Subgroups — #38786997

Order 25664.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20264376	C₂	1	1	yes	maximal, characteristic
2	#27165816	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₄₀₁	C₂	1	1	yes	maximal, characteristic
4	#20264376	—	2	1	no	—
5	#20264376	—	2	1	no	—
6	C₂×#15692006	C₄	1	2	yes	complemented
7	C₄⋊#13107944	—	2	1	no	—
8	C₂²⋊#13107944	C₄	1	2	yes	—
9	C₄×#13107944	—	2	1	no	—
10	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
11	#20264350	C₄	1	1	yes	characteristic, complemented
12	#20264349	—	2	1	no	—
13	C₈×D₄₀₁	—	2	1	no	—
14	M₁₆×C₄₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂×#13107944	—	2	2	no	—
16	#15692006	—	2	2	no	—
17	C₂²×D₄₀₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₄₀₁	D₄	1	1	yes	characteristic
20	C₄×D₄₀₁	D₄	1	1	yes	characteristic
21	C₄×D₄₀₁	D₄	1	1	yes	characteristic
22	C₄×D₄₀₁	Q₈	1	1	yes	characteristic
23	#15691999	—	2	1	no	—
24	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₄₀₁	—	2	1	no	—
26	C₂²×C₄₀₁	C₄²	1	1	yes	characteristic
27	C₂×D₄₀₁	—	4	1	no	—
28	C₂×D₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₄₀₁	C₄⋊C₄	1	1	yes	characteristic
30	#13107944	—	4	2	no	—
31	C₄×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
33	Dic₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₄₀₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄₀₁	—	2	1	no	—
36	C₂×C₄₀₁	#95	1	1	yes	characteristic
37	D₄₀₁	—	2	1	no	—
38	D₄₀₁	—	2	1	no	—
39	C₄₀₁	#344	1	1	yes	characteristic, complemented, Sylow
40	#344	—	401	1	no	maximal, Sylow
41	C₂×M₁₆	—	401	1	no	—
42	C₂×M₁₆	—	401	1	no	—
43	#117	—	401	1	no	—
44	C₂²×C₄	—	401	1	no	—
45	M₁₆	—	802	1	no	—
46	M₁₆	—	802	1	no	—
47	M₁₆	—	802	1	no	—
48	M₁₆	—	401	1	no	—
49	M₁₆	#13107944	1	1	yes	characteristic, complemented
50	C₂×C₈	—	802	1	no	—
51	C₂×C₈	—	401	2	no	—
52	C₄⋊C₄	—	802	1	no	—
53	C₂²⋊C₄	—	401	2	no	—
54	C₄²	—	802	1	no	—
55	C₂³	—	401	1	no	—
56	C₂×C₄	—	802	2	no	—
57	C₂×C₄	—	401	1	no	—
58	C₂×C₄	—	401	1	no	—
59	C₂×C₄	—	401	1	no	—
60	C₂×C₄	—	401	1	no	—
61	C₂×C₄	—	401	1	no	—
62	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	802	2	no	—
65	C₈	—	802	1	no	—
66	C₂²	—	1604	1	no	—
67	C₂²	—	401	1	no	—
68	C₂²	—	401	1	no	—
69	C₂²	C₄×#13107944	1	1	yes	characteristic
70	C₄	—	1604	2	no	—
71	C₄	—	401	1	no	—
72	C₄	—	401	1	no	—
73	C₄	C₂²⋊#13107944	1	1	yes	characteristic
74	C₄	C₄⋊#13107944	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	802	1	no	—
77	C₂	—	802	1	no	—
78	C₂	(C₂×#13107944)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#13107944)⋊C₄
commutator	C₂²×C₄₀₁	C₄²
Frattini	C₂×C₄	C₂×#13107944
Fitting	M₁₆×C₄₀₁	C₄
socle	C₂×C₄₀₁	#95
prime radical	C₂²×D₄₀₁	C₂×C₄
cosocle	C₂×C₄×D₄₀₁	C₂²
hypercenter	M₁₆	#13107944
hypocenter	C₄₀₁	#344
LCS	G ▷ C₂²×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#15692006	C₄	semidirect
11. #20264350	C₄	semidirect
14. M₁₆×C₄₀₁	C₄	semidirect
39. C₄₀₁	#344	semidirect
49. M₁₆	#13107944	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20264376	2
#27165816	2
M₁₆×D₄₀₁	2
#344	401