Subgroups — #42122870

Order 27712.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357295	C₂	1	2	yes	maximal, complemented
2	#28357294	C₂	1	1	yes	maximal, characteristic, complemented
3	#28357293	C₂	1	2	yes	maximal, complemented
4	C₂×#20294100	C₂	1	1	yes	maximal, characteristic, complemented
5	#28357228	C₂	1	1	yes	maximal, characteristic
6	#20294100	C₂²	1	1	yes	characteristic
7	#20294100	C₂²	1	1	yes	characteristic
8	#20294100	C₂²	1	2	yes	—
9	#20294097	C₄	1	1	yes	characteristic
10	#20294080	C₄	1	2	yes	—
11	C₂×#16812358	C₂²	1	1	yes	characteristic
12	C₈×D₄₃₃	C₂²	1	2	yes	—
13	M₁₆×C₄₃₃	C₄	1	1	yes	characteristic
14	Dic₈₆₆	C₈	1	1	yes	characteristic
15	D₁₇₃₂	C₈	1	1	yes	characteristic
16	C₂²⋊D₄₃₃	C₈	1	2	yes	—
17	C₄×D₄₃₃	C₂×C₄	1	2	yes	—
18	#16812358	C₂×C₄	1	1	yes	characteristic
19	#16812358	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
21	C₈×C₄₃₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄₃₃	C₂×C₈	1	1	yes	characteristic
23	C₂×D₄₃₃	C₂×C₈	1	2	yes	—
24	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
25	C₄×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
26	Dic₄₃₃	C₂×C₈	1	2	yes	—
27	C₂×C₄₃₃	—	2	1	no	—
28	C₂×C₄₃₃	C₂²×C₈	1	1	yes	characteristic
29	D₄₃₃	—	2	2	no	—
30	C₄₃₃	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	433	1	no	maximal, Sylow
32	#131	—	433	1	no	—
33	M₃₂	—	433	1	no	—
34	M₃₂	—	433	2	no	—
35	C₂×C₁₆	—	433	1	no	—
36	C₂×C₁₆	—	433	2	no	—
37	#41	—	433	1	no	—
38	M₁₆	—	433	2	no	—
39	M₁₆	#13181884	1	1	yes	characteristic
40	C₂×C₈	—	433	1	no	—
41	C₂×C₈	—	433	2	no	—
42	C₁₆	—	433	1	no	—
43	C₁₆	—	433	1	no	—
44	C₁₆	—	433	2	no	—
45	Q₈	—	433	1	no	—
46	D₄	—	433	2	no	—
47	D₄	—	433	1	no	—
48	C₂×C₄	—	433	2	no	—
49	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
50	C₈	—	433	1	no	—
51	C₈	—	433	1	no	—
52	C₈	C₂×#13181884	1	2	yes	—
53	C₂²	—	433	2	no	—
54	C₂²	#20294105	1	1	yes	characteristic
55	C₄	—	433	2	no	—
56	C₄	#20294105	1	1	yes	characteristic
57	C₄	C₂²×#13181884	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	866	2	no	—
60	C₂	C₂×#20294105	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#13181884
commutator, socle	C₂×C₄₃₃	C₂²×C₈
Fitting	M₁₆×C₄₃₃	C₄
prime radical	#20294097	C₄
cosocle	#16812358	C₂³
hypercenter	M₁₆	#13181884
hypocenter	C₄₃₃	#504
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #28357295	C₂	semidirect
2. #28357294	C₂	semidirect
3. #28357293	C₂	semidirect
4. C₂×#20294100	C₂	semidirect
30. C₄₃₃	#504	semidirect

Maximal subgroups

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

subgroup	index
#28357295	2
#28357294	2
#28357293	2
C₂×#20294100	2
#28357228	2
#504	433