Subgroups — #29507992

Order 15424.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440672	C₂	1	2	yes	maximal
2	C₂×Dic₉₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#21440578	C₂	1	1	yes	maximal, characteristic, complemented
4	#21440560	C₂	1	2	yes	maximal, complemented
5	#131×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₄₈₂	C₂²	1	2	yes	—
7	Dic₉₆₄	—	2	1	no	—
8	Dic₉₆₄	—	2	1	no	—
9	#16838760	—	2	2	no	—
10	#16838758	—	2	2	no	—
11	#16838754	C₂²	1	2	yes	—
12	#41×C₂₄₁	C₂²	1	1	yes	characteristic
13	M₁₆×C₂₄₁	—	2	1	no	—
14	M₁₆×C₂₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₂₄₁	—	2	1	no	—
16	C₂×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
17	Dic₄₈₂	—	2	2	no	—
18	Dic₄₈₂	—	2	2	no	—
19	C₂×Dic₂₄₁	—	2	2	no	—
20	#14515349	—	2	2	no	—
21	Q₈×C₂₄₁	D₄	1	1	yes	characteristic
22	D₄×C₂₄₁	—	2	1	no	—
23	D₄×C₂₄₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₄₁	—	2	1	no	—
25	C₂×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
26	C₈×C₂₄₁	—	2	1	no	—
27	C₈×C₂₄₁	D₄	1	1	yes	characteristic
28	C₈×C₂₄₁	D₄	1	1	yes	characteristic
29	C₂²×C₂₄₁	—	2	1	no	—
30	C₂²×C₂₄₁	#41	1	1	yes	characteristic
31	C₄×C₂₄₁	—	2	1	no	—
32	C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
34	Dic₂₄₁	—	4	2	no	—
35	C₂×C₂₄₁	—	2	1	no	—
36	C₂×C₂₄₁	—	4	1	no	—
37	C₂×C₂₄₁	#121	1	1	yes	characteristic
38	C₂₄₁	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	241	1	no	maximal, Sylow
40	#137	—	241	2	no	—
41	C₂×Q₁₆	—	241	1	no	—
42	#131	D₂₄₁	1	1	yes	characteristic
43	#108	—	241	1	no	—
44	#101	—	241	2	no	—
45	#41	C₂×D₂₄₁	1	1	yes	characteristic
46	C₂×Q₈	—	241	2	no	—
47	Q₁₆	—	482	2	no	—
48	Q₁₆	—	482	1	no	—
49	Q₁₆	—	482	1	no	—
50	SD₁₆	—	482	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	241	2	no	—
53	M₁₆	C₂×D₂₄₁	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₂₄₁	1	1	yes	characteristic
56	Q₈	—	482	2	no	—
57	Q₈	—	482	2	no	—
58	Q₈	D₉₆₄	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₉₆₄	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	482	2	no	—
63	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	482	2	no	—
66	C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
67	C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#16838770	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	964	2	no	—
72	C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
73	C₄	C₂×D₉₆₄	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#21440616	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21440616
commutator, cosocle	C₂×C₄×C₂₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₂₄₁
Fitting	#131×C₂₄₁	C₂
socle	C₂×C₂₄₁	#121
prime radical	#41×C₂₄₁	C₂²
hypercenter	#131	D₂₄₁
hypocenter	C₂₄₁	#473
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₉₆₄	C₂	semidirect
3. #21440578	C₂	semidirect
4. #21440560	C₂	semidirect
38. C₂₄₁	#473	semidirect

Maximal subgroups

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

subgroup	index
#21440672	2
C₂×Dic₉₆₄	2
#21440578	2
#21440560	2
#131×C₂₄₁	2
#473	241