Subgroups — #37588712

Order 24512.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133840	C₂	1	1	yes	maximal, characteristic, complemented
2	#27133830	C₂	1	1	yes	maximal, characteristic
3	#27133765	C₂	1	1	yes	maximal, characteristic, complemented
4	#27133763	C₂	1	1	yes	maximal, characteristic
5	#27133761	C₂	1	1	yes	maximal, characteristic
6	#27133751	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₇₆₆	—	2	1	no	—
9	C₂×D₁₅₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₃₈₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₃₈₃	C₂²	1	1	yes	characteristic
12	Dic₃₈₃⋊C₄	—	2	1	no	—
13	(C₂×D₃₈₃)⋊C₄	—	2	1	no	—
14	(C₂×D₃₈₃)⋊C₄	—	2	1	no	—
15	C₄×Dic₃₈₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₃₈₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₈₃	C₂²	1	1	yes	characteristic
19	C₂²×D₃₈₃	—	2	1	no	—
20	Dic₇₆₆	—	4	2	no	—
21	D₁₅₃₂	—	2	1	no	—
22	D₁₅₃₂	—	2	1	no	—
23	C₂×Dic₃₈₃	—	2	1	no	—
24	C₂×Dic₃₈₃	D₄	1	1	yes	characteristic
25	C₂×Dic₃₈₃	D₄	1	1	yes	characteristic
26	C₃₈₃⋊C₈	—	2	1	no	—
27	Q₈×C₃₈₃	—	2	1	no	—
28	Q₈×C₃₈₃	—	2	1	no	—
29	C₂×C₄×C₃₈₃	—	2	1	no	—
30	C₂×C₄×C₃₈₃	—	2	1	no	—
31	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
32	C₈×C₃₈₃	—	2	1	no	—
33	C₂²×C₃₈₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₈₃	—	4	1	no	—
35	C₂×D₃₈₃	—	4	1	no	—
36	C₂×D₃₈₃	—	4	1	no	—
37	C₄×C₃₈₃	—	4	1	no	—
38	C₄×C₃₈₃	—	4	1	no	—
39	C₄×C₃₈₃	#41	1	1	yes	characteristic
40	C₄×C₃₈₃	#41	1	1	yes	characteristic
41	Dic₃₈₃	—	2	1	no	—
42	Dic₃₈₃	—	2	1	no	—
43	Dic₃₈₃	—	4	1	no	—
44	C₂×C₃₈₃	#124	1	1	yes	characteristic
45	C₂×C₃₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₃₈₃	#137	1	1	yes	characteristic
47	D₃₈₃	—	8	1	no	—
48	C₃₈₃	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	383	1	no	maximal, Sylow
50	C₄⋊Q₈	—	383	1	no	—
51	#124	—	383	1	no	—
52	#103	—	383	1	no	—
53	#103	D₃₈₃	1	1	yes	characteristic, complemented
54	#102	—	383	1	no	—
55	#102	—	383	1	no	—
56	#97	—	383	1	no	—
57	C₂×Q₈	—	766	1	no	—
58	C₂×Q₈	C₂×D₃₈₃	1	1	yes	characteristic
59	C₂×D₄	—	383	1	no	—
60	C₂×C₈	—	383	1	no	—
61	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
62	C₄⋊C₄	—	383	1	no	—
63	C₄⋊C₄	—	766	1	no	—
64	C₄⋊C₄	C₂×D₃₈₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	766	1	no	—
66	C₂²⋊C₄	—	766	1	no	—
67	C₄²	—	383	1	no	—
68	C₂³	—	766	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	1532	2	no	—
72	D₄	—	766	1	no	—
73	D₄	—	766	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	383	1	no	—
77	C₂×C₄	—	383	1	no	—
78	C₂×C₄	—	766	1	no	—
79	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	766	1	no	—
82	C₂²	—	1532	1	no	—
83	C₂²	—	1532	1	no	—
84	C₂²	—	1532	1	no	—
85	C₂²	D₄×D₃₈₃	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	1532	1	no	—
89	C₄	—	766	1	no	—
90	C₄	—	766	1	no	—
91	C₄	#20259456	1	1	yes	characteristic
92	C₄	#20259457	1	1	yes	characteristic
93	C₂	—	3064	1	no	—
94	C₂	#27133827	1	1	yes	characteristic
95	C₂	#27133868	1	1	yes	characteristic
96	C₂	#27133873	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₈₃
commutator, cosocle	C₂×C₄×C₃₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₈₃
Fitting	#103×C₃₈₃	C₂
socle	C₂²×C₃₈₃	C₂×D₄
prime radical	C₂×D₁₅₃₂	C₂²
hypercenter	#103	D₃₈₃
hypocenter	C₃₈₃	#489
LCS	G ▷ C₂×C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #27133840	C₂	semidirect
3. #27133765	C₂	semidirect
6. #27133751	C₂	semidirect
7. #103×C₃₈₃	C₂	semidirect
48. C₃₈₃	#489	semidirect
53. #103	D₃₈₃	semidirect

Maximal subgroups

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

subgroup	index
#27133840	2
#27133830	2
#27133765	2
#27133763	2
#27133761	2
#27133751	2
#103×C₃₈₃	2
#489	383