Subgroups — #11772200

Order 1152.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590175	C₂	1	1	yes	maximal, characteristic
2	#10589135	C₂	1	2	yes	maximal
3	C₂×#3708	C₄	1	1	yes	characteristic
4	C₂×#3708	C₄	1	1	yes	characteristic
5	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₃×#812	—	2	2	no	—
7	#4511	—	6	2	no	—
8	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
9	C₄×C₃⋊Dic₃	Q₈	1	1	yes	characteristic
10	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
11	#3708	—	2	1	no	—
12	#3708	C₈	1	2	yes	—
13	C₃×C₃⋊C₁₆	—	4	2	no	—
14	#1369	—	9	1	no	maximal, Sylow
15	C₃×M₃₂	—	6	2	no	—
16	C₈×Dic₃	—	6	2	no	—
17	#812	—	2	2	no	—
18	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₃⋊Dic₃	—	2	1	no	—
20	C₃²×C₈	SD₁₆	1	2	yes	—
21	C₃⋊(C₃⋊C₈)	C₂×C₈	1	1	yes	characteristic
22	C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
23	#364	—	9	2	no	—
24	#346	—	9	1	no	—
25	C₂×C₃×C₈	—	2	2	no	—
26	C₄×Dic₃	—	6	2	no	—
27	C₂×C₃⋊C₈	—	6	2	no	—
28	C₃×C₁₆	—	12	2	no	—
29	C₃⋊C₁₆	—	4	2	no	—
30	C₂²×C₃²	#108	1	1	yes	characteristic
31	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
32	C₃²×C₄	#106	1	1	yes	characteristic
33	C₃⋊Dic₃	—	4	1	no	—
34	M₃₂	—	6	2	no	—
35	C₂×C₁₆	—	9	1	no	—
36	C₂×C₁₆	—	9	1	no	—
37	C₄×C₈	—	9	1	no	—
38	C₂×C₃×C₄	—	2	2	no	—
39	C₂×Dic₃	—	12	2	no	—
40	C₃×C₈	—	2	2	no	—
41	C₃×C₈	—	2	2	no	—
42	C₃⋊C₈	—	6	2	no	—
43	C₃⋊C₈	—	6	2	no	—
44	C₂×C₃²	—	2	1	no	—
45	C₂×C₃²	#334	1	1	yes	characteristic
46	C₂×C₈	—	9	1	no	—
47	C₂×C₈	GO⁺(4,𝔽₂)	1	1	yes	characteristic
48	C₄²	—	9	1	no	—
49	C₁₆	—	9	2	no	—
50	C₁₆	—	12	2	no	—
51	C₁₆	—	18	1	no	—
52	C₂²×C₃	—	2	2	no	—
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	2	2	no	—
55	Dic₃	—	12	4	no	—
56	C₃²	#1369	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	18	1	no	—
58	C₂×C₄	#3773	1	1	yes	characteristic
59	C₈	—	9	1	no	—
60	C₈	—	9	1	no	—
61	C₈	#3775	1	2	yes	—
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	—	4	2	no	—
64	C₂²	#63733	1	1	yes	characteristic
65	C₄	—	36	1	no	—
66	C₄	#63732	1	1	yes	characteristic
67	C₄	#63742	1	1	yes	characteristic
68	C₃	—	2	2	no	—
69	C₂	—	2	1	no	—
70	C₂	#10590041	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#63742
commutator	C₃⋊(C₃⋊C₈)	C₂×C₈
Frattini, hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₈	D₄
socle	C₂×C₃²	#334
prime radical	C₂²×C₃²	#108
cosocle	C₈×C₃⋊Dic₃	C₂²
hypocenter	C₃²	#1369
LCS	G ▷ C₃⋊(C₃⋊C₈) ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
56. C₃²	#1369	semidirect

Maximal subgroups

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

subgroup	index
#10590175	2
#10589135	2
#1369	9