Subgroups — #11786125

Order 1152.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
2	#10588200	C₂	1	6	yes	maximal
3	#69393	—	3	1	no	maximal
4	C₂×C₄²×C₉	C₄	1	3	yes	—
5	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₉	C₂²	1	3	yes	—
7	C₂²×C₉⋊C₈	C₂²	1	4	yes	—
8	C₃×C₄³	D₃	1	1	yes	characteristic
9	#4524	—	3	6	no	—
10	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
11	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
12	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
13	C₄²×C₉	—	2	6	no	—
14	C₄²×C₉	—	2	6	no	—
15	C₄²×C₉	C₈	1	4	yes	complemented
16	C₂×C₉⋊C₈	—	2	12	no	—
17	#1839	—	9	1	no	Sylow
18	C₂×C₃×C₄²	Dic₃	1	3	yes	—
19	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
20	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
21	C₂²×C₃⋊C₈	—	3	4	no	—
22	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₉	—	2	3	no	—
24	C₂×C₄×C₉	—	2	3	no	—
25	C₂×C₄×C₉	—	2	3	no	—
26	C₂×C₄×C₉	—	2	3	no	—
27	C₂×C₄×C₉	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₉	M₁₆	1	6	yes	—
29	C₂×C₄×C₉	#41	1	6	yes	—
30	C₉⋊C₈	—	4	4	no	—
31	C₄³	D₉	1	1	yes	characteristic
32	#336	—	9	6	no	—
33	C₂²×C₃×C₄	C₂×Dic₃	1	3	yes	—
34	C₂²×C₃×C₄	C₂×Dic₃	1	3	yes	—
35	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
36	C₃×C₄²	—	2	6	no	—
37	C₃×C₄²	—	2	6	no	—
38	C₃×C₄²	C₃⋊C₈	1	4	yes	—
39	C₂×C₃⋊C₈	—	6	12	no	—
40	C₂²×C₉	#117	1	3	yes	—
41	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₉	C₂×M₁₆	1	3	yes	—
43	C₄×C₉	—	2	6	no	—
44	C₄×C₉	—	2	6	no	—
45	C₄×C₉	#126	1	4	yes	—
46	C₂²×C₈	—	9	4	no	—
47	C₂×C₄²	Dic₉	1	3	yes	—
48	C₂×C₄²	Dic₉	1	1	yes	characteristic
49	C₂×C₄²	C₂×D₉	1	3	yes	—
50	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
51	C₂×C₃×C₄	—	2	3	no	—
52	C₂×C₃×C₄	—	2	3	no	—
53	C₂×C₃×C₄	—	2	3	no	—
54	C₂×C₃×C₄	—	2	3	no	—
55	C₂×C₃×C₄	C₂×C₃⋊C₈	1	6	yes	—
56	C₂×C₃×C₄	#208	1	6	yes	—
57	C₂×C₃×C₄	#235	1	6	yes	—
58	C₃⋊C₈	—	12	4	no	—
59	C₂×C₉	#383	1	1	yes	characteristic
60	C₂×C₉	#431	1	3	yes	—
61	C₂×C₉	#432	1	3	yes	—
62	C₂²×C₄	C₂×Dic₉	1	3	yes	—
63	C₂²×C₄	C₂×Dic₉	1	3	yes	—
64	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
65	C₂×C₈	—	18	12	no	—
66	C₄²	—	2	6	no	—
67	C₄²	—	2	6	no	—
68	C₄²	C₉⋊C₈	1	4	yes	complemented
69	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
70	C₂²×C₃	C₂×#208	1	3	yes	—
71	C₂²×C₃	#926	1	3	yes	—
72	C₃×C₄	—	2	6	no	—
73	C₃×C₄	—	2	6	no	—
74	C₃×C₄	#876	1	4	yes	—
75	C₉	#1839	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂²×Dic₉	1	1	yes	characteristic
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	C₂×C₉⋊C₈	1	6	yes	—
82	C₂×C₄	#3667	1	6	yes	—
83	C₂×C₄	#3697	1	6	yes	—
84	C₈	—	36	4	no	—
85	C₂×C₃	#4925	1	3	yes	—
86	C₂×C₃	#4926	1	3	yes	—
87	C₂×C₃	#4937	1	1	yes	characteristic
88	C₂²	C₂²×C₉⋊C₈	1	1	yes	characteristic
89	C₂²	C₂×#3667	1	3	yes	—
90	C₂²	#63488	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	#63438	1	4	yes	—
94	C₃	#69393	1	1	yes	characteristic
95	C₂	#10588605	1	3	yes	—
96	C₂	#10588606	1	3	yes	—
97	C₂	#10588617	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₈
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₄³×C₉	C₂
socle, prime radical	C₂³×C₃	C₂²×Dic₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₄³	D₉
hypocenter	C₉	#1839
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
15. C₄²×C₉	C₈	semidirect
68. C₄²	C₉⋊C₈	semidirect
75. C₉	#1839	semidirect

Maximal subgroups

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

subgroup	index
C₄³×C₉	2
#10588200	2
#69393	3