Subgroups — #35233169

Order 21184.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24902548	C₂	1	1	yes	maximal, characteristic
2	#24902518	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₃₁⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₃₃₁	C₄	1	1	yes	characteristic
6	C₃₃₁⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₃₃₁	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₃₁	C₄	1	2	yes	complemented
9	C₂×Dic₃₃₁	—	2	1	no	—
10	C₃₃₁⋊C₈	—	2	1	no	—
11	C₂×C₄×C₃₃₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₃₁	C₂×C₄	1	1	yes	characteristic
13	C₈×C₃₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃₃₁	M₁₆	1	1	yes	characteristic
15	C₄×C₃₃₁	C₄²	1	1	yes	characteristic
16	C₄×C₃₃₁	M₁₆	1	1	yes	characteristic
17	Dic₃₃₁	—	4	1	no	—
18	C₂×C₃₃₁	—	2	1	no	—
19	C₂×C₃₃₁	#97	1	1	yes	characteristic
20	C₃₃₁	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	331	1	no	maximal, Sylow
22	M₃₂	—	331	1	no	—
23	M₃₂	D₃₃₁	1	1	yes	characteristic
24	#97	—	331	1	no	—
25	C₂×C₈	—	331	1	no	—
26	C₂×C₈	C₂×D₃₃₁	1	1	yes	characteristic
27	C₄²	—	331	1	no	—
28	C₁₆	—	331	2	no	—
29	C₁₆	Dic₃₃₁	1	2	yes	complemented
30	C₂×C₄	—	662	1	no	—
31	C₂×C₄	C₄×D₃₃₁	1	1	yes	characteristic
32	C₈	—	662	1	no	—
33	C₈	C₄×D₃₃₁	1	1	yes	characteristic
34	C₈	C₂×Dic₃₃₁	1	1	yes	characteristic
35	C₂²	#19127019	1	1	yes	characteristic
36	C₄	—	1324	1	no	—
37	C₄	C₄×Dic₃₃₁	1	1	yes	characteristic
38	C₄	#19127019	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#24902518	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₃₃₁
commutator	C₄×C₃₃₁	C₄²
Frattini	C₂×C₈	C₂×D₃₃₁
Fitting	M₃₂×C₃₃₁	C₂
socle	C₂×C₃₃₁	#97
prime radical	C₂²×C₃₃₁	M₁₆
cosocle	C₂×C₈×C₃₃₁	C₂²
hypercenter	M₃₂	D₃₃₁
hypocenter	C₃₃₁	#347
LCS	G ▷ C₄×C₃₃₁ ▷ C₃₃₁
UCS	C₁ ◁ C₄ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
6. C₃₃₁⋊C₁₆	C₄	semidirect
8. C₁₆×C₃₃₁	C₄	semidirect
20. C₃₃₁	#347	semidirect
29. C₁₆	Dic₃₃₁	semidirect

Maximal subgroups

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

subgroup	index
#24902548	2
#24902518	2
M₃₂×C₃₃₁	2
#347	331