Subgroups — #11772224

Order 1152.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590171	C₂	1	2	yes	maximal
2	C₁₆×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#622	—	2	2	no	—
4	C₂×C₃²×C₁₆	C₄	1	1	yes	characteristic
5	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
7	Dic₃×C₁₆	—	6	2	no	—
8	C₂×#622	—	4	2	no	—
9	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
10	C₄×C₃⋊Dic₃	D₄	1	1	yes	characteristic
11	C₂×C₃⋊(C₃⋊C₈)	Q₈	1	1	yes	characteristic
12	C₃²×C₁₆	—	2	1	no	—
13	C₃⋊(C₃⋊C₁₆)	C₈	1	2	yes	complemented
14	#1371	—	9	1	no	maximal, Sylow
15	C₂×C₃×C₁₆	—	2	2	no	—
16	C₈×Dic₃	—	6	2	no	—
17	C₂×C₃⋊C₁₆	—	6	2	no	—
18	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₃⋊Dic₃	D₈	1	1	yes	characteristic
20	C₂×C₃⋊Dic₃	Q₁₆	1	1	yes	characteristic
21	#622	—	8	2	no	—
22	C₃²×C₈	C₂×C₈	1	1	yes	characteristic
23	C₃²×C₈	M₁₆	1	1	yes	characteristic
24	C₃⋊(C₃⋊C₈)	—	2	1	no	—
25	C₄×C₁₆	—	9	1	no	—
26	#335	—	9	2	no	—
27	C₂×C₃×C₈	—	2	2	no	—
28	C₄×Dic₃	—	6	2	no	—
29	C₂×C₃⋊C₈	—	6	2	no	—
30	C₃×C₁₆	—	2	4	no	—
31	C₃⋊C₁₆	—	6	4	no	—
32	C₂²×C₃²	#107	1	1	yes	characteristic
33	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
34	C₃²×C₄	#108	1	1	yes	characteristic
35	C₃⋊Dic₃	—	2	1	no	—
36	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
37	C₃⋊Dic₃	Q₃₂	1	1	yes	characteristic
38	C₂×C₁₆	—	9	1	no	—
39	C₂×C₁₆	#157	1	1	yes	characteristic
40	C₄⋊C₈	—	18	2	no	—
41	C₄×C₈	—	9	1	no	—
42	C₂×C₃×C₄	—	2	2	no	—
43	C₂×Dic₃	—	6	2	no	—
44	C₂×Dic₃	—	6	2	no	—
45	C₃×C₈	—	2	2	no	—
46	C₃×C₈	—	2	2	no	—
47	C₃⋊C₈	—	6	4	no	—
48	C₂×C₃²	#335	1	1	yes	characteristic
49	C₂×C₃²	#366	1	1	yes	characteristic
50	C₂×C₃²	#368	1	1	yes	characteristic
51	C₂×C₈	—	9	1	no	—
52	C₂×C₈	—	36	2	no	—
53	C₂×C₈	C₂×#157	1	1	yes	characteristic
54	C₄²	—	9	1	no	—
55	C₁₆	—	2	1	no	—
56	C₁₆	—	9	2	no	—
57	C₂²×C₃	—	2	2	no	—
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	2	2	no	—
60	Dic₃	—	6	2	no	—
61	Dic₃	—	6	2	no	—
62	Dic₃	—	6	4	no	—
63	C₃²	#1371	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄	—	9	1	no	—
65	C₂×C₄	—	9	1	no	—
66	C₂×C₄	C₄⋊#157	1	1	yes	characteristic
67	C₈	—	18	1	no	—
68	C₈	—	72	2	no	—
69	C₈	#3787	1	1	yes	characteristic
70	C₈	#3792	1	1	yes	characteristic
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	—	2	2	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂²	#63769	1	1	yes	characteristic
75	C₄	—	9	1	no	—
76	C₄	—	9	1	no	—
77	C₄	—	18	1	no	—
78	C₄	#63770	1	1	yes	characteristic
79	C₄	#63779	1	1	yes	characteristic
80	C₃	—	2	2	no	—
81	C₂	#10590138	1	1	yes	characteristic
82	C₂	#10590141	1	1	yes	characteristic
83	C₂	#10590173	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63769
commutator	C₃²×C₈	C₂×C₈
Frattini	C₂×C₈	C₂×#157
Fitting	C₂×C₃²×C₁₆	C₄
socle, prime radical	C₂²×C₃²	#107
cosocle	C₈×C₃⋊Dic₃	C₂²
hypercenter	C₂×C₁₆	#157
hypocenter	C₃²	#1371
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. C₃⋊(C₃⋊C₁₆)	C₈	semidirect
63. C₃²	#1371	semidirect

Maximal subgroups

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

subgroup	index
#10590171	2
C₁₆×C₃⋊Dic₃	2
#1371	9