Subgroups — C₄×D₃₈₉₆ #44529134

Order 31168.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₈₉₆	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₉₄₈	C₂	1	2	yes	maximal, complemented
3	#29510149	C₂	1	1	yes	maximal, characteristic, complemented
4	#29510137	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₄₈	C₂²	1	2	yes	—
7	C₂×C₄×D₄₈₇	—	2	2	no	—
8	D₃₈₉₆	C₄	1	4	yes	direct product factor
9	C₄⋊Dic₄₈₇	C₂²	1	2	yes	—
10	(C₂×D₄₈₇)⋊C₄	—	2	2	no	—
11	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
13	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
14	C₂²×D₄₈₇	—	2	2	no	—
15	D₁₉₄₈	—	2	2	no	—
16	D₁₉₄₈	C₂×C₄	1	4	yes	complemented
17	C₂×Dic₄₈₇	—	2	2	no	—
18	C₄×D₄₈₇	—	4	4	no	—
19	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
22	C₈×C₄₈₇	—	2	1	no	—
23	C₈×C₄₈₇	C₂×C₄	1	2	yes	complemented
24	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
25	C₂×D₄₈₇	—	2	4	no	—
26	C₂×D₄₈₇	—	4	2	no	—
27	C₂×D₄₈₇	—	4	2	no	—
28	C₄×C₄₈₇	—	2	1	no	—
29	C₄×C₄₈₇	D₈	1	2	yes	complemented
30	C₄×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₈₇	#41	1	1	yes	characteristic
32	Dic₄₈₇	—	4	2	no	—
33	C₂×C₄₈₇	C₄×D₄	1	1	yes	characteristic
34	C₂×C₄₈₇	C₂×D₈	1	1	yes	characteristic
35	C₂×C₄₈₇	#135	1	1	yes	characteristic
36	D₄₈₇	—	4	4	no	—
37	C₄₈₇	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₄×D₈	—	487	1	no	maximal, Sylow
39	C₂×D₈	—	487	1	no	—
40	C₄×D₄	—	487	2	no	—
41	#107	—	487	1	no	—
42	#102	—	487	2	no	—
43	C₄×C₈	D₄₈₇	1	1	yes	characteristic, complemented
44	C₂×D₄	—	487	2	no	—
45	C₂²×C₄	—	974	2	no	—
46	D₈	—	487	4	no	—
47	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
48	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
49	C₄⋊C₄	—	487	2	no	—
50	C₂²⋊C₄	—	974	2	no	—
51	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
52	C₂³	—	974	2	no	—
53	D₄	—	974	2	no	—
54	D₄	—	487	4	no	—
55	C₂×C₄	—	1948	4	no	—
56	C₂×C₄	—	974	2	no	—
57	C₂×C₄	D₁₉₄₈	1	1	yes	characteristic
58	C₂×C₄	D₁₉₄₈	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	C₄×D₄₈₇	1	2	yes	complemented
62	C₂²	—	1948	2	no	—
63	C₂²	—	1948	2	no	—
64	C₂²	—	974	4	no	—
65	C₂²	C₂×D₁₉₄₈	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	1948	2	no	—
68	C₄	D₃₈₉₆	1	2	yes	direct product factor
69	C₄	C₂×C₄×D₄₈₇	1	1	yes	characteristic
70	C₄	#21441261	1	1	yes	characteristic
71	C₂	—	1948	4	no	—
72	C₂	C₄×D₁₉₄₈	1	1	yes	characteristic
73	C₂	C₂×D₃₈₉₆	1	1	yes	characteristic
74	C₂	#29510237	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₉₄₈
commutator	C₄×C₄₈₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₄×C₈×C₄₈₇	C₂
socle	C₂²×C₄₈₇	C₂×D₄
prime radical	C₂×D₃₈₉₆	C₂
cosocle	C₂×C₄×C₄₈₇	C₂³
hypercenter	C₄×C₈	D₄₈₇
hypocenter	C₄₈₇	C₄×D₈
LCS	G ▷ C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₉₄₈	C₂	semidirect
3. #29510149	C₂	semidirect
4. #29510137	C₂	semidirect
5. C₄×C₈×C₄₈₇	C₂	semidirect
8. D₃₈₉₆	C₄	direct (N × H)
16. D₁₉₄₈	C₂×C₄	semidirect
23. C₈×C₄₈₇	C₂×C₄	semidirect
29. C₄×C₄₈₇	D₈	semidirect
37. C₄₈₇	C₄×D₈	semidirect
43. C₄×C₈	D₄₈₇	semidirect
61. C₈	C₄×D₄₈₇	semidirect
68. C₄	D₃₈₉₆	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×D₃₈₉₆	2
C₄×D₁₉₄₈	2
#29510149	2
#29510137	2
C₄×C₈×C₄₈₇	2
C₄×D₈	487

Subgroups — C4×D3896 #44529134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃₈₉₆ #44529134