Subgroups — #17985795

Order 4544.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556117	C₂	1	1	yes	maximal, characteristic
2	#14556047	C₂	1	1	yes	maximal, characteristic, complemented
3	#101×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₈₄	C₄	1	1	yes	characteristic
5	#11765849	—	2	1	no	—
6	(C₂×D₇₁)⋊C₄	—	2	1	no	—
7	(C₂×D₇₁)⋊C₄	—	2	1	no	—
8	C₄×Dic₇₁	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₇₁	C₂²	1	1	yes	characteristic
10	M₁₆×C₇₁	—	2	1	no	—
11	C₂²×D₇₁	—	2	1	no	—
12	Q₈×C₇₁	—	4	1	no	—
13	C₂×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₇₁	D₄	1	1	yes	characteristic
16	C₂×Dic₇₁	—	2	1	no	—
17	D₂₈₄	—	4	1	no	—
18	C₈×C₇₁	—	4	1	no	—
19	C₇₁⋊C₈	—	4	1	no	—
20	C₂²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₇₁	—	4	2	no	—
22	C₂×D₇₁	—	4	1	no	—
23	C₄×C₇₁	—	2	1	no	—
24	C₄×C₇₁	—	2	1	no	—
25	C₄×C₇₁	—	2	1	no	—
26	Dic₇₁	—	4	1	no	—
27	C₂×C₇₁	—	2	1	no	—
28	C₂×C₇₁	#99	1	1	yes	characteristic
29	D₇₁	—	8	1	no	—
30	C₇₁	#355	1	1	yes	characteristic, complemented, Sylow
31	#355	—	71	1	no	maximal, Sylow
32	#124	—	71	1	no	—
33	#101	—	71	1	no	—
34	#101	D₇₁	1	1	yes	characteristic, complemented
35	C₂×Q₈	C₂×D₇₁	1	1	yes	characteristic
36	C₂×D₄	—	71	1	no	—
37	M₁₆	—	2	1	no	—
38	M₁₆	—	142	1	no	—
39	C₂²⋊C₄	—	142	1	no	—
40	C₂²⋊C₄	—	142	1	no	—
41	C₄²	—	71	1	no	—
42	C₂³	—	142	1	no	—
43	Q₈	—	4	1	no	—
44	D₄	—	284	1	no	—
45	C₂×C₄	—	142	1	no	—
46	C₂×C₄	C₄×D₇₁	1	1	yes	characteristic
47	C₂×C₄	D₂₈₄	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
49	C₈	—	4	1	no	—
50	C₈	—	284	1	no	—
51	C₂²	—	284	2	no	—
52	C₂²	—	284	1	no	—
53	C₂²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	284	1	no	—
58	C₂	—	2	1	no	—
59	C₂	—	568	1	no	—
60	C₂	#14556042	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14556042
commutator	C₂×C₄×C₇₁	C₂×C₄
Frattini	C₂×Q₈	C₂×D₇₁
Fitting	#101×C₇₁	C₂
socle	C₂×C₇₁	#99
prime radical	C₂×D₂₈₄	C₄
cosocle	C₂×Q₈×C₇₁	C₂²
hypercenter	#101	D₇₁
hypocenter	C₇₁	#355
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #14556047	C₂	semidirect
3. #101×C₇₁	C₂	semidirect
30. C₇₁	#355	semidirect
34. #101	D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#14556117	2
#14556047	2
#101×C₇₁	2
#355	71