Subgroups — #29508592

Order 15424.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₄₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#16838778	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#16838780	C₄	1	2	yes	—
5	#16838779	—	2	1	no	—
6	#16838778	—	2	1	no	—
7	#16838778	—	2	1	no	—
8	#16838778	C₄	1	2	yes	—
9	C₂×#14515356	—	2	1	no	—
10	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
11	#16838754	C₄	1	1	yes	characteristic
12	#16838753	—	2	1	no	—
13	C₈×D₂₄₁	—	2	1	no	—
14	M₁₆×C₂₄₁	C₄	1	1	yes	characteristic
15	#14515356	—	2	2	no	—
16	#14515356	—	2	2	no	—
17	C₂²×D₂₄₁	Q₈	1	1	yes	characteristic
18	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
19	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₄×D₂₄₁	D₄	1	1	yes	characteristic
22	C₄×D₂₄₁	D₄	1	1	yes	characteristic
23	#14515349	—	2	1	no	—
24	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₄₁	—	2	1	no	—
26	C₂²×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₂₄₁	—	2	2	no	—
28	C₂×D₂₄₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₂₄₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₂₄₁	C₄²	1	1	yes	characteristic
31	C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
32	Dic₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₂₄₁	—	2	1	no	—
35	C₂×C₂₄₁	#95	1	1	yes	characteristic
36	D₂₄₁	—	2	1	no	—
37	D₂₄₁	#108	1	2	yes	—
38	C₂₄₁	#341	1	1	yes	characteristic, complemented, Sylow
39	#341	—	241	1	no	maximal, Sylow
40	C₂×M₁₆	—	241	1	no	—
41	C₂×M₁₆	—	241	1	no	—
42	C₂²×C₈	—	241	1	no	—
43	C₂²×C₄	—	241	1	no	—
44	M₁₆	—	482	1	no	—
45	M₁₆	—	482	1	no	—
46	M₁₆	—	241	2	no	—
47	M₁₆	—	241	1	no	—
48	M₁₆	#11757210	1	1	yes	characteristic
49	C₂×C₈	—	482	1	no	—
50	C₂×C₈	—	482	1	no	—
51	C₂×C₈	—	482	1	no	—
52	C₂×C₈	—	482	1	no	—
53	C₂×C₈	—	241	2	no	—
54	C₂³	—	241	1	no	—
55	C₂×C₄	—	241	1	no	—
56	C₂×C₄	—	241	1	no	—
57	C₂×C₄	—	241	1	no	—
58	C₂×C₄	—	241	1	no	—
59	C₂×C₄	—	241	1	no	—
60	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	482	2	no	—
63	C₈	—	482	2	no	—
64	C₈	—	482	1	no	—
65	C₂²	—	482	2	no	—
66	C₂²	—	241	1	no	—
67	C₂²	—	241	1	no	—
68	C₂²	C₄⋊#11757210	1	1	yes	characteristic
69	C₄	—	241	1	no	—
70	C₄	—	241	1	no	—
71	C₄	C₄×#11757210	1	1	yes	characteristic
72	C₄	C₂²⋊#11757210	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	482	1	no	—
75	C₂	—	241	2	no	—
76	C₂	(C₂×#11757210)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11757210
commutator	C₄×C₂₄₁	C₄²
Frattini	C₂×C₄	C₂×#11757210
Fitting	M₁₆×C₂₄₁	C₄
socle	C₂×C₂₄₁	#95
prime radical	C₂²×D₂₄₁	Q₈
cosocle	C₂×C₄×D₂₄₁	C₂²
hypercenter	M₁₆	#11757210
hypocenter	C₂₄₁	#341
LCS	G ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
38. C₂₄₁	#341	semidirect

Maximal subgroups

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

subgroup	index
D₂₄₁⋊M₁₆	2
C₂×#16838778	2
M₁₆×D₂₄₁	2
#341	241