Subgroups — #28405487

Order 14464.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14268650	C₂	1	2	yes	maximal
2	C₈×#11744751	C₂	1	1	yes	maximal, characteristic
3	C₂×#14268650	C₄	1	4	yes	—
4	C₄×#11744751	C₄	1	1	yes	characteristic
5	C₄×#11744751	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₁₃	C₄	1	1	yes	characteristic
7	#14268650	—	2	4	no	—
8	C₂×#11744751	C₈	1	2	yes	—
9	C₂×#11744751	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₁₃	C₈	1	2	yes	—
11	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₁₃	C₁₆	1	4	yes	complemented
16	#11744751	—	2	2	no	—
17	#11744751	M₁₆	1	4	yes	—
18	C₂²×C₁₁₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₁₃	#97	1	2	yes	—
20	C₄×C₁₁₃	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₁₃	M₃₂	1	2	yes	—
22	C₂×C₁₁₃	#322	1	1	yes	characteristic
23	C₂×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₁₃	#346	1	1	yes	characteristic
25	#1312	—	113	1	no	maximal, Sylow
26	C₁₁₃	#1312	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₁₆	—	113	2	no	—
28	C₈²	—	113	1	no	—
29	C₂×C₁₆	—	113	4	no	—
30	C₄×C₈	—	113	1	no	—
31	C₄×C₈	—	113	1	no	—
32	C₄×C₈	#90673	1	1	yes	characteristic
33	C₂×C₈	—	113	2	no	—
34	C₂×C₈	—	113	2	no	—
35	C₂×C₈	#11744753	1	2	yes	—
36	C₄²	C₂×#90673	1	1	yes	characteristic
37	C₁₆	—	226	4	no	—
38	C₂×C₄	C₄×#90673	1	1	yes	characteristic
39	C₂×C₄	C₂×#11744753	1	1	yes	characteristic
40	C₂×C₄	#14268655	1	1	yes	characteristic
41	C₈	—	113	4	no	—
42	C₈	—	226	2	no	—
43	C₈	#14268650	1	4	yes	complemented
44	C₂²	C₄×#11744753	1	1	yes	characteristic
45	C₄	#16813676	1	2	yes	—
46	C₄	C₂×#14268650	1	2	yes	—
47	C₄	#16813697	1	2	yes	—
48	C₂	#20299439	1	1	yes	characteristic
49	C₂	C₄×#14268650	1	1	yes	characteristic
50	C₂	#20299487	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#90673
commutator	C₂×C₁₁₃	C₄×C₁₆
Fitting	C₄×C₈×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	C₄×C₈
cosocle	C₄×#11744751	C₂²
hypercenter	C₄×C₈	#90673
hypocenter	C₁₁₃	#1312
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₈×C₁₁₃	C₁₆	semidirect
26. C₁₁₃	#1312	semidirect
43. C₈	#14268650	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14268650	2
C₈×#11744751	2
#1312	113