Subgroups — #28405482

Order 14464.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299601	C₂	1	2	yes	maximal
2	#20298621	C₂	1	1	yes	maximal, characteristic
3	C₂×#14268656	C₄	1	4	yes	—
4	#16813689	—	2	2	no	—
5	C₄⋊#11744753	—	2	2	no	—
6	C₂×#14268631	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
8	#16813551	—	2	2	no	—
9	C₂×M₁₆×C₁₁₃	C₄	1	1	yes	characteristic
10	#14268656	—	4	4	no	—
11	C₂×#11744753	—	2	4	no	—
12	C₂²×Dic₁₁₃	C₂×C₄	1	2	yes	—
13	#14268631	—	4	1	no	—
14	C₂×#11744751	—	2	1	no	—
15	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
16	C₄×Dic₁₁₃	D₄	1	2	yes	—
17	C₄×Dic₁₁₃	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₁₁₃	—	4	1	no	—
20	C₂×C₈×C₁₁₃	—	2	1	no	—
21	C₂³×C₁₁₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	—	2	1	no	—
24	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₁₃	—	2	2	no	—
27	C₂×Dic₁₁₃	—	2	2	no	—
28	C₂×Dic₁₁₃	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₁₁₃	C₄⋊C₄	1	2	yes	—
30	#11744753	—	4	4	no	—
31	C₈×C₁₁₃	—	4	1	no	—
32	#11744751	—	4	1	no	—
33	C₂²×C₁₁₃	—	2	2	no	—
34	C₂²×C₁₁₃	—	2	1	no	—
35	C₂²×C₁₁₃	#95	1	1	yes	characteristic
36	C₄×C₁₁₃	—	2	1	no	—
37	C₄×C₁₁₃	#100	1	1	yes	characteristic
38	C₄×C₁₁₃	#101	1	1	yes	characteristic
39	Dic₁₁₃	—	2	2	no	—
40	Dic₁₁₃	#100	1	2	yes	—
41	Dic₁₁₃	#101	1	2	yes	—
42	C₂×C₁₁₃	—	4	1	no	—
43	C₂×C₁₁₃	#343	1	2	yes	—
44	C₂×C₁₁₃	#343	1	1	yes	characteristic
45	#1309	—	113	1	no	maximal, Sylow
46	C₁₁₃	#1309	1	1	yes	characteristic, complemented, Sylow
47	#423	—	113	2	no	—
48	#423	—	113	1	no	—
49	C₂×M₁₆	—	113	4	no	—
50	C₂×M₁₆	—	113	1	no	—
51	C₂×M₁₆	#90673	1	1	yes	characteristic
52	C₂×C₄²	—	113	1	no	—
53	C₄⋊C₈	—	226	2	no	—
54	C₄⋊C₈	—	226	2	no	—
55	C₄⋊C₈	—	226	2	no	—
56	C₂²×C₄	—	113	2	no	—
57	C₂²×C₄	C₂×#90673	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	452	1	no	—
60	M₁₆	—	452	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	226	4	no	—
63	C₂×C₈	—	226	1	no	—
64	C₄²	—	113	2	no	—
65	C₄²	—	113	1	no	—
66	C₄²	—	113	1	no	—
67	C₂³	C₄×#90673	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	113	2	no	—
71	C₂×C₄	—	113	2	no	—
72	C₂×C₄	—	226	2	no	—
73	C₂×C₄	—	226	2	no	—
74	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	452	4	no	—
78	C₈	—	452	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#90673)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	113	2	no	—
84	C₄	—	113	2	no	—
85	C₄	—	226	2	no	—
86	C₄	#16813682	1	1	yes	characteristic
87	C₄	#16813683	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#20299477	1	2	yes	—
90	C₂	#20299478	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#90673)⋊C₄
commutator, prime radical	C₂³×C₁₁₃	C₄²
Frattini	C₂²×C₄	C₂×#90673
Fitting	C₂×M₁₆×C₁₁₃	C₄
socle	C₂²×C₁₁₃	#95
cosocle	C₂×C₄×Dic₁₁₃	C₂²
hypercenter	C₂×M₁₆	#90673
hypocenter	C₁₁₃	#1309
LCS	G ▷ C₂³×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
46. C₁₁₃	#1309	semidirect

Maximal subgroups

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

subgroup	index
#20299601	2
#20298621	2
#1309	113