Subgroups — #24905458

Order 10624.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127959	C₂	1	1	yes	maximal, characteristic
2	C₈₃⋊#338	C₂	1	1	yes	maximal, characteristic
3	#349×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	C₄	1	1	yes	characteristic
5	C₂×#13050574	—	2	1	no	—
6	#14581771	—	2	1	no	—
7	#14581724	C₄	1	1	yes	characteristic
8	#14581717	—	2	1	no	—
9	C₂×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	M₃₂×C₈₃	—	2	1	no	—
11	C₂×Dic₁₆₆	—	2	1	no	—
12	Dic₃₃₂	—	4	1	no	—
13	#13050574	—	4	1	no	—
14	#13050574	—	4	1	no	—
15	C₂×C₈₃⋊C₈	—	2	2	no	—
16	C₄⋊Dic₈₃	—	2	1	no	—
17	Dic₈₃⋊C₄	—	4	1	no	—
18	C₂²⋊Dic₈₃	—	4	1	no	—
19	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
20	M₁₆×C₈₃	—	4	1	no	—
21	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
23	C₁₆×C₈₃	—	4	1	no	—
24	C₂³×C₈₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₈₃	—	2	1	no	—
26	C₂×C₄×C₈₃	—	2	1	no	—
27	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
29	C₂×Dic₈₃	—	4	1	no	—
30	C₂×Dic₈₃	—	4	1	no	—
31	Dic₁₆₆	—	4	1	no	—
32	Dic₁₆₆	—	4	1	no	—
33	C₈×C₈₃	—	2	1	no	—
34	C₈×C₈₃	—	2	1	no	—
35	C₈₃⋊C₈	—	4	2	no	—
36	C₂²×C₈₃	—	2	1	no	—
37	C₂²×C₈₃	—	4	1	no	—
38	C₂²×C₈₃	#102	1	1	yes	characteristic
39	C₄×C₈₃	—	2	1	no	—
40	C₄×C₈₃	#99	1	1	yes	characteristic
41	C₄×C₈₃	#104	1	1	yes	characteristic
42	Dic₈₃	—	8	1	no	—
43	Dic₈₃	—	8	1	no	—
44	C₂×C₈₃	—	2	1	no	—
45	C₂×C₈₃	—	4	1	no	—
46	C₂×C₈₃	#327	1	1	yes	characteristic
47	#1342	—	83	1	no	maximal, Sylow
48	C₈₃	#1342	1	1	yes	characteristic, complemented, Sylow
49	#470	—	83	1	no	—
50	#349	D₈₃	1	1	yes	characteristic
51	#338	—	83	1	no	—
52	C₂×Q₁₆	—	83	1	no	—
53	C₂×M₁₆	—	166	1	no	—
54	C₂×M₁₆	C₂×D₈₃	1	1	yes	characteristic
55	C₂²⋊Q₈	—	166	1	no	—
56	M₃₂	—	2	1	no	—
57	#106	—	83	1	no	—
58	#103	—	166	1	no	—
59	C₂×Q₈	—	166	1	no	—
60	C₂²×C₄	D₃₃₂	1	1	yes	characteristic
61	Q₁₆	—	332	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	332	1	no	—
64	M₁₆	—	332	1	no	—
65	C₂×C₈	—	166	2	no	—
66	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
68	C₄⋊C₄	—	332	1	no	—
69	C₄⋊C₄	—	166	1	no	—
70	C₂²⋊C₄	—	332	1	no	—
71	C₁₆	—	4	1	no	—
72	C₂³	#13050579	1	1	yes	characteristic
73	Q₈	—	332	1	no	—
74	Q₈	—	332	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	332	1	no	—
78	C₂×C₄	—	332	1	no	—
79	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
80	C₂×C₄	D₆₆₄	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	332	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#14581714	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	664	1	no	—
89	C₄	—	664	1	no	—
90	C₄	#14581706	1	1	yes	characteristic
91	C₄	#14581718	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#19127436	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127436
commutator	C₂×C₈×C₈₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₈₃
Fitting	#349×C₈₃	C₂
socle	C₂×C₈₃	#327
prime radical	C₂³×C₈₃	SD₁₆
cosocle	C₂×M₁₆×C₈₃	C₂²
hypercenter	#349	D₈₃
hypocenter	C₈₃	#1342
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
48. C₈₃	#1342	semidirect