Subgroups — #38786162

Order 25664.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20264350	C₂	1	1	yes	maximal, characteristic
2	C₂×#20264350	C₂	1	1	yes	maximal, characteristic
3	#27165672	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₄₀₁	C₂	1	1	yes	maximal, characteristic
5	#20264350	—	2	1	no	—
6	#20264350	C₄	1	2	yes	—
7	#20264350	C₄	1	2	yes	—
8	#20264350	C₂²	1	2	yes	—
9	C₂×#15691999	—	2	1	no	—
10	C₂×#15691999	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₀₁	C₂²	1	1	yes	characteristic
12	M₁₆×C₄₀₁	—	2	1	no	—
13	M₁₆×C₄₀₁	C₂²	1	2	yes	—
14	C₂×C₈×C₄₀₁	—	2	1	no	—
15	#15691999	—	2	2	no	—
16	#15691999	C₂×C₄	1	4	yes	—
17	C₂³×C₄₀₁	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₀₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₀₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₀₁	Q₈	1	1	yes	characteristic
23	C₂×C₄×C₄₀₁	C₂³	1	1	yes	characteristic
24	C₈×C₄₀₁	—	2	2	no	—
25	C₂²×C₄₀₁	—	4	1	no	—
26	C₂²×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄₀₁	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₀₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄₀₁	—	2	1	no	—
34	C₂×C₄₀₁	—	2	1	no	—
35	C₂×C₄₀₁	—	2	1	no	—
36	C₂×C₄₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄₀₁	#430	1	1	yes	characteristic, complemented, Sylow
38	#430	—	401	1	no	maximal, Sylow
39	C₂×M₁₆	—	401	1	no	—
40	C₂×M₁₆	—	401	1	no	—
41	C₂×M₁₆	D₄₀₁	1	1	yes	characteristic
42	#108	—	401	4	no	—
43	C₂²×C₄	C₂×D₄₀₁	1	1	yes	characteristic
44	M₁₆	—	2	1	no	—
45	M₁₆	—	802	1	no	—
46	M₁₆	—	401	2	no	—
47	M₁₆	—	401	2	no	—
48	M₁₆	—	401	2	no	—
49	M₁₆	C₂×D₄₀₁	1	2	yes	—
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	—	802	1	no	—
52	C₂×C₈	—	401	2	no	—
53	C₂³	Dic₈₀₂	1	1	yes	characteristic
54	C₂×C₄	C₄×D₄₀₁	1	1	yes	characteristic
55	C₂×C₄	C₄×D₄₀₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₄₀₁	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₄₀₁	1	1	yes	characteristic
58	C₂×C₄	Dic₈₀₂	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₄₀₁	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	802	2	no	—
62	C₈	—	401	4	no	—
63	C₂²	—	4	1	no	—
64	C₂²	#20264345	1	1	yes	characteristic
65	C₂²	#20264345	1	1	yes	characteristic
66	C₂²	C₂×Dic₈₀₂	1	1	yes	characteristic
67	C₄	#20264345	1	1	yes	characteristic
68	C₄	#20264345	1	1	yes	characteristic
69	C₄	C₂×C₄×D₄₀₁	1	1	yes	characteristic
70	C₄	C₂×C₂²⋊D₄₀₁	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×#20264345	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊D₄₀₁
commutator	C₄×C₄₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₀₁
Fitting	C₂×M₁₆×C₄₀₁	C₂
socle	C₂×C₄₀₁	C₂×C₄⋊C₄
prime radical	C₂³×C₄₀₁	Q₈
cosocle	C₂×C₄×C₄₀₁	C₂³
hypercenter	C₂×M₁₆	D₄₀₁
hypocenter	C₄₀₁	#430
LCS	G ▷ C₄×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #27165672	C₂	semidirect
37. C₄₀₁	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20264350	2
#27165672	2
C₂×M₁₆×C₄₀₁	2
#430	401