Subgroups — #49119308

Order 36224.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826842	C₂	1	1	yes	maximal, characteristic
2	#31826218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₁₆×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₂₆₄	—	2	1	no	—
5	C₂×D₂₂₆₄	C₄	1	2	yes	—
6	#22583607	—	2	1	no	—
7	C₄⋊(C₂₈₃⋊C₈)	—	2	1	no	—
8	C₂×C₁₆×C₂₈₃	—	2	1	no	—
9	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₂×D₁₁₃₂	—	2	2	no	—
11	C₂×D₁₁₃₂	—	4	1	no	—
12	C₂×D₁₁₃₂	—	4	1	no	—
13	D₂₂₆₄	—	4	2	no	—
14	D₂₂₆₄	—	4	1	no	—
15	D₂₂₆₄	—	4	1	no	—
16	C₂×C₂₈₃⋊C₈	—	4	1	no	—
17	C₂×C₈×C₂₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
19	C₄²×C₂₈₃	D₄	1	1	yes	characteristic
20	C₁₆×C₂₈₃	—	4	1	no	—
21	C₂²×D₂₈₃	—	4	2	no	—
22	D₁₁₃₂	—	4	2	no	—
23	D₁₁₃₂	—	4	2	no	—
24	D₁₁₃₂	—	8	2	no	—
25	D₁₁₃₂	—	8	1	no	—
26	D₁₁₃₂	—	8	1	no	—
27	C₂₈₃⋊C₈	—	8	1	no	—
28	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₂₈₃	SD₁₆	1	1	yes	characteristic
31	C₈×C₂₈₃	—	2	1	no	—
32	C₈×C₂₈₃	D₈	1	1	yes	characteristic
33	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
34	C₂²×C₂₈₃	#102	1	1	yes	characteristic
35	C₂×D₂₈₃	—	8	2	no	—
36	C₂×D₂₈₃	—	8	2	no	—
37	C₂×D₂₈₃	—	8	2	no	—
38	C₄×C₂₈₃	—	2	1	no	—
39	C₄×C₂₈₃	#100	1	1	yes	characteristic
40	C₄×C₂₈₃	#102	1	1	yes	characteristic
41	C₄×C₂₈₃	D₁₆	1	1	yes	characteristic
42	C₄×C₂₈₃	SD₃₂	1	1	yes	characteristic
43	C₂×C₂₈₃	#331	1	1	yes	characteristic
44	C₂×C₂₈₃	#357	1	1	yes	characteristic
45	C₂×C₂₈₃	#361	1	1	yes	characteristic
46	D₂₈₃	—	16	2	no	—
47	C₂₈₃	#1361	1	1	yes	characteristic, complemented, Sylow
48	#1361	—	283	1	no	maximal, Sylow
49	#493	—	283	1	no	—
50	C₄⋊C₁₆	D₂₈₃	1	1	yes	characteristic, complemented
51	#335	—	283	1	no	—
52	C₂×D₈	—	283	2	no	—
53	C₂×D₈	—	566	1	no	—
54	#127	—	566	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₄⋊C₈	—	566	1	no	—
57	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
58	C₂×D₄	—	566	2	no	—
59	C₂×D₄	—	1132	1	no	—
60	C₂×D₄	—	1132	1	no	—
61	D₈	—	1132	2	no	—
62	D₈	—	1132	1	no	—
63	D₈	—	1132	1	no	—
64	C₂×C₈	—	1132	1	no	—
65	C₂×C₈	C₄×D₂₈₃	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
67	C₄²	D₁₁₃₂	1	1	yes	characteristic
68	C₁₆	—	4	1	no	—
69	C₂³	—	1132	2	no	—
70	D₄	—	1132	2	no	—
71	D₄	—	1132	2	no	—
72	D₄	—	2264	2	no	—
73	D₄	—	2264	1	no	—
74	D₄	—	2264	1	no	—
75	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
76	C₂×C₄	D₂₂₆₄	1	1	yes	characteristic
77	C₂×C₄	#17985381	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	2264	1	no	—
80	C₈	#17985377	1	1	yes	characteristic
81	C₈	#17985379	1	1	yes	characteristic
82	C₂²	—	2264	2	no	—
83	C₂²	—	2264	2	no	—
84	C₂²	—	2264	2	no	—
85	C₂²	#22583532	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	#22583526	1	1	yes	characteristic
88	C₄	#22583530	1	1	yes	characteristic
89	C₄	D₄₅₂₈	1	1	yes	characteristic
90	C₄	#22583555	1	1	yes	characteristic
91	C₂	—	4528	2	no	—
92	C₂	#31826208	1	1	yes	characteristic
93	C₂	#31826267	1	1	yes	characteristic
94	C₂	#31826279	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22583532
commutator	C₂×C₈×C₂₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₃
Fitting	C₄⋊C₁₆×C₂₈₃	C₂
socle	C₂²×C₂₈₃	#102
prime radical	#31826842	C₂
cosocle	C₄×C₈×C₂₈₃	C₂²
hypercenter	C₄⋊C₁₆	D₂₈₃
hypocenter	C₂₈₃	#1361
LCS	G ▷ C₂×C₈×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #31826218	C₂	semidirect
3. C₄⋊C₁₆×C₂₈₃	C₂	semidirect
47. C₂₈₃	#1361	semidirect
50. C₄⋊C₁₆	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#31826842	2
#31826218	2
C₄⋊C₁₆×C₂₈₃	2
#1361	283