Subgroups — #11773066

Order 1152.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590141	C₂	1	2	yes	maximal
2	#10590132	C₂	1	1	yes	maximal, characteristic
3	#63771	—	2	2	no	—
4	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	#63540	C₄	1	2	yes	—
6	#3788	—	4	2	no	—
7	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
8	C₃²×C₁₆	Q₈	1	1	yes	characteristic
9	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	1	yes	characteristic
10	#1425	—	9	1	no	maximal, Sylow
11	D₃×C₁₆	—	12	1	no	—
12	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
13	#622	—	8	2	no	—
14	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
15	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
16	C₂×C₃₂	—	9	1	no	—
17	#368	—	9	2	no	—
18	D₃×C₈	—	12	1	no	—
19	C₃×C₁₆	—	4	1	no	—
20	C₃⋊C₁₆	—	12	1	no	—
21	C₂×C₃⋊D₃	Q₃₂	1	1	yes	characteristic
22	C₃²×C₄	#107	1	1	yes	characteristic
23	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
24	C₂×C₁₆	—	9	1	no	—
25	#108	—	18	2	no	—
26	C₃₂	—	9	2	no	—
27	C₄×D₃	—	12	1	no	—
28	C₃×C₈	—	4	1	no	—
29	C₃⋊C₈	—	12	1	no	—
30	C₂×C₃²	#366	1	1	yes	characteristic
31	C₃⋊D₃	—	2	1	no	—
32	M₁₆	—	36	2	no	—
33	C₂×C₈	—	9	1	no	—
34	C₁₆	—	9	1	no	—
35	C₁₆	PSU(3,𝔽₂)	1	1	yes	characteristic
36	C₂×D₃	—	12	1	no	—
37	C₃×C₄	—	4	1	no	—
38	Dic₃	—	12	1	no	—
39	C₃²	#1425	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	—	9	1	no	—
41	C₈	—	9	1	no	—
42	C₈	—	72	2	no	—
43	C₈	#3777	1	1	yes	characteristic
44	C₂×C₃	—	4	1	no	—
45	D₃	—	12	2	no	—
46	C₂²	—	9	1	no	—
47	C₄	—	9	1	no	—
48	C₄	#63746	1	1	yes	characteristic
49	C₃	—	4	1	no	—
50	C₂	—	18	1	no	—
51	C₂	#10590085	1	1	yes	characteristic

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

N	H ≅ G/N	type
39. C₃²	#1425	semidirect

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