Subgroups — #28405439

Order 14464.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299619	C₂	1	2	yes	maximal
2	C₂×#16813551	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11744753	—	2	2	no	—
4	C₂²⋊#11744753	—	2	2	no	—
5	#16813677	C₄	1	4	yes	—
6	C₂²×#11744751	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
8	#16813551	—	2	2	no	—
9	C₂²×C₈×C₁₁₃	C₄	1	1	yes	characteristic
10	C₂×#11744753	—	2	4	no	—
11	C₂²×Dic₁₁₃	D₄	1	1	yes	characteristic
12	C₂²×Dic₁₁₃	Q₈	1	1	yes	characteristic
13	C₂×#11744751	—	2	1	no	—
14	C₂×#11744751	—	4	1	no	—
15	C₄×Dic₁₁₃	C₂×C₄	1	2	yes	—
16	C₄×Dic₁₁₃	D₄	1	2	yes	—
17	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁₃	—	2	1	no	—
19	C₂×C₈×C₁₁₃	—	4	1	no	—
20	C₂³×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	—	2	1	no	—
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₁₃	—	2	1	no	—
26	C₂×Dic₁₁₃	—	2	1	no	—
27	C₂×Dic₁₁₃	—	4	1	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	1	no	—
34	C₂²×C₁₁₃	—	2	1	no	—
35	C₂²×C₁₁₃	#95	1	1	yes	characteristic
36	C₂²×C₁₁₃	#108	1	1	yes	characteristic
37	C₂²×C₁₁₃	#108	1	1	yes	characteristic
38	C₄×C₁₁₃	—	2	1	no	—
39	C₄×C₁₁₃	#100	1	1	yes	characteristic
40	C₄×C₁₁₃	#101	1	1	yes	characteristic
41	Dic₁₁₃	—	2	2	no	—
42	Dic₁₁₃	—	2	2	no	—
43	C₂×C₁₁₃	—	2	1	no	—
44	C₂×C₁₁₃	—	2	1	no	—
45	C₂×C₁₁₃	H(3,ℤ/4)	1	1	yes	characteristic
46	C₂×C₁₁₃	#341	1	1	yes	characteristic
47	C₂×C₁₁₃	#343	1	1	yes	characteristic
48	#1290	—	113	1	no	maximal, Sylow
49	C₁₁₃	#1290	1	1	yes	characteristic, complemented, Sylow
50	#432	—	113	2	no	—
51	C₂×C₄⋊C₈	—	113	1	no	—
52	C₂²×C₈	—	113	1	no	—
53	C₂²×C₈	#90673	1	1	yes	characteristic
54	C₂×C₄²	—	113	1	no	—
55	C₄⋊C₈	—	226	2	no	—
56	C₄⋊C₈	—	226	2	no	—
57	C₂²⋊C₈	—	226	2	no	—
58	#97	—	113	4	no	—
59	C₂²×C₄	—	113	1	no	—
60	C₂²×C₄	—	113	1	no	—
61	C₂²×C₄	C₂×#90673	1	1	yes	characteristic
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	—	452	1	no	—
65	C₂×C₈	—	226	4	no	—
66	C₂×C₈	—	226	1	no	—
67	C₄²	—	113	2	no	—
68	C₄²	—	113	2	no	—
69	C₂³	C₄⋊#90673	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	113	2	no	—
73	C₂×C₄	—	113	2	no	—
74	C₂×C₄	—	452	1	no	—
75	C₂×C₄	—	226	1	no	—
76	C₂×C₄	—	226	1	no	—
77	C₂×C₄	C₄×#90673	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
79	C₈	—	4	1	no	—
80	C₈	—	452	4	no	—
81	C₈	—	452	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	1	no	—
84	C₂²	(C₂×#90673)⋊C₄	1	1	yes	characteristic
85	C₂²	#16813692	1	1	yes	characteristic
86	C₂²	#16813693	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	226	2	no	—
89	C₄	—	226	2	no	—
90	C₄	#16813682	1	1	yes	characteristic
91	C₄	#16813683	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#20299466	1	1	yes	characteristic
95	C₂	#20299474	1	1	yes	characteristic
96	C₂	#20299478	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#90673)⋊C₄
commutator	C₂×C₄×C₁₁₃	C₄²
Frattini	C₂²×C₄	C₂×#90673
Fitting	C₂²×C₈×C₁₁₃	C₄
socle	C₂²×C₁₁₃	#95
prime radical	C₂³×C₁₁₃	C₄⋊C₄
cosocle	C₂×C₄×Dic₁₁₃	C₂²
hypercenter	C₂²×C₈	#90673
hypocenter	C₁₁₃	#1290
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
49. C₁₁₃	#1290	semidirect

Maximal subgroups

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

subgroup	index
#20299619	2
C₂×#16813551	2
#1290	113