Subgroups — #28416813

Order 14912.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#16836584	C₂	1	2	yes	maximal
3	#21418533	C₂	1	2	yes	maximal
4	C₈×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₂₃₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₄₆₆	C₂²	1	2	yes	—
7	Dic₉₃₂	—	2	2	no	—
8	#16836584	—	2	4	no	—
9	C₂×#14272338	C₂²	1	1	yes	characteristic
10	#16836573	—	2	4	no	—
11	C₄×Dic₂₃₃	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₂₃₃	C₂²	1	2	yes	—
13	Q₁₆×C₂₃₃	—	2	2	no	—
14	C₂×C₈×C₂₃₃	C₂²	1	1	yes	characteristic
15	Dic₄₆₆	—	2	2	no	—
16	Dic₄₆₆	—	2	2	no	—
17	C₂×Dic₂₃₃	—	2	2	no	—
18	C₂×Dic₂₃₃	D₄	1	2	yes	—
19	#14272338	D₄	1	2	yes	—
20	Q₈×C₂₃₃	—	2	2	no	—
21	Q₈×C₂₃₃	—	2	2	no	—
22	C₂×C₄×C₂₃₃	—	2	2	no	—
23	C₂×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
24	C₈×C₂₃₃	D₄	1	2	yes	—
25	C₂²×C₂₃₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₃₃	—	4	2	no	—
27	C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
29	Dic₂₃₃	—	4	2	no	—
30	Dic₂₃₃	Q₁₆	1	4	yes	complemented
31	C₂×C₂₃₃	#127	1	1	yes	characteristic
32	C₂×C₂₃₃	C₂×Q₁₆	1	2	yes	—
33	C₂₃₃	#494	1	1	yes	characteristic, complemented, Sylow
34	#494	—	233	1	no	maximal, Sylow
35	C₂×Q₁₆	—	233	2	no	—
36	C₂×Q₁₆	—	233	1	no	—
37	C₂×Q₁₆	D₂₃₃	1	1	yes	characteristic
38	C₄⋊Q₈	—	233	2	no	—
39	C₄×C₈	—	233	1	no	—
40	C₂×Q₈	—	233	2	no	—
41	C₂×Q₈	C₂×D₂₃₃	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	466	4	no	—
44	Q₁₆	—	466	2	no	—
45	C₂×C₈	—	233	1	no	—
46	C₂×C₈	C₂×D₂₃₃	1	1	yes	characteristic
47	C₄⋊C₄	—	466	4	no	—
48	C₄²	—	233	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	466	2	no	—
52	Q₈	—	466	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	466	2	no	—
55	C₂×C₄	—	233	2	no	—
56	C₂×C₄	C₂²×D₂₃₃	1	1	yes	characteristic
57	C₈	—	233	2	no	—
58	C₈	C₂²⋊D₂₃₃	1	2	yes	—
59	C₂²	D₄×D₂₃₃	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	932	2	no	—
62	C₄	—	233	4	no	—
63	C₄	D₄×D₂₃₃	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₂₃₃	1	1	yes	characteristic
65	C₂	#21418531	1	1	yes	characteristic
66	C₂	Q₁₆×D₂₃₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₃₃
commutator, cosocle	C₂×C₄×C₂₃₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃₃
Fitting	C₂×Q₁₆×C₂₃₃	C₂
socle, prime radical	C₂²×C₂₃₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₂₃₃
hypocenter	C₂₃₃	#494
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₂₃₃	Q₁₆	semidirect
33. C₂₃₃	#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₉₃₂	2
C₂×#16836584	2
#21418533	2
C₈×Dic₂₃₃	2
C₂×Q₁₆×C₂₃₃	2
#494	233