Subgroups — #13070933

Order 1408.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#508	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622160	C₂	1	2	yes	maximal, complemented
4	#10622158	C₂	1	2	yes	maximal, complemented
5	#10622137	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#135	—	2	1	no	—
7	C₂×Dic₄₄	—	2	1	no	—
8	C₁₁×Q₃₂	C₂²	1	1	yes	characteristic
9	C₁₁×SD₃₂	—	2	1	no	—
10	C₁₁×D₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	Dic₈₈	—	2	1	no	—
13	Dic₈₈	C₂²	1	2	yes	—
14	C₁₁⋊C₃₂	C₂²	1	2	yes	—
15	C₁₁×#41	—	4	1	no	—
16	C₂×Dic₂₂	—	4	1	no	—
17	C₁₁×Q₁₆	—	2	1	no	—
18	C₁₁×SD₁₆	—	4	1	no	—
19	C₁₁×D₈	—	2	1	no	—
20	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
21	Dic₄₄	—	2	2	no	—
22	Dic₄₄	—	4	1	no	—
23	C₁₁×C₁₆	D₄	1	1	yes	characteristic
24	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
25	#2264	—	11	1	no	maximal, Sylow
26	Q₈×C₁₁	—	4	1	no	—
27	D₄×C₁₁	—	4	1	no	—
28	D₄×C₁₁	—	8	1	no	—
29	C₂×C₄×C₁₁	—	8	1	no	—
30	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
31	C₂×Dic₁₁	—	8	1	no	—
32	Dic₂₂	—	4	2	no	—
33	Dic₂₂	—	8	1	no	—
34	C₈×C₁₁	D₈	1	1	yes	characteristic
35	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
36	#508	D₁₁	1	1	yes	characteristic
37	C₂×Q₃₂	—	11	1	no	—
38	Q₆₄	—	11	2	no	—
39	SD₆₄	—	11	2	no	—
40	M₆₄	—	11	1	no	—
41	C₂²×C₁₁	—	8	1	no	—
42	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
43	C₄×C₁₁	—	8	1	no	—
44	C₄×C₁₁	D₁₆	1	1	yes	characteristic
45	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
46	Dic₁₁	—	8	2	no	—
47	#135	—	2	1	no	—
48	C₂×Q₁₆	—	22	1	no	—
49	Q₃₂	—	11	2	no	—
50	Q₃₂	—	22	1	no	—
51	Q₃₂	C₂×D₁₁	1	1	yes	characteristic
52	SD₃₂	—	2	1	no	—
53	D₁₆	C₂×D₁₁	1	1	yes	characteristic
54	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
55	C₃₂	—	11	2	no	—
56	C₂×C₁₁	—	2	1	no	—
57	C₂×C₁₁	—	16	1	no	—
58	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
59	#41	—	4	1	no	—
60	C₂×Q₈	—	44	1	no	—
61	Q₁₆	—	2	1	no	—
62	Q₁₆	—	22	2	no	—
63	Q₁₆	—	44	1	no	—
64	SD₁₆	—	4	1	no	—
65	D₈	—	2	1	no	—
66	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
67	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
68	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
69	C₁₁	#2264	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	4	1	no	—
71	Q₈	—	44	2	no	—
72	Q₈	—	88	1	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	88	1	no	—
77	C₂×C₄	#4323	1	1	yes	characteristic
78	C₈	#4323	1	1	yes	characteristic
79	C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	#66890	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	88	2	no	—
84	C₄	#66890	1	1	yes	characteristic
85	C₄	C₂×#4323	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#66890	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#66890
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting, prime radical	C₁₁×#508	C₂
socle	C₂×C₁₁	C₂×D₁₆
hypercenter	#508	D₁₁
hypocenter	C₁₁	#2264
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₈₈	C₂	semidirect
3. #10622160	C₂	semidirect
4. #10622158	C₂	semidirect
5. #10622137	C₂	semidirect
69. C₁₁	#2264	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#508	2
C₂×Dic₈₈	2
#10622160	2
#10622158	2
#10622137	2
#2264	11