Subgroups — #11773687

Order 1152.

321 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#3663	C₂	1	3	yes	maximal
2	C₈²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588132	C₂	1	3	yes	maximal, complemented
4	#68050	—	3	1	no	maximal
5	C₂×#3663	C₄	1	6	yes	—
6	C₄²×D₉	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₉	C₂²	1	3	yes	—
8	#63375	C₄	1	6	yes	—
9	C₄×C₉⋊C₈	C₂²	1	3	yes	—
10	C₄×ΓL(1,𝔽₂₅)	—	3	3	no	—
11	C₃×C₈²	D₃	1	1	yes	characteristic
12	#4455	—	3	3	no	—
13	C₂×C₄×D₉	C₂×C₄	1	3	yes	—
14	C₂×C₈×C₉	C₂×C₄	1	6	yes	—
15	C₄²×C₉	C₂³	1	1	yes	characteristic
16	C₄×Dic₉	C₂×C₄	1	3	yes	—
17	C₂×C₉⋊C₈	C₂×C₄	1	6	yes	—
18	#3663	—	2	12	no	—
19	#1455	—	9	1	no	Sylow
20	C₂×ΓL(1,𝔽₂₅)	—	3	6	no	—
21	C₄²×D₃	—	3	1	no	—
22	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
23	#815	—	3	6	no	—
24	C₄×C₃⋊C₈	—	3	3	no	—
25	C₂²×D₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₉	C₂²×C₄	1	3	yes	—
27	C₂×Dic₉	C₄²	1	3	yes	—
28	C₄×D₉	—	2	6	no	—
29	C₈×C₉	M₁₆	1	12	yes	complemented
30	C₉⋊C₈	—	2	6	no	—
31	C₄×M₁₆	—	9	3	no	—
32	#322	—	9	3	no	—
33	C₈²	D₉	1	1	yes	characteristic, complemented
34	C₂×C₄×D₃	—	3	3	no	—
35	C₂×C₃×C₈	C₄×D₃	1	6	yes	—
36	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
37	C₄×Dic₃	—	3	3	no	—
38	C₂×C₃⋊C₈	—	3	6	no	—
39	ΓL(1,𝔽₂₅)	—	6	12	no	—
40	C₂²×C₉	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₉	—	2	3	no	—
42	C₄×C₉	C₂×M₁₆	1	6	yes	—
43	Dic₉	—	2	3	no	—
44	C₂×M₁₆	—	9	6	no	—
45	C₂×C₄²	—	9	1	no	—
46	#97	—	9	6	no	—
47	C₄×C₈	—	9	3	no	—
48	C₄×C₈	C₂×D₉	1	3	yes	—
49	C₂²×D₃	—	3	1	no	—
50	C₂×C₃×C₄	C₂×C₄×D₃	1	3	yes	—
51	C₂×Dic₃	—	3	3	no	—
52	C₄×D₃	—	6	6	no	—
53	C₃×C₈	ΓL(1,𝔽₂₅)	1	12	yes	—
54	C₃⋊C₈	—	6	6	no	—
55	C₂×C₉	C₄×M₁₆	1	3	yes	—
56	D₉	—	4	1	no	—
57	C₂²×C₄	—	9	3	no	—
58	M₁₆	—	18	12	no	—
59	C₂×C₈	—	9	6	no	—
60	C₂×C₈	C₄×D₉	1	6	yes	—
61	C₄²	—	9	3	no	—
62	C₄²	C₂²×D₉	1	1	yes	characteristic
63	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
64	C₂×D₃	—	6	3	no	—
65	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	6	yes	—
66	Dic₃	—	6	3	no	—
67	C₉	#1455	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	9	1	no	—
69	C₂×C₄	—	9	3	no	—
70	C₂×C₄	—	18	6	no	—
71	C₂×C₄	C₂×C₄×D₉	1	3	yes	—
72	C₈	—	18	6	no	—
73	C₈	#3663	1	12	yes	complemented
74	C₂×C₃	C₄×ΓL(1,𝔽₂₅)	1	3	yes	—
75	D₃	—	12	1	no	—
76	C₂²	—	18	3	no	—
77	C₂²	C₄²×D₉	1	1	yes	characteristic
78	C₄	—	18	3	no	—
79	C₄	C₂×#3663	1	6	yes	—
80	C₃	#68050	1	1	yes	characteristic
81	C₂	—	36	1	no	—
82	C₂	C₄×#3663	1	3	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₉
commutator	C₂²×C₉	C₂×C₄²
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₈²×C₉	C₂
socle	C₂²×C₃	C₄²×D₃
prime radical	C₂²×D₉	C₄²
cosocle	C₄²×C₉	C₂³
hypercenter	C₈²	D₉
hypocenter	C₉	#1455
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₈²×C₉	C₂	semidirect
3. #10588132	C₂	semidirect
29. C₈×C₉	M₁₆	semidirect
33. C₈²	D₉	semidirect
67. C₉	#1455	semidirect
73. C₈	#3663	semidirect

Maximal subgroups

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

subgroup	index
C₄×#3663	2
C₈²×C₉	2
#10588132	2
#68050	3