Subgroups — #14580726

Order 2624.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620284	C₂	1	2	yes	maximal, complemented
2	C₂×#10620282	C₂	1	2	yes	maximal, complemented
3	#13050161	C₂	1	1	yes	maximal, characteristic, complemented
4	#13050075	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×D₁₆₄	—	2	2	no	—
9	C₂×D₁₆₄	C₂²	1	2	yes	—
10	C₂²⋊C₄×C₄₁	—	2	2	no	—
11	C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	#10620284	—	2	4	no	—
13	#10620282	—	2	4	no	—
14	C₂×#66491	C₂²	1	2	yes	—
15	C₂³×C₄₁	—	2	1	no	—
16	C₂²×D₄₁	—	2	2	no	—
17	Q₈×C₄₁	—	2	2	no	—
18	D₄×C₄₁	—	2	2	no	—
19	C₂×C₄×C₄₁	—	2	1	no	—
20	C₂×C₄×C₄₁	D₄	1	2	yes	—
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	D₁₆₄	—	2	2	no	—
23	D₁₆₄	—	2	2	no	—
24	D₁₆₄	—	4	4	no	—
25	#66491	D₄	1	4	yes	complemented
26	C₂²×C₄₁	—	4	1	no	—
27	C₂²×C₄₁	—	4	2	no	—
28	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
29	C₂×D₄₁	—	4	2	no	—
30	C₂×D₄₁	—	4	4	no	—
31	C₄×C₄₁	—	2	2	no	—
32	C₄×C₄₁	—	4	1	no	—
33	C₄×C₄₁	C₂×D₄	1	2	yes	—
34	C₂×C₄₁	—	8	1	no	—
35	C₂×C₄₁	#127	1	1	yes	characteristic
36	C₂×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
37	D₄₁	—	8	2	no	—
38	#496	—	41	1	no	maximal, Sylow
39	C₄₁	#496	1	1	yes	characteristic, complemented, Sylow
40	C₂×SD₁₆	—	41	2	no	—
41	C₂×D₈	—	41	2	no	—
42	#127	—	41	1	no	—
43	#124	D₄₁	1	1	yes	characteristic, complemented
44	#97	—	41	1	no	—
45	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
46	C₂×D₄	—	41	2	no	—
47	C₂×D₄	—	82	2	no	—
48	C₂×D₄	C₂×D₄₁	1	1	yes	characteristic
49	SD₁₆	—	82	4	no	—
50	D₈	—	82	4	no	—
51	C₂×C₈	—	41	2	no	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂×D₄₁	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	C₂³	—	82	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	82	2	no	—
59	D₄	—	82	2	no	—
60	D₄	—	164	4	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
63	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
64	C₈	—	41	4	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	—	164	2	no	—
68	C₂²	—	164	4	no	—
69	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	4	1	no	—
72	C₄	D₄×D₄₁	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	—	328	2	no	—
75	C₂	#13050160	1	1	yes	characteristic
76	C₂	#13050189	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#124×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
hypercenter	#124	D₄₁
hypocenter	C₄₁	#496
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. C₂×#10620284	C₂	semidirect
2. C₂×#10620282	C₂	semidirect
3. #13050161	C₂	semidirect
4. #13050075	C₂	semidirect
5. #124×C₄₁	C₂	semidirect
25. #66491	D₄	semidirect
39. C₄₁	#496	semidirect
43. #124	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620284	2
C₂×#10620282	2
#13050161	2
#13050075	2
#124×C₄₁	2
#496	41