Subgroups — #14581382

Order 2624.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050252	C₂	1	2	yes	maximal, complemented
2	#13050234	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050229	C₂	1	2	yes	maximal, complemented
4	#13050218	C₂	1	1	yes	maximal, characteristic, complemented
5	#13050187	C₂	1	1	yes	maximal, characteristic
6	#10620310	C₂²	1	2	yes	—
7	C₄×#4223	C₂²	1	1	yes	characteristic
8	#10620297	—	2	2	no	—
9	#10620297	C₂²	1	2	yes	—
10	#10620296	—	2	2	no	—
11	#10620296	C₂²	1	1	yes	characteristic
12	Q₁₆×C₄₁	C₄	1	1	yes	characteristic, complemented
13	#10620284	C₄	1	2	yes	complemented
14	D₃₂₈	C₄	1	1	yes	characteristic, complemented
15	C₈×D₄₁	C₂²	1	1	yes	characteristic
16	C₂×#4223	—	2	1	no	—
17	Q₈×C₄₁	C₂×C₄	1	2	yes	—
18	D₁₆₄	—	2	2	no	—
19	D₁₆₄	C₂×C₄	1	2	yes	—
20	C₄×D₄₁	—	2	2	no	—
21	C₄×D₄₁	C₂³	1	1	yes	characteristic
22	#66493	—	2	2	no	—
23	#66493	D₄	1	2	yes	—
24	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
25	#66491	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄₁	—	2	2	no	—
27	C₂×D₄₁	#41	1	1	yes	characteristic
28	#4223	—	4	1	no	—
29	C₄×C₄₁	—	2	2	no	—
30	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	Dic₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
33	D₄₁	—	2	1	no	—
34	D₄₁	—	4	2	no	—
35	#444	—	41	1	no	maximal, Sylow
36	C₄₁	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	—	41	1	no	—
38	#131	—	41	2	no	—
39	#108	—	41	1	no	—
40	#104	—	41	2	no	—
41	#97	—	41	1	no	—
42	#41	—	41	2	no	—
43	Q₁₆	#4223	1	1	yes	characteristic, complemented
44	SD₁₆	—	41	2	no	—
45	D₈	—	41	1	no	—
46	M₁₆	—	41	2	no	—
47	M₁₆	—	82	2	no	—
48	C₂×C₈	—	41	1	no	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	82	2	no	—
51	C₄²	—	41	1	no	—
52	Q₈	C₂×#4223	1	2	yes	—
53	D₄	—	41	2	no	—
54	D₄	—	82	2	no	—
55	C₂×C₄	—	41	1	no	—
56	C₂×C₄	—	82	2	no	—
57	C₂×C₄	—	82	1	no	—
58	C₈	—	41	2	no	—
59	C₈	—	41	1	no	—
60	C₈	—	82	2	no	—
61	C₈	C₂×#4223	1	1	yes	characteristic
62	C₂²	—	41	1	no	—
63	C₂²	—	82	2	no	—
64	C₄	—	2	2	no	—
65	C₄	—	41	1	no	—
66	C₄	—	164	1	no	—
67	C₄	C₂²×#4223	1	1	yes	characteristic
68	C₂	—	82	1	no	—
69	C₂	—	164	2	no	—
70	C₂	D₄×#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#4223
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₄	C₂²×#4223
Fitting	Q₁₆×C₄₁	C₄
socle	C₂×C₄₁	C₄×D₄
prime radical	#13050187	C₂
cosocle	C₄×D₄₁	C₂³
hypercenter	Q₁₆	#4223
hypocenter	C₄₁	#444
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #13050252	C₂	semidirect
2. #13050234	C₂	semidirect
3. #13050229	C₂	semidirect
4. #13050218	C₂	semidirect
12. Q₁₆×C₄₁	C₄	semidirect
13. #10620284	C₄	semidirect
14. D₃₂₈	C₄	semidirect
36. C₄₁	#444	semidirect
43. Q₁₆	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050252	2
#13050234	2
#13050229	2
#13050218	2
#13050187	2
#444	41