Subgroups — #42122653

Order 27712.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16812365	C₂	1	1	yes	maximal, characteristic
2	C₄×#16812365	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#16812365	C₄	1	2	yes	—
5	C₂×#16812365	C₄	1	2	yes	—
6	C₂×#16812358	C₄	1	1	yes	characteristic
7	C₄×Dic₄₃₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₃₃	C₄	1	1	yes	characteristic
9	#16812365	—	2	2	no	—
10	#16812365	C₈	1	4	yes	complemented
11	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
13	#16812358	—	2	1	no	—
14	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₄₃₃	—	2	1	no	—
16	C₂²×C₄₃₃	C₄²	1	1	yes	characteristic
17	C₄×C₄₃₃	M₁₆	1	1	yes	characteristic
18	C₄×C₄₃₃	M₁₆	1	1	yes	characteristic
19	Dic₄₃₃	C₂×C₈	1	2	yes	—
20	Dic₄₃₃	M₁₆	1	2	yes	—
21	C₂×C₄₃₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₄₃₃	#97	1	1	yes	characteristic
23	C₂×C₄₃₃	#97	1	1	yes	characteristic
24	C₄₃₃	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	433	1	no	maximal, Sylow
26	C₄×C₈	—	433	1	no	—
27	C₄×C₈	—	433	1	no	—
28	C₄×C₈	—	433	1	no	—
29	C₂×C₈	—	433	2	no	—
30	C₂×C₈	—	433	1	no	—
31	C₂×C₈	—	433	2	no	—
32	C₂×C₈	#13181884	1	1	yes	characteristic
33	C₄²	—	433	1	no	—
34	C₂×C₄	—	433	1	no	—
35	C₂×C₄	—	433	1	no	—
36	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	866	2	no	—
39	C₈	—	866	1	no	—
40	C₈	—	433	4	no	—
41	C₂²	C₄×#13181884	1	1	yes	characteristic
42	C₄	—	433	2	no	—
43	C₄	—	433	2	no	—
44	C₄	#20294106	1	1	yes	characteristic
45	C₄	#20294107	1	1	yes	characteristic
46	C₂	C₈×#13181884	1	1	yes	characteristic
47	C₂	#28357274	1	1	yes	characteristic
48	C₂	#28357275	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#13181884
commutator	C₂×C₄₃₃	C₄×C₈
Fitting	C₂×C₈×C₄₃₃	C₄
socle, prime radical	C₂²×C₄₃₃	C₄²
cosocle	C₄×Dic₄₃₃	C₂²
hypercenter	C₂×C₈	#13181884
hypocenter	C₄₃₃	#322
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #16812365	C₈	semidirect
24. C₄₃₃	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×#16812365	2
C₈×Dic₄₃₃	2
#322	433