Subgroups — #14581189

Order 2624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050221	C₂	1	1	yes	maximal, characteristic
2	(C₂×#4223)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#13050144	C₂	1	1	yes	maximal, characteristic
4	C₂²×#4223	—	2	1	no	—
5	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
6	C₂×Dic₈₂	C₄	1	1	yes	characteristic, complemented
7	C₂×#66493	—	2	1	no	—
8	C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic, complemented
9	#10620281	—	2	1	no	—
10	C₄⋊Dic₄₁	—	2	1	no	—
11	C₂²×D₄₁	D₄	1	1	yes	characteristic
12	C₂×#4223	—	2	2	no	—
13	C₂×#4223	—	4	1	no	—
14	C₂×#4223	—	4	1	no	—
15	C₂×C₄×C₄₁	—	2	1	no	—
16	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₁	—	2	1	no	—
18	C₂×Dic₄₁	D₄	1	1	yes	characteristic
19	C₄×D₄₁	—	4	1	no	—
20	Dic₈₂	—	4	1	no	—
21	#66493	—	4	1	no	—
22	C₂²×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₄₁	—	2	1	no	—
24	C₂×D₄₁	—	2	1	no	—
25	C₂×D₄₁	SD₁₆	1	1	yes	characteristic
26	C₂×D₄₁	Q₁₆	1	1	yes	characteristic
27	#4223	—	4	2	no	—
28	C₄×C₄₁	—	2	1	no	—
29	C₄×C₄₁	—	4	1	no	—
30	Dic₄₁	—	2	1	no	—
31	Dic₄₁	—	4	1	no	—
32	C₂×C₄₁	#99	1	1	yes	characteristic
33	C₂×C₄₁	#103	1	1	yes	characteristic
34	C₂×C₄₁	#104	1	1	yes	characteristic
35	D₄₁	—	2	1	no	—
36	D₄₁	—	2	1	no	—
37	#328	—	41	1	no	maximal, Sylow
38	C₄₁	#328	1	1	yes	characteristic, complemented, Sylow
39	C₂²⋊Q₈	—	41	1	no	—
40	C₂²⋊C₈	—	41	1	no	—
41	#95	—	41	1	no	—
42	C₂×Q₈	—	41	1	no	—
43	C₂²×C₄	—	41	1	no	—
44	C₂²×C₄	—	82	1	no	—
45	C₂×C₈	—	82	1	no	—
46	C₄⋊C₄	—	82	1	no	—
47	C₄⋊C₄	#4223	1	1	yes	characteristic, complemented
48	C₂²⋊C₄	—	82	1	no	—
49	C₂³	—	41	1	no	—
50	Q₈	—	164	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	41	1	no	—
53	C₂×C₄	—	82	2	no	—
54	C₂×C₄	—	82	1	no	—
55	C₂×C₄	—	164	1	no	—
56	C₂×C₄	—	164	1	no	—
57	C₂×C₄	—	164	1	no	—
58	C₂×C₄	C₂×#4223	1	1	yes	characteristic
59	C₈	—	164	1	no	—
60	C₂²	—	41	1	no	—
61	C₂²	—	41	1	no	—
62	C₂²	—	82	1	no	—
63	C₂²	—	82	1	no	—
64	C₂²	C₂²⋊#4223	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	1	no	—
67	C₄	—	82	1	no	—
68	C₄	—	164	2	no	—
69	C₄	—	164	1	no	—
70	C₂	—	82	1	no	—
71	C₂	—	82	1	no	—
72	C₂	#13050223	1	1	yes	characteristic
73	C₂	#13050227	1	1	yes	characteristic
74	C₂	#13050228	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#4223
commutator	C₂×C₄×C₄₁	C₂×C₄
Frattini	C₂×C₄	C₂×#4223
Fitting	C₄⋊C₄×C₄₁	C₄
socle	C₂²×C₄₁	C₂²⋊C₄
prime radical	C₂²×D₄₁	D₄
cosocle	C₂×C₄×D₄₁	C₂²
hypercenter	C₄⋊C₄	#4223
hypocenter	C₄₁	#328
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. C₂×Dic₈₂	C₄	semidirect
8. C₄⋊C₄×C₄₁	C₄	semidirect
38. C₄₁	#328	semidirect
47. C₄⋊C₄	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050221	2
(C₂×#4223)⋊C₄	2
#13050144	2
#328	41