Subgroups — D₄₁⋊#101 #14581321

Order 2624.

146 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	#13050225	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₁	C₄	1	1	yes	characteristic
5	Q₈×D₄₁	—	2	2	no	—
6	Q₈×D₄₁	—	2	2	no	—
7	C₂×C₄×D₄₁	C₄	1	2	yes	—
8	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₂	C₄	1	1	yes	characteristic
10	C₂×Dic₈₂	C₂²	1	2	yes	—
11	#10620301	C₂²	1	4	yes	—
12	#10620297	—	2	2	no	—
13	#10620296	—	2	2	no	—
14	C₂²×D₄₁	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₄₁	—	2	2	no	—
16	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
19	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
20	C₄×D₄₁	—	2	2	no	—
21	C₄×D₄₁	—	2	2	no	—
22	C₄×D₄₁	D₄	1	2	yes	—
23	C₄×D₄₁	D₄	1	2	yes	—
24	Dic₈₂	—	2	2	no	—
25	Dic₈₂	—	2	4	no	—
26	#66493	—	2	4	no	—
27	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₁	—	2	2	no	—
29	C₂×D₄₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₄₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₁	—	2	2	no	—
32	C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
33	Dic₄₁	—	2	2	no	—
34	Dic₄₁	C₂×D₄	1	2	yes	—
35	C₂×C₄₁	—	2	1	no	—
36	C₂×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₄₁	—	2	1	no	—
38	D₄₁	#101	1	2	yes	complemented
39	C₂×#101	—	41	1	no	maximal, Sylow
40	C₄₁	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂²×Q₈	—	41	1	no	—
42	C₂×M₁₆	—	41	2	no	—
43	#101	—	41	4	no	—
44	C₂×Q₈	—	41	2	no	—
45	C₂×Q₈	—	41	1	no	—
46	C₂×Q₈	—	82	2	no	—
47	C₂×Q₈	—	82	2	no	—
48	C₂×Q₈	#4223	1	1	yes	characteristic
49	C₂²×C₄	—	41	1	no	—
50	C₂²×C₄	—	41	2	no	—
51	M₁₆	—	41	4	no	—
52	M₁₆	—	82	2	no	—
53	C₂×C₈	—	82	2	no	—
54	C₂³	—	41	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	82	4	no	—
57	Q₈	—	82	2	no	—
58	C₂×C₄	—	41	1	no	—
59	C₂×C₄	—	41	2	no	—
60	C₂×C₄	—	41	2	no	—
61	C₂×C₄	—	41	2	no	—
62	C₂×C₄	—	82	2	no	—
63	C₂×C₄	—	82	2	no	—
64	C₂×C₄	C₂×#4223	1	2	yes	—
65	C₂×C₄	C₂×#4223	1	1	yes	characteristic
66	C₈	—	82	4	no	—
67	C₂²	—	41	1	no	—
68	C₂²	—	41	1	no	—
69	C₂²	—	82	2	no	—
70	C₂²	C₂²×#4223	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	41	2	no	—
73	C₄	—	82	2	no	—
74	C₄	C₂²⋊#4223	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	41	2	no	—
77	C₂	—	82	1	no	—
78	C₂	C₂×C₂²⋊#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#4223
commutator	C₂²×C₄₁	C₂²×C₄
Frattini	C₂²	C₂²×#4223
Fitting	C₂×Q₈×C₄₁	C₄
socle	C₂×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂²×D₄₁	C₂×C₄
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₂×Q₈	#4223
hypocenter	C₄₁	C₂×#101
LCS	G ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #13050225	C₂	semidirect
38. D₄₁	#101	semidirect
40. C₄₁	C₂×#101	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
#13050225	2
C₂×Q₈×D₄₁	2
C₂×#101	41

Subgroups — D41⋊#101 #14581321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁⋊#101 #14581321