Subgroups — #14640752

Order 2816.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070419	C₂	1	2	yes	maximal
2	C₁₁×#1452	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#431	C₄	1	2	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₁₁×#322	—	2	2	no	—
6	C₂²⋊(C₁₁⋊C₁₆)	C₄	1	4	yes	—
7	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
8	#10622099	—	2	2	no	—
9	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
10	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₁₁×C₄⋊C₈	—	2	2	no	—
12	C₁₁×C₂²⋊C₈	C₈	1	4	yes	—
13	C₄×C₈×C₁₁	—	2	2	no	—
14	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₁	D₄	1	2	yes	—
16	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
17	C₂×C₁₁⋊C₁₆	—	2	4	no	—
18	#7197	—	11	1	no	maximal, Sylow
19	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
21	C₂×C₈×C₁₁	—	2	4	no	—
22	C₂×C₈×C₁₁	—	4	2	no	—
23	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
25	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
27	C₄²×C₁₁	M₁₆	1	2	yes	—
28	C₁₁⋊C₁₆	—	4	4	no	—
29	#2163	—	11	2	no	—
30	#1452	D₁₁	1	1	yes	characteristic
31	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₁	—	2	2	no	—
33	C₂×C₄×C₁₁	—	4	2	no	—
34	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
35	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
36	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
37	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
38	C₈×C₁₁	—	2	2	no	—
39	C₈×C₁₁	—	2	2	no	—
40	C₈×C₁₁	—	4	4	no	—
41	#431	Dic₁₁	1	2	yes	—
42	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
43	C₄⋊C₁₆	—	22	2	no	—
44	C₂²⋊C₁₆	—	11	4	no	—
45	#346	—	22	2	no	—
46	#322	—	2	2	no	—
47	C₂²×C₁₁	—	2	1	no	—
48	C₂²×C₁₁	—	2	2	no	—
49	C₂²×C₁₁	#336	1	1	yes	characteristic
50	C₄×C₁₁	—	2	1	no	—
51	C₄×C₁₁	—	2	2	no	—
52	C₄×C₁₁	—	2	2	no	—
53	C₄×C₁₁	#344	1	2	yes	—
54	C₂²×C₈	C₄×D₁₁	1	2	yes	—
55	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
56	C₂×C₁₆	—	22	4	no	—
57	C₄⋊C₈	—	2	2	no	—
58	C₂²⋊C₈	C₁₁⋊C₈	1	4	yes	—
59	C₄×C₈	—	2	2	no	—
60	C₄×C₈	Dic₂₂	1	1	yes	characteristic
61	C₄×C₈	D₄₄	1	1	yes	characteristic
62	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
63	C₂×C₁₁	—	4	1	no	—
64	C₂×C₁₁	#1281	1	1	yes	characteristic
65	C₂×C₁₁	#1378	1	2	yes	—
66	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
67	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
68	C₂×C₈	—	2	4	no	—
69	C₂×C₈	—	4	2	no	—
70	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
71	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
72	C₄²	#4318	1	2	yes	—
73	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
74	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
75	C₁₆	—	44	4	no	—
76	C₁₁	#7197	1	1	yes	characteristic, complemented, Sylow
77	C₂³	C₄×C₁₁⋊C₈	1	1	yes	characteristic
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#66867	1	1	yes	characteristic
81	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
82	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
83	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
84	C₈	—	2	2	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	4	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#10622162	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	#10622194	1	2	yes	—
94	C₂	—	4	1	no	—
95	C₂	#13066461	1	1	yes	characteristic
96	C₂	#13066702	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₁₁⋊#95
commutator, prime radical	C₂³×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#1452	C₂
socle	C₂²×C₁₁	#336
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	#1452	D₁₁
hypocenter	C₁₁	#7197
LCS	G ▷ C₂³×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
76. C₁₁	#7197	semidirect

Maximal subgroups

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

subgroup	index
#13070419	2
C₁₁×#1452	2
#7197	11