Subgroups — #28405632

Order 14464.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813691	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#90673	—	2	2	no	—
4	#16813691	—	2	2	no	—
5	#16813691	C₄	1	4	yes	complemented
6	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
7	C₂×#14268622	C₄	1	1	yes	characteristic, complemented
8	C₁₆×D₁₁₃	—	2	2	no	—
9	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
10	C₂²×#90673	—	4	2	no	—
11	C₄⋊#90673	—	2	4	no	—
12	C₄⋊#90673	—	4	2	no	—
13	C₂×C₄×D₁₁₃	D₄	1	1	yes	characteristic
14	C₂×#11744751	Q₈	1	1	yes	characteristic
15	C₈×D₁₁₃	C₂×C₄	1	2	yes	—
16	C₈×D₁₁₃	D₄	1	2	yes	—
17	#14268622	—	2	1	no	—
18	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₁₃	—	2	1	no	—
20	C₂²×D₁₁₃	D₈	1	1	yes	characteristic
21	C₂×#90673	—	4	4	no	—
22	C₂×#90673	—	8	2	no	—
23	C₂×#90673	—	8	2	no	—
24	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₁₃	Q₁₆	1	1	yes	characteristic
26	C₄×D₁₁₃	C₂²⋊C₄	1	2	yes	—
27	C₄×D₁₁₃	SD₁₆	1	2	yes	—
28	C₈×C₁₁₃	C₄²	1	1	yes	characteristic
29	C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	#11744751	C₄⋊C₄	1	2	yes	—
31	C₂²×C₁₁₃	#107	1	1	yes	characteristic
32	C₂×D₁₁₃	#102	1	2	yes	—
33	C₂×D₁₁₃	D₁₆	1	1	yes	characteristic
34	C₂×D₁₁₃	SD₃₂	1	2	yes	—
35	C₂×D₁₁₃	Q₃₂	1	1	yes	characteristic
36	#90673	—	8	4	no	—
37	C₄×C₁₁₃	#95	1	1	yes	characteristic
38	C₄×C₁₁₃	#106	1	1	yes	characteristic
39	Dic₁₁₃	#103	1	2	yes	—
40	C₂×C₁₁₃	#340	1	1	yes	characteristic
41	C₂×C₁₁₃	#366	1	1	yes	characteristic
42	C₂×C₁₁₃	#367	1	1	yes	characteristic
43	D₁₁₃	#357	1	2	yes	—
44	D₁₁₃	#358	1	2	yes	—
45	#1380	—	113	1	no	maximal, Sylow
46	C₁₁₃	#1380	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₁₆	—	113	1	no	—
48	C₂×#107	—	113	2	no	—
49	C₂²×C₈	—	113	1	no	—
50	C₂×C₄⋊C₄	—	226	2	no	—
51	C₂×C₁₆	—	113	1	no	—
52	C₂×C₁₆	—	226	2	no	—
53	C₂×C₁₆	#90673	1	1	yes	characteristic, complemented
54	#107	—	113	4	no	—
55	#107	—	226	2	no	—
56	C₂²×C₄	—	113	1	no	—
57	C₂²×C₄	—	452	2	no	—
58	C₂×C₈	—	113	1	no	—
59	C₂×C₈	—	113	2	no	—
60	C₂×C₈	—	113	2	no	—
61	C₂×C₈	C₂×#90673	1	1	yes	characteristic
62	C₄⋊C₄	—	452	2	no	—
63	C₄⋊C₄	—	226	4	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	226	1	no	—
66	C₂³	—	113	1	no	—
67	C₂×C₄	—	113	1	no	—
68	C₂×C₄	—	113	2	no	—
69	C₂×C₄	—	113	2	no	—
70	C₂×C₄	—	904	2	no	—
71	C₂×C₄	—	904	2	no	—
72	C₂×C₄	—	452	4	no	—
73	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
74	C₈	—	113	2	no	—
75	C₈	C₄×#90673	1	1	yes	characteristic
76	C₈	C₂²⋊#90673	1	1	yes	characteristic
77	C₂²	—	113	1	no	—
78	C₂²	—	113	1	no	—
79	C₂²	—	113	2	no	—
80	C₂²	—	113	2	no	—
81	C₂²	#16813691	1	1	yes	characteristic
82	C₄	—	113	2	no	—
83	C₄	—	904	4	no	—
84	C₄	(C₂×#90673)⋊C₄	1	1	yes	characteristic
85	C₄	#16813690	1	1	yes	characteristic
86	C₂	—	113	2	no	—
87	C₂	—	113	2	no	—
88	C₂	#20299472	1	1	yes	characteristic
89	C₂	#20299524	1	1	yes	characteristic
90	C₂	#20299525	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813691
commutator	C₈×C₁₁₃	C₄²
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle	C₂²×C₁₁₃	#107
prime radical	C₂²×D₁₁₃	D₈
cosocle	C₂×C₈×D₁₁₃	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1380
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #16813691	C₄	semidirect
7. C₂×#14268622	C₄	semidirect
9. C₂×C₁₆×C₁₁₃	C₄	semidirect
46. C₁₁₃	#1380	semidirect
53. C₂×C₁₆	#90673	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813691	2
C₂×C₁₆×D₁₁₃	2
#1380	113