Subgroups — C₄×#19097544 #34094102

Order 20032.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097544	C₂	1	2	yes	maximal
2	C₄²×D₃₁₃	C₂	1	1	yes	maximal, characteristic
3	#23756407	C₂	1	2	yes	maximal, complemented
4	C₄×#14578809	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁₃	C₄	1	2	yes	—
7	C₂×C₄×D₃₁₃	C₂²	1	1	yes	characteristic
8	#19097544	C₄	1	8	yes	direct product factor
9	C₂×#14578809	C₂²	1	2	yes	—
10	C₄×Dic₃₁₃	C₄	1	2	yes	—
11	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₁₃	C₂²	1	2	yes	—
13	C₄²×C₃₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₃₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₃₁₃	C₂×C₄	1	2	yes	—
16	C₂×Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×D₃₁₃	—	2	4	no	—
18	C₄×D₃₁₃	C₂×C₄	1	4	yes	—
19	#14578809	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₃₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₁₃	C₂³	1	1	yes	characteristic
22	C₈×C₃₁₃	C₂×C₄	1	4	yes	complemented
23	C₂²×C₃₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₃₁₃	—	2	2	no	—
25	C₂×D₃₁₃	C₄²	1	2	yes	—
26	C₄×C₃₁₃	M₁₆	1	4	yes	complemented
27	C₄×C₃₁₃	C₂²×C₄	1	2	yes	—
28	Dic₃₁₃	—	2	2	no	—
29	Dic₃₁₃	C₄²	1	2	yes	—
30	C₂×C₃₁₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₃₁₃	C₂×M₁₆	1	2	yes	—
32	D₃₁₃	—	2	2	no	—
33	C₃₁₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×M₁₆	—	313	1	no	maximal, Sylow
35	C₂×M₁₆	—	313	2	no	—
36	C₂×C₄²	—	313	1	no	—
37	#97	—	313	2	no	—
38	C₄×C₈	—	313	1	no	—
39	C₄×C₈	D₃₁₃	1	1	yes	characteristic, complemented
40	C₂²×C₄	—	313	1	no	—
41	C₂²×C₄	—	313	2	no	—
42	M₁₆	—	313	8	no	—
43	C₂×C₈	—	313	2	no	—
44	C₂×C₈	C₂×D₃₁₃	1	2	yes	—
45	C₄²	—	313	2	no	—
46	C₄²	—	313	1	no	—
47	C₄²	C₂×D₃₁₃	1	1	yes	characteristic
48	C₂³	—	313	1	no	—
49	C₂×C₄	—	313	1	no	—
50	C₂×C₄	—	313	4	no	—
51	C₂×C₄	—	313	2	no	—
52	C₂×C₄	—	626	4	no	—
53	C₂×C₄	C₄×D₃₁₃	1	2	yes	—
54	C₂×C₄	C₂²×D₃₁₃	1	1	yes	characteristic
55	C₈	—	313	4	no	—
56	C₈	C₄×D₃₁₃	1	4	yes	complemented
57	C₂²	—	313	2	no	—
58	C₂²	—	626	2	no	—
59	C₂²	C₂×C₄×D₃₁₃	1	1	yes	characteristic
60	C₄	—	313	2	no	—
61	C₄	—	626	2	no	—
62	C₄	#19097544	1	4	yes	direct product factor
63	C₄	C₂×C₄×D₃₁₃	1	2	yes	—
64	C₂	—	626	2	no	—
65	C₂	C₄²×D₃₁₃	1	1	yes	characteristic
66	C₂	C₂×#19097544	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₃₁₃
commutator	C₂×C₃₁₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃₁₃
Fitting	C₄×C₈×C₃₁₃	C₂
socle	C₂²×C₃₁₃	C₂²×C₄
prime radical	C₂²×D₃₁₃	C₂×C₄
cosocle	C₂×C₄×C₃₁₃	C₂³
hypercenter	C₄×C₈	D₃₁₃
hypocenter	C₃₁₃	C₄×M₁₆
LCS	G ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #23756407	C₂	semidirect
4. C₄×#14578809	C₂	semidirect
5. C₄×C₈×C₃₁₃	C₂	semidirect
8. #19097544	C₄	direct (N × H)
19. #14578809	C₂×C₄	semidirect
22. C₈×C₃₁₃	C₂×C₄	semidirect
26. C₄×C₃₁₃	M₁₆	semidirect
33. C₃₁₃	C₄×M₁₆	semidirect
39. C₄×C₈	D₃₁₃	semidirect
56. C₈	C₄×D₃₁₃	semidirect
62. C₄	#19097544	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19097544	2
C₄²×D₃₁₃	2
#23756407	2
C₄×#14578809	2
C₄×C₈×C₃₁₃	2
C₄×M₁₆	313

Subgroups — C4×#19097544 #34094102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19097544 #34094102