Subgroups — #14520213

Order 1968.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758315	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Dic₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758299	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758297	C₂	1	1	yes	maximal, characteristic, complemented
6	#11758295	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#10620306	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×D₁₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₄₁	C₂²	1	1	yes	characteristic
12	Dic₁₂₃	C₂²	1	1	yes	characteristic
13	C₃×Dic₄₁	C₂²	1	1	yes	characteristic
14	Dic₃×C₄₁	C₂²	1	1	yes	characteristic
15	Dic₃×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄₁	—	3	1	no	—
17	C₂²⋊D₄₁	—	3	1	no	—
18	C₂²⋊D₄₁	D₃	1	1	yes	characteristic, complemented
19	D₁₆₄	—	3	1	no	—
20	C₄×D₄₁	—	3	1	no	—
21	C₄×D₄₁	—	3	1	no	—
22	Dic₈₂	—	3	1	no	—
23	C₂×C₃×C₄₁	—	2	1	no	—
24	C₂×C₃×C₄₁	C₂³	1	1	yes	characteristic
25	D₁₂₃	—	2	1	no	—
26	C₃×D₄₁	—	2	1	no	—
27	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
28	C₂×D₄₁	—	3	1	no	—
29	C₂×D₄₁	C₂×D₃	1	1	yes	characteristic
30	C₄×C₄₁	—	3	1	no	—
31	C₄×C₄₁	—	3	1	no	—
32	Dic₄₁	—	3	1	no	—
33	Dic₄₁	C₂×D₃	1	1	yes	characteristic
34	C₃×C₄₁	#41	1	1	yes	characteristic, complemented, Hall
35	C₂×C₄₁	—	2	1	no	—
36	C₂×C₄₁	C₂²×D₃	1	1	yes	characteristic
37	D₄₁	—	2	1	no	—
38	D₄₁	—	6	1	no	—
39	#237	—	41	1	no	maximal, Hall
40	C₄₁	#237	1	1	yes	characteristic, complemented, Sylow
41	C₃×D₄	—	41	1	no	—
42	#67	—	41	1	no	—
43	#67	—	41	1	no	—
44	C₂×Dic₃	—	41	1	no	—
45	C₂×Dic₃	D₄₁	1	1	yes	characteristic, complemented
46	C₄×D₃	—	41	1	no	—
47	Dic₆	—	41	1	no	—
48	#41	—	123	1	no	Sylow
49	C₂²×C₃	—	41	1	no	—
50	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic
51	C₂×D₃	—	41	1	no	—
52	C₃×C₄	—	41	1	no	—
53	Dic₃	—	41	1	no	—
54	Dic₃	C₂×D₄₁	1	1	yes	characteristic
55	Dic₃	C₂×D₄₁	1	1	yes	characteristic
56	Q₈	—	123	1	no	—
57	D₄	—	41	1	no	—
58	D₄	—	123	1	no	—
59	D₄	—	123	1	no	—
60	C₂×C₄	—	3	1	no	—
61	C₂×C₄	—	123	1	no	—
62	C₂×C₄	—	123	1	no	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	—	82	1	no	—
65	C₂×C₃	C₂²×D₄₁	1	1	yes	characteristic
66	D₃	—	82	1	no	—
67	C₂²	—	41	1	no	—
68	C₂²	—	123	1	no	—
69	C₂²	D₃×D₄₁	1	1	yes	characteristic
70	C₄	—	3	1	no	—
71	C₄	—	3	1	no	—
72	C₄	—	41	1	no	—
73	C₄	—	123	1	no	—
74	C₃	#10620306	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	2	1	no	—
76	C₂	—	82	1	no	—
77	C₂	—	246	1	no	—
78	C₂	C₂×D₃×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×D₄₁
commutator, socle, cosocle	C₂×C₃×C₄₁	C₂³
Fitting	C₂²×C₃×C₄₁	C₂²
hypercenter	C₂²	D₃×D₄₁
hypocenter	C₃×C₄₁	#41
LCS	G ▷ C₂×C₃×C₄₁ ▷ C₃×C₄₁
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. #11758315	C₂	semidirect
2. C₂×Dic₃×C₄₁	C₂	semidirect
3. C₃×C₂²⋊D₄₁	C₂	semidirect
4. #11758299	C₂	semidirect
5. #11758297	C₂	semidirect
6. #11758295	C₂	semidirect
7. Dic₃×D₄₁	C₂	semidirect
18. C₂²⋊D₄₁	D₃	semidirect
34. C₃×C₄₁	#41	semidirect
40. C₄₁	#237	semidirect
45. C₂×Dic₃	D₄₁	semidirect
74. C₃	#10620306	semidirect

Maximal subgroups

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

subgroup	index
#11758315	2
C₂×Dic₃×C₄₁	2
C₃×C₂²⋊D₄₁	2
#11758299	2
#11758297	2
#11758295	2
Dic₃×D₄₁	2
#10620306	3
#237	41