Subgroups — #29507844

Order 15424.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₄₈₂	C₂	1	1	yes	maximal, characteristic
2	#21440571	C₂	1	2	yes	maximal
3	#21440552	C₂	1	2	yes	maximal
4	C₄×#14515349	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₈×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₄₈₂	C₄	1	1	yes	characteristic
7	C₂×#14515349	C₂²	1	1	yes	characteristic
8	C₂×#14515349	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₄₁	C₄	1	1	yes	characteristic
10	#16838749	C₄	1	2	yes	—
11	C₄×Dic₂₄₁	C₂²	1	2	yes	—
12	C₂×C₈×C₂₄₁	C₂²	1	2	yes	—
13	C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
14	Dic₄₈₂	—	2	2	no	—
15	C₂×Dic₂₄₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₂₄₁	C₂×C₄	1	2	yes	—
17	#14515349	—	2	1	no	—
18	#14515349	Q₈	1	2	yes	complemented
19	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
22	C₈×C₂₄₁	—	2	2	no	—
23	C₂²×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₄₁	—	2	1	no	—
25	C₄×C₂₄₁	M₁₆	1	2	yes	—
26	C₄×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₂₄₁	#41	1	1	yes	characteristic
28	Dic₂₄₁	—	2	2	no	—
29	Dic₂₄₁	—	2	2	no	—
30	C₂×C₂₄₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₂₄₁	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₂₄₁	#131	1	1	yes	characteristic
33	C₂₄₁	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	241	1	no	maximal, Sylow
35	C₄×Q₈	—	241	1	no	—
36	C₄⋊C₈	—	241	2	no	—
37	C₄⋊C₈	D₂₄₁	1	1	yes	characteristic
38	#97	—	241	2	no	—
39	C₄×C₈	—	241	1	no	—
40	C₂×Q₈	—	241	1	no	—
41	C₂×C₈	—	241	1	no	—
42	C₂×C₈	—	241	1	no	—
43	C₂×C₈	C₂×D₂₄₁	1	2	yes	—
44	C₄⋊C₄	—	241	2	no	—
45	C₄⋊C₄	—	241	1	no	—
46	C₄²	—	241	2	no	—
47	C₄²	C₂×D₂₄₁	1	1	yes	characteristic
48	Q₈	—	482	2	no	—
49	C₂×C₄	—	241	2	no	—
50	C₂×C₄	—	241	2	no	—
51	C₂×C₄	C₄×D₂₄₁	1	1	yes	characteristic
52	C₂×C₄	C₄×D₂₄₁	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	482	1	no	—
56	C₈	—	241	2	no	—
57	C₂²	C₂×C₄×D₂₄₁	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	482	2	no	—
60	C₄	—	482	2	no	—
61	C₄	#16838753	1	2	yes	—
62	C₄	Q₈×D₂₄₁	1	1	yes	characteristic
63	C₄	#16838769	1	1	yes	characteristic
64	C₂	#21440607	1	1	yes	characteristic
65	C₂	C₂×#16838753	1	1	yes	characteristic
66	C₂	#21440650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₄₁
commutator, socle, prime radical	C₂²×C₂₄₁	C₂²×C₄
Fitting	C₄⋊C₈×C₂₄₁	C₂
cosocle	C₂×C₄×C₂₄₁	C₂³
hypercenter	C₄⋊C₈	D₂₄₁
hypocenter	C₂₄₁	#446
LCS	G ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
18. #14515349	Q₈	semidirect
33. C₂₄₁	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₄₈₂	2
#21440571	2
#21440552	2
C₄×#14515349	2
C₄⋊C₈×C₂₄₁	2
#446	241