Subgroups — C₂×C₄⋊#11745400 #21418613

Order 7456.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11745400	C₂	1	2	yes	maximal
2	C₄⋊#11745400	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745400	—	2	4	no	—
5	C₂×#11745400	C₂²	1	4	yes	—
6	C₂²×D₂₃₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₃₃	C₄	1	1	yes	characteristic, complemented
8	C₄×D₂₃₃	C₄	1	2	yes	complemented
9	C₄×D₂₃₃	C₂²	1	2	yes	—
10	C₂×C₄×C₂₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
12	C₂×D₂₃₃	C₂×C₄	1	1	yes	characteristic
13	C₂×D₂₃₃	D₄	1	2	yes	—
14	C₂×D₂₃₃	Q₈	1	2	yes	—
15	C₂×D₂₃₃	C₂³	1	1	yes	characteristic
16	#11745400	—	2	4	no	—
17	C₄×C₂₃₃	C₂×C₄	1	2	yes	complemented
18	Dic₂₃₃	C₂×C₄	1	2	yes	complemented
19	C₂×C₂₃₃	C₄⋊C₄	1	2	yes	complemented
20	C₂×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
21	D₂₃₃	C₄⋊C₄	1	2	yes	complemented
22	D₂₃₃	C₂×D₄	1	1	yes	characteristic
23	D₂₃₃	C₂×Q₈	1	1	yes	characteristic
24	C₂₃₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₄⋊C₄	—	233	1	no	maximal, Sylow
26	C₂²×C₄	—	233	2	no	—
27	C₂²×C₄	—	233	1	no	—
28	C₄⋊C₄	—	233	4	no	—
29	C₂³	—	233	1	no	—
30	C₂×C₄	—	466	4	no	—
31	C₂×C₄	—	233	4	no	—
32	C₂×C₄	—	233	1	no	—
33	C₂×C₄	—	233	2	no	—
34	C₂×C₄	—	233	2	no	—
35	C₂×C₄	#11745400	1	1	yes	characteristic, complemented
36	C₂²	—	233	2	no	—
37	C₂²	—	233	2	no	—
38	C₂²	—	233	1	no	—
39	C₂²	—	233	1	no	—
40	C₂²	C₂×#11745400	1	1	yes	characteristic
41	C₄	—	466	4	no	—
42	C₄	—	233	2	no	—
43	C₄	C₂×#11745400	1	2	yes	complemented
44	C₂	—	233	1	no	—
45	C₂	—	233	2	no	—
46	C₂	—	233	1	no	—
47	C₂	C₄⋊#11745400	1	2	yes	direct product factor
48	C₂	C₂²×#11745400	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄⋊#11745400	C₂	direct (N × H)
7. C₂×Dic₂₃₃	C₄	semidirect
8. C₄×D₂₃₃	C₄	semidirect
10. C₂×C₄×C₂₃₃	C₄	semidirect
17. C₄×C₂₃₃	C₂×C₄	semidirect
18. Dic₂₃₃	C₂×C₄	semidirect
19. C₂×C₂₃₃	C₄⋊C₄	semidirect
21. D₂₃₃	C₄⋊C₄	semidirect
24. C₂₃₃	C₂×C₄⋊C₄	semidirect
35. C₂×C₄	#11745400	semidirect
43. C₄	C₂×#11745400	semidirect
47. C₂	C₄⋊#11745400	direct (N × H)

Subgroups — C2×C4⋊#11745400 #21418613

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄⋊#11745400 #21418613