Subgroups — #11772667

Order 1152.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃⋊C₃₂	C₂	1	2	yes	maximal
3	#67589	—	3	2	no	maximal
4	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
5	C₈×C₃⋊Dic₃	C₄	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
7	C₃×C₃⋊C₃₂	C₄	1	4	yes	complemented
8	C₂×C₃×C₃₂	—	3	2	no	—
9	Dic₃×C₁₆	—	3	2	no	—
10	Dic₃×C₁₆	—	6	1	no	—
11	C₂×C₃⋊C₃₂	D₃	1	2	yes	—
12	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
13	C₄×C₃⋊Dic₃	C₈	1	1	yes	characteristic
14	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
15	C₃²×C₁₆	C₂×C₄	1	2	yes	—
16	C₃⋊(C₃⋊C₁₆)	C₈	1	2	yes	—
17	#1397	—	9	1	no	Sylow
18	C₂×C₃×C₁₆	—	2	1	no	—
19	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
20	C₈×Dic₃	—	3	2	no	—
21	C₈×Dic₃	—	6	1	no	—
22	C₂×C₃⋊C₁₆	—	3	2	no	—
23	C₂×C₃⋊C₁₆	—	6	1	no	—
24	C₃×C₃₂	—	3	4	no	—
25	C₃⋊C₃₂	Dic₃	1	4	yes	complemented
26	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
27	C₂×C₃⋊Dic₃	C₁₆	1	2	yes	—
28	C₃²×C₈	C₄²	1	1	yes	characteristic
29	C₃²×C₈	C₂×C₈	1	1	yes	characteristic
30	C₃⋊(C₃⋊C₈)	C₁₆	1	2	yes	—
31	C₂×C₃₂	—	3	2	no	—
32	C₄×C₁₆	—	9	1	no	—
33	C₂×C₃×C₈	—	2	1	no	—
34	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
35	C₄×Dic₃	—	3	2	no	—
36	C₄×Dic₃	—	6	1	no	—
37	C₂×C₃⋊C₈	—	3	2	no	—
38	C₂×C₃⋊C₈	—	6	1	no	—
39	C₃×C₁₆	—	2	2	no	—
40	C₃×C₁₆	C₄×D₃	1	2	yes	—
41	C₃×C₁₆	C₂×Dic₃	1	2	yes	—
42	C₃⋊C₁₆	—	3	4	no	—
43	C₃⋊C₁₆	—	6	2	no	—
44	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
45	C₃²×C₄	C₄×C₈	1	1	yes	characteristic
46	C₃²×C₄	C₂×C₁₆	1	1	yes	characteristic
47	C₃⋊Dic₃	—	2	2	no	—
48	C₂×C₁₆	—	9	1	no	—
49	C₂×C₁₆	D₃²	1	1	yes	characteristic
50	C₄×C₈	—	9	1	no	—
51	C₃₂	—	3	4	no	—
52	C₂×C₃×C₄	—	2	1	no	—
53	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
54	C₂×Dic₃	—	3	4	no	—
55	C₂×Dic₃	—	6	2	no	—
56	C₃×C₈	—	2	1	no	—
57	C₃×C₈	—	2	1	no	—
58	C₃×C₈	D₃×C₈	1	2	yes	—
59	C₃×C₈	C₄×Dic₃	1	2	yes	—
60	C₃⋊C₈	—	3	4	no	—
61	C₃⋊C₈	—	6	2	no	—
62	C₂×C₃²	C₄×C₁₆	1	1	yes	characteristic
63	C₂×C₃²	M₆₄	1	2	yes	—
64	C₂×C₈	—	9	1	no	—
65	C₂×C₈	#624	1	1	yes	characteristic
66	C₄²	—	9	1	no	—
67	C₁₆	—	9	2	no	—
68	C₁₆	D₃×Dic₃	1	2	yes	—
69	C₂²×C₃	—	2	1	no	—
70	C₂²×C₃	D₃×C₁₆	1	2	yes	—
71	C₃×C₄	—	2	1	no	—
72	C₃×C₄	—	2	1	no	—
73	C₃×C₄	D₃×C₁₆	1	2	yes	—
74	C₃×C₄	C₈×Dic₃	1	2	yes	—
75	Dic₃	—	6	4	no	—
76	Dic₃	—	6	4	no	—
77	C₃²	#1397	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₄	—	9	2	no	—
79	C₂×C₄	#3710	1	1	yes	characteristic
80	C₈	—	9	2	no	—
81	C₈	#3710	1	1	yes	characteristic
82	C₈	Dic₃²	1	1	yes	characteristic
83	C₂×C₃	—	2	2	no	—
84	C₂×C₃	—	2	1	no	—
85	C₂×C₃	#4447	1	4	yes	—
86	C₂×C₃	Dic₃×C₁₆	1	2	yes	—
87	C₂²	#63542	1	1	yes	characteristic
88	C₄	—	18	2	no	—
89	C₄	#63542	1	1	yes	characteristic
90	C₄	#63553	1	1	yes	characteristic
91	C₃	—	2	1	no	—
92	C₃	#67589	1	2	yes	complemented
93	C₂	#10589069	1	2	yes	—
94	C₂	#10589102	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₁₆	D₃²
commutator	C₂×C₃²	C₄×C₁₆
Fitting, cosocle	C₂×C₃²×C₁₆	C₂²
socle, prime radical	C₂²×C₃²	C₂×C₁₆
hypocenter	C₃²	#1397
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
7. C₃×C₃⋊C₃₂	C₄	semidirect
25. C₃⋊C₃₂	Dic₃	semidirect
77. C₃²	#1397	semidirect
92. C₃	#67589	semidirect

Maximal subgroups

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

subgroup	index
C₁₆×C₃⋊Dic₃	2
C₂×C₃×C₃⋊C₃₂	2
#67589	3