Subgroups — #29508006

Order 15424.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440641	C₂	1	1	yes	maximal, characteristic, complemented
2	#21440604	C₂	1	1	yes	maximal, characteristic
3	#21440573	C₂	1	1	yes	maximal, characteristic, complemented
4	#21440571	C₂	1	1	yes	maximal, characteristic, complemented
5	#21440564	C₂	1	1	yes	maximal, characteristic
6	#21440562	C₂	1	1	yes	maximal, characteristic
7	#106×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₄₈₂	—	2	1	no	—
9	C₂×D₉₆₄	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₂₄₁	—	2	1	no	—
11	C₂×#14515349	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₄₁	C₂²	1	1	yes	characteristic
13	#16838749	—	2	1	no	—
14	#16838747	—	2	1	no	—
15	C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₂₄₁	—	2	1	no	—
20	Dic₄₈₂	—	4	2	no	—
21	D₉₆₄	—	2	1	no	—
22	D₉₆₄	Q₈	1	2	yes	complemented
23	C₂×Dic₂₄₁	—	2	1	no	—
24	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
25	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
26	C₄×D₂₄₁	—	4	2	no	—
27	#14515349	—	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	C₂×D₂₄₁	—	2	2	no	—
34	C₂×D₂₄₁	—	4	1	no	—
35	C₂×D₂₄₁	—	4	1	no	—
36	C₄×C₂₄₁	—	4	1	no	—
37	C₄×C₂₄₁	—	4	1	no	—
38	C₄×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₂₄₁	#41	1	1	yes	characteristic
40	Dic₂₄₁	—	2	1	no	—
41	Dic₂₄₁	—	4	1	no	—
42	Dic₂₄₁	SD₁₆	1	2	yes	—
43	C₂×C₂₄₁	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₂₄₁	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₂₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₂₄₁	—	4	2	no	—
47	C₂₄₁	#476	1	1	yes	characteristic, complemented, Sylow
48	#476	—	241	1	no	maximal, Sylow
49	C₄⋊Q₈	—	241	1	no	—
50	C₄×D₄	—	241	1	no	—
51	#106	—	241	1	no	—
52	#106	D₂₄₁	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	241	1	no	—
54	#102	—	241	1	no	—
55	#102	—	241	1	no	—
56	C₂×Q₈	—	482	1	no	—
57	C₂×D₄	—	241	1	no	—
58	C₂²×C₄	—	482	1	no	—
59	C₂×C₈	—	241	1	no	—
60	C₂×C₈	C₂×D₂₄₁	1	1	yes	characteristic
61	C₄⋊C₄	—	482	1	no	—
62	C₄⋊C₄	—	241	1	no	—
63	C₄⋊C₄	C₂×D₂₄₁	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₂₄₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	482	1	no	—
66	C₄²	—	241	1	no	—
67	C₂³	—	482	1	no	—
68	Q₈	—	964	2	no	—
69	D₄	—	482	1	no	—
70	D₄	—	241	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	964	2	no	—
74	C₂×C₄	—	482	1	no	—
75	C₂×C₄	—	241	1	no	—
76	C₂×C₄	—	241	1	no	—
77	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	482	1	no	—
80	C₂²	—	964	1	no	—
81	C₂²	—	964	1	no	—
82	C₂²	—	482	2	no	—
83	C₂²	D₄×D₂₄₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	964	1	no	—
87	C₄	—	482	1	no	—
88	C₄	—	241	2	no	—
89	C₄	Q₈×D₂₄₁	1	1	yes	characteristic
90	C₄	#16838770	1	1	yes	characteristic
91	C₂	—	964	2	no	—
92	C₂	#21440620	1	1	yes	characteristic
93	C₂	SD₁₆×D₂₄₁	1	1	yes	characteristic
94	C₂	#21440669	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₄₁
commutator, cosocle	C₂×C₄×C₂₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₂₄₁
Fitting	#106×C₂₄₁	C₂
socle	C₂²×C₂₄₁	C₂×D₄
prime radical	C₂×D₉₆₄	C₂²
hypercenter	#106	D₂₄₁
hypocenter	C₂₄₁	#476
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. #21440641	C₂	semidirect
3. #21440573	C₂	semidirect
4. #21440571	C₂	semidirect
7. #106×C₂₄₁	C₂	semidirect
22. D₉₆₄	Q₈	semidirect
47. C₂₄₁	#476	semidirect
52. #106	D₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#21440641	2
#21440604	2
#21440573	2
#21440571	2
#21440564	2
#21440562	2
#106×C₂₄₁	2
#476	241