Subgroups — #11772701

Order 1152.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#10588176	C₂	1	2	yes	maximal, complemented
3	#67809	—	3	1	no	maximal
4	C₂²×C₈×C₉	C₄	1	1	yes	characteristic
5	C₉×M₃₂	—	2	2	no	—
6	C₂×C₉×C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
8	C₉⋊C₃₂	—	2	2	no	—
9	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic
10	#4499	—	3	2	no	—
11	C₂²×C₄×C₉	C₈	1	1	yes	characteristic
12	C₂×C₈×C₉	—	2	1	no	—
13	C₂×C₈×C₉	—	2	1	no	—
14	C₂×C₈×C₉	C₈	1	1	yes	characteristic
15	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×C₁₆	—	2	1	no	—
17	C₉×C₁₆	D₄	1	2	yes	—
18	#1400	—	9	1	no	Sylow
19	C₂²×C₃×C₈	Dic₃	1	1	yes	characteristic
20	C₃×M₃₂	—	2	2	no	—
21	C₂×C₃×C₁₆	Dic₃	1	1	yes	characteristic
22	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
23	C₃⋊C₃₂	—	6	2	no	—
24	C₂³×C₉	C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₉	—	2	1	no	—
26	C₂×C₄×C₉	—	2	1	no	—
27	C₂×C₄×C₉	C₁₆	1	1	yes	characteristic
28	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
29	C₈×C₉	—	2	1	no	—
30	C₈×C₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₉	M₁₆	1	1	yes	characteristic
32	C₂×M₃₂	D₉	1	1	yes	characteristic
33	M₆₄	—	9	2	no	—
34	C₂²×C₃×C₄	C₃⋊C₈	1	1	yes	characteristic
35	C₂×C₃×C₈	—	2	1	no	—
36	C₂×C₃×C₈	—	2	1	no	—
37	C₂×C₃×C₈	C₃⋊C₈	1	1	yes	characteristic
38	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
39	C₃×C₁₆	—	2	1	no	—
40	C₃×C₁₆	#67	1	2	yes	—
41	C₂²×C₉	—	2	1	no	—
42	C₂²×C₉	—	4	1	no	—
43	C₂²×C₉	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₉	—	2	1	no	—
45	C₄×C₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₄×C₉	M₃₂	1	1	yes	characteristic
47	C₂²×C₈	Dic₉	1	1	yes	characteristic
48	M₃₂	—	2	2	no	—
49	C₂×C₁₆	Dic₉	1	1	yes	characteristic
50	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
51	C₃₂	—	18	2	no	—
52	C₂³×C₃	C₃⋊C₁₆	1	1	yes	characteristic
53	C₂×C₃×C₄	—	2	1	no	—
54	C₂×C₃×C₄	—	2	1	no	—
55	C₂×C₃×C₄	C₃⋊C₁₆	1	1	yes	characteristic
56	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
57	C₃×C₈	—	2	1	no	—
58	C₃×C₈	#208	1	1	yes	characteristic
59	C₃×C₈	#217	1	1	yes	characteristic
60	C₂×C₉	—	2	1	no	—
61	C₂×C₉	—	4	1	no	—
62	C₂×C₉	C₂²⋊C₁₆	1	1	yes	characteristic
63	C₂²×C₄	C₉⋊C₈	1	1	yes	characteristic
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	C₉⋊C₈	1	1	yes	characteristic
67	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	#611	1	2	yes	—
70	C₂²×C₃	—	2	1	no	—
71	C₂²×C₃	—	4	1	no	—
72	C₂²×C₃	C₂×C₃⋊C₁₆	1	1	yes	characteristic
73	C₃×C₄	—	2	1	no	—
74	C₃×C₄	#812	1	1	yes	characteristic
75	C₃×C₄	#830	1	1	yes	characteristic
76	C₉	#1400	1	1	yes	characteristic, complemented, Sylow
77	C₂³	C₉⋊C₁₆	1	1	yes	characteristic
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	C₉⋊C₁₆	1	1	yes	characteristic
81	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	#3667	1	1	yes	characteristic
84	C₈	#3676	1	1	yes	characteristic
85	C₂×C₃	—	2	1	no	—
86	C₂×C₃	—	4	1	no	—
87	C₂×C₃	#4549	1	1	yes	characteristic
88	C₂²	—	2	1	no	—
89	C₂²	—	4	1	no	—
90	C₂²	C₂×C₉⋊C₁₆	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	#63371	1	1	yes	characteristic
93	C₄	#63389	1	1	yes	characteristic
94	C₃	#67809	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	4	1	no	—
97	C₂	#10588226	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#3676
commutator	C₂²×C₉	C₂×C₁₆
Frattini	C₂×C₃×C₁₆	C₂×D₃
Fitting	C₂×C₉×M₃₂	C₂
socle	C₂×C₃	#4549
prime radical	C₂³×C₃	C₃⋊C₁₆
cosocle	C₂×C₉×C₁₆	C₂²
hypercenter	C₂×M₃₂	D₉
hypocenter	C₉	#1400
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #10588176	C₂	semidirect
76. C₉	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×M₃₂	2
#10588176	2
#67809	3