Subgroups — #49129658

Order 36224.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22583609	C₂	1	6	yes	maximal
2	#31826335	C₂	1	1	yes	maximal, characteristic
3	#31826334	C₂	1	6	yes	maximal
4	C₄²×Dic₂₈₃	C₂	1	1	yes	maximal, characteristic
5	#384×C₂₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₆₆	C₂²	1	4	yes	—
7	#22583609	—	2	24	no	—
8	C₂×C₄⋊Dic₂₈₃	C₂²	1	6	yes	—
9	C₂×Dic₂₈₃⋊C₄	C₂²	1	12	yes	—
10	C₂×C₄×Dic₂₈₃	C₂²	1	3	yes	—
11	C₂×C₄×Dic₂₈₃	C₂²	1	3	yes	—
12	C₂×C₄⋊C₄×C₂₈₃	C₂²	1	6	yes	—
13	C₂×C₄²×C₂₈₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₅₆₆	—	2	24	no	—
15	C₂²×Dic₂₈₃	C₂³	1	4	yes	—
16	C₂²×Dic₂₈₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₈₃	C₂³	1	3	yes	—
18	C₄⋊Dic₂₈₃	—	2	12	no	—
19	Dic₂₈₃⋊C₄	—	2	24	no	—
20	C₄×Dic₂₈₃	D₄	1	12	yes	—
21	C₄×Dic₂₈₃	Q₈	1	12	yes	complemented
22	C₂²×C₄×C₂₈₃	C₂³	1	4	yes	—
23	C₂²×C₄×C₂₈₃	C₂³	1	3	yes	—
24	C₄⋊C₄×C₂₈₃	—	2	12	no	—
25	C₄²×C₂₈₃	Q₈	1	4	yes	complemented
26	Dic₅₆₆	—	4	16	no	—
27	C₂×Dic₂₈₃	—	2	12	no	—
28	C₂×Dic₂₈₃	C₂×D₄	1	6	yes	—
29	C₂×Dic₂₈₃	C₂×D₄	1	6	yes	—
30	C₂×Dic₂₈₃	C₂×Q₈	1	12	yes	—
31	C₂³×C₂₈₃	C₂⁴	1	1	yes	characteristic
32	C₂×C₄×C₂₈₃	—	2	12	no	—
33	C₂×C₄×C₂₈₃	C₂×D₄	1	6	yes	—
34	C₂×C₄×C₂₈₃	C₂×Q₈	1	6	yes	—
35	C₂×C₄×C₂₈₃	C₂×Q₈	1	6	yes	—
36	C₂²×C₂₈₃	C₂²×D₄	1	3	yes	—
37	C₂²×C₂₈₃	C₂²×Q₈	1	3	yes	—
38	C₂²×C₂₈₃	C₂²×Q₈	1	1	yes	characteristic
39	C₄×C₂₈₃	—	4	4	no	—
40	C₄×C₂₈₃	C₄⋊Q₈	1	12	yes	complemented
41	Dic₂₈₃	—	4	4	no	—
42	Dic₂₈₃	#127	1	4	yes	—
43	Dic₂₈₃	C₄⋊Q₈	1	12	yes	complemented
44	C₂×C₂₈₃	C₂×#127	1	1	yes	characteristic
45	C₂×C₂₈₃	C₂×C₄⋊Q₈	1	3	yes	—
46	C₂×C₂₈₃	C₂×C₄⋊Q₈	1	3	yes	—
47	C₂₈₃	#2868	1	1	yes	characteristic, complemented, Sylow
48	#2868	—	283	1	no	maximal, Sylow
49	C₂×C₄⋊Q₈	—	283	6	no	—
50	#384	—	283	6	no	—
51	#384	—	283	1	no	—
52	#384	D₂₈₃	1	1	yes	characteristic
53	C₄³	—	283	1	no	—
54	C₂²×Q₈	—	283	4	no	—
55	C₄⋊Q₈	—	566	24	no	—
56	C₂×C₄⋊C₄	—	283	12	no	—
57	C₂×C₄⋊C₄	—	283	6	no	—
58	C₂×C₄⋊C₄	C₂×D₂₈₃	1	6	yes	—
59	C₂×C₄²	—	283	3	no	—
60	C₂×C₄²	—	283	3	no	—
61	C₂×C₄²	C₂×D₂₈₃	1	1	yes	characteristic
62	C₂×Q₈	—	566	24	no	—
63	C₂²×C₄	—	283	3	no	—
64	C₂²×C₄	—	283	1	no	—
65	C₂²×C₄	—	283	4	no	—
66	C₂²×C₄	C₂²×D₂₈₃	1	4	yes	—
67	C₂²×C₄	C₂²×D₂₈₃	1	3	yes	—
68	C₄⋊C₄	—	2	12	no	—
69	C₄⋊C₄	—	566	24	no	—
70	C₄⋊C₄	—	566	12	no	—
71	C₄²	—	283	12	no	—
72	C₄²	—	283	12	no	—
73	C₄²	Dic₅₆₆	1	4	yes	complemented
74	C₂³	C₂³×D₂₈₃	1	1	yes	characteristic
75	Q₈	—	1132	16	no	—
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	283	6	no	—
78	C₂×C₄	—	283	6	no	—
79	C₂×C₄	—	283	12	no	—
80	C₂×C₄	—	566	12	no	—
81	C₂×C₄	D₄×D₂₈₃	1	6	yes	—
82	C₂×C₄	Q₈×D₂₈₃	1	6	yes	—
83	C₂×C₄	C₂×Dic₅₆₆	1	6	yes	—
84	C₂²	C₂×D₄×D₂₈₃	1	3	yes	—
85	C₂²	C₂×Q₈×D₂₈₃	1	3	yes	—
86	C₂²	C₂²×Dic₅₆₆	1	1	yes	characteristic
87	C₄	—	4	4	no	—
88	C₄	—	283	4	no	—
89	C₄	—	283	12	no	—
90	C₄	—	1132	4	no	—
91	C₄	#22583609	1	12	yes	complemented
92	C₂	#127×D₂₈₃	1	1	yes	characteristic
93	C₂	C₄⋊Q₈×D₂₈₃	1	3	yes	—
94	C₂	C₂×#22583609	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₈₃
commutator, socle, prime radical, cosocle	C₂³×C₂₈₃	C₂⁴
Fitting	#384×C₂₈₃	C₂
hypercenter	#384	D₂₈₃
hypocenter	C₂₈₃	#2868
LCS	G ▷ C₂³×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂³ ◁ #384

Complements

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

N	H ≅ G/N	type
21. C₄×Dic₂₈₃	Q₈	semidirect
25. C₄²×C₂₈₃	Q₈	semidirect
40. C₄×C₂₈₃	C₄⋊Q₈	semidirect
43. Dic₂₈₃	C₄⋊Q₈	semidirect
47. C₂₈₃	#2868	semidirect
73. C₄²	Dic₅₆₆	semidirect
91. C₄	#22583609	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22583609	2
#31826335	2
#31826334	2
C₄²×Dic₂₈₃	2
#384×C₂₈₃	2
#2868	283