Subgroups — #11770703

Order 1152.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#3787	C₂	1	3	yes	maximal
2	C₂×#3787	C₄	1	6	yes	—
3	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	C₄×#622	—	2	6	no	—
5	C₂×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
6	C₂×#622	—	2	6	no	—
7	#3787	—	2	6	no	—
8	#3787	C₈	1	12	yes	complemented
9	C₃²×C₄²	Q₈	1	1	yes	characteristic
10	C₄×C₃⋊Dic₃	D₄	1	3	yes	—
11	#1273	—	9	1	no	maximal, Sylow
12	C₄²×D₃	—	12	1	no	—
13	C₂²×C₃⋊D₃	C₄²	1	1	yes	characteristic
14	C₂×C₃²×C₄	C₄⋊C₄	1	3	yes	—
15	C₂×C₃⋊Dic₃	C₂²⋊C₄	1	3	yes	—
16	C₄×C₃⋊D₃	C₂×C₈	1	6	yes	—
17	C₄×C₃⋊D₃	M₁₆	1	6	yes	—
18	#622	—	2	12	no	—
19	C₂×C₄×C₈	—	9	3	no	—
20	C₂×C₄×D₃	—	12	3	no	—
21	C₃×C₄²	—	4	1	no	—
22	C₄×Dic₃	—	12	3	no	—
23	C₂²×C₃²	#95	1	1	yes	characteristic
24	C₂×C₃⋊D₃	C₄×C₈	1	3	yes	—
25	C₂×C₃⋊D₃	#97	1	3	yes	—
26	C₃²×C₄	C₄⋊C₈	1	6	yes	—
27	C₃⋊Dic₃	C₂²⋊C₈	1	6	yes	—
28	C₂²×C₈	—	9	6	no	—
29	C₂×C₄²	—	9	1	no	—
30	C₄×C₈	—	18	6	no	—
31	C₂²×D₃	—	12	1	no	—
32	C₂×C₃×C₄	—	4	3	no	—
33	C₂×Dic₃	—	12	3	no	—
34	C₄×D₃	—	12	6	no	—
35	C₄×D₃	—	12	6	no	—
36	C₂×C₃²	#336	1	3	yes	—
37	C₃⋊D₃	C₈²	1	1	yes	characteristic
38	C₃⋊D₃	#322	1	3	yes	—
39	C₂²×C₄	—	9	3	no	—
40	C₂×C₈	—	9	12	no	—
41	C₂×C₈	—	18	6	no	—
42	C₂×C₈	—	18	6	no	—
43	C₄²	—	9	3	no	—
44	C₄²	PSU(3,𝔽₂)	1	1	yes	characteristic
45	C₂²×C₃	—	4	1	no	—
46	C₂×D₃	—	12	3	no	—
47	C₂×D₃	—	12	3	no	—
48	C₃×C₄	—	4	6	no	—
49	Dic₃	—	12	6	no	—
50	C₃²	#1273	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	9	1	no	—
52	C₂×C₄	—	9	3	no	—
53	C₂×C₄	—	9	6	no	—
54	C₂×C₄	—	9	6	no	—
55	C₂×C₄	#3777	1	3	yes	—
56	C₈	—	18	12	no	—
57	C₂×C₃	—	4	3	no	—
58	D₃	—	12	1	no	—
59	D₃	—	12	3	no	—
60	C₂²	—	9	3	no	—
61	C₂²	—	9	3	no	—
62	C₂²	#63747	1	1	yes	characteristic
63	C₄	—	9	6	no	—
64	C₄	#63744	1	6	yes	—
65	C₃	—	4	1	no	—
66	C₂	—	9	1	no	—
67	C₂	—	9	3	no	—
68	C₂	#10590090	1	3	yes	—

	subgroup	G/H
center, Frattini, hypercenter	C₄²	PSU(3,𝔽₂)
commutator	C₃⋊D₃	C₈²
Fitting	C₃²×C₄²	Q₈
socle	C₂²×C₃²	#95
prime radical	C₂²×C₃⋊D₃	C₄²
cosocle	C₄²×C₃⋊D₃	C₂²
hypocenter	C₃²	#1273
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
8. #3787	C₈	semidirect
50. C₃²	#1273	semidirect

Maximal subgroups

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

subgroup	index
C₄×#3787	2
#1273	9