Subgroups — #14580452

Order 2624.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050186	C₂	1	1	yes	maximal, characteristic
2	#13050172	C₂	1	2	yes	maximal, complemented
3	#13050090	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#108×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10620306	C₂²	1	2	yes	—
7	M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
10	C₂×#66491	C₂²	1	1	yes	characteristic
11	Dic₁₆₄	C₄	1	1	yes	characteristic, complemented
12	D₃₂₈	C₄	1	1	yes	characteristic, complemented
13	#10620273	C₄	1	2	yes	complemented
14	#10620272	—	2	2	no	—
15	C₈×D₄₁	—	2	2	no	—
16	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
17	C₂²⋊D₄₁	—	2	2	no	—
18	C₂×Dic₄₁	—	2	1	no	—
19	D₁₆₄	C₂×C₄	1	2	yes	—
20	C₄×D₄₁	—	2	2	no	—
21	Dic₈₂	C₂×C₄	1	2	yes	—
22	C₈×C₄₁	—	2	2	no	—
23	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
25	#66491	D₄	1	1	yes	characteristic
26	#66491	D₄	1	1	yes	characteristic
27	C₂²×C₄₁	#41	1	1	yes	characteristic
28	C₂×D₄₁	—	2	2	no	—
29	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
31	Dic₄₁	—	2	2	no	—
32	Dic₄₁	—	2	2	no	—
33	C₂×C₄₁	—	2	1	no	—
34	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
35	D₄₁	—	4	2	no	—
36	#443	—	41	1	no	maximal, Sylow
37	C₄₁	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	—	41	1	no	—
39	#131	—	41	2	no	—
40	#108	D₄₁	1	1	yes	characteristic, complemented
41	#104	—	41	2	no	—
42	C₄×C₈	—	41	1	no	—
43	#41	—	41	2	no	—
44	Q₁₆	—	41	1	no	—
45	SD₁₆	—	41	2	no	—
46	D₈	—	41	1	no	—
47	M₁₆	—	82	2	no	—
48	M₁₆	C₂×D₄₁	1	2	yes	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	82	2	no	—
51	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
52	C₄²	—	41	1	no	—
53	Q₈	—	41	2	no	—
54	D₄	—	41	2	no	—
55	D₄	—	82	2	no	—
56	C₂×C₄	—	82	1	no	—
57	C₂×C₄	—	82	2	no	—
58	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	41	1	no	—
61	C₈	—	41	1	no	—
62	C₈	C₄×D₄₁	1	1	yes	characteristic
63	C₈	C₄×D₄₁	1	1	yes	characteristic
64	C₂²	—	82	2	no	—
65	C₂²	#10620310	1	1	yes	characteristic
66	C₄	—	82	2	no	—
67	C₄	—	82	2	no	—
68	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
69	C₄	D₄×D₄₁	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	164	2	no	—
72	C₂	#13050126	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₁
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#108×C₄₁	C₂
socle	C₂×C₄₁	C₄×D₄
prime radical	#13050186	C₂
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	#108	D₄₁
hypocenter	C₄₁	#443
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #13050172	C₂	semidirect
3. #13050090	C₂	semidirect
4. C₈×Dic₄₁	C₂	semidirect
5. #108×C₄₁	C₂	semidirect
11. Dic₁₆₄	C₄	semidirect
12. D₃₂₈	C₄	semidirect
13. #10620273	C₄	semidirect
37. C₄₁	#443	semidirect
40. #108	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050186	2
#13050172	2
#13050090	2
C₈×Dic₄₁	2
#108×C₄₁	2
#443	41