Subgroups — #34093924

Order 20032.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097545	C₂	1	1	yes	maximal, characteristic
2	#23756456	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic
4	#19097545	—	2	1	no	—
5	#19097545	—	2	1	no	—
6	C₂×#14578809	C₄	1	2	yes	complemented
7	C₄⋊Dic₃₁₃	—	2	1	no	—
8	C₂²⋊Dic₃₁₃	C₄	1	2	yes	—
9	C₄×Dic₃₁₃	—	2	1	no	—
10	C₂²×C₄×C₃₁₃	C₂²	1	1	yes	characteristic
11	M₁₆×C₃₁₃	—	2	1	no	—
12	M₁₆×C₃₁₃	C₄	1	2	yes	complemented
13	C₂×C₈×C₃₁₃	—	2	1	no	—
14	C₂×Dic₃₁₃	—	2	2	no	—
15	#14578809	—	2	2	no	—
16	C₂³×C₃₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁₃	Q₈	1	1	yes	characteristic
23	C₈×C₃₁₃	—	2	2	no	—
24	C₂²×C₃₁₃	—	4	1	no	—
25	C₂²×C₃₁₃	C₄²	1	1	yes	characteristic
26	C₂²×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₃₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₃₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₃₁₃	C₄⋊C₄	1	1	yes	characteristic
32	Dic₃₁₃	—	4	2	no	—
33	C₂×C₃₁₃	—	2	1	no	—
34	C₂×C₃₁₃	—	2	1	no	—
35	C₂×C₃₁₃	—	2	1	no	—
36	C₂×C₃₁₃	#95	1	1	yes	characteristic
37	C₃₁₃	#344	1	1	yes	characteristic, complemented, Sylow
38	#344	—	313	1	no	maximal, Sylow
39	C₂×M₁₆	—	313	1	no	—
40	C₂×M₁₆	D₃₁₃	1	1	yes	characteristic
41	#117	—	313	1	no	—
42	C₂²×C₄	C₂×D₃₁₃	1	1	yes	characteristic
43	M₁₆	—	2	1	no	—
44	M₁₆	—	626	1	no	—
45	M₁₆	—	626	1	no	—
46	M₁₆	Dic₃₁₃	1	2	yes	complemented
47	C₂×C₈	—	2	1	no	—
48	C₂×C₈	—	313	2	no	—
49	C₄⋊C₄	—	626	1	no	—
50	C₂²⋊C₄	—	313	2	no	—
51	C₄²	—	626	1	no	—
52	C₂³	C₄×D₃₁₃	1	1	yes	characteristic
53	C₂×C₄	—	626	2	no	—
54	C₂×C₄	C₄×D₃₁₃	1	1	yes	characteristic
55	C₂×C₄	C₂×Dic₃₁₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₃₁₃	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₃₁₃	1	1	yes	characteristic
58	C₂×C₄	D₁₂₅₂	1	1	yes	characteristic
59	C₂×C₄	Dic₆₂₆	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	626	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄×Dic₃₁₃	1	1	yes	characteristic
64	C₂²	#19097538	1	1	yes	characteristic
65	C₂²	#19097540	1	1	yes	characteristic
66	C₄	—	1252	2	no	—
67	C₄	#19097538	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₃₁₃	1	1	yes	characteristic
69	C₄	#19097540	1	1	yes	characteristic
70	C₄	C₄⋊Dic₃₁₃	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#23756404	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19097538
commutator	C₂²×C₃₁₃	C₄²
Frattini	C₂²×C₄	C₂×D₃₁₃
Fitting	C₂×M₁₆×C₃₁₃	C₂
socle	C₂×C₃₁₃	#95
prime radical	C₂³×C₃₁₃	C₂×C₄
cosocle	C₂²×C₄×C₃₁₃	C₂²
hypercenter	C₂×M₁₆	D₃₁₃
hypocenter	C₃₁₃	#344
LCS	G ▷ C₂²×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#14578809	C₄	semidirect
12. M₁₆×C₃₁₃	C₄	semidirect
37. C₃₁₃	#344	semidirect
46. M₁₆	Dic₃₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19097545	2
#23756456	2
C₂×M₁₆×C₃₁₃	2
#344	313