Subgroups — #28417331

Order 14912.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418609	C₂	1	2	yes	maximal, complemented
2	C₂×#16836578	C₂	1	1	yes	maximal, characteristic
3	#16836597	—	2	2	no	—
4	#16836578	—	2	2	no	—
5	C₂×#14272338	C₄	1	1	yes	characteristic
6	C₂×#14272338	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₂₃₃	C₄	1	1	yes	characteristic
8	#14272338	—	2	1	no	—
9	#14272338	D₄	1	2	yes	—
10	C₂³×C₂₃₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₂₃₃	—	2	1	no	—
12	C₂×C₄×C₂₃₃	—	2	1	no	—
13	C₂×C₄×C₂₃₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₂₃₃	—	2	1	no	—
16	C₂²×C₂₃₃	—	4	1	no	—
17	C₂²×C₂₃₃	C₂×C₈	1	1	yes	characteristic
18	C₄×C₂₃₃	—	2	1	no	—
19	C₄×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₃₃	M₁₆	1	1	yes	characteristic
21	C₂×C₂₃₃	—	2	1	no	—
22	C₂×C₂₃₃	—	4	1	no	—
23	C₂×C₂₃₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₂₃₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	233	1	no	maximal, Sylow
26	C₂×M₁₆	—	233	1	no	—
27	M₃₂	—	233	2	no	—
28	C₂²×C₄	#11745400	1	1	yes	characteristic
29	M₁₆	—	466	2	no	—
30	C₂×C₈	—	233	1	no	—
31	C₂×C₈	—	233	1	no	—
32	C₁₆	—	466	2	no	—
33	C₂³	#14272345	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	#14272345	1	1	yes	characteristic
37	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
38	C₈	—	466	1	no	—
39	C₈	—	233	2	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#14272345	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊#11745400	1	1	yes	characteristic
45	C₄	#16836603	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#14272345	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11745400
commutator	C₂²×C₂₃₃	C₂×C₈
Frattini	C₂×C₄	C₂×#11745400
Fitting	C₂²×C₄×C₂₃₃	C₄
socle	C₂×C₂₃₃	C₂²⋊C₈
prime radical	C₂³×C₂₃₃	C₈
cosocle	C₂×#14272338	C₂²
hypercenter	C₂²×C₄	#11745400
hypocenter	C₂₃₃	#349
LCS	G ▷ C₂²×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #21418609	C₂	semidirect
24. C₂₃₃	#349	semidirect

Maximal subgroups

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

subgroup	index
#21418609	2
C₂×#16836578	2
#349	233