Subgroups — #14580255

Order 2624.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620279	C₂	1	3	yes	maximal
2	#13050071	C₂	1	3	yes	maximal
3	C₂²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₁	—	2	6	no	—
5	C₂²×C₄×C₄₁	C₂²	1	3	yes	—
6	C₂²×Dic₄₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₂²	1	3	yes	—
8	#10620279	—	2	6	no	—
9	C₂³×C₄₁	C₂³	1	1	yes	characteristic
10	Q₈×C₄₁	—	2	8	no	—
11	C₂×C₄×C₄₁	—	2	6	no	—
12	C₂×C₄×C₄₁	D₄	1	6	yes	—
13	C₂×Dic₄₁	—	2	3	no	—
14	C₂×Dic₄₁	—	2	3	no	—
15	C₂×Dic₄₁	—	2	3	no	—
16	C₂×Dic₄₁	Q₈	1	6	yes	complemented
17	C₂²×C₄₁	C₂×D₄	1	3	yes	—
18	C₂²×C₄₁	C₂×Q₈	1	3	yes	—
19	C₂²×C₄₁	#41	1	1	yes	characteristic
20	C₄×C₄₁	—	2	6	no	—
21	Dic₄₁	—	2	6	no	—
22	Dic₄₁	—	4	1	no	—
23	C₂×C₄₁	#120	1	1	yes	characteristic
24	C₂×C₄₁	C₂²⋊Q₈	1	3	yes	—
25	C₂×C₄₁	C₄⋊Q₈	1	3	yes	—
26	#395	—	41	1	no	maximal, Sylow
27	C₄₁	#395	1	1	yes	characteristic, complemented, Sylow
28	C₂²×Q₈	D₄₁	1	1	yes	characteristic
29	C₂×C₄⋊C₄	—	41	3	no	—
30	#95	—	41	3	no	—
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	—	41	3	no	—
33	C₂²×C₄	—	41	1	no	—
34	C₂²×C₄	C₂×D₄₁	1	3	yes	—
35	C₄⋊C₄	—	82	6	no	—
36	C₂³	C₂²×D₄₁	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	41	6	no	—
40	C₂×C₄	—	82	3	no	—
41	C₂×C₄	—	82	3	no	—
42	C₂×C₄	—	82	3	no	—
43	C₂×C₄	C₂²⋊D₄₁	1	6	yes	—
44	C₂²	Q₈×D₄₁	1	3	yes	—
45	C₂²	#10620310	1	1	yes	characteristic
46	C₂²	C₂×C₂²⋊D₄₁	1	3	yes	—
47	C₄	—	2	6	no	—
48	C₄	—	82	6	no	—
49	C₄	—	164	1	no	—
50	C₂	#13050133	1	1	yes	characteristic
51	C₂	#13050140	1	3	yes	—
52	C₂	#13050162	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₁
commutator, socle, prime radical, cosocle	C₂³×C₄₁	C₂³
Fitting	C₂²×Q₈×C₄₁	C₂
hypercenter	C₂²×Q₈	D₄₁
hypocenter	C₄₁	#395
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
16. C₂×Dic₄₁	Q₈	semidirect
27. C₄₁	#395	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620279	2
#13050071	2
C₂²×Q₈×C₄₁	2
#395	41