Subgroups — #17986271

Order 4544.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556159	C₂	1	2	yes	maximal
2	#14556134	C₂	1	1	yes	maximal, characteristic
3	#14556064	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556047	C₂	1	2	yes	maximal, complemented
5	C₂×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#11765865	C₂²	1	1	yes	characteristic
7	#11765855	—	2	2	no	—
8	#11765852	—	2	2	no	—
9	#11765849	C₂²	1	1	yes	characteristic
10	#11765849	C₂²	1	2	yes	—
11	#11765848	—	2	1	no	—
12	C₈×D₇₁	—	2	1	no	—
13	C₂×Q₈×C₇₁	C₂²	1	2	yes	—
14	Q₁₆×C₇₁	—	2	1	no	—
15	Q₁₆×C₇₁	—	2	1	no	—
16	C₂×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	Q₈×C₇₁	—	2	2	no	—
18	Q₈×C₇₁	—	2	2	no	—
19	C₂×C₄×C₇₁	—	2	2	no	—
20	C₂×C₄×C₇₁	C₂³	1	1	yes	characteristic
21	C₂²⋊D₇₁	—	2	1	no	—
22	D₂₈₄	D₄	1	1	yes	characteristic
23	C₄×D₇₁	—	2	1	no	—
24	Dic₁₄₂	D₄	1	1	yes	characteristic
25	C₈×C₇₁	D₄	1	1	yes	characteristic
26	C₈×C₇₁	D₄	1	1	yes	characteristic
27	C₇₁⋊C₈	—	2	1	no	—
28	C₇₁⋊C₈	—	2	2	no	—
29	C₂²×C₇₁	#41	1	1	yes	characteristic
30	C₂×D₇₁	—	2	1	no	—
31	C₄×C₇₁	—	4	2	no	—
32	C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
34	Dic₇₁	—	2	1	no	—
35	C₂×C₇₁	—	2	1	no	—
36	C₂×C₇₁	#121	1	1	yes	characteristic
37	D₇₁	—	4	1	no	—
38	C₇₁	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	71	1	no	maximal, Sylow
40	#137	—	71	2	no	—
41	C₂×Q₁₆	D₇₁	1	1	yes	characteristic, complemented
42	#131	—	71	1	no	—
43	#108	—	71	1	no	—
44	#101	—	71	2	no	—
45	#41	—	71	1	no	—
46	C₂×Q₈	C₂×D₇₁	1	2	yes	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	2	1	no	—
49	Q₁₆	—	142	2	no	—
50	SD₁₆	—	142	2	no	—
51	M₁₆	—	71	1	no	—
52	M₁₆	—	71	2	no	—
53	M₁₆	—	142	1	no	—
54	C₂×C₈	—	142	1	no	—
55	C₂×C₈	C₂×D₇₁	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	—	71	1	no	—
59	D₄	—	71	1	no	—
60	D₄	—	142	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	142	1	no	—
63	C₂×C₄	C₂²×D₇₁	1	1	yes	characteristic
64	C₈	—	142	2	no	—
65	C₈	—	142	1	no	—
66	C₈	C₂²⋊D₇₁	1	1	yes	characteristic
67	C₈	C₂²⋊D₇₁	1	1	yes	characteristic
68	C₂²	—	142	1	no	—
69	C₂²	#11765864	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	142	1	no	—
72	C₄	D₄×D₇₁	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	284	1	no	—
76	C₂	#14556099	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14556099
commutator, cosocle	C₂×C₄×C₇₁	C₂³
Frattini	C₂×C₄	C₂²×D₇₁
Fitting	C₂×Q₁₆×C₇₁	C₂
socle	C₂×C₇₁	#121
prime radical	#11765865	C₂²
hypercenter	C₂×Q₁₆	D₇₁
hypocenter	C₇₁	#473
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #14556064	C₂	semidirect
4. #14556047	C₂	semidirect
5. C₂×Q₁₆×C₇₁	C₂	semidirect
38. C₇₁	#473	semidirect
41. C₂×Q₁₆	D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#14556159	2
#14556134	2
#14556064	2
#14556047	2
C₂×Q₁₆×C₇₁	2
#473	71