Subgroups — #28405682

Order 14464.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813672	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813672	C₄	1	4	yes	complemented
4	C₂×#14268622	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₁₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#11744751	C₈	1	1	yes	characteristic
8	C₄×Dic₁₁₃	C₈	1	1	yes	characteristic
9	#14268622	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
11	C₁₆×C₁₁₃	C₈	1	2	yes	—
12	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
13	C₂×Dic₁₁₃	C₁₆	1	2	yes	—
14	C₈×C₁₁₃	C₄²	1	1	yes	characteristic
15	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	#11744751	C₁₆	1	2	yes	—
17	C₂²×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
20	Dic₁₁₃	—	2	2	no	—
21	C₂×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₁₁₃	M₆₄	1	2	yes	—
23	#1397	—	113	1	no	maximal, Sylow
24	C₁₁₃	#1397	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	113	2	no	—
26	C₄×C₁₆	—	113	1	no	—
27	C₂×C₁₆	—	113	1	no	—
28	C₂×C₁₆	#90673	1	1	yes	characteristic
29	C₄×C₈	—	113	1	no	—
30	C₃₂	—	113	4	no	—
31	C₂×C₈	—	113	1	no	—
32	C₂×C₈	C₂×#90673	1	1	yes	characteristic
33	C₄²	—	113	1	no	—
34	C₁₆	—	113	2	no	—
35	C₁₆	#11744753	1	2	yes	—
36	C₂×C₄	—	113	2	no	—
37	C₂×C₄	#14268655	1	1	yes	characteristic
38	C₈	—	113	2	no	—
39	C₈	C₄×#90673	1	1	yes	characteristic
40	C₈	C₂×#11744753	1	1	yes	characteristic
41	C₂²	#16813695	1	1	yes	characteristic
42	C₄	—	226	2	no	—
43	C₄	C₄×#11744753	1	1	yes	characteristic
44	C₄	#16813695	1	1	yes	characteristic
45	C₂	#20299484	1	1	yes	characteristic
46	C₂	#20299531	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#90673
commutator	C₂×C₁₁₃	C₄×C₁₆
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	C₂×C₁₆
cosocle	C₂×#14268622	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1397
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
3. #16813672	C₄	semidirect
24. C₁₁₃	#1397	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813672	2
C₁₆×Dic₁₁₃	2
#1397	113