Subgroups — C₄×Q₈×D₄₁ #14580799

Order 2624.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₄₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₈₂	C₂	1	3	yes	maximal, complemented
4	#13050129	C₂	1	3	yes	maximal, complemented
5	C₄⋊C₄×D₄₁	C₂	1	3	yes	maximal
6	C₄²×D₄₁	C₂	1	3	yes	maximal
7	C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	Q₈×D₄₁	C₄	1	8	yes	direct product factor
10	C₂×C₄×D₄₁	C₂²	1	3	yes	—
11	C₂×C₄×D₄₁	C₂²	1	3	yes	—
12	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₈₂	C₂²	1	3	yes	—
14	C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
15	C₄²×C₄₁	C₂²	1	3	yes	—
16	C₄⋊Dic₄₁	C₂²	1	3	yes	—
17	#10620279	C₂²	1	6	yes	—
18	C₄×Dic₄₁	C₂²	1	3	yes	—
19	C₄×Dic₄₁	C₂²	1	3	yes	—
20	C₄×Dic₄₁	C₂²	1	3	yes	—
21	C₂²×D₄₁	C₂³	1	1	yes	characteristic
22	Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
23	C₂×C₄×C₄₁	C₂³	1	3	yes	—
24	C₂×C₄×C₄₁	C₂³	1	3	yes	—
25	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₁	C₂³	1	3	yes	—
27	C₂×Dic₄₁	C₂³	1	3	yes	—
28	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
29	C₄×D₄₁	—	2	6	no	—
30	C₄×D₄₁	C₂×C₄	1	12	yes	—
31	C₄×D₄₁	Q₈	1	4	yes	direct product factor
32	Dic₈₂	C₂×C₄	1	12	yes	complemented
33	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
34	C₂×D₄₁	C₂²×C₄	1	2	yes	—
35	C₂×D₄₁	C₂×Q₈	1	2	yes	—
36	C₂×D₄₁	#41	1	2	yes	—
37	C₄×C₄₁	—	2	3	no	—
38	C₄×C₄₁	C₂²×C₄	1	6	yes	—
39	C₄×C₄₁	C₂×Q₈	1	2	yes	complemented
40	Dic₄₁	—	2	3	no	—
41	Dic₄₁	C₂²×C₄	1	6	yes	—
42	Dic₄₁	C₂×Q₈	1	2	yes	complemented
43	C₂×C₄₁	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₄₁	C₂²×Q₈	1	1	yes	characteristic
45	C₂×C₄₁	C₂×#41	1	1	yes	characteristic
46	D₄₁	C₄×Q₈	1	4	yes	direct product factor
47	C₂×C₄×Q₈	—	41	1	no	maximal, Sylow
48	C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
49	C₂²×Q₈	—	41	1	no	—
50	C₄×Q₈	—	41	1	no	—
51	C₄×Q₈	—	41	3	no	—
52	C₄×Q₈	—	41	3	no	—
53	C₄×Q₈	D₄₁	1	1	yes	characteristic, direct product factor
54	C₂×C₄⋊C₄	—	41	3	no	—
55	C₂×C₄²	—	41	3	no	—
56	C₂×Q₈	—	41	8	no	—
57	C₂×Q₈	—	41	3	no	—
58	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
59	C₂²×C₄	—	41	3	no	—
60	C₂²×C₄	—	41	1	no	—
61	C₂²×C₄	—	41	3	no	—
62	C₄⋊C₄	—	41	6	no	—
63	C₄⋊C₄	—	41	3	no	—
64	C₄⋊C₄	C₂×D₄₁	1	3	yes	—
65	C₄²	—	41	3	no	—
66	C₄²	—	41	3	no	—
67	C₄²	—	41	3	no	—
68	C₄²	C₂×D₄₁	1	3	yes	—
69	C₂³	—	41	1	no	—
70	Q₈	—	41	12	no	—
71	Q₈	C₄×D₄₁	1	4	yes	direct product factor
72	C₂×C₄	—	41	1	no	—
73	C₂×C₄	—	41	3	no	—
74	C₂×C₄	—	41	12	no	—
75	C₂×C₄	—	41	4	no	—
76	C₂×C₄	—	41	3	no	—
77	C₂×C₄	—	82	6	no	—
78	C₂×C₄	C₂²×D₄₁	1	3	yes	—
79	C₂×C₄	C₂²×D₄₁	1	3	yes	—
80	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
81	C₂²	—	41	2	no	—
82	C₂²	—	41	2	no	—
83	C₂²	—	41	2	no	—
84	C₂²	C₂³×D₄₁	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	41	6	no	—
87	C₄	—	41	2	no	—
88	C₄	—	82	3	no	—
89	C₄	C₂×C₄×D₄₁	1	6	yes	—
90	C₄	Q₈×D₄₁	1	2	yes	direct product factor
91	C₂	—	41	4	no	—
92	C₂	C₂²×C₄×D₄₁	1	1	yes	characteristic
93	C₂	C₂×Q₈×D₄₁	1	1	yes	characteristic
94	C₂	#41×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₁
commutator	C₂×C₄₁	C₂³×C₄
Frattini	C₂²	C₂³×D₄₁
Fitting	C₄×Q₈×C₄₁	C₂
socle, cosocle	C₂²×C₄₁	C₂⁴
prime radical	C₂²×D₄₁	C₂³
hypercenter	C₄×Q₈	D₄₁
hypocenter	C₄₁	C₂×C₄×Q₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₄₁	C₂	semidirect
3. C₄×Dic₈₂	C₂	semidirect
4. #13050129	C₂	semidirect
7. C₄×Q₈×C₄₁	C₂	semidirect
9. Q₈×D₄₁	C₄	direct (N × H)
22. Q₈×C₄₁	C₂×C₄	semidirect
31. C₄×D₄₁	Q₈	direct (N × H)
32. Dic₈₂	C₂×C₄	semidirect
39. C₄×C₄₁	C₂×Q₈	semidirect
42. Dic₄₁	C₂×Q₈	semidirect
46. D₄₁	C₄×Q₈	direct (N × H)
48. C₄₁	C₂×C₄×Q₈	semidirect
53. C₄×Q₈	D₄₁	direct (N × H)
71. Q₈	C₄×D₄₁	direct (N × H)
90. C₄	Q₈×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₄₁	2
Q₈×Dic₄₁	2
C₄×Dic₈₂	2
#13050129	2
C₄⋊C₄×D₄₁	2
C₄²×D₄₁	2
C₄×Q₈×C₄₁	2
C₂×C₄×Q₈	41

Subgroups — C4×Q8×D41 #14580799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×D₄₁ #14580799