Subgroups — #14643138

Order 2816.

526 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068362	C₂	1	2	yes	maximal
2	C₂×#10622092	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
6	C₄³×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₁⋊C₈	C₂²	1	4	yes	—
8	#10622162	C₄	1	8	yes	—
9	#10622092	C₄	1	16	yes	complemented
10	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
14	C₂²×C₁₁⋊C₈	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₁	—	2	8	no	—
16	C₄×C₈×C₁₁	C₂×C₄	1	8	yes	—
17	C₄×C₁₁⋊C₈	C₂×C₄	1	16	yes	—
18	#7843	—	11	1	no	maximal, Sylow
19	C₂²×C₄×C₁₁	C₄²	1	4	yes	—
20	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
22	C₂×C₈×C₁₁	—	2	8	no	—
23	C₂×C₈×C₁₁	C₄²	1	8	yes	—
24	C₄²×C₁₁	—	2	8	no	—
25	C₄²×C₁₁	M₁₆	1	8	yes	—
26	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
27	C₂×C₁₁⋊C₈	—	2	16	no	—
28	C₂×C₁₁⋊C₈	C₄²	1	16	yes	—
29	#1744	—	11	2	no	—
30	C₄²×C₈	D₁₁	1	1	yes	characteristic
31	C₂×#322	—	11	4	no	—
32	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄×C₁₁	—	2	8	no	—
34	C₂×C₄×C₁₁	#97	1	8	yes	—
35	C₂×C₄×C₁₁	C₂×C₄²	1	4	yes	—
36	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
37	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
38	C₂×C₄×C₁₁	#131	1	8	yes	—
39	C₈×C₁₁	—	2	8	no	—
40	C₁₁⋊C₈	—	2	16	no	—
41	C₂×C₄×C₈	—	11	4	no	—
42	C₂×C₄×C₈	Dic₁₁	1	4	yes	—
43	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
44	C₄³	C₂×D₁₁	1	1	yes	characteristic
45	#336	—	11	8	no	—
46	#322	—	11	16	no	—
47	C₂²×C₁₁	C₄³	1	1	yes	characteristic
48	C₂²×C₁₁	C₂×#97	1	2	yes	—
49	C₂²×C₁₁	#405	1	4	yes	—
50	C₄×C₁₁	—	2	8	no	—
51	C₄×C₁₁	C₄×M₁₆	1	4	yes	—
52	C₄×C₁₁	#405	1	8	yes	—
53	C₂²×C₈	—	11	8	no	—
54	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
55	C₂×C₄²	C₄×D₁₁	1	4	yes	—
56	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
57	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
58	C₄×C₈	—	2	8	no	—
59	C₄×C₈	—	11	16	no	—
60	C₄×C₈	C₄×D₁₁	1	8	yes	—
61	C₂×C₁₁	#1452	1	4	yes	—
62	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
63	C₂×C₁₁	#1726	1	2	yes	—
64	C₂²×C₄	C₄×Dic₁₁	1	4	yes	—
65	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
66	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
67	C₂×C₈	—	2	8	no	—
68	C₂×C₈	—	11	16	no	—
69	C₂×C₈	—	22	16	no	—
70	C₂×C₈	C₄×Dic₁₁	1	8	yes	—
71	C₄²	—	2	8	no	—
72	C₄²	#4318	1	8	yes	—
73	C₄²	C₂×C₄×D₁₁	1	4	yes	—
74	C₁₁	#7843	1	1	yes	characteristic, complemented, Sylow
75	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
76	C₂×C₄	—	2	8	no	—
77	C₂×C₄	#66867	1	8	yes	—
78	C₂×C₄	C₄²×D₁₁	1	4	yes	—
79	C₂×C₄	#66954	1	8	yes	—
80	C₂×C₄	C₂×#4318	1	4	yes	—
81	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
82	C₈	—	2	8	no	—
83	C₈	—	22	16	no	—
84	C₂²	C₂×#66867	1	2	yes	—
85	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
86	C₂²	#10622714	1	4	yes	—
87	C₄	—	2	8	no	—
88	C₄	#10622302	1	8	yes	—
89	C₄	C₄×#4318	1	4	yes	—
90	C₂	#13066908	1	4	yes	—
91	C₂	C₄×#66867	1	1	yes	characteristic
92	C₂	#13068302	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₄²×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄²×C₈	D₁₁
hypocenter	C₁₁	#7843
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
9. #10622092	C₄	semidirect
74. C₁₁	#7843	semidirect

Maximal subgroups

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

subgroup	index
#13068362	2
C₂×#10622092	2
C₄²×C₈×C₁₁	2
#7843	11