Subgroups — #22586372

Order 9088.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986364	C₂	1	1	yes	maximal, characteristic
2	#17985777	C₂	1	1	yes	maximal, characteristic, complemented
3	#347×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556125	C₄	1	1	yes	characteristic
5	#14556120	C₄	1	1	yes	characteristic
6	#14556068	—	2	1	no	—
7	#14556050	—	2	1	no	—
8	#14556050	—	2	1	no	—
9	M₃₂×C₇₁	—	2	1	no	—
10	#97×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₈₄	—	2	1	no	—
12	C₂×D₂₈₄	—	4	1	no	—
13	C₄⋊Dic₇₁	—	2	1	no	—
14	Dic₇₁⋊C₄	—	4	1	no	—
15	C₇₁⋊C₁₆	—	2	2	no	—
16	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
18	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₇₁	—	2	2	no	—
20	C₂²×D₇₁	—	4	1	no	—
21	C₂×C₄×C₇₁	—	2	1	no	—
22	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₇₁	—	4	1	no	—
24	D₂₈₄	—	4	1	no	—
25	D₂₈₄	—	4	1	no	—
26	D₂₈₄	—	8	2	no	—
27	C₈×C₇₁	—	2	1	no	—
28	C₈×C₇₁	—	2	1	no	—
29	C₂²×C₇₁	#100	1	1	yes	characteristic
30	C₂×D₇₁	—	8	2	no	—
31	C₂×D₇₁	—	8	1	no	—
32	C₄×C₇₁	—	4	1	no	—
33	C₄×C₇₁	#104	1	1	yes	characteristic
34	C₄×C₇₁	#104	1	1	yes	characteristic
35	Dic₇₁	—	8	1	no	—
36	C₂×C₇₁	—	2	1	no	—
37	C₂×C₇₁	#329	1	1	yes	characteristic
38	D₇₁	—	16	1	no	—
39	#1355	—	71	1	no	maximal, Sylow
40	C₇₁	#1355	1	1	yes	characteristic, complemented, Sylow
41	#490	—	71	1	no	—
42	#347	—	71	1	no	—
43	#347	D₇₁	1	1	yes	characteristic, complemented
44	#127	—	71	1	no	—
45	#125	—	71	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	142	1	no	—
48	#102	—	142	1	no	—
49	#102	—	142	1	no	—
50	#97	C₂×D₇₁	1	1	yes	characteristic
51	C₂×D₄	—	284	1	no	—
52	C₂×D₄	—	142	1	no	—
53	C₂×C₈	D₂₈₄	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
55	C₄⋊C₄	—	284	1	no	—
56	C₄⋊C₄	—	142	1	no	—
57	C₄²	C₄×D₇₁	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	142	2	no	—
60	C₂³	—	284	1	no	—
61	D₄	—	284	1	no	—
62	D₄	—	284	1	no	—
63	D₄	—	568	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	284	1	no	—
66	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	568	2	no	—
70	C₂²	—	568	1	no	—
71	C₂²	#14556044	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	568	1	no	—
74	C₄	#14556054	1	1	yes	characteristic
75	C₄	#14556056	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	1136	1	no	—
78	C₂	#17985738	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985738
commutator	C₄²×C₇₁	C₂×C₄
Frattini	#97	C₂×D₇₁
Fitting	#347×C₇₁	C₂
socle	C₂×C₇₁	#329
hypercenter	#347	D₇₁
hypocenter	C₇₁	#1355
LCS	G ▷ C₄²×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #17985777	C₂	semidirect
3. #347×C₇₁	C₂	semidirect
40. C₇₁	#1355	semidirect
43. #347	D₇₁	semidirect