Subgroups — #14670175

Order 2816.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066694	C₂	1	6	yes	maximal
2	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#97	C₄	1	3	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
5	C₁₁×#376	C₄	1	1	yes	characteristic
6	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
10	C₁₁×#97	—	2	6	no	—
11	C₄×C₈×C₁₁	—	2	6	no	—
12	C₁₁×#95	C₈	1	4	yes	—
13	C₂×C₁₁⋊C₁₆	—	2	12	no	—
14	#12895	—	11	1	no	maximal, Sylow
15	C₂²×C₄×C₁₁	C₂×C₈	1	6	yes	—
16	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁	—	2	3	no	—
18	C₂×C₈×C₁₁	—	2	3	no	—
19	C₂×C₈×C₁₁	M₁₆	1	6	yes	—
20	C₂×C₈×C₁₁	#41	1	6	yes	—
21	C₄²×C₁₁	—	2	3	no	—
22	C₄²×C₁₁	—	2	3	no	—
23	C₁₁⋊C₁₆	—	4	4	no	—
24	#1726	D₁₁	1	1	yes	characteristic
25	#1374	—	11	6	no	—
26	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₁	—	2	6	no	—
28	C₂×C₄×C₁₁	—	2	12	no	—
29	C₂×C₄×C₁₁	#117	1	3	yes	—
30	C₂×C₄×C₁₁	C₂×M₁₆	1	3	yes	—
31	C₈×C₁₁	—	2	6	no	—
32	C₈×C₁₁	#126	1	4	yes	—
33	C₂²×C₁₆	—	11	4	no	—
34	C₂×#97	Dic₁₁	1	3	yes	—
35	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
36	#376	Dic₁₁	1	1	yes	characteristic
37	C₂²×C₁₁	#431	1	3	yes	—
38	C₂²×C₁₁	#504	1	4	yes	—
39	C₄×C₁₁	—	4	6	no	—
40	C₄×C₁₁	#383	1	1	yes	characteristic
41	C₄×C₁₁	#432	1	3	yes	—
42	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
43	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
44	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
45	C₂×C₁₆	—	22	12	no	—
46	#97	—	2	6	no	—
47	C₄×C₈	—	2	6	no	—
48	#95	C₁₁⋊C₈	1	4	yes	—
49	C₂×C₁₁	#1839	1	1	yes	characteristic
50	C₂×C₁₁	#2164	1	6	yes	—
51	C₂²×C₄	C₂×C₁₁⋊C₈	1	6	yes	—
52	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
53	C₂×C₈	—	2	3	no	—
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	#4318	1	6	yes	—
56	C₂×C₈	#4339	1	6	yes	—
57	C₄²	—	2	3	no	—
58	C₄²	—	2	3	no	—
59	C₁₆	—	44	4	no	—
60	C₁₁	#12895	1	1	yes	characteristic, complemented, Sylow
61	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	—	2	6	no	—
64	C₂×C₄	C₂×#4318	1	3	yes	—
65	C₂×C₄	#66979	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	#66929	1	4	yes	—
68	C₂²	#10622538	1	3	yes	—
69	C₂²	#10622753	1	4	yes	—
70	C₄	—	4	6	no	—
71	C₄	#10622539	1	3	yes	—
72	C₄	#10622550	1	1	yes	characteristic
73	C₂	#13068759	1	1	yes	characteristic
74	C₂	#13070423	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator, socle, prime radical	C₂³×C₁₁	C₂²×C₈
Fitting	C₁₁×#1726	C₂
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1726	D₁₁
hypocenter	C₁₁	#12895
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
60. C₁₁	#12895	semidirect

Maximal subgroups

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

subgroup	index
#13066694	2
C₁₁×#1726	2
#12895	11