Subgroups — D₄×#11745021 #20301068

Order 7328.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11745021	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11745021	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11745021	C₂	1	2	yes	maximal, complemented
4	C₄×#11745021	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₂₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745021	—	2	4	no	—
7	C₂×#11745021	C₂²	1	1	yes	characteristic
8	C₂×#11745021	C₂²	1	2	yes	—
9	C₂×#11745021	C₂²	1	1	yes	characteristic
10	C₂²×D₂₂₉	C₂²	1	2	yes	—
11	D₉₁₆	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₂₂₉	C₄	1	2	yes	complemented
13	C₄×D₂₂₉	C₂²	1	1	yes	characteristic
14	D₄×C₂₂₉	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₂₂₉	C₂×C₄	1	2	yes	complemented
16	C₂×D₂₂₉	—	2	2	no	—
17	C₂×D₂₂₉	—	2	2	no	—
18	C₂×D₂₂₉	C₂×C₄	1	2	yes	complemented
19	C₂×D₂₂₉	C₂³	1	1	yes	characteristic
20	#11745021	—	2	2	no	—
21	#11745021	—	2	1	no	—
22	#11745021	D₄	1	2	yes	direct product factor
23	C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₂₂₉	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₂₂₉	—	2	2	no	—
26	C₂×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
27	D₂₂₉	—	2	2	no	—
28	D₂₂₉	C₂×D₄	1	1	yes	characteristic
29	D₂₂₉	#41	1	1	yes	characteristic
30	C₂₂₉	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	229	1	no	maximal, Sylow
32	C₂×D₄	—	229	1	no	—
33	C₂²×C₄	—	229	2	no	—
34	C₄⋊C₄	—	229	1	no	—
35	C₂²⋊C₄	—	229	2	no	—
36	C₄²	—	229	1	no	—
37	C₂³	—	229	2	no	—
38	D₄	—	229	2	no	—
39	D₄	—	229	1	no	—
40	D₄	#11745021	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	458	4	no	—
42	C₂×C₄	—	229	1	no	—
43	C₂×C₄	—	229	2	no	—
44	C₂×C₄	—	229	1	no	—
45	C₂×C₄	—	229	1	no	—
46	C₂²	—	458	2	no	—
47	C₂²	—	458	2	no	—
48	C₂²	—	229	2	no	—
49	C₂²	—	229	1	no	—
50	C₂²	C₂×#11745021	1	2	yes	complemented
51	C₄	—	458	2	no	—
52	C₄	—	458	1	no	—
53	C₄	—	229	2	no	—
54	C₄	—	229	1	no	—
55	C₄	C₂×#11745021	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	458	2	no	—
58	C₂	—	229	1	no	—
59	C₂	—	229	1	no	—
60	C₂	C₂²×#11745021	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11745021
commutator, socle	C₂×C₂₂₉	C₂²×C₄
Fitting	D₄×C₂₂₉	C₄
hypercenter	D₄	#11745021
hypocenter	C₂₂₉	C₄×D₄
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#11745021	C₂	semidirect
2. C₄⋊#11745021	C₂	semidirect
3. C₂²⋊#11745021	C₂	semidirect
4. C₄×#11745021	C₂	semidirect
11. D₉₁₆	C₄	semidirect
12. C₂²⋊D₂₂₉	C₄	semidirect
14. D₄×C₂₂₉	C₄	semidirect
15. C₂²×C₂₂₉	C₂×C₄	semidirect
18. C₂×D₂₂₉	C₂×C₄	semidirect
22. #11745021	D₄	direct (N × H)
23. C₄×C₂₂₉	C₂×C₄	semidirect
24. Dic₂₂₉	C₂×C₄	semidirect
30. C₂₂₉	C₄×D₄	semidirect
40. D₄	#11745021	direct (N × H)
50. C₂²	C₂×#11745021	semidirect
55. C₄	C₂×#11745021	semidirect

Subgroups — D4×#11745021 #20301068

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#11745021 #20301068