Subgroups — D₄×#261 #88239

Order 416.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#261	C₂	1	2	yes	maximal, complemented
2	D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#261	C₂	1	2	yes	maximal, complemented
4	C₄⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#261	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₃	C₂²	1	2	yes	—
7	C₂×#261	—	2	4	no	—
8	C₂×#261	C₂²	1	1	yes	characteristic
9	C₂×#261	C₂²	1	2	yes	—
10	C₂×#261	C₂²	1	1	yes	characteristic
11	D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₁₃	C₄	1	2	yes	complemented
13	D₅₂	C₄	1	1	yes	characteristic, complemented
14	C₄×D₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃	C₂×C₄	1	2	yes	complemented
16	C₂×D₁₃	—	2	2	no	—
17	C₂×D₁₃	—	2	2	no	—
18	C₂×D₁₃	C₂×C₄	1	2	yes	complemented
19	C₂×D₁₃	C₂³	1	1	yes	characteristic
20	#261	—	2	2	no	—
21	#261	—	2	1	no	—
22	#261	D₄	1	2	yes	direct product factor
23	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
25	C₄×D₄	—	13	1	no	maximal, Sylow
26	C₂×C₁₃	—	2	2	no	—
27	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	D₁₃	—	2	2	no	—
29	D₁₃	C₂×D₄	1	1	yes	characteristic
30	D₁₃	#41	1	1	yes	characteristic
31	C₂×D₄	—	13	1	no	—
32	C₂²×C₄	—	13	2	no	—
33	C₄⋊C₄	—	13	1	no	—
34	C₂²⋊C₄	—	13	2	no	—
35	C₄²	—	13	1	no	—
36	C₁₃	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
37	C₂³	—	13	2	no	—
38	D₄	—	13	2	no	—
39	D₄	—	13	1	no	—
40	D₄	#261	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	13	1	no	—
42	C₂×C₄	—	13	1	no	—
43	C₂×C₄	—	13	1	no	—
44	C₂×C₄	—	13	2	no	—
45	C₂×C₄	—	26	4	no	—
46	C₂²	—	13	1	no	—
47	C₂²	—	13	2	no	—
48	C₂²	—	26	2	no	—
49	C₂²	—	26	2	no	—
50	C₂²	C₂×#261	1	2	yes	complemented
51	C₄	—	13	2	no	—
52	C₄	—	13	1	no	—
53	C₄	—	26	1	no	—
54	C₄	—	26	2	no	—
55	C₄	C₂×#261	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	13	1	no	—
58	C₂	—	13	1	no	—
59	C₂	—	26	2	no	—
60	C₂	C₂²×#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#261
commutator, socle	C₂×C₁₃	C₂²×C₄
Fitting	D₄×C₁₃	C₄
prime radical	D₄×D₁₃	C₂
cosocle	C₂×D₁₃	C₂³
hypercenter	D₄	#261
hypocenter	C₁₃	C₄×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#261	C₂	semidirect
3. C₂²⋊#261	C₂	semidirect
4. C₄⋊#261	C₂	semidirect
5. C₄×#261	C₂	semidirect
11. D₄×C₁₃	C₄	semidirect
12. C₂²⋊D₁₃	C₄	semidirect
13. D₅₂	C₄	semidirect
15. C₂²×C₁₃	C₂×C₄	semidirect
18. C₂×D₁₃	C₂×C₄	semidirect
22. #261	D₄	direct (N × H)
23. C₄×C₁₃	C₂×C₄	semidirect
24. Dic₁₃	C₂×C₄	semidirect
36. C₁₃	C₄×D₄	semidirect
40. D₄	#261	direct (N × H)
50. C₂²	C₂×#261	semidirect
55. C₄	C₂×#261	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#261	2
D₄×D₁₃	2
C₂²⋊#261	2
C₄⋊#261	2
C₄×#261	2
C₄×D₄	13

Subgroups — D4×#261 #88239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#261 #88239