Subgroups — #34042897

Order 19072.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23749455	C₂	1	1	yes	maximal, characteristic
2	#23749453	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#18011847	—	2	1	no	—
5	#18011845	—	2	1	no	—
6	C₂×C₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₃₂×C₁₄₉	C₄	1	2	yes	complemented
8	#14558720	—	4	1	no	—
9	C₄⋊Dic₁₄₉	—	4	1	no	—
10	C₂×C₈×C₁₄₉	D₄	1	1	yes	characteristic
11	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₄₉	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₄₉	—	8	1	no	—
14	#11924746	—	8	1	no	—
15	C₂×C₄×C₁₄₉	D₈	1	1	yes	characteristic
16	C₈×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₄₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₄₉	SD₃₂	1	1	yes	characteristic
19	C₄×C₁₄₉	#107	1	1	yes	characteristic
20	C₄×C₁₄₉	SD₃₂	1	1	yes	characteristic
21	Dic₁₄₉	—	16	1	no	—
22	C₂×C₁₄₉	—	2	1	no	—
23	C₂×C₁₄₉	#367	1	1	yes	characteristic
24	C₁₄₉	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	149	1	no	maximal, Sylow
26	M₆₄	D₁₄₉	1	1	yes	characteristic
27	#368	—	149	1	no	—
28	#367	—	149	1	no	—
29	C₂×C₁₆	C₂×D₁₄₉	1	1	yes	characteristic
30	#108	—	298	1	no	—
31	#107	—	298	1	no	—
32	C₃₂	Dic₁₄₉	1	2	yes	complemented
33	M₁₆	—	596	1	no	—
34	C₂×C₈	D₅₉₆	1	1	yes	characteristic
35	C₄⋊C₄	—	596	1	no	—
36	C₁₆	C₂×Dic₁₄₉	1	1	yes	characteristic
37	C₁₆	Dic₂₉₈	1	1	yes	characteristic
38	C₂×C₄	—	1192	1	no	—
39	C₂×C₄	D₁₁₉₂	1	1	yes	characteristic
40	C₈	—	1192	1	no	—
41	C₈	C₄⋊Dic₁₄₉	1	1	yes	characteristic
42	C₈	Dic₅₉₆	1	1	yes	characteristic
43	C₂²	#18011856	1	1	yes	characteristic
44	C₄	—	2384	1	no	—
45	C₄	#18011845	1	1	yes	characteristic
46	C₄	#18011856	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#23749453	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23749453
commutator	C₁₆×C₁₄₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₄₉
Fitting	M₆₄×C₁₄₉	C₂
socle	C₂×C₁₄₉	#367
prime radical	C₂²×C₁₄₉	SD₃₂
cosocle	C₂×C₁₆×C₁₄₉	C₂²
hypercenter	M₆₄	D₁₄₉
hypocenter	C₁₄₉	#1426
LCS	G ▷ C₁₆×C₁₄₉ ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₁₄₉	C₄	semidirect
24. C₁₄₉	#1426	semidirect
32. C₃₂	Dic₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23749455	2
#23749453	2
M₆₄×C₁₄₉	2
#1426	149