Subgroups — #14581235

Order 2624.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050238	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10620270	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050172	C₂	1	1	yes	maximal, characteristic
4	#10620306	C₄	1	1	yes	characteristic
5	M₁₆×C₄₁	C₄	1	1	yes	characteristic
6	C₂×#66491	C₂²	1	1	yes	characteristic
7	#10620272	—	2	1	no	—
8	C₈×D₄₁	—	2	1	no	—
9	#10620270	—	2	1	no	—
10	#10620270	—	2	1	no	—
11	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₄₁	—	2	1	no	—
13	D₁₆₄	C₈	1	1	yes	characteristic
14	C₄×D₄₁	—	2	1	no	—
15	Dic₈₂	C₈	1	1	yes	characteristic
16	C₈×C₄₁	—	2	1	no	—
17	#66491	D₄	1	1	yes	characteristic
18	#66491	D₄	1	1	yes	characteristic
19	C₂²×C₄₁	M₁₆	1	1	yes	characteristic
20	C₂×D₄₁	—	2	1	no	—
21	C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₄₁	C₂×C₈	1	1	yes	characteristic
23	Dic₄₁	—	2	1	no	—
24	C₂×C₄₁	—	2	1	no	—
25	C₂×C₄₁	C₂²⋊C₈	1	1	yes	characteristic
26	D₄₁	—	4	1	no	—
27	#350	—	41	1	no	maximal, Sylow
28	C₄₁	#350	1	1	yes	characteristic, complemented, Sylow
29	#131	—	41	1	no	—
30	M₃₂	—	41	1	no	—
31	C₂×C₁₆	—	41	1	no	—
32	#41	—	41	1	no	—
33	M₁₆	—	82	1	no	—
34	M₁₆	#4223	1	1	yes	characteristic
35	C₂×C₈	—	41	1	no	—
36	C₂×C₈	—	82	1	no	—
37	C₁₆	—	82	1	no	—
38	C₁₆	—	82	1	no	—
39	Q₈	—	41	1	no	—
40	D₄	—	41	1	no	—
41	D₄	—	82	1	no	—
42	C₂×C₄	—	82	1	no	—
43	C₂×C₄	C₂×#4223	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	41	1	no	—
46	C₈	—	41	1	no	—
47	C₂²	—	82	1	no	—
48	C₂²	#10620297	1	1	yes	characteristic
49	C₄	—	82	1	no	—
50	C₄	#10620296	1	1	yes	characteristic
51	C₄	C₂²⋊#4223	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	164	1	no	—
54	C₂	#13050221	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#4223
commutator	C₄×C₄₁	C₂×C₈
Frattini	C₂×C₄	C₂×#4223
Fitting	M₁₆×C₄₁	C₄
socle	C₂×C₄₁	C₂²⋊C₈
prime radical	#10620306	C₄
cosocle	C₂×#66491	C₂²
hypercenter	M₁₆	#4223
hypocenter	C₄₁	#350
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #13050238	C₂	semidirect
2. C₂×#10620270	C₂	semidirect
28. C₄₁	#350	semidirect

Maximal subgroups

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

subgroup	index
#13050238	2
C₂×#10620270	2
#13050172	2
#350	41