Subgroups — #11722389

Order 864.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#3688	C₂	1	2	yes	maximal, complemented
3	#64160	—	3	1	no	maximal
4	#63690	—	3	3	no	maximal
5	#6226	—	4	1	no	maximal
6	C₃×Q₈⋊C₉	C₂²	1	1	yes	characteristic
7	C₃²×#41	D₃	1	1	yes	characteristic
8	C₂×#634	—	3	1	no	—
9	#3756	—	3	2	no	—
10	#3754	—	3	2	no	—
11	#3748	—	3	1	no	—
12	#41⋊C₉	D₃	1	3	yes	—
13	#3688	—	3	6	no	—
14	C₃×C₄×C₉	—	4	1	no	—
15	C₃⋊Dic₉	—	4	2	no	—
16	#951	—	9	3	no	—
17	#951	—	9	1	no	—
18	C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
19	C₃²×D₄	—	3	1	no	—
20	C₂×C₃²×C₄	—	3	1	no	—
21	C₂×C₃⋊Dic₃	—	6	1	no	—
22	#634	—	3	2	no	—
23	#634	—	6	1	no	—
24	C₃⋊(C₃⋊C₈)	—	3	2	no	—
25	Dic₁₈	—	12	3	no	—
26	Q₈⋊C₉	C₂×D₃	1	3	yes	—
27	C₂×C₃×C₉	—	4	1	no	—
28	C₃×#41	D₉	1	3	yes	—
29	C₃×#41	C₃⋊D₃	1	1	yes	characteristic
30	C₂×Dic₆	—	9	3	no	—
31	C₂×Dic₆	—	9	1	no	—
32	#216	—	9	6	no	—
33	#216	—	9	2	no	—
34	#214	—	9	6	no	—
35	#214	—	9	2	no	—
36	#208	—	9	3	no	—
37	#208	—	9	1	no	—
38	C₂²×C₃²	—	3	1	no	—
39	C₃²×C₄	—	3	1	no	—
40	C₃²×C₄	S₄	1	1	yes	characteristic
41	C₃⋊Dic₃	—	6	2	no	—
42	C₄×C₉	—	4	3	no	—
43	Dic₉	—	12	6	no	—
44	#137	—	27	1	no	Sylow
45	C₃×C₉	—	4	1	no	Sylow
46	C₃×Q₈	C₂×D₉	1	3	yes	—
47	C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
48	C₃×D₄	—	3	3	no	—
49	C₃×D₄	—	3	1	no	—
50	C₂×C₃×C₄	—	3	3	no	—
51	C₂×C₃×C₄	—	3	1	no	—
52	C₂×Dic₃	—	18	1	no	—
53	C₂×Dic₃	—	18	3	no	—
54	Dic₆	—	9	2	no	—
55	Dic₆	—	9	6	no	—
56	Dic₆	—	18	3	no	—
57	Dic₆	—	18	1	no	—
58	C₃⋊C₈	—	9	2	no	—
59	C₃⋊C₈	—	9	6	no	—
60	C₂×C₃²	—	6	1	no	—
61	C₂×C₃²	C₂×S₄	1	1	yes	characteristic
62	C₂×C₉	—	4	3	no	—
63	#41	C₃⋊D₉	1	1	yes	characteristic
64	C₂×Q₈	—	27	1	no	—
65	Q₁₆	—	27	2	no	—
66	SD₁₆	—	27	2	no	—
67	M₁₆	—	27	1	no	—
68	C₂²×C₃	—	3	1	no	—
69	C₂²×C₃	—	3	3	no	—
70	C₃×C₄	—	3	1	no	—
71	C₃×C₄	—	3	3	no	—
72	C₃×C₄	(C₂²⋊C₉)⋊C₂	1	3	yes	—
73	C₃×C₄	C₃⋊S₄	1	1	yes	characteristic
74	Dic₃	—	18	2	no	—
75	Dic₃	—	18	6	no	—
76	C₃²	#984	1	1	yes	characteristic
77	C₉	—	4	3	no	—
78	Q₈	—	27	2	no	—
79	Q₈	—	54	1	no	—
80	Q₈	C₂×C₃⋊D₉	1	1	yes	characteristic
81	D₄	—	3	1	no	—
82	C₂×C₄	—	3	1	no	—
83	C₂×C₄	—	54	1	no	—
84	C₈	—	27	2	no	—
85	C₂×C₃	—	6	1	no	—
86	C₂×C₃	—	6	3	no	—
87	C₂×C₃	C₂×(C₂²⋊C₉)⋊C₂	1	3	yes	—
88	C₂×C₃	C₂×C₃⋊S₄	1	1	yes	characteristic
89	C₂²	—	3	1	no	—
90	C₄	—	3	1	no	—
91	C₄	—	54	2	no	—
92	C₄	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic
93	C₃	#63690	1	3	yes	complemented
94	C₃	#64265	1	1	yes	characteristic
95	C₂	—	6	1	no	—
96	C₂	C₂×C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊((C₂²⋊C₉)⋊C₂)
commutator, cosocle, hypocenter	C₃×Q₈⋊C₉	C₂²
Frattini	C₂×C₃	C₂×C₃⋊S₄
Fitting, prime radical	C₃²×#41	D₃
socle	C₂×C₃²	C₂×S₄
hypercenter	C₄	C₃⋊((C₂²⋊C₉)⋊C₂)
LCS	G ▷ C₃×Q₈⋊C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊#3688	C₂	semidirect
93. C₃	#63690	semidirect

Maximal subgroups

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

subgroup	index
C₃×#41⋊C₉	2
C₃⋊#3688	2
#64160	3
#63690	3
#6226	4