Subgroups — #29508764

Order 15424.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440729	C₂	1	2	yes	maximal, complemented
2	#21440712	C₂	1	1	yes	maximal, characteristic, complemented
3	#21440706	C₂	1	2	yes	maximal, complemented
4	#21440696	C₂	1	1	yes	maximal, characteristic, complemented
5	#21440661	C₂	1	1	yes	maximal, characteristic
6	#16838780	C₂²	1	2	yes	—
7	#16838779	—	2	2	no	—
8	#16838778	C₂²	1	1	yes	characteristic
9	C₂×#14515356	—	2	2	no	—
10	C₄×#11757210	C₂²	1	1	yes	characteristic
11	#16838769	C₂²	1	2	yes	—
12	Dic₉₆₄	C₄	1	1	yes	characteristic, complemented
13	#16838758	C₄	1	2	yes	complemented
14	C₈×D₂₄₁	C₂²	1	1	yes	characteristic
15	D₈×C₂₄₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#11757210	—	2	1	no	—
17	#14515356	—	2	2	no	—
18	#14515356	D₄	1	2	yes	—
19	Dic₄₈₂	C₂×C₄	1	2	yes	—
20	C₂²⋊D₂₄₁	—	2	2	no	—
21	C₂×Dic₂₄₁	—	2	2	no	—
22	C₄×D₂₄₁	C₂³	1	1	yes	characteristic
23	#14515349	C₂×C₄	1	1	yes	characteristic
24	D₄×C₂₄₁	C₂×C₄	1	2	yes	—
25	C₈×C₂₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₂₄₁	—	2	2	no	—
27	C₂×D₂₄₁	#41	1	1	yes	characteristic
28	#11757210	—	4	1	no	—
29	C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
30	Dic₂₄₁	—	2	2	no	—
31	Dic₂₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₂₄₁	—	4	2	no	—
33	C₂×C₂₄₁	C₄×D₄	1	1	yes	characteristic
34	D₂₄₁	—	2	1	no	—
35	C₂₄₁	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	241	1	no	maximal, Sylow
37	#135	—	241	1	no	—
38	#131	—	241	2	no	—
39	#108	—	241	1	no	—
40	#104	—	241	2	no	—
41	#97	—	241	1	no	—
42	#41	—	241	2	no	—
43	Q₁₆	—	241	1	no	—
44	SD₁₆	—	241	2	no	—
45	D₈	#11757210	1	1	yes	characteristic, complemented
46	M₁₆	—	482	2	no	—
47	M₁₆	—	241	2	no	—
48	C₂×C₈	—	482	2	no	—
49	C₂×C₈	—	241	1	no	—
50	C₂×C₈	—	241	1	no	—
51	C₄²	—	241	1	no	—
52	Q₈	—	241	2	no	—
53	D₄	—	482	2	no	—
54	D₄	C₂×#11757210	1	2	yes	—
55	C₂×C₄	—	482	1	no	—
56	C₂×C₄	—	482	2	no	—
57	C₂×C₄	—	241	1	no	—
58	C₈	—	482	2	no	—
59	C₈	—	241	2	no	—
60	C₈	—	241	1	no	—
61	C₈	C₂×#11757210	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	241	1	no	—
64	C₄	—	964	1	no	—
65	C₄	—	482	2	no	—
66	C₄	—	241	1	no	—
67	C₄	C₂²×#11757210	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	482	1	no	—
70	C₂	D₄×#11757210	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11757210
commutator	C₄×C₂₄₁	C₂²×C₄
Frattini	C₄	C₂²×#11757210
Fitting	D₈×C₂₄₁	C₄
socle	C₂×C₂₄₁	C₄×D₄
prime radical	#21440661	C₂
cosocle	C₄×D₂₄₁	C₂³
hypercenter	D₈	#11757210
hypocenter	C₂₄₁	#444
LCS	G ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #21440729	C₂	semidirect
2. #21440712	C₂	semidirect
3. #21440706	C₂	semidirect
4. #21440696	C₂	semidirect
12. Dic₉₆₄	C₄	semidirect
13. #16838758	C₄	semidirect
15. D₈×C₂₄₁	C₄	semidirect
35. C₂₄₁	#444	semidirect
45. D₈	#11757210	semidirect

Maximal subgroups

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

subgroup	index
#21440729	2
#21440712	2
#21440706	2
#21440696	2
#21440661	2
#444	241