Subgroups — #14580201

Order 2624.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	#13050071	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	2	yes	—
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₂²	1	2	yes	—
8	C₂²×Dic₄₁	C₂²	1	2	yes	—
9	C₄⋊C₄×C₄₁	—	2	2	no	—
10	C₄⋊Dic₄₁	—	2	2	no	—
11	C₄×Dic₄₁	C₄	1	4	yes	complemented
12	C₂³×C₄₁	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₄₁	—	2	2	no	—
14	C₂×C₄×C₄₁	—	2	4	no	—
15	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₁	D₄	1	2	yes	—
17	C₂×C₄×C₄₁	Q₈	1	2	yes	—
18	C₂×Dic₄₁	—	2	2	no	—
19	C₂×Dic₄₁	—	2	2	no	—
20	C₂×Dic₄₁	—	2	2	no	—
21	C₂×Dic₄₁	—	2	4	no	—
22	C₂×Dic₄₁	C₂×C₄	1	4	yes	—
23	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄₁	C₂×Q₈	1	1	yes	characteristic
26	C₂²×C₄₁	#41	1	2	yes	—
27	C₂²×C₄₁	#41	1	2	yes	—
28	C₄×C₄₁	—	4	2	no	—
29	C₄×C₄₁	C₄⋊C₄	1	4	yes	—
30	Dic₄₁	—	2	4	no	—
31	Dic₄₁	—	4	2	no	—
32	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄₁	#117	1	2	yes	—
34	C₂×C₄₁	#124	1	1	yes	characteristic
35	C₂×C₄₁	#124	1	1	yes	characteristic
36	C₂×C₄₁	#125	1	2	yes	—
37	#382	—	41	1	no	maximal, Sylow
38	C₄₁	#382	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄⋊C₄	—	41	1	no	—
40	C₂×C₄⋊C₄	D₄₁	1	1	yes	characteristic
41	C₂×C₄²	—	41	1	no	—
42	#95	—	41	4	no	—
43	C₂²×C₄	—	41	2	no	—
44	C₂²×C₄	—	41	2	no	—
45	C₂²×C₄	C₂×D₄₁	1	2	yes	—
46	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
47	C₄⋊C₄	—	2	2	no	—
48	C₄⋊C₄	—	82	2	no	—
49	C₄²	—	41	4	no	—
50	C₂³	C₂²×D₄₁	1	1	yes	characteristic
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	41	4	no	—
54	C₂×C₄	—	82	2	no	—
55	C₂×C₄	—	82	2	no	—
56	C₂×C₄	—	82	4	no	—
57	C₂×C₄	—	82	2	no	—
58	C₂×C₄	Dic₈₂	1	2	yes	—
59	C₂×C₄	C₄×D₄₁	1	2	yes	—
60	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
61	C₂²	C₂×Dic₈₂	1	1	yes	characteristic
62	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
63	C₂²	#10620308	1	2	yes	—
64	C₂²	#10620310	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	82	4	no	—
68	C₄	—	164	2	no	—
69	C₄	#10620279	1	4	yes	—
70	C₂	C₂×#10620279	1	1	yes	characteristic
71	C₂	#13050122	1	2	yes	—
72	C₂	#13050151	1	1	yes	characteristic
73	C₂	#13050153	1	1	yes	characteristic
74	C₂	#13050155	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₁
commutator	C₂²×C₄₁	C₂²×C₄
Fitting	C₂×C₄⋊C₄×C₄₁	C₂
socle, prime radical, cosocle	C₂³×C₄₁	C₂³
hypercenter	C₂×C₄⋊C₄	D₄₁
hypocenter	C₄₁	#382
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. C₄×Dic₄₁	C₄	semidirect
38. C₄₁	#382	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₄₁	2
C₂×C₄×Dic₄₁	2
#13050071	2
C₂×C₄⋊C₄×C₄₁	2
#382	41