Subgroups — #13066586

Order 1408.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#10622099	C₂	1	1	yes	maximal, characteristic
3	#10622095	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
5	C₄×Q₈×C₁₁	—	2	1	no	—
6	C₁₁×#107	C₄	1	1	yes	characteristic
7	C₁₁×#103	—	2	1	no	—
8	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁⋊C₁₆	—	2	1	no	—
10	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
11	C₂×Q₈×C₁₁	—	2	1	no	—
12	C₁₁×Q₁₆	—	2	1	no	—
13	C₁₁×Q₁₆	C₈	1	2	yes	complemented
14	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₁₁×C₄⋊C₄	—	2	1	no	—
17	C₁₁×C₄⋊C₄	—	4	1	no	—
18	C₄²×C₁₁	—	4	1	no	—
19	C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₁₁⋊C₈	—	4	1	no	—
21	C₁₁⋊C₁₆	—	2	2	no	—
22	#1334	—	11	1	no	maximal, Sylow
23	Q₈×C₁₁	—	2	2	no	—
24	Q₈×C₁₁	—	4	1	no	—
25	C₂×C₄×C₁₁	—	4	1	no	—
26	C₂×C₄×C₁₁	—	4	1	no	—
27	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₁	—	2	1	no	—
31	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₁	M₁₆	1	1	yes	characteristic
33	C₁₁⋊C₈	—	8	1	no	—
34	C₄×Q₁₆	D₁₁	1	1	yes	characteristic
35	#346	—	11	1	no	—
36	#334	—	11	1	no	—
37	C₂²×C₁₁	#102	1	1	yes	characteristic
38	C₄×C₁₁	—	2	1	no	—
39	C₄×C₁₁	—	2	1	no	—
40	C₄×C₁₁	—	4	2	no	—
41	C₄×C₁₁	—	8	1	no	—
42	C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₁	#104	1	1	yes	characteristic
44	C₂×Q₁₆	Dic₁₁	1	1	yes	characteristic
45	C₄×Q₈	—	2	1	no	—
46	C₂×C₁₆	—	22	1	no	—
47	#107	Dic₁₁	1	1	yes	characteristic
48	C₄⋊C₈	—	22	1	no	—
49	#103	—	2	1	no	—
50	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
51	C₂×C₁₁	D₄⋊C₈	1	1	yes	characteristic
52	C₂×C₁₁	#360	1	1	yes	characteristic
53	C₂×C₁₁	#362	1	1	yes	characteristic
54	C₂×Q₈	—	2	1	no	—
55	Q₁₆	—	2	1	no	—
56	Q₁₆	C₁₁⋊C₈	1	2	yes	complemented
57	C₂×C₈	—	44	1	no	—
58	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
59	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄²	—	4	1	no	—
63	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
64	C₁₆	—	22	2	no	—
65	C₁₁	#1334	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	#4323	1	1	yes	characteristic
71	C₂×C₄	#4324	1	1	yes	characteristic
72	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	88	1	no	—
75	C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
76	C₈	#4318	1	1	yes	characteristic
77	C₂²	#66896	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
83	C₄	#66901	1	1	yes	characteristic
84	C₂	D₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
85	C₂	#10622203	1	1	yes	characteristic
86	C₂	#10622204	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66896
commutator	C₈×C₁₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₄×C₁₁×Q₁₆	C₂
socle, prime radical	C₂²×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₄×Q₁₆	D₁₁
hypocenter	C₁₁	#1334
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
13. C₁₁×Q₁₆	C₈	semidirect
56. Q₁₆	C₁₁⋊C₈	semidirect
65. C₁₁	#1334	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×Q₁₆	2
#10622099	2
#10622095	2
#1334	11