Subgroups — #11771273

Order 1152.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593730	C₂	1	3	yes	maximal
2	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
3	#63778	C₄	1	6	yes	—
4	#63777	—	2	3	no	—
5	C₄⋊#622	—	2	3	no	—
6	C₂×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
7	C₂×#622	—	2	6	no	—
8	C₃²×C₄²	Q₈	1	1	yes	characteristic
9	C₄×C₃⋊Dic₃	D₄	1	3	yes	—
10	#1308	—	9	1	no	maximal, Sylow
11	C₄²×D₃	—	12	1	no	—
12	C₂²×C₃⋊D₃	C₄²	1	1	yes	characteristic
13	C₂×C₃²×C₄	C₄⋊C₄	1	3	yes	—
14	C₂×C₃⋊Dic₃	C₂²⋊C₄	1	3	yes	—
15	C₄×C₃⋊D₃	—	4	3	no	—
16	#622	—	4	6	no	—
17	#432	—	9	3	no	—
18	C₂×C₄×D₃	—	12	3	no	—
19	C₃×C₄²	—	4	1	no	—
20	C₄×Dic₃	—	12	3	no	—
21	C₂²×C₃²	#95	1	1	yes	characteristic
22	C₂×C₃⋊D₃	—	2	3	no	—
23	C₃²×C₄	—	2	3	no	—
24	C₃⋊Dic₃	—	2	3	no	—
25	C₂×C₄²	—	9	1	no	—
26	C₄⋊C₈	—	18	3	no	—
27	C₂²⋊C₈	—	9	6	no	—
28	#97	—	18	3	no	—
29	C₂²×D₃	—	12	1	no	—
30	C₂×C₃×C₄	—	4	3	no	—
31	C₂×Dic₃	—	12	3	no	—
32	C₄×D₃	—	12	12	no	—
33	C₂×C₃²	#344	1	3	yes	—
34	C₃⋊D₃	—	4	1	no	—
35	C₂²×C₄	—	9	3	no	—
36	C₂×C₈	—	18	6	no	—
37	C₄²	—	9	3	no	—
38	C₄²	PSU(3,𝔽₂)	1	1	yes	characteristic
39	C₂²×C₃	—	4	1	no	—
40	C₂×D₃	—	12	6	no	—
41	C₃×C₄	—	4	6	no	—
42	Dic₃	—	12	6	no	—
43	C₃²	#1308	1	1	yes	characteristic, complemented, Sylow
44	C₂³	—	9	1	no	—
45	C₂×C₄	—	9	3	no	—
46	C₂×C₄	—	36	3	no	—
47	C₂×C₄	#3777	1	3	yes	—
48	C₈	—	36	6	no	—
49	C₂×C₃	—	4	3	no	—
50	D₃	—	12	4	no	—
51	C₂²	—	18	3	no	—
52	C₂²	#63747	1	1	yes	characteristic
53	C₄	—	2	3	no	—
54	C₄	—	18	3	no	—
55	C₃	—	4	1	no	—
56	C₂	—	36	1	no	—
57	C₂	#10590095	1	3	yes	—

	subgroup	G/H
center	C₂²	#63747
commutator, prime radical	C₂²×C₃⋊D₃	C₄²
Frattini, hypercenter	C₄²	PSU(3,𝔽₂)
Fitting	C₃²×C₄²	Q₈
socle	C₂²×C₃²	#95
cosocle	C₄²×C₃⋊D₃	C₂²
hypocenter	C₃²	#1308
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
43. C₃²	#1308	semidirect

Maximal subgroups

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

subgroup	index
#10593730	2
#1308	9