Subgroups — #14580275

Order 2624.

134 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	#13050071	C₂	1	2	yes	maximal
3	#13050071	C₂	1	2	yes	maximal
4	#13050071	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₁	C₂²	1	2	yes	—
10	C₂²×Dic₄₁	C₂²	1	2	yes	—
11	C₄⋊C₄×C₄₁	—	2	2	no	—
12	C₄⋊Dic₄₁	—	2	2	no	—
13	C₂³×C₄₁	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₄₁	—	2	1	no	—
15	C₂×C₄×C₄₁	—	2	1	no	—
16	C₂×C₄×C₄₁	—	2	2	no	—
17	C₂×C₄×C₄₁	—	2	1	no	—
18	C₂×C₄×C₄₁	—	2	2	no	—
19	C₂×C₄×C₄₁	D₄	1	2	yes	—
20	C₂×C₄×C₄₁	Q₈	1	2	yes	—
21	C₂×Dic₄₁	—	2	2	no	—
22	C₂×Dic₄₁	—	2	2	no	—
23	C₂×Dic₄₁	—	2	2	no	—
24	C₂×Dic₄₁	—	2	4	no	—
25	C₂×Dic₄₁	—	2	2	no	—
26	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄₁	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₄₁	#41	1	1	yes	characteristic
29	C₂²×C₄₁	#41	1	2	yes	—
30	C₂²×C₄₁	#41	1	2	yes	—
31	C₄×C₄₁	—	2	2	no	—
32	C₄×C₄₁	—	2	2	no	—
33	C₄×C₄₁	—	4	1	no	—
34	Dic₄₁	—	4	2	no	—
35	Dic₄₁	—	4	2	no	—
36	C₂×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
37	C₂×C₄₁	#123	1	1	yes	characteristic
38	C₂×C₄₁	#124	1	1	yes	characteristic
39	C₂×C₄₁	#125	1	2	yes	—
40	C₂×C₄₁	#126	1	2	yes	—
41	#400	—	41	1	no	maximal, Sylow
42	C₄₁	#400	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄⋊C₄	—	41	1	no	—
44	C₂×C₄⋊C₄	D₄₁	1	1	yes	characteristic
45	#95	—	41	1	no	—
46	#95	—	41	2	no	—
47	#95	—	41	2	no	—
48	C₂²×C₄	—	41	2	no	—
49	C₂²×C₄	—	41	2	no	—
50	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
51	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
52	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	82	2	no	—
55	C₂³	C₂²×D₄₁	1	1	yes	characteristic
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	82	2	no	—
62	C₂×C₄	—	82	2	no	—
63	C₂×C₄	—	82	4	no	—
64	C₂×C₄	—	82	2	no	—
65	C₂×C₄	—	82	2	no	—
66	C₂×C₄	Dic₈₂	1	2	yes	—
67	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
68	C₂²	C₂×Dic₈₂	1	1	yes	characteristic
69	C₂²	#10620306	1	1	yes	characteristic
70	C₂²	#10620308	1	2	yes	—
71	C₂²	#10620310	1	2	yes	—
72	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	2	2	no	—
75	C₄	—	4	1	no	—
76	C₄	—	164	2	no	—
77	C₄	—	164	2	no	—
78	C₂	#13050143	1	1	yes	characteristic
79	C₂	#13050145	1	1	yes	characteristic
80	C₂	#13050153	1	1	yes	characteristic
81	C₂	#13050155	1	2	yes	—
82	C₂	#13050159	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₁
commutator, socle, prime radical, cosocle	C₂³×C₄₁	C₂³
Fitting	C₂×C₄⋊C₄×C₄₁	C₂
hypercenter	C₂×C₄⋊C₄	D₄₁
hypocenter	C₄₁	#400
LCS	G ▷ C₂³×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
42. C₄₁	#400	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
#13050071	2
C₂×C₄⋊C₄×C₄₁	2
#400	41