Subgroups — #14668597

Order 2816.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622099	C₂	1	3	yes	maximal
2	C₂×C₄×C₁₁⋊C₁₆	C₂	1	3	yes	maximal
3	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
6	C₁₁×#376	C₄	1	1	yes	characteristic
7	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₁⋊C₁₆	C₂²	1	3	yes	—
9	#10622099	C₄	1	12	yes	complemented
10	C₄×C₁₁⋊C₁₆	C₄	1	12	yes	complemented
11	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
12	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
14	C₁₁×#97	C₈	1	12	yes	—
15	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
16	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
17	C₁₁×#95	C₈	1	4	yes	—
18	C₂×C₁₁⋊C₁₆	C₂×C₄	1	6	yes	—
19	C₂×C₁₁⋊C₁₆	C₂×C₄	1	6	yes	—
20	C₂×C₁₁⋊C₁₆	C₂×C₄	1	12	yes	—
21	#12539	—	11	1	no	maximal, Sylow
22	C₂²×C₄×C₁₁	C₂×C₈	1	6	yes	—
23	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₁	C₄²	1	6	yes	—
25	C₂×C₈×C₁₁	C₂×C₈	1	12	yes	—
26	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
27	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
28	C₄²×C₁₁	C₄²	1	6	yes	—
29	C₄²×C₁₁	C₂×C₈	1	6	yes	—
30	C₁₁⋊C₁₆	C₄²	1	4	yes	—
31	C₁₁⋊C₁₆	C₄²	1	12	yes	—
32	C₂×#346	—	11	3	no	—
33	C₂×C₄×C₁₆	—	11	3	no	—
34	#1726	D₁₁	1	1	yes	characteristic
35	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₁	—	2	12	no	—
37	C₂×C₄×C₁₁	C₄×C₈	1	12	yes	—
38	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
39	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
40	C₈×C₁₁	C₄×C₈	1	12	yes	—
41	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
42	C₈×C₁₁	C₂×C₄²	1	3	yes	—
43	C₂²×C₁₆	—	11	1	no	—
44	C₂²×C₁₆	—	11	3	no	—
45	C₂×#97	Dic₁₁	1	3	yes	—
46	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
47	#376	Dic₁₁	1	1	yes	characteristic
48	#346	—	11	12	no	—
49	C₄×C₁₆	—	11	12	no	—
50	C₂²×C₁₁	C₂×C₄×C₈	1	3	yes	—
51	C₂²×C₁₁	#504	1	4	yes	—
52	C₄×C₁₁	—	2	12	no	—
53	C₄×C₁₁	C₄³	1	1	yes	characteristic
54	C₄×C₁₁	C₂×C₄×C₈	1	3	yes	—
55	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
56	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
57	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
58	C₂×C₁₆	—	11	6	no	—
59	C₂×C₁₆	—	11	6	no	—
60	C₂×C₁₆	—	11	12	no	—
61	#97	C₁₁⋊C₈	1	12	yes	—
62	C₄×C₈	C₄×D₁₁	1	6	yes	—
63	C₄×C₈	C₄×D₁₁	1	6	yes	—
64	#95	C₁₁⋊C₈	1	4	yes	—
65	C₂×C₁₁	C₄²×C₈	1	1	yes	characteristic
66	C₂×C₁₁	#2108	1	6	yes	—
67	C₂²×C₄	C₂×C₁₁⋊C₈	1	6	yes	—
68	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
69	C₂×C₈	C₂×C₁₁⋊C₈	1	12	yes	—
70	C₂×C₈	C₄×Dic₁₁	1	6	yes	—
71	C₂×C₈	C₂×C₄×D₁₁	1	3	yes	—
72	C₂×C₈	C₂×C₄×D₁₁	1	3	yes	—
73	C₄²	C₂×C₁₁⋊C₈	1	6	yes	—
74	C₄²	C₄×Dic₁₁	1	6	yes	—
75	C₁₆	—	11	4	no	—
76	C₁₆	—	11	12	no	—
77	C₁₁	#12539	1	1	yes	characteristic, complemented, Sylow
78	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
79	C₂×C₄	—	2	12	no	—
80	C₂×C₄	C₄×C₁₁⋊C₈	1	12	yes	—
81	C₂×C₄	C₂²×C₁₁⋊C₈	1	3	yes	—
82	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
83	C₈	C₄×C₁₁⋊C₈	1	12	yes	—
84	C₈	C₄²×D₁₁	1	1	yes	characteristic
85	C₈	C₄²×D₁₁	1	3	yes	—
86	C₂²	C₂×C₄×C₁₁⋊C₈	1	3	yes	—
87	C₂²	#10622753	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	C₂×C₄×C₁₁⋊C₈	1	3	yes	—
90	C₄	C₄²×Dic₁₁	1	1	yes	characteristic
91	C₂	C₄²×C₁₁⋊C₈	1	1	yes	characteristic
92	C₂	#13070213	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator	C₂×C₁₁	C₄²×C₈
Fitting	C₁₁×#1726	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1726	D₁₁
hypocenter	C₁₁	#12539
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
9. #10622099	C₄	semidirect
10. C₄×C₁₁⋊C₁₆	C₄	semidirect
77. C₁₁	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622099	2
C₂×C₄×C₁₁⋊C₁₆	2
C₁₁×#1726	2
#12539	11