Subgroups — #14641425

Order 2816.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070891	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₁⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1371	C₂	1	1	yes	maximal, characteristic
4	#10622295	—	2	1	no	—
5	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₁×#335	—	2	1	no	—
7	#10622142	—	2	1	no	—
8	#10622142	C₄	1	2	yes	—
9	C₂×C₁₁⋊C₃₂	—	2	1	no	—
10	#66922	—	4	1	no	—
11	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₁₁×C₄⋊C₈	—	4	1	no	—
14	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
15	#66882	—	2	2	no	—
16	#66882	—	4	1	no	—
17	C₁₁⋊C₃₂	—	4	1	no	—
18	#7450	—	11	1	no	maximal, Sylow
19	C₂×Dic₂₂	—	8	1	no	—
20	C₂×C₈×C₁₁	—	8	1	no	—
21	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
23	C₄²×C₁₁	D₈	1	1	yes	characteristic
24	C₄⋊Dic₁₁	—	4	2	no	—
25	C₄⋊Dic₁₁	—	8	1	no	—
26	C₁₁×C₁₆	—	2	1	no	—
27	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
29	#2252	—	11	1	no	—
30	C₄⋊C₃₂	—	11	1	no	—
31	#1371	D₁₁	1	1	yes	characteristic
32	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
33	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₁	SD₃₂	1	1	yes	characteristic
35	C₂×Dic₁₁	—	8	2	no	—
36	Dic₂₂	—	16	1	no	—
37	Dic₂₂	—	16	1	no	—
38	C₈×C₁₁	—	2	1	no	—
39	C₈×C₁₁	—	16	1	no	—
40	C₈×C₁₁	#101	1	1	yes	characteristic
41	C₈×C₁₁	#103	1	1	yes	characteristic
42	#500	—	22	1	no	—
43	C₂×C₃₂	—	22	1	no	—
44	#366	—	11	2	no	—
45	#366	—	22	1	no	—
46	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
47	#335	—	2	1	no	—
48	C₂²×C₁₁	#357	1	1	yes	characteristic
49	C₄×C₁₁	—	2	1	no	—
50	C₄×C₁₁	#332	1	1	yes	characteristic
51	C₄×C₁₁	#362	1	1	yes	characteristic
52	C₄×C₁₁	D₃₂	1	1	yes	characteristic
53	C₄×C₁₁	SD₆₄	1	1	yes	characteristic
54	Dic₁₁	—	16	2	no	—
55	C₄⋊Q₈	—	44	1	no	—
56	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
57	C₂×C₁₆	D₄₄	1	1	yes	characteristic
58	#107	—	22	2	no	—
59	#107	—	44	1	no	—
60	C₄⋊C₈	—	4	1	no	—
61	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
62	C₃₂	—	44	1	no	—
63	C₂×C₁₁	#1364	1	1	yes	characteristic
64	C₂×C₁₁	#1415	1	1	yes	characteristic
65	C₂×C₁₁	#1420	1	1	yes	characteristic
66	C₂×Q₈	—	88	1	no	—
67	C₂×C₈	—	8	1	no	—
68	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
69	C₂×C₈	#4325	1	1	yes	characteristic
70	C₄⋊C₄	—	44	2	no	—
71	C₄⋊C₄	—	88	1	no	—
72	C₄²	#4323	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	#4314	1	1	yes	characteristic
75	C₁₆	Dic₄₄	1	1	yes	characteristic
76	C₁₁	#7450	1	1	yes	characteristic, complemented, Sylow
77	Q₈	—	176	1	no	—
78	Q₈	—	176	1	no	—
79	C₂×C₄	—	88	2	no	—
80	C₂×C₄	#66873	1	1	yes	characteristic
81	C₂×C₄	#66890	1	1	yes	characteristic
82	C₂×C₄	#66892	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	16	1	no	—
85	C₈	#66880	1	1	yes	characteristic
86	C₈	#66888	1	1	yes	characteristic
87	C₂²	#10622129	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	176	2	no	—
90	C₄	#10622120	1	1	yes	characteristic
91	C₄	#10622134	1	1	yes	characteristic
92	C₄	#10622157	1	1	yes	characteristic
93	C₄	#10622159	1	1	yes	characteristic
94	C₂	#13066672	1	1	yes	characteristic
95	C₂	#13066793	1	1	yes	characteristic
96	C₂	#13066808	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622129
commutator	C₂×C₁₁×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1371	C₂
socle, prime radical	C₂²×C₁₁	#357
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1371	D₁₁
hypocenter	C₁₁	#7450
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
76. C₁₁	#7450	semidirect

Maximal subgroups

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

subgroup	index
#13070891	2
C₄⋊(C₁₁⋊C₃₂)	2
C₁₁×#1371	2
#7450	11