Subgroups — #24907134

Order 10624.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128106	C₂	1	2	yes	maximal, complemented
2	#19128081	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128074	C₂	1	1	yes	maximal, characteristic
4	#19128048	C₂	1	2	yes	maximal
5	#322×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₃₂	—	2	2	no	—
7	C₂×#13050579	—	2	2	no	—
8	#14581792	C₂²	1	1	yes	characteristic
9	#14581792	C₂²	1	2	yes	—
10	#14581789	C₂²	1	1	yes	characteristic
11	#14581726	—	2	4	no	—
12	#14581714	—	2	4	no	—
13	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₈₃	C₂²	1	2	yes	—
15	C₂×Dic₁₆₆	—	2	1	no	—
16	C₂×Dic₁₆₆	—	2	2	no	—
17	C₂×D₃₃₂	—	2	1	no	—
18	C₂×D₃₃₂	—	2	2	no	—
19	Dic₃₃₂	—	4	4	no	—
20	#13050579	—	4	4	no	—
21	C₄⋊Dic₈₃	—	2	2	no	—
22	C₄⋊Dic₈₃	—	2	2	no	—
23	C₄⋊Dic₈₃	—	2	2	no	—
24	C₂×C₈×C₈₃	D₄	1	4	yes	—
25	C₂×C₈×C₈₃	D₄	1	2	yes	—
26	C₄²×C₈₃	C₂³	1	1	yes	characteristic
27	C₂²×D₈₃	—	4	1	no	—
28	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
30	C₂×Dic₈₃	—	4	2	no	—
31	C₂×Dic₈₃	—	4	1	no	—
32	D₃₃₂	—	4	2	no	—
33	D₃₃₂	—	4	4	no	—
34	Dic₁₆₆	—	4	2	no	—
35	Dic₁₆₆	—	4	4	no	—
36	C₈×C₈₃	—	2	4	no	—
37	C₈×C₈₃	D₈	1	4	yes	—
38	C₂²×C₈₃	#127	1	1	yes	characteristic
39	C₂×D₈₃	—	8	1	no	—
40	C₂×D₈₃	—	8	2	no	—
41	C₄×C₈₃	C₂×D₈	1	2	yes	—
42	C₄×C₈₃	#137	1	4	yes	—
43	Dic₈₃	—	8	1	no	—
44	Dic₈₃	—	8	2	no	—
45	C₂×C₈₃	#493	1	1	yes	characteristic
46	C₂×C₈₃	#497	1	2	yes	—
47	D₈₃	—	16	1	no	—
48	#1722	—	83	1	no	maximal, Sylow
49	C₈₃	#1722	1	1	yes	characteristic, complemented, Sylow
50	#500	—	83	2	no	—
51	#494	—	83	1	no	—
52	#492	—	83	1	no	—
53	#486	—	83	2	no	—
54	#322	D₈₃	1	1	yes	characteristic, complemented
55	C₂×Q₁₆	—	166	2	no	—
56	C₂×SD₁₆	—	166	2	no	—
57	C₄⋊Q₈	—	83	2	no	—
58	C₄⋊Q₈	—	83	1	no	—
59	#127	—	83	1	no	—
60	#107	—	166	4	no	—
61	#102	—	166	4	no	—
62	C₄×C₈	C₂×D₈₃	1	2	yes	—
63	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
64	C₂×Q₈	—	166	1	no	—
65	C₂×Q₈	—	166	2	no	—
66	C₂×D₄	—	166	2	no	—
67	C₂×D₄	—	166	1	no	—
68	Q₁₆	—	332	4	no	—
69	SD₁₆	—	332	4	no	—
70	C₂×C₈	D₃₃₂	1	4	yes	—
71	C₂×C₈	D₃₃₂	1	2	yes	—
72	C₄⋊C₄	—	166	2	no	—
73	C₄⋊C₄	—	166	2	no	—
74	C₄⋊C₄	—	166	2	no	—
75	C₄²	C₂²×D₈₃	1	1	yes	characteristic
76	C₂³	—	332	1	no	—
77	Q₈	—	332	2	no	—
78	Q₈	—	332	4	no	—
79	D₄	—	332	2	no	—
80	D₄	—	332	4	no	—
81	C₂×C₄	—	332	2	no	—
82	C₂×C₄	—	332	1	no	—
83	C₂×C₄	C₂×D₃₃₂	1	1	yes	characteristic
84	C₂×C₄	C₂×D₃₃₂	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₆₆₄	1	4	yes	—
87	C₂²	—	664	1	no	—
88	C₂²	—	664	2	no	—
89	C₂²	#14581789	1	1	yes	characteristic
90	C₄	—	664	1	no	—
91	C₄	—	664	2	no	—
92	C₄	C₂×D₆₆₄	1	2	yes	—
93	C₄	#14581825	1	4	yes	—
94	C₂	—	1328	1	no	—
95	C₂	#19128078	1	1	yes	characteristic
96	C₂	#19128095	1	2	yes	—

	subgroup	G/H
center	C₂²	#14581789
commutator, cosocle	C₄²×C₈₃	C₂³
Frattini	C₄²	C₂²×D₈₃
Fitting	#322×C₈₃	C₂
socle	C₂²×C₈₃	#127
prime radical	#14581789	C₂²
hypercenter	#322	D₈₃
hypocenter	C₈₃	#1722
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #19128106	C₂	semidirect
2. #19128081	C₂	semidirect
5. #322×C₈₃	C₂	semidirect
49. C₈₃	#1722	semidirect
54. #322	D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128106	2
#19128081	2
#19128074	2
#19128048	2
#322×C₈₃	2
#1722	83