Subgroups — #42122908

Order 27712.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294109	C₂	1	2	yes	maximal, complemented
2	C₂×#20294105	C₂	1	1	yes	maximal, characteristic
3	#20294109	—	2	2	no	—
4	#20294105	—	2	2	no	—
5	C₂×#16812365	C₄	1	1	yes	characteristic
6	C₂×#16812365	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄₃₃	C₄	1	1	yes	characteristic
8	#16812365	—	2	1	no	—
9	#16812365	D₄	1	2	yes	—
10	C₂²×D₄₃₃	C₈	1	1	yes	characteristic
11	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
12	C₄×D₄₃₃	—	2	1	no	—
13	C₄×D₄₃₃	—	2	1	no	—
14	C₂×C₄×C₄₃₃	C₈	1	1	yes	characteristic
15	C₂²×C₄₃₃	C₂×C₈	1	1	yes	characteristic
16	C₂×D₄₃₃	—	2	1	no	—
17	C₂×D₄₃₃	—	2	1	no	—
18	C₂×D₄₃₃	C₁₆	1	2	yes	complemented
19	C₄×C₄₃₃	—	2	1	no	—
20	Dic₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₄₃₃	M₁₆	1	1	yes	characteristic
22	C₂×C₄₃₃	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₄₃₃	M₃₂	1	1	yes	characteristic
25	D₄₃₃	—	2	2	no	—
26	C₄₃₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	433	1	no	maximal, Sylow
28	C₂²×C₈	—	433	1	no	—
29	C₂×C₁₆	—	433	2	no	—
30	C₂²×C₄	—	433	1	no	—
31	C₂×C₈	—	866	2	no	—
32	C₂×C₈	—	433	1	no	—
33	C₂×C₈	—	433	1	no	—
34	C₁₆	—	866	2	no	—
35	C₂³	—	433	1	no	—
36	C₂×C₄	—	866	1	no	—
37	C₂×C₄	—	866	1	no	—
38	C₂×C₄	—	433	1	no	—
39	C₂×C₄	#16812367	1	1	yes	characteristic
40	C₈	—	866	1	no	—
41	C₈	—	433	2	no	—
42	C₂²	—	866	1	no	—
43	C₂²	—	866	1	no	—
44	C₂²	—	433	2	no	—
45	C₂²	C₂×#16812367	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	433	1	no	—
48	C₄	—	433	1	no	—
49	C₂	—	866	2	no	—
50	C₂	C₂²⋊#16812367	1	1	yes	characteristic
51	C₂	#28357315	1	1	yes	characteristic
52	C₂	#28357317	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#16812367
commutator	C₂×C₄₃₃	C₂×C₁₆
Fitting	C₂×C₄×C₄₃₃	C₈
socle	C₂²×C₄₃₃	C₂×C₈
prime radical	C₂²×D₄₃₃	C₈
cosocle	C₂×#16812365	C₂²
hypercenter	C₂×C₄	#16812367
hypocenter	C₄₃₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#20294109	C₂	semidirect
18. C₂×D₄₃₃	C₁₆	semidirect
26. C₄₃₃	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20294109	2
C₂×#20294105	2
C₂²⋊C₁₆	433