Subgroups — #37548880

Order 23168.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042211	C₂	1	2	yes	maximal
2	C₄×#15668424	C₂	1	1	yes	maximal, characteristic
3	#19153866	—	2	2	no	—
4	C₂×#15668424	C₄	1	1	yes	characteristic
5	C₂×#15668424	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
7	#15668424	—	2	1	no	—
8	#15668424	D₄	1	1	yes	characteristic
9	#15668424	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₁₈₁	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₁₈₁	C₈	1	1	yes	characteristic
13	C₂×C₄×C₁₈₁	—	2	1	no	—
14	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₈₁	C₁₆	1	2	yes	—
16	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
18	C₂²×C₁₈₁	M₃₂	1	1	yes	characteristic
19	C₄×C₁₈₁	—	2	2	no	—
20	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₈₁	—	2	1	no	—
23	C₂×C₁₈₁	C₄⋊C₁₆	1	1	yes	characteristic
24	C₁₈₁	#1422	1	1	yes	characteristic, complemented, Sylow
25	#1422	—	181	1	no	maximal, Sylow
26	M₆₄	—	181	2	no	—
27	C₄×C₁₆	—	181	1	no	—
28	C₂×C₁₆	—	181	1	no	—
29	C₂×C₁₆	—	181	1	no	—
30	C₄×C₈	#10624382	1	1	yes	characteristic
31	C₃₂	—	362	2	no	—
32	C₂×C₈	#13089685	1	1	yes	characteristic
33	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
34	C₄²	#13089685	1	1	yes	characteristic
35	C₁₆	—	362	1	no	—
36	C₁₆	—	181	1	no	—
37	C₁₆	—	181	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
40	C₈	#15668452	1	2	yes	—
41	C₈	C₄⋊#10624382	1	1	yes	characteristic
42	C₈	#15668459	1	1	yes	characteristic
43	C₂²	#19153890	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊#13089685	1	1	yes	characteristic
46	C₄	C₂×#15668452	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#15668452	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#10624382
commutator	C₄×C₁₈₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₄×C₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₄⋊C₁₆
prime radical	C₂²×C₁₈₁	M₃₂
cosocle	C₂×#15668424	C₂²
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1422
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
24. C₁₈₁	#1422	semidirect

Maximal subgroups

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

subgroup	index
#26042211	2
C₄×#15668424	2
#1422	181