1	no	—
9	#14579261	D₄	1	2	yes	—
10	C₂³×C₃₁₇	C₈	1	1	yes	characteristic
11	C₂×C₄×C₃₁₇	—	2	1	no	—
12	C₂×C₄×C₃₁₇	—	2	1	no	—
13	C₂×C₄×C₃₁₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₁₇	—	2	1	no	—
16	C₂²×C₃₁₇	—	2	1	no	—
17	C₂²×C₃₁₇	C₁₆	1	2	yes	complemented
18	C₂²×C₃₁₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₃₁₇	—	2	1	no	—
20	C₄×C₃₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₁₇	M₁₆	1	1	yes	characteristic
22	C₂×C₃₁₇	—	2	2	no	—
23	C₂×C₃₁₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₃₁₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₃₁₇	M₃₂	1	1	yes	characteristic
26	C₃₁₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	317	1	no	maximal, Sylow
28	C₂²×C₈	—	317	1	no	—
29	C₂×C₁₆	—	317	2	no	—
30	C₂²×C₄	#11929639	1	1	yes	characteristic
31	C₂×C₈	—	317	1	no	—
32	C₂×C₈	—	317	1	no	—
33	C₂×C₈	—	634	2	no	—
34	C₁₆	—	634	2	no	—
35	C₂³	#14579268	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#14579268	1	1	yes	characteristic
39	C₂×C₄	C₂×#11929639	1	1	yes	characteristic
40	C₈	—	317	2	no	—
41	C₈	—	634	1	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#19099577	1	2	yes	complemented
45	C₂²	C₂×#14579268	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊#11929639	1	1	yes	characteristic
48	C₄	#19099583	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#14579268	1	1	yes	characteristic
51	C₂	C₂×#19099577	1	1	yes	characteristic
52	C₂	#23778854	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11929639
commutator	C₂×C₃₁₇	C₂×C₁₆
Fitting	C₂²×C₄×C₃₁₇	C₄
socle	C₂²×C₃₁₇	C₂×C₈
prime radical	C₂³×C₃₁₇	C₈
cosocle	C₂×#14579261	C₂²
hypercenter	C₂²×C₄	#11929639
hypocenter	C₃₁₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₃₁₇ ▷ C₃₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#19099577	C₂	semidirect
17. C₂²×C₃₁₇	C₁₆	semidirect
26. C₃₁₇	C₂²⋊C₁₆	semidirect
44. C₂²	#19099577	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19099577	2
C₂²×#14579261	2
C₂²⋊C₁₆	317

Subgroups — C22⋊#19099577 #35204117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19099577 #35204117