Subgroups — #11772995

Order 1152.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₂	C₂	1	1	yes	maximal, characteristic
2	C₉×M₆₄	C₂	1	1	yes	maximal, characteristic
3	#10588183	C₂	1	1	yes	maximal, characteristic
4	#67605	—	3	1	no	maximal
5	C₂×Dic₃₆	—	2	1	no	—
6	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
7	#63372	—	2	1	no	—
8	Dic₇₂	—	2	1	no	—
9	Dic₇₂	C₄	1	2	yes	—
10	C₉×C₃₂	—	2	1	no	—
11	C₂×Dic₂₄	—	3	1	no	—
12	C₃×M₆₄	D₃	1	1	yes	characteristic
13	#4506	—	3	1	no	—
14	C₂×Dic₁₈	—	4	1	no	—
15	C₂×C₈×C₉	D₄	1	1	yes	characteristic
16	#3667	—	4	1	no	—
17	Dic₃₆	—	2	2	no	—
18	Dic₃₆	—	4	1	no	—
19	C₉×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₉×C₁₆	D₄	1	1	yes	characteristic
21	#1420	—	9	1	no	Sylow
22	C₂×Dic₁₂	—	6	1	no	—
23	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
24	#819	—	6	1	no	—
25	Dic₂₄	—	3	2	no	—
26	Dic₂₄	—	6	1	no	—
27	C₃×C₃₂	—	2	1	no	—
28	C₂×C₄×C₉	D₈	1	1	yes	characteristic
29	C₂×Dic₉	—	8	1	no	—
30	Dic₁₈	—	4	2	no	—
31	Dic₁₈	—	8	1	no	—
32	C₈×C₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₉	SD₁₆	1	1	yes	characteristic
34	C₉⋊C₈	—	8	1	no	—
35	C₂×Q₃₂	—	9	1	no	—
36	M₆₄	D₉	1	1	yes	characteristic
37	#368	—	9	1	no	—
38	C₂×Dic₆	—	12	1	no	—
39	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
40	#208	—	12	1	no	—
41	Dic₁₂	—	6	2	no	—
42	Dic₁₂	—	12	1	no	—
43	C₃×C₁₆	C₄×D₃	1	1	yes	characteristic
44	C₃×C₁₆	#67	1	1	yes	characteristic
45	C₂²×C₉	SD₃₂	1	1	yes	characteristic
46	C₄×C₉	#102	1	1	yes	characteristic
47	C₄×C₉	D₁₆	1	1	yes	characteristic
48	Dic₉	—	8	2	no	—
49	C₂×Q₁₆	—	18	1	no	—
50	Q₃₂	—	9	2	no	—
51	Q₃₂	—	18	1	no	—
52	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
53	#108	—	18	1	no	—
54	C₃₂	—	2	1	no	—
55	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
56	C₂×Dic₃	—	24	1	no	—
57	Dic₆	—	12	2	no	—
58	Dic₆	—	24	1	no	—
59	C₃×C₈	#204	1	1	yes	characteristic
60	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
61	C₃⋊C₈	—	24	1	no	—
62	C₂×C₉	—	2	1	no	—
63	C₂×C₉	#357	1	1	yes	characteristic
64	C₂×Q₈	—	36	1	no	—
65	Q₁₆	—	18	2	no	—
66	Q₁₆	—	36	1	no	—
67	M₁₆	—	36	1	no	—
68	C₂×C₈	D₃₆	1	1	yes	characteristic
69	C₁₆	C₄×D₉	1	1	yes	characteristic
70	C₁₆	#611	1	1	yes	characteristic
71	C₂²×C₃	#800	1	1	yes	characteristic
72	C₃×C₄	D₄₈	1	1	yes	characteristic
73	C₃×C₄	#821	1	1	yes	characteristic
74	Dic₃	—	24	2	no	—
75	C₉	#1420	1	1	yes	characteristic, complemented, Sylow
76	Q₈	—	36	2	no	—
77	Q₈	—	72	1	no	—
78	C₂×C₄	—	72	1	no	—
79	C₂×C₄	D₇₂	1	1	yes	characteristic
80	C₈	—	72	1	no	—
81	C₈	#3664	1	1	yes	characteristic
82	C₈	(C₂×D₉)⋊C₄	1	1	yes	characteristic
83	C₂×C₃	—	2	1	no	—
84	C₂×C₃	#4509	1	1	yes	characteristic
85	C₂²	#63359	1	1	yes	characteristic
86	C₄	—	72	2	no	—
87	C₄	D₁₄₄	1	1	yes	characteristic
88	C₄	#63380	1	1	yes	characteristic
89	C₃	#67605	1	1	yes	characteristic
90	C₂	—	2	1	no	—
91	C₂	#10588186	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10588186
commutator	C₉×C₁₆	C₂×C₄
Frattini	C₂×C₃×C₁₆	C₂×D₃
Fitting	C₉×M₆₄	C₂
socle	C₂×C₃	#4509
prime radical	C₂²×C₃	#800
cosocle	C₂×C₉×C₁₆	C₂²
hypercenter	M₆₄	D₉
hypocenter	C₉	#1420
LCS	G ▷ C₉×C₁₆ ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
75. C₉	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₇₂	2
C₉×M₆₄	2
#10588183	2
#67605	3