Subgroups — #14580359

Order 2624.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620277	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050093	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₁	C₄	1	2	yes	—
7	M₁₆×C₄₁	—	2	2	no	—
8	C₂×C₈×C₄₁	C₂²	1	2	yes	—
9	C₄×Dic₄₁	C₄	1	1	yes	characteristic
10	C₄×Dic₄₁	C₄	1	1	yes	characteristic
11	C₄×Dic₄₁	C₂²	1	2	yes	—
12	#10620277	—	2	2	no	—
13	C₂×#66491	C₂²	1	2	yes	—
14	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁	D₄	1	2	yes	—
17	C₂×C₄×C₄₁	Q₈	1	2	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	—	2	4	no	—
20	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
21	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
22	C₈×C₄₁	—	2	2	no	—
23	#66491	—	2	2	no	—
24	C₂²×C₄₁	—	2	2	no	—
25	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
26	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
28	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
29	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
30	Dic₄₁	—	2	2	no	—
31	Dic₄₁	M₁₆	1	4	yes	complemented
32	C₂×C₄₁	—	2	2	no	—
33	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄₁	C₂×M₁₆	1	2	yes	—
35	#423	—	41	1	no	maximal, Sylow
36	C₄₁	#423	1	1	yes	characteristic, complemented, Sylow
37	C₂×M₁₆	—	41	1	no	—
38	C₂×M₁₆	D₄₁	1	1	yes	characteristic
39	C₂×C₄²	—	41	1	no	—
40	C₄⋊C₈	—	41	4	no	—
41	C₂²×C₄	—	41	2	no	—
42	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
43	M₁₆	—	2	2	no	—
44	M₁₆	—	82	2	no	—
45	C₂×C₈	—	41	2	no	—
46	C₂×C₈	C₂×D₄₁	1	2	yes	—
47	C₄²	—	41	1	no	—
48	C₄²	—	41	1	no	—
49	C₄²	—	41	2	no	—
50	C₂³	C₄×D₄₁	1	1	yes	characteristic
51	C₂×C₄	—	41	2	no	—
52	C₂×C₄	—	41	2	no	—
53	C₂×C₄	—	82	4	no	—
54	C₂×C₄	Dic₈₂	1	2	yes	—
55	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
57	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	82	2	no	—
60	C₂²	—	2	2	no	—
61	C₂²	#10620279	1	2	yes	—
62	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
63	C₄	—	41	4	no	—
64	C₄	—	82	2	no	—
65	C₄	#10620279	1	2	yes	—
66	C₄	C₂×Dic₈₂	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	C₂×#10620279	1	1	yes	characteristic
70	C₂	M₁₆×D₄₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₂×M₁₆×C₄₁	C₂
prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂×M₁₆	D₄₁
hypocenter	C₄₁	#423
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13050093	C₂	semidirect
31. Dic₄₁	M₁₆	semidirect
36. C₄₁	#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620277	2
C₂×C₄×Dic₄₁	2
#13050093	2
C₂×M₁₆×C₄₁	2
#423	41