Subgroups — #22588480

Order 9088.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986023	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556039	C₂	1	1	yes	maximal, characteristic
3	#17985763	C₂	1	4	yes	maximal
4	#423×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	C₂²	1	2	yes	—
6	C₂²×C₇₁⋊C₈	C₂²	1	2	yes	—
7	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
8	#14556039	C₄	1	4	yes	—
9	C₂×M₁₆×C₇₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₇₁	—	2	2	no	—
12	#11765849	—	2	4	no	—
13	C₂×C₇₁⋊C₈	—	2	2	no	—
14	C₂×C₇₁⋊C₈	—	2	2	no	—
15	C₂×C₇₁⋊C₈	—	2	2	no	—
16	C₂×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₇₁	Q₈	1	2	yes	—
18	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
19	M₁₆×C₇₁	—	2	4	no	—
20	C₂×C₈×C₇₁	—	2	2	no	—
21	C₄²×C₇₁	C₂×C₄	1	2	yes	—
22	C₄²×C₇₁	D₄	1	2	yes	—
23	C₂³×C₇₁	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₇₁	—	4	2	no	—
25	C₂×C₄×C₇₁	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₇₁	#41	1	2	yes	—
29	C₂×C₄×C₇₁	#41	1	2	yes	—
30	C₈×C₇₁	—	4	2	no	—
31	C₇₁⋊C₈	—	2	4	no	—
32	C₇₁⋊C₈	—	4	2	no	—
33	C₂²×C₇₁	—	2	2	no	—
34	C₂²×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₇₁	#125	1	2	yes	—
36	C₄×C₇₁	—	2	4	no	—
37	C₄×C₇₁	#117	1	2	yes	—
38	C₄×C₇₁	#124	1	1	yes	characteristic
39	C₄×C₇₁	#124	1	1	yes	characteristic
40	C₂×C₇₁	—	2	2	no	—
41	C₂×C₇₁	#382	1	1	yes	characteristic
42	C₂×C₇₁	#430	1	2	yes	—
43	#1838	—	71	1	no	maximal, Sylow
44	C₇₁	#1838	1	1	yes	characteristic, complemented, Sylow
45	#423	—	71	1	no	—
46	#423	D₇₁	1	1	yes	characteristic
47	C₂×#97	—	71	1	no	—
48	#341	—	71	4	no	—
49	C₂×M₁₆	—	71	2	no	—
50	C₂×M₁₆	C₂×D₇₁	1	2	yes	—
51	C₂²×C₈	—	71	2	no	—
52	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	142	2	no	—
55	#97	—	71	4	no	—
56	C₂²×C₄	Dic₁₄₂	1	2	yes	—
57	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	142	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	71	4	no	—
62	C₂×C₈	—	142	2	no	—
63	C₂×C₈	—	142	2	no	—
64	C₂×C₈	—	142	2	no	—
65	C₄²	C₄×D₇₁	1	2	yes	—
66	C₄²	C₂²⋊D₇₁	1	2	yes	—
67	C₂³	C₂×Dic₁₄₂	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	Dic₇₁⋊C₄	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
71	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
72	C₂×C₄	#11765864	1	2	yes	—
73	C₂×C₄	#11765866	1	2	yes	—
74	C₈	—	4	2	no	—
75	C₈	—	284	2	no	—
76	C₈	—	142	4	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
79	C₂²	#14556119	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#14556086	1	2	yes	—
82	C₄	#14556115	1	1	yes	characteristic
83	C₄	#14556117	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#17985864	1	1	yes	characteristic
86	C₂	#17986047	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#423×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄⋊C₄
hypercenter	#423	D₇₁
hypocenter	C₇₁	#1838
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
44. C₇₁	#1838	semidirect