Subgroups — Q₈×Dic₇₄ #14558264

Order 2368.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924536	C₂	1	3	yes	maximal
2	#11924535	C₂	1	6	yes	maximal
3	Q₈×Dic₃₇	C₂	1	2	yes	maximal
4	C₄×Dic₇₄	C₂	1	3	yes	maximal
5	C₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₄	C₂²	1	6	yes	—
8	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₃₇	C₂²	1	3	yes	—
10	C₄²×C₃₇	C₂²	1	3	yes	—
11	C₄⋊Dic₃₇	C₂²	1	3	yes	—
12	C₄⋊Dic₃₇	C₂²	1	6	yes	—
13	#10596936	C₂²	1	6	yes	—
14	C₄×Dic₃₇	C₂²	1	6	yes	—
15	Q₈×C₃₇	Q₈	1	4	yes	complemented
16	C₂×C₄×C₃₇	C₂³	1	3	yes	—
17	C₂×C₄×C₃₇	C₂³	1	3	yes	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₇	C₂³	1	6	yes	—
20	C₂×Dic₃₇	C₂³	1	2	yes	—
21	Dic₇₄	—	4	6	no	—
22	Dic₇₄	Q₈	1	4	yes	direct product factor
23	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
24	C₄×C₃₇	—	2	3	no	—
25	C₄×C₃₇	C₂×Q₈	1	6	yes	—
26	C₄×C₃₇	C₂×Q₈	1	2	yes	—
27	Dic₃₇	—	2	6	no	—
28	Dic₃₇	C₂×Q₈	1	4	yes	—
29	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
30	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
31	C₂×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
32	Q₈²	—	37	1	no	maximal, Sylow
33	C₃₇	Q₈²	1	1	yes	characteristic, complemented, Sylow
34	C₄⋊Q₈	—	37	6	no	—
35	C₄⋊Q₈	—	37	3	no	—
36	C₄×Q₈	—	37	2	no	—
37	C₄×Q₈	—	37	3	no	—
38	C₄×Q₈	D₃₇	1	1	yes	characteristic
39	C₂×Q₈	—	37	1	no	—
40	C₂×Q₈	—	37	6	no	—
41	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
42	C₄⋊C₄	—	37	6	no	—
43	C₄⋊C₄	—	37	6	no	—
44	C₄⋊C₄	—	37	3	no	—
45	C₄⋊C₄	C₂×D₃₇	1	3	yes	—
46	C₄²	—	37	6	no	—
47	C₄²	C₂×D₃₇	1	3	yes	—
48	Q₈	—	37	4	no	—
49	Q₈	—	148	6	no	—
50	Q₈	Dic₇₄	1	4	yes	direct product factor
51	C₂×C₄	—	37	2	no	—
52	C₂×C₄	—	37	6	no	—
53	C₂×C₄	C₂²×D₃₇	1	3	yes	—
54	C₂×C₄	C₂²×D₃₇	1	3	yes	—
55	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
56	C₂²	C₂³×D₃₇	1	1	yes	characteristic
57	C₄	—	2	3	no	—
58	C₄	—	37	4	no	—
59	C₄	—	74	6	no	—
60	C₄	C₂×Dic₇₄	1	6	yes	—
61	C₄	Q₈×D₃₇	1	2	yes	—
62	C₂	C₂×Q₈×D₃₇	1	1	yes	characteristic
63	C₂	C₂²×Dic₇₄	1	1	yes	characteristic
64	C₂	#11924582	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, prime radical, cosocle	C₂²×C₃₇	C₂⁴
Fitting	C₄×Q₈×C₃₇	C₂
hypercenter	C₄×Q₈	D₃₇
hypocenter	C₃₇	Q₈²
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
15. Q₈×C₃₇	Q₈	semidirect
22. Dic₇₄	Q₈	direct (N × H)
33. C₃₇	Q₈²	semidirect
50. Q₈	Dic₇₄	direct (N × H)

Maximal subgroups

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

subgroup	index
#11924536	2
#11924535	2
Q₈×Dic₃₇	2
C₄×Dic₇₄	2
C₄×Q₈×C₃₇	2
Q₈²	37

Subgroups — Q8×Dic74 #14558264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₇₄ #14558264