Subgroups — Q₈×#64436 #14557659

Order 2368.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#64436	C₂	1	3	yes	maximal
2	C₄×#64436	C₂	1	3	yes	maximal
3	C₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
5	C₄⋊C₄×C₃₇	C₄	1	3	yes	—
6	C₄²×C₃₇	C₂²	1	3	yes	—
7	C₂×#64436	C₂²	1	3	yes	—
8	C₂×#64436	C₂²	1	1	yes	characteristic
9	Q₈×C₃₇	C₈	1	4	yes	complemented
10	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
13	#64436	—	2	3	no	—
14	#64436	Q₈	1	2	yes	direct product factor
15	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₃₇	—	2	3	no	—
17	C₄×C₃₇	C₂×C₈	1	6	yes	—
18	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₃₇	#41	1	1	yes	characteristic
20	C₂×C₃₇	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₃₇	#131	1	1	yes	characteristic
23	C₈×Q₈	—	37	1	no	maximal, Sylow
24	C₃₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₄×Q₈	D₃₇	1	1	yes	characteristic
26	C₄⋊C₈	—	37	3	no	—
27	C₄×C₈	—	37	3	no	—
28	C₂×Q₈	Dic₃₇	1	1	yes	characteristic
29	C₂×C₈	—	37	1	no	—
30	C₂×C₈	—	37	3	no	—
31	C₄⋊C₄	Dic₃₇	1	3	yes	—
32	C₄²	C₂×D₃₇	1	3	yes	—
33	Q₈	#64436	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₃₇	1	3	yes	—
35	C₂×C₄	C₂×Dic₃₇	1	3	yes	—
36	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
37	C₈	—	37	2	no	—
38	C₈	—	74	3	no	—
39	C₂²	C₂²×Dic₃₇	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#64436	1	6	yes	—
42	C₄	Q₈×D₃₇	1	1	yes	characteristic
43	C₄	#10596966	1	1	yes	characteristic
44	C₂	Q₈×Dic₃₇	1	1	yes	characteristic
45	C₂	C₂²×#64436	1	1	yes	characteristic
46	C₂	#11924543	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₇
commutator	C₂×C₃₇	C₂²×C₈
Fitting	C₄×Q₈×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂²×C₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₄×Q₈	D₃₇
hypocenter	C₃₇	C₈×Q₈
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₃₇	C₈	semidirect
14. #64436	Q₈	direct (N × H)
24. C₃₇	C₈×Q₈	semidirect
33. Q₈	#64436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#64436	2
C₄×#64436	2
C₄×Q₈×C₃₇	2
C₈×Q₈	37

Subgroups — Q8×#64436 #14557659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#64436 #14557659