Subgroups — D₄₁⋊#100 #14581319

Order 2624.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₁⋊M₁₆	C₂	1	2	yes	maximal, complemented
2	#13050224	C₂	1	4	yes	maximal, complemented
3	C₂×D₄×D₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×D₄₁	C₄	1	2	yes	—
5	C₂×D₄×C₄₁	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊D₄₁	C₂²	1	2	yes	—
7	D₄×D₄₁	—	2	2	no	—
8	D₄×D₄₁	—	2	2	no	—
9	C₂×D₁₆₄	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
11	#10620301	C₂²	1	4	yes	complemented
12	#10620297	—	2	2	no	—
13	#10620296	—	2	2	no	—
14	C₂³×C₄₁	C₂×C₄	1	2	yes	—
15	C₂²×D₄₁	—	2	2	no	—
16	C₂²×D₄₁	—	2	2	no	—
17	C₂²×D₄₁	—	4	4	no	—
18	C₂²×D₄₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₄₁	C₂×C₄	1	2	yes	—
20	D₄×C₄₁	—	2	2	no	—
21	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
22	C₂²⋊D₄₁	—	2	4	no	—
23	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
24	D₁₆₄	—	2	2	no	—
25	C₄×D₄₁	D₄	1	2	yes	—
26	C₄×D₄₁	D₄	1	2	yes	—
27	#66493	—	2	4	no	—
28	C₂²×C₄₁	—	2	2	no	—
29	C₂²×C₄₁	—	4	2	no	—
30	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₄₁	—	2	2	no	—
32	C₂×D₄₁	—	2	2	no	—
33	C₂×D₄₁	—	4	4	no	—
34	C₂×D₄₁	—	4	4	no	—
35	C₂×D₄₁	—	4	2	no	—
36	C₂×D₄₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×D₄₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
39	Dic₄₁	C₂×D₄	1	2	yes	—
40	C₂×C₄₁	—	2	1	no	—
41	C₂×C₄₁	—	4	2	no	—
42	C₂×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	D₄₁	—	2	1	no	—
44	D₄₁	—	4	2	no	—
45	D₄₁	#100	1	2	yes	complemented
46	C₂×#100	—	41	1	no	maximal, Sylow
47	C₄₁	C₂×#100	1	1	yes	characteristic, complemented, Sylow
48	C₂²×D₄	—	41	1	no	—
49	C₂×M₁₆	—	41	2	no	—
50	#100	—	41	4	no	—
51	C₂⁴	—	41	2	no	—
52	C₂×D₄	—	41	2	no	—
53	C₂×D₄	—	41	1	no	—
54	C₂×D₄	—	82	2	no	—
55	C₂×D₄	—	82	2	no	—
56	C₂×D₄	#4223	1	1	yes	characteristic
57	C₂²×C₄	—	41	1	no	—
58	M₁₆	—	41	4	no	—
59	M₁₆	—	82	2	no	—
60	C₂×C₈	—	82	2	no	—
61	C₂³	—	41	1	no	—
62	C₂³	—	41	2	no	—
63	C₂³	—	82	2	no	—
64	C₂³	—	82	2	no	—
65	C₂³	—	164	4	no	—
66	C₂³	C₂×#4223	1	2	yes	—
67	D₄	—	2	2	no	—
68	D₄	—	82	4	no	—
69	D₄	—	82	2	no	—
70	C₂×C₄	—	41	1	no	—
71	C₂×C₄	—	41	2	no	—
72	C₂×C₄	—	41	2	no	—
73	C₂×C₄	C₂×#4223	1	1	yes	characteristic
74	C₈	—	82	4	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	4	2	no	—
77	C₂²	—	41	1	no	—
78	C₂²	—	41	1	no	—
79	C₂²	—	82	2	no	—
80	C₂²	—	82	2	no	—
81	C₂²	—	164	2	no	—
82	C₂²	—	164	4	no	—
83	C₂²	—	164	4	no	—
84	C₂²	C₂²×#4223	1	1	yes	characteristic
85	C₄	—	41	2	no	—
86	C₄	C₂²⋊#4223	1	2	yes	—
87	C₂	—	2	1	no	—
88	C₂	—	4	2	no	—
89	C₂	—	41	2	no	—
90	C₂	—	82	1	no	—
91	C₂	—	164	2	no	—
92	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×D₄×C₄₁	C₄
socle	C₂×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂×D₄×D₄₁	C₂
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₂×D₄	#4223
hypocenter	C₄₁	C₂×#100
LCS	G ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. D₄₁⋊M₁₆	C₂	semidirect
2. #13050224	C₂	semidirect
11. #10620301	C₂²	semidirect
45. D₄₁	#100	semidirect
47. C₄₁	C₂×#100	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
#13050224	2
C₂×D₄×D₄₁	2
C₂×#100	41

Subgroups — D41⋊#100 #14581319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁⋊#100 #14581319