Subgroups — D₄×#11745400 #21418615

Order 7456.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11745400	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11745400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11745400	C₂	1	2	yes	maximal, complemented
4	C₄×#11745400	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₂₃₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745400	—	2	4	no	—
7	C₂×#11745400	C₂²	1	1	yes	characteristic
8	C₂×#11745400	C₂²	1	2	yes	—
9	C₂×#11745400	C₂²	1	1	yes	characteristic
10	C₂²×D₂₃₃	C₂²	1	2	yes	—
11	D₉₃₂	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₂₃₃	C₄	1	2	yes	complemented
13	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
14	D₄×C₂₃₃	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₂₃₃	C₂×C₄	1	2	yes	complemented
16	C₂×D₂₃₃	—	2	2	no	—
17	C₂×D₂₃₃	—	2	2	no	—
18	C₂×D₂₃₃	C₂×C₄	1	2	yes	complemented
19	C₂×D₂₃₃	C₂³	1	1	yes	characteristic
20	#11745400	—	2	2	no	—
21	#11745400	—	2	1	no	—
22	#11745400	D₄	1	2	yes	direct product factor
23	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₂₃₃	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₂₃₃	—	2	2	no	—
26	C₂×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
27	D₂₃₃	—	2	2	no	—
28	D₂₃₃	C₂×D₄	1	1	yes	characteristic
29	D₂₃₃	#41	1	1	yes	characteristic
30	C₂₃₃	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	233	1	no	maximal, Sylow
32	C₂×D₄	—	233	1	no	—
33	C₂²×C₄	—	233	2	no	—
34	C₄⋊C₄	—	233	1	no	—
35	C₂²⋊C₄	—	233	2	no	—
36	C₄²	—	233	1	no	—
37	C₂³	—	233	2	no	—
38	D₄	—	233	2	no	—
39	D₄	—	233	1	no	—
40	D₄	#11745400	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	466	4	no	—
42	C₂×C₄	—	233	1	no	—
43	C₂×C₄	—	233	2	no	—
44	C₂×C₄	—	233	1	no	—
45	C₂×C₄	—	233	1	no	—
46	C₂²	—	466	2	no	—
47	C₂²	—	466	2	no	—
48	C₂²	—	233	2	no	—
49	C₂²	—	233	1	no	—
50	C₂²	C₂×#11745400	1	2	yes	complemented
51	C₄	—	466	2	no	—
52	C₄	—	466	1	no	—
53	C₄	—	233	2	no	—
54	C₄	—	233	1	no	—
55	C₄	C₂×#11745400	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	466	2	no	—
58	C₂	—	233	1	no	—
59	C₂	—	233	1	no	—
60	C₂	C₂²×#11745400	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11745400
commutator, socle	C₂×C₂₃₃	C₂²×C₄
Fitting	D₄×C₂₃₃	C₄
hypercenter	D₄	#11745400
hypocenter	C₂₃₃	C₄×D₄
LCS	G ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#11745400	C₂	semidirect
2. C₄⋊#11745400	C₂	semidirect
3. C₂²⋊#11745400	C₂	semidirect
4. C₄×#11745400	C₂	semidirect
11. D₉₃₂	C₄	semidirect
12. C₂²⋊D₂₃₃	C₄	semidirect
14. D₄×C₂₃₃	C₄	semidirect
15. C₂²×C₂₃₃	C₂×C₄	semidirect
18. C₂×D₂₃₃	C₂×C₄	semidirect
22. #11745400	D₄	direct (N × H)
23. C₄×C₂₃₃	C₂×C₄	semidirect
24. Dic₂₃₃	C₂×C₄	semidirect
30. C₂₃₃	C₄×D₄	semidirect
40. D₄	#11745400	direct (N × H)
50. C₂²	C₂×#11745400	semidirect
55. C₄	C₂×#11745400	semidirect

Subgroups — D4×#11745400 #21418615

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#11745400 #21418615