Subgroups — C₄×#10620285 #14580429

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	C₄×Dic₈₂	C₂	1	1	yes	maximal, characteristic
3	#13050097	C₂	1	1	yes	maximal, characteristic
4	#13050088	C₂	1	1	yes	maximal, characteristic
5	#13050087	C₂	1	1	yes	maximal, characteristic
6	C₄×#66491	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×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	C₄⋊C₄×C₄₁	—	2	1	no	—
11	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₄²×C₄₁	—	2	1	no	—
13	C₄²×C₄₁	C₂²	1	1	yes	characteristic
14	#10620285	C₄	1	4	yes	direct product factor
15	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
16	#10620279	—	2	1	no	—
17	C₄×Dic₄₁	—	2	1	no	—
18	C₂×#66491	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	D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
27	C₂×Dic₄₁	—	2	1	no	—
28	C₂×Dic₄₁	—	2	1	no	—
29	Dic₈₂	—	2	1	no	—
30	Dic₈₂	C₂×C₄	1	2	yes	—
31	#66491	—	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	—	2	1	no	—
36	C₄×C₄₁	—	4	1	no	—
37	C₄×C₄₁	Q₁₆	1	2	yes	complemented
38	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₄₁	#41	1	1	yes	characteristic
40	Dic₄₁	—	2	2	no	—
41	Dic₄₁	—	4	1	no	—
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	D₄₁	1	1	yes	characteristic
50	#107	—	41	1	no	—
51	#103	—	41	1	no	—
52	#103	—	41	1	no	—
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	—	41	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	41	1	no	—
61	C₄⋊C₄	—	82	1	no	—
62	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
63	C₄²	—	2	1	no	—
64	C₄²	—	82	1	no	—
65	C₄²	C₂×D₄₁	1	1	yes	characteristic
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	—	82	1	no	—
73	C₂×C₄	—	82	1	no	—
74	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
77	C₈	—	41	2	no	—
78	C₈	—	82	1	no	—
79	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	2	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	82	2	no	—
84	C₄	—	164	1	no	—
85	C₄	#10620285	1	2	yes	direct product factor
86	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
87	C₄	#10620306	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₄₁	1	1	yes	characteristic
89	C₂	C₂×#10620285	1	1	yes	characteristic
90	C₂	#13050184	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₁
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₄×Q₈×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄×Q₈	D₄₁
hypocenter	C₄₁	C₄×Q₁₆
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
14. #10620285	C₄	direct (N × H)
37. C₄×C₄₁	Q₁₆	semidirect
46. C₄₁	C₄×Q₁₆	semidirect
85. C₄	#10620285	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×#10620285	2
C₄×Dic₈₂	2
#13050097	2
#13050088	2
#13050087	2
C₄×#66491	2
C₄×Q₈×C₄₁	2
C₄×Q₁₆	41

Subgroups — C4×#10620285 #14580429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10620285 #14580429