Subgroups — #29508084

Order 15424.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440640	C₂	1	1	yes	maximal, characteristic
2	#21440633	C₂	1	1	yes	maximal, characteristic
3	#21440567	C₂	1	1	yes	maximal, characteristic
4	#21440566	C₂	1	1	yes	maximal, characteristic
5	#21440565	C₂	1	1	yes	maximal, characteristic
6	#21440552	C₂	1	1	yes	maximal, characteristic
7	#103×C₂₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₄₈₂	C₂²	1	1	yes	characteristic
9	C₂×#14515349	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₄₁	—	2	1	no	—
11	C₄⋊Dic₂₄₁	C₂²	1	1	yes	characteristic
12	#16838749	—	2	1	no	—
13	#16838749	—	2	1	no	—
14	#16838749	—	2	1	no	—
15	C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₂₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
19	Dic₄₈₂	—	2	1	no	—
20	Dic₄₈₂	—	2	1	no	—
21	C₂×Dic₂₄₁	—	2	1	no	—
22	C₂×Dic₂₄₁	—	2	1	no	—
23	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
24	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
25	#14515349	—	2	1	no	—
26	Q₈×C₂₄₁	—	2	1	no	—
27	Q₈×C₂₄₁	—	2	1	no	—
28	C₂×C₄×C₂₄₁	—	2	1	no	—
29	C₂×C₄×C₂₄₁	—	2	1	no	—
30	C₂×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
31	C₈×C₂₄₁	—	2	1	no	—
32	C₂²×C₂₄₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₄₁	—	4	1	no	—
34	C₄×C₂₄₁	—	4	1	no	—
35	C₄×C₂₄₁	#41	1	1	yes	characteristic
36	C₄×C₂₄₁	#41	1	1	yes	characteristic
37	Dic₂₄₁	—	2	1	no	—
38	Dic₂₄₁	—	2	1	no	—
39	Dic₂₄₁	—	4	1	no	—
40	Dic₂₄₁	—	4	1	no	—
41	C₂×C₂₄₁	#124	1	1	yes	characteristic
42	C₂×C₂₄₁	#137	1	1	yes	characteristic
43	C₂×C₂₄₁	#137	1	1	yes	characteristic
44	C₂₄₁	#491	1	1	yes	characteristic, complemented, Sylow
45	#491	—	241	1	no	maximal, Sylow
46	C₄⋊Q₈	—	241	1	no	—
47	#125	—	241	1	no	—
48	#103	—	241	1	no	—
49	#103	—	241	1	no	—
50	#103	—	241	1	no	—
51	#103	D₂₄₁	1	1	yes	characteristic
52	#97	—	241	1	no	—
53	C₂×Q₈	—	241	1	no	—
54	C₂×Q₈	C₂×D₂₄₁	1	1	yes	characteristic
55	C₂×C₈	—	241	1	no	—
56	C₂×C₈	C₂×D₂₄₁	1	1	yes	characteristic
57	C₄⋊C₄	—	482	1	no	—
58	C₄⋊C₄	—	482	1	no	—
59	C₄⋊C₄	—	482	1	no	—
60	C₄⋊C₄	—	482	1	no	—
61	C₄⋊C₄	—	241	1	no	—
62	C₄⋊C₄	C₂×D₂₄₁	1	1	yes	characteristic
63	C₄²	—	241	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	482	1	no	—
67	Q₈	—	482	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	482	1	no	—
71	C₂×C₄	—	482	1	no	—
72	C₂×C₄	—	241	1	no	—
73	C₂×C₄	—	241	1	no	—
74	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	482	1	no	—
77	C₂²	D₄×D₂₄₁	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	964	1	no	—
81	C₄	—	964	1	no	—
82	C₄	—	482	1	no	—
83	C₄	—	482	1	no	—
84	C₄	#16838769	1	1	yes	characteristic
85	C₄	#16838770	1	1	yes	characteristic
86	C₂	#21440628	1	1	yes	characteristic
87	C₂	#21440671	1	1	yes	characteristic
88	C₂	#21440674	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₄₁
commutator, cosocle	C₂×C₄×C₂₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₂₄₁
Fitting	#103×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	C₂×D₄
hypercenter	#103	D₂₄₁
hypocenter	C₂₄₁	#491
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. C₂₄₁	#491	semidirect

Maximal subgroups

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

subgroup	index
#21440640	2
#21440633	2
#21440567	2
#21440566	2
#21440565	2
#21440552	2
#103×C₂₄₁	2
#491	241