Subgroups — #14580428

Order 2624.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620285	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050129	C₂	1	1	yes	maximal, characteristic
4	#13050097	C₂	1	1	yes	maximal, characteristic
5	#13050089	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	#10620285	C₄	1	4	yes	complemented
13	C₄⋊Dic₄₁	—	2	1	no	—
14	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
15	#10620279	—	2	1	no	—
16	C₄×Dic₄₁	—	2	1	no	—
17	C₄×Dic₄₁	—	2	1	no	—
18	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
19	C₂×#66491	C₂²	1	1	yes	characteristic
20	Q₈×C₄₁	—	2	1	no	—
21	Q₈×C₄₁	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₁	—	2	1	no	—
23	C₂×C₄×C₄₁	—	2	1	no	—
24	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₁	—	2	1	no	—
26	C₂×Dic₄₁	—	2	1	no	—
27	C₂×Dic₄₁	D₄	1	1	yes	characteristic
28	C₂×Dic₄₁	D₄	1	1	yes	characteristic
29	Dic₈₂	—	2	1	no	—
30	Dic₈₂	C₂×C₄	1	2	yes	—
31	C₈×C₄₁	—	2	1	no	—
32	#66491	C₂×C₄	1	2	yes	—
33	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₁	—	2	2	no	—
35	C₄×C₄₁	—	4	1	no	—
36	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₄₁	#41	1	1	yes	characteristic
38	Dic₄₁	—	2	2	no	—
39	Dic₄₁	—	2	1	no	—
40	Dic₄₁	—	4	1	no	—
41	Dic₄₁	Q₁₆	1	2	yes	complemented
42	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
43	C₂×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₄₁	#135	1	1	yes	characteristic
45	C₄×Q₁₆	—	41	1	no	maximal, Sylow
46	C₄₁	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₁₆	—	41	1	no	—
48	C₄×Q₈	—	41	1	no	—
49	C₄×Q₈	—	41	1	no	—
50	#107	—	41	1	no	—
51	#103	—	41	1	no	—
52	#103	D₄₁	1	1	yes	characteristic
53	C₄×C₈	—	41	1	no	—
54	C₂×Q₈	—	41	1	no	—
55	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
56	Q₁₆	—	41	4	no	—
57	C₂×C₈	—	41	1	no	—
58	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
59	C₄⋊C₄	—	41	1	no	—
60	C₄⋊C₄	—	82	1	no	—
61	C₄⋊C₄	—	82	1	no	—
62	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
63	C₄²	—	41	1	no	—
64	C₄²	—	82	1	no	—
65	C₄²	—	82	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	41	2	no	—
68	Q₈	—	82	1	no	—
69	Q₈	C₄×D₄₁	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	41	1	no	—
73	C₂×C₄	—	41	1	no	—
74	C₂×C₄	—	82	1	no	—
75	C₂×C₄	—	82	1	no	—
76	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	41	2	no	—
79	C₂²	D₄×D₄₁	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	41	2	no	—
83	C₄	—	82	2	no	—
84	C₄	—	82	1	no	—
85	C₄	—	164	1	no	—
86	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
87	C₄	#10620308	1	1	yes	characteristic
88	C₂	#13050124	1	1	yes	characteristic
89	C₂	Q₁₆×D₄₁	1	1	yes	characteristic
90	C₂	#13050185	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#103×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	#103	D₄₁
hypocenter	C₄₁	C₄×Q₁₆
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
12. #10620285	C₄	semidirect
41. Dic₄₁	Q₁₆	semidirect
46. C₄₁	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620285	2
Q₈×Dic₄₁	2
#13050129	2
#13050097	2
#13050089	2
C₈×Dic₄₁	2
#103×C₄₁	2
C₄×Q₁₆	41