Subgroups — #29508732

Order 15424.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838780	C₂	1	1	yes	maximal, characteristic
2	D₂₄₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#21440713	C₂	1	2	yes	maximal, complemented
4	#21440712	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₂₄₁	C₂	1	1	yes	maximal, characteristic
6	#16838780	—	2	1	no	—
7	#16838780	C₂²	1	1	yes	characteristic
8	#16838780	C₂²	1	2	yes	—
9	#16838780	C₂²	1	1	yes	characteristic
10	#16838779	—	2	1	no	—
11	#16838778	—	2	1	no	—
12	C₂×#14515356	—	2	1	no	—
13	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
14	#16838754	C₄	1	1	yes	characteristic
15	#16838753	C₄	1	2	yes	—
16	C₈×D₂₄₁	C₂²	1	2	yes	—
17	M₁₆×C₂₄₁	C₄	1	1	yes	characteristic
18	#14515356	—	2	2	no	—
19	#14515356	—	2	1	no	—
20	#14515356	—	2	1	no	—
21	C₂²×D₂₄₁	Q₈	1	1	yes	characteristic
22	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
23	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₂₄₁	D₄	1	1	yes	characteristic
25	C₄×D₂₄₁	Q₈	1	1	yes	characteristic
26	C₄×D₂₄₁	C₂³	1	1	yes	characteristic
27	#14515349	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
29	C₈×C₂₄₁	C₂×C₄	1	2	yes	—
30	C₂²×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₂₄₁	—	4	1	no	—
32	C₂×D₂₄₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₂₄₁	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
36	Dic₂₄₁	C₄⋊C₄	1	1	yes	characteristic
37	Dic₂₄₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₂₄₁	—	2	1	no	—
39	C₂×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	D₂₄₁	—	2	1	no	—
41	D₂₄₁	—	2	1	no	—
42	C₂₄₁	#430	1	1	yes	characteristic, complemented, Sylow
43	#430	—	241	1	no	maximal, Sylow
44	C₂×M₁₆	—	241	1	no	—
45	C₂×M₁₆	—	241	1	no	—
46	C₂×M₁₆	—	241	1	no	—
47	#108	—	241	2	no	—
48	#108	—	241	2	no	—
49	C₂²×C₄	—	241	1	no	—
50	M₁₆	—	482	1	no	—
51	M₁₆	—	482	1	no	—
52	M₁₆	—	241	1	no	—
53	M₁₆	—	241	2	no	—
54	M₁₆	—	241	1	no	—
55	M₁₆	—	241	1	no	—
56	M₁₆	—	241	2	no	—
57	M₁₆	#11757210	1	1	yes	characteristic
58	C₂×C₈	—	482	1	no	—
59	C₂×C₈	—	482	1	no	—
60	C₂×C₈	—	241	2	no	—
61	C₂³	—	241	1	no	—
62	C₂×C₄	—	241	1	no	—
63	C₂×C₄	—	241	1	no	—
64	C₂×C₄	—	241	1	no	—
65	C₂×C₄	—	241	1	no	—
66	C₂×C₄	—	241	1	no	—
67	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
68	C₈	—	482	2	no	—
69	C₈	—	482	1	no	—
70	C₈	—	482	1	no	—
71	C₈	—	241	2	no	—
72	C₈	C₂×#11757210	1	2	yes	—
73	C₂²	—	964	1	no	—
74	C₂²	—	241	1	no	—
75	C₂²	—	241	1	no	—
76	C₂²	C₄⋊#11757210	1	1	yes	characteristic
77	C₄	—	241	1	no	—
78	C₄	—	241	1	no	—
79	C₄	C₄⋊#11757210	1	1	yes	characteristic
80	C₄	C₂²×#11757210	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	482	1	no	—
83	C₂	—	482	1	no	—
84	C₂	C₂×C₄⋊#11757210	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#11757210
commutator	C₄×C₂₄₁	C₂²×C₄
Frattini	C₄	C₂²×#11757210
Fitting	M₁₆×C₂₄₁	C₄
socle	C₂×C₂₄₁	C₂×C₄⋊C₄
prime radical	C₂²×D₂₄₁	Q₈
cosocle	C₄×D₂₄₁	C₂³
hypercenter	M₁₆	#11757210
hypocenter	C₂₄₁	#430
LCS	G ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #21440713	C₂	semidirect
4. #21440712	C₂	semidirect
42. C₂₄₁	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16838780	2
D₂₄₁⋊M₁₆	2
#21440713	2
#21440712	2
M₁₆×D₂₄₁	2
#430	241