Subgroups — D₄₁⋊#108 #14581349

Order 2624.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₁⋊M₁₆	C₂	1	2	yes	maximal
2	#13050235	C₂	1	2	yes	maximal, complemented
3	#13050234	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
6	#10620301	—	2	2	no	—
7	#10620297	C₂²	1	4	yes	—
8	#10620296	—	2	2	no	—
9	C₂×C₈×C₄₁	C₄	1	1	yes	characteristic
10	C₂×#66491	C₄	1	1	yes	characteristic
11	C₈×D₄₁	C₄	1	1	yes	characteristic
12	C₈×D₄₁	C₄	1	1	yes	characteristic
13	C₈×D₄₁	C₂²	1	1	yes	characteristic
14	C₈×D₄₁	C₂²	1	1	yes	characteristic
15	C₂²×D₄₁	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₁	D₄	1	1	yes	characteristic
18	C₄×D₄₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₄₁	D₄	1	1	yes	characteristic
20	C₄×D₄₁	Q₈	1	1	yes	characteristic
21	C₄×D₄₁	C₂³	1	1	yes	characteristic
22	#66493	—	2	4	no	—
23	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
25	#66491	C₂×C₄	1	1	yes	characteristic
26	#66491	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₄₁	—	2	2	no	—
29	C₂×D₄₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₄₁	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
33	Dic₄₁	C₄⋊C₄	1	1	yes	characteristic
34	Dic₄₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄₁	—	2	1	no	—
36	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₄₁	—	2	1	no	—
38	D₄₁	#108	1	2	yes	complemented
39	C₂×#108	—	41	1	no	maximal, Sylow
40	C₄₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	41	2	no	—
42	C₂²×C₈	—	41	1	no	—
43	#108	—	41	2	no	—
44	#108	—	41	2	no	—
45	C₂²×C₄	—	41	1	no	—
46	M₁₆	—	41	4	no	—
47	M₁₆	—	82	2	no	—
48	C₂×C₈	—	41	1	no	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	41	1	no	—
51	C₂×C₈	—	41	1	no	—
52	C₂×C₈	—	41	1	no	—
53	C₂×C₈	—	82	2	no	—
54	C₂×C₈	#4223	1	1	yes	characteristic
55	C₂³	—	41	1	no	—
56	C₂×C₄	—	41	1	no	—
57	C₂×C₄	—	41	1	no	—
58	C₂×C₄	—	41	1	no	—
59	C₂×C₄	—	41	1	no	—
60	C₂×C₄	—	41	1	no	—
61	C₂×C₄	C₂×#4223	1	1	yes	characteristic
62	C₈	—	41	1	no	—
63	C₈	—	41	1	no	—
64	C₈	—	82	4	no	—
65	C₈	C₂×#4223	1	1	yes	characteristic
66	C₈	C₂×#4223	1	1	yes	characteristic
67	C₂²	—	41	1	no	—
68	C₂²	—	41	1	no	—
69	C₂²	—	82	2	no	—
70	C₂²	C₄⋊#4223	1	1	yes	characteristic
71	C₄	—	41	1	no	—
72	C₄	—	41	1	no	—
73	C₄	C₄⋊#4223	1	1	yes	characteristic
74	C₄	C₂²×#4223	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	41	2	no	—
77	C₂	—	82	1	no	—
78	C₂	C₂×C₄⋊#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#4223
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₄	C₂²×#4223
Fitting	C₂×C₈×C₄₁	C₄
socle	C₂×C₄₁	C₂×C₄⋊C₄
prime radical	C₂²×D₄₁	Q₈
cosocle	C₄×D₄₁	C₂³
hypercenter	C₂×C₈	#4223
hypocenter	C₄₁	C₂×#108
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #13050235	C₂	semidirect
3. #13050234	C₂	semidirect
38. D₄₁	#108	semidirect
40. C₄₁	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₄₁⋊M₁₆	2
#13050235	2
#13050234	2
C₂×C₈×D₄₁	2
C₂×#108	41

Subgroups — D41⋊#108 #14581349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁⋊#108 #14581349