Subgroups — #11782566

Order 1152.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593379	C₂	1	4	yes	maximal
2	#10590902	C₂	1	2	yes	maximal
3	C₈×#622	C₂	1	1	yes	maximal, characteristic
4	#63919	C₂²	1	4	yes	—
5	C₄×#622	C₂²	1	2	yes	—
6	#63740	—	2	8	no	—
7	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
8	C₃×#818	—	2	2	no	—
9	#63576	—	2	2	no	—
10	#4874	—	6	2	no	—
11	C₂×#627	—	2	4	no	—
12	C₂×#622	D₄	1	4	yes	—
13	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
14	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
15	C₂×C₃⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
16	C₃×C₄⋊Dic₃	—	2	4	no	—
17	#3724	—	2	4	no	—
18	#1710	—	9	1	no	maximal, Sylow
19	#888	—	6	4	no	—
20	C₃×#107	—	6	2	no	—
21	#818	—	2	2	no	—
22	C₈×Dic₃	—	6	2	no	—
23	#807	—	6	4	no	—
24	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
25	C₂×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
26	C₂×C₃×Dic₃	—	4	4	no	—
27	#627	—	4	8	no	—
28	#622	—	2	4	no	—
29	C₃²×C₈	Q₁₆	1	2	yes	—
30	C₃⋊(C₃⋊C₈)	Q₁₆	1	2	yes	—
31	#500	—	9	2	no	—
32	#487	—	9	4	no	—
33	C₈²	—	9	1	no	—
34	C₂×Dic₆	—	12	4	no	—
35	C₂×C₃×C₈	—	2	2	no	—
36	C₃×C₄⋊C₄	—	6	4	no	—
37	C₄⋊Dic₃	—	2	4	no	—
38	Dic₃⋊C₄	—	12	4	no	—
39	C₄×Dic₃	—	6	2	no	—
40	C₂×C₃⋊C₈	—	6	2	no	—
41	C₂²×C₃²	#127	1	1	yes	characteristic
42	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
43	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
44	C₃⋊Dic₃	#135	1	4	yes	—
45	C₃×Dic₃	—	8	4	no	—
46	C₄⋊Q₈	—	9	4	no	—
47	#107	—	6	2	no	—
48	#107	—	18	2	no	—
49	#103	—	18	8	no	—
50	C₄×C₈	—	9	2	no	—
51	C₄×C₈	—	9	1	no	—
52	C₂×C₃×C₄	—	2	2	no	—
53	C₂×C₃×C₄	—	12	4	no	—
54	C₂×Dic₃	—	4	4	no	—
55	C₂×Dic₃	—	6	2	no	—
56	C₂×Dic₃	—	6	2	no	—
57	Dic₆	—	24	8	no	—
58	C₃×C₈	—	2	4	no	—
59	C₃⋊C₈	—	6	4	no	—
60	C₂×C₃²	#494	1	1	yes	characteristic
61	C₂×C₃²	#495	1	2	yes	—
62	C₂×Q₈	—	18	4	no	—
63	C₂×C₈	—	9	1	no	—
64	C₂×C₈	—	9	4	no	—
65	C₂×C₈	GO⁺(4,𝔽₂)	1	1	yes	characteristic
66	C₄⋊C₄	—	6	4	no	—
67	C₄⋊C₄	—	18	4	no	—
68	C₄²	—	9	1	no	—
69	C₂²×C₃	—	2	2	no	—
70	C₃×C₄	—	2	2	no	—
71	C₃×C₄	—	2	2	no	—
72	C₃×C₄	—	24	4	no	—
73	Dic₃	—	6	4	no	—
74	Dic₃	—	6	4	no	—
75	Dic₃	—	8	4	no	—
76	C₃²	#1710	1	1	yes	characteristic, complemented, Sylow
77	Q₈	—	36	8	no	—
78	C₂×C₄	—	9	2	no	—
79	C₂×C₄	—	12	4	no	—
80	C₂×C₄	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic
81	C₈	—	9	2	no	—
82	C₈	—	18	4	no	—
83	C₈	#3776	1	2	yes	—
84	C₂×C₃	—	2	2	no	—
85	C₂×C₃	—	2	2	no	—
86	C₂×C₃	—	2	2	no	—
87	C₂²	#64231	1	1	yes	characteristic
88	C₄	—	9	4	no	—
89	C₄	—	24	4	no	—
90	C₄	#64228	1	1	yes	characteristic
91	C₄	C₂×#3776	1	1	yes	characteristic
92	C₃	—	2	2	no	—
93	C₂	#10593290	1	2	yes	—
94	C₂	#10593450	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64231
commutator, cosocle	C₄×C₃⋊Dic₃	C₂³
Frattini	C₂×C₄	C₂×GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₈	D₄
socle, prime radical	C₂²×C₃²	#127
hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
hypocenter	C₃²	#1710
LCS	G ▷ C₄×C₃⋊Dic₃ ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
76. C₃²	#1710	semidirect

Maximal subgroups

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

subgroup	index
#10593379	2
#10590902	2
C₈×#622	2
#1710	9