Subgroups — #28417277

Order 14912.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14272345	C₂	1	1	yes	maximal, characteristic
2	C₄×#14272345	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14272345	C₄	1	2	yes	—
5	C₂×#14272345	C₄	1	2	yes	—
6	C₂×#14272338	C₄	1	1	yes	characteristic
7	C₄×Dic₂₃₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃₃	C₄	1	1	yes	characteristic
9	#14272345	—	2	2	no	—
10	#14272345	C₈	1	4	yes	complemented
11	C₂×Dic₂₃₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₂₃₃	C₂×C₄	1	1	yes	characteristic
13	#14272338	—	2	1	no	—
14	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₃₃	—	2	1	no	—
16	C₂²×C₂₃₃	C₄²	1	1	yes	characteristic
17	C₄×C₂₃₃	M₁₆	1	1	yes	characteristic
18	C₄×C₂₃₃	M₁₆	1	1	yes	characteristic
19	Dic₂₃₃	C₂×C₈	1	2	yes	—
20	Dic₂₃₃	M₁₆	1	2	yes	—
21	C₂×C₂₃₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₂₃₃	#97	1	1	yes	characteristic
23	C₂×C₂₃₃	#97	1	1	yes	characteristic
24	C₂₃₃	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	233	1	no	maximal, Sylow
26	C₄×C₈	—	233	1	no	—
27	C₄×C₈	—	233	1	no	—
28	C₄×C₈	—	233	1	no	—
29	C₂×C₈	—	233	2	no	—
30	C₂×C₈	—	233	1	no	—
31	C₂×C₈	—	233	2	no	—
32	C₂×C₈	#11745400	1	1	yes	characteristic
33	C₄²	—	233	1	no	—
34	C₂×C₄	—	233	1	no	—
35	C₂×C₄	—	233	1	no	—
36	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	466	2	no	—
39	C₈	—	466	1	no	—
40	C₈	—	233	4	no	—
41	C₂²	C₄×#11745400	1	1	yes	characteristic
42	C₄	—	233	2	no	—
43	C₄	—	233	2	no	—
44	C₄	#16836603	1	1	yes	characteristic
45	C₄	#16836604	1	1	yes	characteristic
46	C₂	C₈×#11745400	1	1	yes	characteristic
47	C₂	#21418589	1	1	yes	characteristic
48	C₂	#21418590	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11745400
commutator	C₂×C₂₃₃	C₄×C₈
Fitting	C₂×C₈×C₂₃₃	C₄
socle, prime radical	C₂²×C₂₃₃	C₄²
cosocle	C₄×Dic₂₃₃	C₂²
hypercenter	C₂×C₈	#11745400
hypocenter	C₂₃₃	#322
LCS	G ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #14272345	C₈	semidirect
24. C₂₃₃	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14272345	2
C₈×Dic₂₃₃	2
#322	233