Subgroups — #14581062

Order 2624.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050163	C₂	1	3	yes	maximal
2	#13050156	C₂	1	3	yes	maximal
3	#13050155	C₂	1	3	yes	maximal
4	Q₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
5	Q₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₈₂	C₂	1	3	yes	maximal
7	C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₂	C₂²	1	3	yes	—
10	C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
11	C₄²×C₄₁	C₂²	1	3	yes	—
12	C₄⋊Dic₄₁	C₂²	1	3	yes	—
13	C₄⋊Dic₄₁	C₂²	1	3	yes	—
14	C₄⋊Dic₄₁	C₂²	1	3	yes	—
15	#10620279	C₂²	1	1	yes	characteristic
16	#10620279	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	Q₈×C₄₁	Q₈	1	4	yes	complemented
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₄₁	C₂³	1	3	yes	—
23	C₂×C₄×C₄₁	C₂³	1	3	yes	—
24	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₁	C₂³	1	3	yes	—
26	C₂×Dic₄₁	C₂³	1	3	yes	—
27	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
28	Dic₈₂	—	2	6	no	—
29	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
30	C₄×C₄₁	—	2	3	no	—
31	C₄×C₄₁	—	2	1	no	—
32	C₄×C₄₁	C₂×Q₈	1	6	yes	—
33	Dic₄₁	—	2	3	no	—
34	Dic₄₁	—	2	1	no	—
35	Dic₄₁	—	2	3	no	—
36	Dic₄₁	#41	1	2	yes	—
37	C₂×C₄₁	C₂²×Q₈	1	1	yes	characteristic
38	C₂×C₄₁	C₂×#41	1	1	yes	characteristic
39	C₂×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
40	#557	—	41	1	no	maximal, Sylow
41	C₄₁	#557	1	1	yes	characteristic, complemented, Sylow
42	C₄⋊Q₈	—	41	3	no	—
43	#125	—	41	3	no	—
44	#125	—	41	3	no	—
45	C₄×Q₈	—	41	1	no	—
46	C₄×Q₈	—	41	1	no	—
47	C₄×Q₈	—	41	3	no	—
48	C₄×Q₈	D₄₁	1	1	yes	characteristic
49	C₂×Q₈	—	41	3	no	—
50	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
51	C₄⋊C₄	—	41	1	no	—
52	C₄⋊C₄	—	41	3	no	—
53	C₄⋊C₄	—	41	3	no	—
54	C₄⋊C₄	—	41	3	no	—
55	C₄⋊C₄	—	41	3	no	—
56	C₄⋊C₄	—	41	6	no	—
57	C₄⋊C₄	C₂×D₄₁	1	3	yes	—
58	C₄²	—	41	3	no	—
59	C₄²	—	41	3	no	—
60	C₄²	C₂×D₄₁	1	3	yes	—
61	Q₈	—	82	6	no	—
62	Q₈	Dic₈₂	1	4	yes	complemented
63	C₂×C₄	—	41	1	no	—
64	C₂×C₄	—	41	1	no	—
65	C₂×C₄	—	41	3	no	—
66	C₂×C₄	—	41	3	no	—
67	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
68	C₂×C₄	C₂²×D₄₁	1	3	yes	—
69	C₂×C₄	C₂²×D₄₁	1	3	yes	—
70	C₂²	C₂³×D₄₁	1	1	yes	characteristic
71	C₄	—	2	3	no	—
72	C₄	—	2	1	no	—
73	C₄	—	41	2	no	—
74	C₄	—	82	3	no	—
75	C₄	—	82	1	no	—
76	C₄	—	82	3	no	—
77	C₄	C₂×Dic₈₂	1	6	yes	—
78	C₂	C₂²×Dic₈₂	1	1	yes	characteristic
79	C₂	#41×D₄₁	1	1	yes	characteristic
80	C₂	#13050212	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₁
commutator, socle, prime radical, cosocle	C₂²×C₄₁	C₂⁴
Fitting	C₄×Q₈×C₄₁	C₂
hypercenter	C₄×Q₈	D₄₁
hypocenter	C₄₁	#557
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
20. Q₈×C₄₁	Q₈	semidirect
41. C₄₁	#557	semidirect
62. Q₈	Dic₈₂	semidirect

Maximal subgroups

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

subgroup	index
#13050163	2
#13050156	2
#13050155	2
Q₈×Dic₄₁	2
C₄×Dic₈₂	2
C₄×Q₈×C₄₁	2
#557	41