Subgroups — #35233173

Order 21184.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19127019	C₂	1	1	yes	maximal, characteristic
2	#24902548	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₃₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₃₃₁	C₄	1	1	yes	characteristic
5	#19127019	—	2	1	no	—
6	#19127019	—	2	1	no	—
7	C₂×C₃₃₁⋊C₈	C₄	1	1	yes	characteristic
8	C₃₃₁⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₃₃₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₃₃₁	—	2	1	no	—
11	C₂²×D₃₃₁	C₈	1	1	yes	characteristic
12	C₂×Dic₃₃₁	C₈	1	1	yes	characteristic
13	C₄×D₃₃₁	—	2	1	no	—
14	C₄×D₃₃₁	—	2	1	no	—
15	C₃₃₁⋊C₈	—	2	1	no	—
16	C₂×C₄×C₃₃₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₃₃₁	D₄	1	1	yes	characteristic
18	C₈×C₃₃₁	D₄	1	1	yes	characteristic
19	C₂²×C₃₃₁	C₂×C₈	1	1	yes	characteristic
20	C₂×D₃₃₁	—	2	1	no	—
21	C₂×D₃₃₁	—	4	1	no	—
22	C₄×C₃₃₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₃₃₁	M₁₆	1	1	yes	characteristic
24	Dic₃₃₁	—	2	1	no	—
25	C₂×C₃₃₁	—	2	1	no	—
26	C₂×C₃₃₁	C₂²⋊C₈	1	1	yes	characteristic
27	D₃₃₁	—	4	1	no	—
28	C₃₃₁	#349	1	1	yes	characteristic, complemented, Sylow
29	#349	—	331	1	no	maximal, Sylow
30	C₂×M₁₆	—	331	1	no	—
31	M₃₂	—	331	1	no	—
32	M₃₂	D₃₃₁	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	331	1	no	—
34	M₁₆	—	662	1	no	—
35	M₁₆	—	662	1	no	—
36	C₂×C₈	—	331	1	no	—
37	C₂×C₈	C₂×D₃₃₁	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	—	662	1	no	—
40	C₂³	—	331	1	no	—
41	C₂×C₄	—	331	1	no	—
42	C₂×C₄	—	662	1	no	—
43	C₂×C₄	—	662	1	no	—
44	C₂×C₄	C₄×D₃₃₁	1	1	yes	characteristic
45	C₈	—	662	1	no	—
46	C₈	C₂²⋊D₃₃₁	1	1	yes	characteristic
47	C₈	D₁₃₂₄	1	1	yes	characteristic
48	C₂²	—	1324	1	no	—
49	C₂²	—	662	1	no	—
50	C₂²	C₈×D₃₃₁	1	1	yes	characteristic
51	C₄	—	662	1	no	—
52	C₄	(C₂×D₃₃₁)⋊C₄	1	1	yes	characteristic
53	C₄	#19127019	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	1324	1	no	—
56	C₂	(C₂×D₃₃₁)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	(C₂×D₃₃₁)⋊C₄
commutator	C₂²×C₃₃₁	C₂×C₈
Frattini	C₂×C₈	C₂×D₃₃₁
Fitting	M₃₂×C₃₃₁	C₂
socle	C₂×C₃₃₁	C₂²⋊C₈
prime radical	C₂²×D₃₃₁	C₈
cosocle	C₂×C₈×C₃₃₁	C₂²
hypercenter	M₃₂	D₃₃₁
hypocenter	C₃₃₁	#349
LCS	G ▷ C₂²×C₃₃₁ ▷ C₂×C₃₃₁ ▷ C₃₃₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #24902548	C₂	semidirect
3. M₃₂×C₃₃₁	C₂	semidirect
28. C₃₃₁	#349	semidirect
32. M₃₂	D₃₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19127019	2
#24902548	2
M₃₂×C₃₃₁	2
#349	331