Subgroups — #22586506

Order 9088.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986373	C₂	1	1	yes	maximal, characteristic
2	#17985798	C₂	1	1	yes	maximal, characteristic, complemented
3	#356×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11765852	—	2	1	no	—
5	C₂×#11765852	—	2	1	no	—
6	#14556125	C₄	1	1	yes	characteristic
7	#14556047	—	2	1	no	—
8	C₄×C₇₁⋊C₈	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
10	#101×C₇₁	—	2	1	no	—
11	C₂×D₂₈₄	—	2	1	no	—
12	C₂×D₂₈₄	—	4	1	no	—
13	#11765852	—	4	2	no	—
14	#11765852	—	4	2	no	—
15	#11765849	—	4	1	no	—
16	C₂×C₇₁⋊C₈	—	2	1	no	—
17	C₂×Q₈×C₇₁	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₇₁	D₄	1	1	yes	characteristic
19	M₁₆×C₇₁	—	4	1	no	—
20	C₄⋊C₄×C₇₁	—	4	1	no	—
21	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₇₁	—	4	1	no	—
23	Q₈×C₇₁	—	4	1	no	—
24	Q₈×C₇₁	—	4	1	no	—
25	C₂×C₄×C₇₁	—	2	1	no	—
26	C₂×C₄×C₇₁	—	2	1	no	—
27	C₂×C₄×C₇₁	—	2	1	no	—
28	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
29	D₂₈₄	—	4	1	no	—
30	D₂₈₄	—	4	1	no	—
31	D₂₈₄	—	8	2	no	—
32	C₈×C₇₁	—	8	1	no	—
33	C₇₁⋊C₈	—	2	2	no	—
34	C₇₁⋊C₈	—	8	1	no	—
35	C₂²×C₇₁	#99	1	1	yes	characteristic
36	C₂×D₇₁	—	8	2	no	—
37	C₂×D₇₁	—	8	1	no	—
38	C₄×C₇₁	—	2	2	no	—
39	C₄×C₇₁	—	2	1	no	—
40	C₄×C₇₁	—	4	1	no	—
41	C₄×C₇₁	—	4	1	no	—
42	C₂×C₇₁	—	2	1	no	—
43	C₂×C₇₁	#353	1	1	yes	characteristic
44	D₇₁	—	16	1	no	—
45	#1410	—	71	1	no	maximal, Sylow
46	C₇₁	#1410	1	1	yes	characteristic, complemented, Sylow
47	#492	—	71	1	no	—
48	#356	—	71	1	no	—
49	#356	D₇₁	1	1	yes	characteristic, complemented
50	C₂×SD₁₆	—	142	1	no	—
51	C₂×SD₁₆	—	142	1	no	—
52	C₄⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
53	#127	—	71	1	no	—
54	#101	—	2	1	no	—
55	#101	—	142	1	no	—
56	C₄×C₈	—	71	1	no	—
57	C₂×Q₈	D₂₈₄	1	1	yes	characteristic
58	C₂×Q₈	C₂²⋊D₇₁	1	1	yes	characteristic
59	C₂×D₄	—	284	1	no	—
60	C₂×D₄	—	142	1	no	—
61	SD₁₆	—	284	2	no	—
62	SD₁₆	—	284	2	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	284	1	no	—
65	C₂×C₈	—	142	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₇₁	1	1	yes	characteristic
68	C₂³	—	284	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	D₄	—	284	1	no	—
72	D₄	—	284	1	no	—
73	D₄	—	568	2	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	568	1	no	—
80	C₈	—	142	2	no	—
81	C₂²	—	568	2	no	—
82	C₂²	—	568	1	no	—
83	C₂²	#14556042	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	2	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	1136	1	no	—
90	C₂	#17985791	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985791
commutator	C₄²×C₇₁	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₇₁
Fitting	#356×C₇₁	C₂
socle	C₂×C₇₁	#353
hypercenter	#356	D₇₁
hypocenter	C₇₁	#1410
LCS	G ▷ C₄²×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
2. #17985798	C₂	semidirect
3. #356×C₇₁	C₂	semidirect
46. C₇₁	#1410	semidirect
49. #356	D₇₁	semidirect