Subgroups — #49121436

Order 36224.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22583546	C₂	1	4	yes	maximal
2	#31826489	C₂	1	2	yes	maximal
3	C₂×#97×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985376	C₂²	1	4	yes	—
5	#22583546	—	2	8	no	—
6	C₄⋊(C₂₈₃⋊C₈)	—	2	4	no	—
7	C₂²×C₈×C₂₈₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₈₃	C₂²	1	1	yes	characteristic
9	#97×C₂₈₃	C₄	1	4	yes	—
10	#17985376	—	2	8	no	—
11	C₂×C₂₈₃⋊C₈	—	2	4	no	—
12	C₂²×C₄×C₂₈₃	Q₈	1	2	yes	—
13	C₂²×C₄×C₂₈₃	C₂³	1	1	yes	characteristic
14	C₂×C₈×C₂₈₃	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₂₈₃	D₄	1	4	yes	—
16	C₂×C₈×C₂₈₃	Q₈	1	4	yes	—
17	C₄²×C₂₈₃	C₂×C₄	1	2	yes	—
18	C₄²×C₂₈₃	D₄	1	2	yes	—
19	C₂₈₃⋊C₈	—	4	4	no	—
20	C₂³×C₂₈₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₂₈₃	—	4	2	no	—
22	C₂×C₄×C₂₈₃	C₄⋊C₄	1	4	yes	—
23	C₂×C₄×C₂₈₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₈₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×C₂₈₃	C₂×Q₈	1	2	yes	—
27	C₈×C₂₈₃	C₄⋊C₄	1	8	yes	—
28	C₂²×C₂₈₃	—	2	2	no	—
29	C₂²×C₂₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₂₈₃	C₄⋊Q₈	1	2	yes	—
31	C₄×C₂₈₃	—	2	4	no	—
32	C₄×C₂₈₃	C₂×C₄⋊C₄	1	2	yes	—
33	C₄×C₂₈₃	#127	1	1	yes	characteristic
34	C₄×C₂₈₃	C₄⋊Q₈	1	1	yes	characteristic
35	C₂×C₂₈₃	—	2	2	no	—
36	C₂×C₂₈₃	#384	1	1	yes	characteristic
37	C₂×C₂₈₃	#430	1	2	yes	—
38	C₂₈₃	#1849	1	1	yes	characteristic, complemented, Sylow
39	#1849	—	283	1	no	maximal, Sylow
40	C₂×#108	—	283	4	no	—
41	#423	—	283	2	no	—
42	C₂×#97	D₂₈₃	1	1	yes	characteristic
43	C₂×M₁₆	—	283	4	no	—
44	C₂²×C₈	C₂×D₂₈₃	1	2	yes	—
45	C₂×C₄²	C₂×D₂₈₃	1	1	yes	characteristic
46	#108	—	566	8	no	—
47	C₄⋊C₈	—	566	4	no	—
48	#97	Dic₂₈₃	1	4	yes	—
49	C₂²×C₄	Dic₅₆₆	1	2	yes	—
50	C₂²×C₄	C₂²×D₂₈₃	1	1	yes	characteristic
51	M₁₆	—	566	8	no	—
52	C₂×C₈	—	566	4	no	—
53	C₂×C₈	C₂×Dic₂₈₃	1	4	yes	—
54	C₂×C₈	D₁₁₃₂	1	4	yes	—
55	C₂×C₈	Dic₅₆₆	1	4	yes	—
56	C₄²	C₂×Dic₂₈₃	1	2	yes	—
57	C₄²	D₁₁₃₂	1	2	yes	—
58	C₂³	C₂×Dic₅₆₆	1	1	yes	characteristic
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₄⋊Dic₂₈₃	1	4	yes	—
61	C₂×C₄	C₂²×Dic₂₈₃	1	1	yes	characteristic
62	C₂×C₄	C₂×D₁₁₃₂	1	2	yes	—
63	C₂×C₄	C₂×D₁₁₃₂	1	1	yes	characteristic
64	C₂×C₄	C₂×Dic₅₆₆	1	2	yes	—
65	C₈	—	1132	4	no	—
66	C₈	C₄⋊Dic₂₈₃	1	8	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₂₈₃	1	1	yes	characteristic
69	C₂²	#22583610	1	2	yes	—
70	C₄	—	2	4	no	—
71	C₄	C₂×C₄⋊Dic₂₈₃	1	2	yes	—
72	C₄	#22583607	1	1	yes	characteristic
73	C₄	#22583610	1	1	yes	characteristic
74	C₂	—	2	2	no	—
75	C₂	#31826335	1	1	yes	characteristic
76	C₂	#31826514	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₃₂
commutator	C₂×C₄×C₂₈₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₃
Fitting	C₂×#97×C₂₈₃	C₂
socle	C₂²×C₂₈₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₃	C₂³
hypercenter	C₂×#97	D₂₈₃
hypocenter	C₂₈₃	#1849
LCS	G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
38. C₂₈₃	#1849	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22583546	2
#31826489	2
C₂×#97×C₂₈₃	2
#1849	283