Subgroups — #14580294

Order 2624.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	1	yes	maximal, characteristic
2	#13050123	C₂	1	1	yes	maximal, characteristic
3	#13050074	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₁	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	M₁₆×C₄₁	C₄	1	4	yes	complemented
8	C₂×C₈×C₄₁	C₂²	1	2	yes	—
9	C₂²⋊Dic₄₁	C₄	1	2	yes	—
10	C₄⋊Dic₄₁	C₄	1	2	yes	—
11	C₄×Dic₄₁	C₂²	1	2	yes	—
12	C₂×#66491	C₄	1	4	yes	complemented
13	C₂×#66491	C₂²	1	1	yes	characteristic
14	C₂×#66491	C₂²	1	1	yes	characteristic
15	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₁	C₂×C₄	1	4	yes	—
21	C₈×C₄₁	C₂×C₄	1	4	yes	—
22	#66491	C₂×C₄	1	2	yes	—
23	#66491	C₂×C₄	1	2	yes	—
24	C₂²×C₄₁	—	2	2	no	—
25	C₂²×C₄₁	C₄²	1	2	yes	—
26	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₁	C₄²	1	2	yes	—
28	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	Dic₄₁	—	2	4	no	—
31	C₂×C₄₁	—	2	2	no	—
32	C₂×C₄₁	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄₁	#131	1	2	yes	—
34	#405	—	41	1	no	maximal, Sylow
35	C₄₁	#405	1	1	yes	characteristic, complemented, Sylow
36	C₂×M₁₆	D₄₁	1	1	yes	characteristic
37	C₂²×C₈	—	41	1	no	—
38	#117	—	41	1	no	—
39	#97	—	41	2	no	—
40	C₄×C₈	—	41	2	no	—
41	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
42	M₁₆	Dic₄₁	1	4	yes	complemented
43	C₂×C₈	—	41	4	no	—
44	C₂×C₈	—	41	1	no	—
45	C₂×C₈	—	41	1	no	—
46	C₂×C₈	C₂×D₄₁	1	2	yes	—
47	C₄⋊C₄	—	41	2	no	—
48	C₂²⋊C₄	—	41	2	no	—
49	C₄²	—	41	2	no	—
50	C₂³	C₄×D₄₁	1	1	yes	characteristic
51	C₂×C₄	—	41	4	no	—
52	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
53	C₂×C₄	C₄×D₄₁	1	2	yes	—
54	C₂×C₄	C₂×Dic₄₁	1	2	yes	—
55	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
56	C₈	—	41	2	no	—
57	C₈	—	41	2	no	—
58	C₈	C₂×Dic₄₁	1	4	yes	—
59	C₂²	—	2	2	no	—
60	C₂²	C₄×Dic₄₁	1	2	yes	—
61	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
62	C₄	—	82	4	no	—
63	C₄	C₄×Dic₄₁	1	2	yes	—
64	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
65	C₄	C₂²×Dic₄₁	1	1	yes	characteristic
66	C₂	—	2	2	no	—
67	C₂	C₂×C₄×Dic₄₁	1	1	yes	characteristic
68	C₂	#13050172	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator	C₂×C₄₁	C₂×C₄²
Fitting	C₂×M₁₆×C₄₁	C₂
socle	C₂²×C₄₁	C₂²×C₄
prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂×M₁₆	D₄₁
hypocenter	C₄₁	#405
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13050074	C₂	semidirect
4. C₈×Dic₄₁	C₂	semidirect
7. M₁₆×C₄₁	C₄	semidirect
12. C₂×#66491	C₄	semidirect
35. C₄₁	#405	semidirect
42. M₁₆	Dic₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66491	2
#13050123	2
#13050074	2
C₈×Dic₄₁	2
C₂×M₁₆×C₄₁	2
#405	41