Subgroups — D₄×#13062438 #24925039

Order 10784.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13062438	C₂	1	2	yes	maximal, complemented
2	C₄⋊#13062438	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#13062438	C₂	1	2	yes	maximal, complemented
4	C₄×#13062438	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₃₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13062438	—	2	4	no	—
7	C₂×#13062438	C₂²	1	1	yes	characteristic
8	C₂×#13062438	C₂²	1	2	yes	—
9	C₂×#13062438	C₂²	1	1	yes	characteristic
10	C₂²×D₃₃₇	C₂²	1	2	yes	—
11	D₁₃₄₈	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₃₃₇	C₄	1	2	yes	complemented
13	C₄×D₃₃₇	C₂²	1	1	yes	characteristic
14	D₄×C₃₃₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₃₃₇	C₂×C₄	1	2	yes	complemented
16	C₂×D₃₃₇	—	2	2	no	—
17	C₂×D₃₃₇	—	2	2	no	—
18	C₂×D₃₃₇	C₂×C₄	1	2	yes	complemented
19	C₂×D₃₃₇	C₂³	1	1	yes	characteristic
20	#13062438	—	2	2	no	—
21	#13062438	—	2	1	no	—
22	#13062438	D₄	1	2	yes	direct product factor
23	C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₃₃₇	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₃₃₇	—	2	2	no	—
26	C₂×C₃₃₇	C₂²×C₄	1	1	yes	characteristic
27	D₃₃₇	—	2	2	no	—
28	D₃₃₇	C₂×D₄	1	1	yes	characteristic
29	D₃₃₇	#41	1	1	yes	characteristic
30	C₃₃₇	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	337	1	no	maximal, Sylow
32	C₂×D₄	—	337	1	no	—
33	C₂²×C₄	—	337	2	no	—
34	C₄⋊C₄	—	337	1	no	—
35	C₂²⋊C₄	—	337	2	no	—
36	C₄²	—	337	1	no	—
37	C₂³	—	337	2	no	—
38	D₄	—	337	2	no	—
39	D₄	—	337	1	no	—
40	D₄	#13062438	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	337	1	no	—
42	C₂×C₄	—	337	1	no	—
43	C₂×C₄	—	337	1	no	—
44	C₂×C₄	—	337	2	no	—
45	C₂×C₄	—	674	4	no	—
46	C₂²	—	337	1	no	—
47	C₂²	—	337	2	no	—
48	C₂²	—	674	2	no	—
49	C₂²	—	674	2	no	—
50	C₂²	C₂×#13062438	1	2	yes	complemented
51	C₄	—	337	2	no	—
52	C₄	—	337	1	no	—
53	C₄	—	674	2	no	—
54	C₄	—	674	1	no	—
55	C₄	C₂×#13062438	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	337	1	no	—
58	C₂	—	337	1	no	—
59	C₂	—	674	2	no	—
60	C₂	C₂²×#13062438	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#13062438
commutator, socle	C₂×C₃₃₇	C₂²×C₄
Fitting	D₄×C₃₃₇	C₄
prime radical	D₄×D₃₃₇	C₂
cosocle	C₂×D₃₃₇	C₂³
hypercenter	D₄	#13062438
hypocenter	C₃₃₇	C₄×D₄
LCS	G ▷ C₂×C₃₃₇ ▷ C₃₃₇
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#13062438	C₂	semidirect
2. C₄⋊#13062438	C₂	semidirect
3. C₂²⋊#13062438	C₂	semidirect
4. C₄×#13062438	C₂	semidirect
11. D₁₃₄₈	C₄	semidirect
12. C₂²⋊D₃₃₇	C₄	semidirect
14. D₄×C₃₃₇	C₄	semidirect
15. C₂²×C₃₃₇	C₂×C₄	semidirect
18. C₂×D₃₃₇	C₂×C₄	semidirect
22. #13062438	D₄	direct (N × H)
23. C₄×C₃₃₇	C₂×C₄	semidirect
24. Dic₃₃₇	C₂×C₄	semidirect
30. C₃₃₇	C₄×D₄	semidirect
40. D₄	#13062438	direct (N × H)
50. C₂²	C₂×#13062438	semidirect
55. C₄	C₂×#13062438	semidirect

Subgroups — D4×#13062438 #24925039

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#13062438 #24925039