Subgroups — #29507926

Order 15424.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#16838760	C₂	1	1	yes	maximal, characteristic
3	#21440640	C₂	1	1	yes	maximal, characteristic
4	#21440607	C₂	1	1	yes	maximal, characteristic
5	#21440571	C₂	1	1	yes	maximal, characteristic
6	#21440565	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×Dic₄₈₂	C₂²	1	1	yes	characteristic
10	Dic₉₆₄	—	2	2	no	—
11	#16838760	—	2	2	no	—
12	C₂×#14515349	C₂²	1	1	yes	characteristic
13	#16838749	—	2	1	no	—
14	#16838749	—	2	1	no	—
15	#16838749	—	2	1	no	—
16	C₄×Dic₂₄₁	—	2	1	no	—
17	C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₂₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
21	Dic₄₈₂	—	2	1	no	—
22	Dic₄₈₂	—	2	1	no	—
23	Dic₄₈₂	—	2	1	no	—
24	Dic₄₈₂	D₄	1	2	yes	—
25	C₂×Dic₂₄₁	—	2	1	no	—
26	C₂×Dic₂₄₁	—	2	1	no	—
27	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
28	C₂×Dic₂₄₁	D₄	1	1	yes	characteristic
29	#14515349	—	2	1	no	—
30	Q₈×C₂₄₁	—	2	1	no	—
31	Q₈×C₂₄₁	—	2	1	no	—
32	C₂×C₄×C₂₄₁	—	2	1	no	—
33	C₂×C₄×C₂₄₁	—	2	1	no	—
34	C₂×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
35	C₈×C₂₄₁	—	2	1	no	—
36	C₂²×C₂₄₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₂₄₁	—	4	1	no	—
38	C₄×C₂₄₁	—	4	1	no	—
39	C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
40	C₄×C₂₄₁	#41	1	1	yes	characteristic
41	Dic₂₄₁	—	2	2	no	—
42	Dic₂₄₁	—	2	1	no	—
43	Dic₂₄₁	—	4	1	no	—
44	Dic₂₄₁	Q₁₆	1	2	yes	complemented
45	C₂×C₂₄₁	#121	1	1	yes	characteristic
46	C₂×C₂₄₁	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₂₄₁	#137	1	1	yes	characteristic
48	C₂₄₁	#462	1	1	yes	characteristic, complemented, Sylow
49	#462	—	241	1	no	maximal, Sylow
50	C₂×Q₁₆	—	241	1	no	—
51	C₂×Q₁₆	—	241	1	no	—
52	C₄⋊Q₈	—	241	1	no	—
53	C₄×Q₈	—	241	1	no	—
54	C₄⋊C₈	—	241	1	no	—
55	#103	—	241	1	no	—
56	#103	D₂₄₁	1	1	yes	characteristic
57	C₂×Q₈	—	241	1	no	—
58	C₂×Q₈	—	241	1	no	—
59	C₂×Q₈	C₂×D₂₄₁	1	1	yes	characteristic
60	Q₁₆	—	482	2	no	—
61	Q₁₆	—	482	2	no	—
62	C₂×C₈	—	241	1	no	—
63	C₂×C₈	C₂×D₂₄₁	1	1	yes	characteristic
64	C₄⋊C₄	—	482	1	no	—
65	C₄⋊C₄	—	482	1	no	—
66	C₄⋊C₄	—	482	1	no	—
67	C₄⋊C₄	C₂×D₂₄₁	1	1	yes	characteristic
68	C₄²	—	482	1	no	—
69	C₄²	—	241	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	482	1	no	—
73	Q₈	—	482	1	no	—
74	Q₈	—	482	1	no	—
75	Q₈	—	241	2	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	482	1	no	—
79	C₂×C₄	—	482	1	no	—
80	C₂×C₄	—	241	1	no	—
81	C₂×C₄	—	241	1	no	—
82	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	482	1	no	—
85	C₂²	D₄×D₂₄₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	964	1	no	—
89	C₄	—	482	2	no	—
90	C₄	—	482	1	no	—
91	C₄	—	241	2	no	—
92	C₄	D₄×D₂₄₁	1	1	yes	characteristic
93	C₄	#16838770	1	1	yes	characteristic
94	C₂	#21440615	1	1	yes	characteristic
95	C₂	Q₁₆×D₂₄₁	1	1	yes	characteristic
96	C₂	#21440671	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	#462
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. Dic₂₄₁	Q₁₆	semidirect
48. C₂₄₁	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₉₆₄	2
C₂×#16838760	2
#21440640	2
#21440607	2
#21440571	2
#21440565	2
#103×C₂₄₁	2
#462	241