Subgroups — #14580247

Order 2624.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620281	C₂	1	3	yes	maximal
2	#13050071	C₂	1	3	yes	maximal, complemented
3	C₂²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄₁	C₂²	1	1	yes	characteristic
5	C₂×Q₈×C₄₁	—	2	6	no	—
6	C₂²×C₄×C₄₁	C₂²	1	3	yes	—
7	C₂²×Dic₄₁	C₂²	1	3	yes	—
8	#10620281	—	2	6	no	—
9	C₂³×C₄₁	C₂³	1	1	yes	characteristic
10	C₂²×D₄₁	—	2	3	no	—
11	C₂²×D₄₁	—	2	3	no	—
12	C₂²×D₄₁	Q₈	1	2	yes	complemented
13	Q₈×C₄₁	—	2	8	no	—
14	C₂×C₄×C₄₁	—	2	6	no	—
15	C₂×C₄×C₄₁	D₄	1	6	yes	—
16	C₂×Dic₄₁	—	2	3	no	—
17	C₂×Dic₄₁	—	2	6	no	—
18	C₂²×C₄₁	C₂×D₄	1	3	yes	—
19	C₂²×C₄₁	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₄₁	#41	1	3	yes	—
21	C₂×D₄₁	—	2	6	no	—
22	C₂×D₄₁	—	4	1	no	—
23	C₂×D₄₁	—	4	3	no	—
24	C₄×C₄₁	—	2	6	no	—
25	Dic₄₁	—	4	3	no	—
26	C₂×C₄₁	#120	1	1	yes	characteristic
27	C₂×C₄₁	C₂²⋊Q₈	1	3	yes	—
28	C₂×C₄₁	#124	1	3	yes	—
29	D₄₁	—	4	2	no	—
30	#393	—	41	1	no	maximal, Sylow
31	C₄₁	#393	1	1	yes	characteristic, complemented, Sylow
32	C₂²×Q₈	D₄₁	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊C₄	—	41	3	no	—
34	#95	—	41	3	no	—
35	C₂⁴	—	41	1	no	—
36	C₂×Q₈	—	2	6	no	—
37	C₂²×C₄	—	41	3	no	—
38	C₂²×C₄	C₂×D₄₁	1	3	yes	—
39	C₂²⋊C₄	—	82	6	no	—
40	C₂³	—	41	2	no	—
41	C₂³	—	82	3	no	—
42	C₂³	—	82	3	no	—
43	C₂³	C₂²×D₄₁	1	1	yes	characteristic
44	Q₈	—	2	8	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	82	6	no	—
47	C₂×C₄	—	82	3	no	—
48	C₂×C₄	C₂²⋊D₄₁	1	6	yes	—
49	C₂²	—	82	6	no	—
50	C₂²	—	164	1	no	—
51	C₂²	—	164	3	no	—
52	C₂²	Q₈×D₄₁	1	1	yes	characteristic
53	C₂²	#10620310	1	3	yes	—
54	C₂²	C₂×C₂²⋊D₄₁	1	3	yes	—
55	C₄	—	2	6	no	—
56	C₄	—	164	3	no	—
57	C₂	—	164	2	no	—
58	C₂	#13050133	1	1	yes	characteristic
59	C₂	#13050140	1	3	yes	—
60	C₂	#13050153	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₁
commutator, socle, cosocle	C₂³×C₄₁	C₂³
Fitting	C₂²×Q₈×C₄₁	C₂
prime radical	C₂³×D₄₁	C₂²
hypercenter	C₂²×Q₈	D₄₁
hypocenter	C₄₁	#393
LCS	G ▷ C₂³×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #13050071	C₂	semidirect
3. C₂²×Q₈×C₄₁	C₂	semidirect
12. C₂²×D₄₁	Q₈	semidirect
31. C₄₁	#393	semidirect
32. C₂²×Q₈	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620281	2
#13050071	2
C₂²×Q₈×C₄₁	2
#393	41