Subgroups — C₄⋊Q₈×D₃₁ #14521590

Order 1984.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₃₁	C₂	1	2	yes	maximal
2	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758521	C₂	1	2	yes	maximal, complemented
4	C₄⋊C₄×D₃₁	C₂	1	4	yes	maximal
5	#11758465	C₂	1	4	yes	maximal, complemented
6	C₄²×D₃₁	C₂	1	1	yes	maximal, characteristic
7	#11758446	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
9	Q₈×D₃₁	—	2	8	no	—
10	C₂×C₄×D₃₁	C₂²	1	4	yes	—
11	C₂×C₄×D₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₃₁	C₂²	1	2	yes	—
13	C₂×Dic₆₂	C₂²	1	2	yes	—
14	C₂×Dic₆₂	C₂²	1	4	yes	—
15	C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
16	C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₃₁	C₂²	1	4	yes	—
18	Dic₃₁⋊C₄	C₂²	1	8	yes	—
19	C₄×Dic₃₁	C₂²	1	2	yes	—
20	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
21	C₂²×D₃₁	C₂³	1	1	yes	characteristic
22	Q₈×C₃₁	—	2	4	no	—
23	C₂×C₄×C₃₁	C₂³	1	4	yes	—
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₃₁	C₂³	1	2	yes	—
26	C₂×Dic₃₁	C₂³	1	4	yes	—
27	C₂×Dic₃₁	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₁	C₂³	1	2	yes	—
29	C₄×D₃₁	—	2	8	no	—
30	C₄×D₃₁	D₄	1	4	yes	—
31	C₄×D₃₁	Q₈	1	8	yes	complemented
32	Dic₆₂	—	2	4	no	—
33	Dic₆₂	—	2	8	no	—
34	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
35	C₂×D₃₁	C₂×D₄	1	2	yes	—
36	C₂×D₃₁	C₂×Q₈	1	4	yes	—
37	C₄×C₃₁	—	2	4	no	—
38	C₄×C₃₁	C₂×D₄	1	2	yes	—
39	C₄×C₃₁	C₂×Q₈	1	4	yes	complemented
40	Dic₃₁	—	2	4	no	—
41	Dic₃₁	C₂×D₄	1	2	yes	—
42	Dic₃₁	C₂×Q₈	1	4	yes	complemented
43	C₂×C₄⋊Q₈	—	31	1	no	maximal, Sylow
44	C₂×C₃₁	C₂²×D₄	1	1	yes	characteristic
45	C₂×C₃₁	C₂²×Q₈	1	2	yes	—
46	D₃₁	C₄⋊Q₈	1	4	yes	direct product factor
47	C₂²×Q₈	—	31	2	no	—
48	C₄⋊Q₈	—	31	2	no	—
49	C₄⋊Q₈	—	31	4	no	—
50	C₄⋊Q₈	—	31	1	no	—
51	C₄⋊Q₈	D₃₁	1	1	yes	characteristic, direct product factor
52	C₂×C₄⋊C₄	—	31	4	no	—
53	C₂×C₄²	—	31	1	no	—
54	C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	31	4	no	—
56	C₂×Q₈	—	31	2	no	—
57	C₂×Q₈	—	62	8	no	—
58	C₂×Q₈	C₂×D₃₁	1	2	yes	—
59	C₂²×C₄	—	31	2	no	—
60	C₂²×C₄	—	31	1	no	—
61	C₂²×C₄	—	31	4	no	—
62	C₄⋊C₄	—	31	8	no	—
63	C₄⋊C₄	—	31	4	no	—
64	C₄⋊C₄	C₂×D₃₁	1	4	yes	—
65	C₄²	—	31	1	no	—
66	C₄²	—	31	2	no	—
67	C₄²	C₂×D₃₁	1	1	yes	characteristic
68	C₂³	—	31	1	no	—
69	Q₈	—	2	4	no	—
70	Q₈	—	62	8	no	—
71	Q₈	—	62	4	no	—
72	C₂×C₄	—	31	2	no	—
73	C₂×C₄	—	31	1	no	—
74	C₂×C₄	—	31	4	no	—
75	C₂×C₄	—	31	8	no	—
76	C₂×C₄	—	31	4	no	—
77	C₂×C₄	—	62	8	no	—
78	C₂×C₄	C₂²×D₃₁	1	4	yes	—
79	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₃₁	1	2	yes	—
81	C₂²	—	31	2	no	—
82	C₂²	—	31	4	no	—
83	C₂²	C₂³×D₃₁	1	1	yes	characteristic
84	C₄	—	2	4	no	—
85	C₄	—	31	2	no	—
86	C₄	—	31	4	no	—
87	C₄	—	62	4	no	—
88	C₄	D₄×D₃₁	1	2	yes	—
89	C₄	Q₈×D₃₁	1	4	yes	complemented
90	C₂	—	31	4	no	—
91	C₂	C₂×D₄×D₃₁	1	1	yes	characteristic
92	C₂	C₂×Q₈×D₃₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁴
Fitting	C₃₁×C₄⋊Q₈	C₂
prime radical	C₂²×D₃₁	C₂³
hypercenter	C₄⋊Q₈	D₃₁
hypocenter	C₃₁	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃₁×C₄⋊Q₈	C₂	semidirect
3. #11758521	C₂	semidirect
5. #11758465	C₂	semidirect
7. #11758446	C₂	semidirect
31. C₄×D₃₁	Q₈	semidirect
39. C₄×C₃₁	C₂×Q₈	semidirect
42. Dic₃₁	C₂×Q₈	semidirect
46. D₃₁	C₄⋊Q₈	direct (N × H)
51. C₄⋊Q₈	D₃₁	direct (N × H)
54. C₃₁	C₂×C₄⋊Q₈	semidirect
89. C₄	Q₈×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₃₁	2
C₃₁×C₄⋊Q₈	2
#11758521	2
C₄⋊C₄×D₃₁	2
#11758465	2
C₄²×D₃₁	2
#11758446	2
C₂×C₄⋊Q₈	31

Subgroups — C4⋊Q8×D31 #14521590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊Q₈×D₃₁ #14521590