Subgroups — #34059857

Order 19072.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750554	C₂	1	1	yes	maximal, characteristic
2	#23750552	C₂	1	1	yes	maximal, characteristic
3	#23749458	C₂	1	1	yes	maximal, characteristic
4	#18011982	—	2	1	no	—
5	#18011980	—	2	1	no	—
6	C₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
7	#18011817	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₁₄₉	C₄	1	1	yes	characteristic, complemented
9	#14558746	—	4	1	no	—
10	C₄⋊#10597010	—	4	1	no	—
11	C₈×D₁₄₉	D₄	1	1	yes	characteristic
12	#14558711	Q₈	1	1	yes	characteristic
13	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×#10597010	—	8	1	no	—
15	#11924753	—	8	1	no	—
16	C₄×D₁₄₉	D₈	1	1	yes	characteristic
17	#11924746	Q₁₆	1	1	yes	characteristic
18	C₈×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₄₉	SD₃₂	1	1	yes	characteristic
20	#10597010	—	16	1	no	—
21	C₄×C₁₄₉	#107	1	1	yes	characteristic
22	Dic₁₄₉	SD₃₂	1	1	yes	characteristic
23	C₂×C₁₄₉	#367	1	1	yes	characteristic
24	D₁₄₉	—	2	1	no	—
25	C₁₄₉	#1426	1	1	yes	characteristic, complemented, Sylow
26	#1426	—	149	1	no	maximal, Sylow
27	M₆₄	—	149	1	no	—
28	#368	—	149	1	no	—
29	#367	—	149	1	no	—
30	C₂×C₁₆	—	149	1	no	—
31	#108	—	298	1	no	—
32	#107	—	298	1	no	—
33	C₃₂	—	149	1	no	—
34	C₃₂	#10597010	1	1	yes	characteristic, complemented
35	M₁₆	—	596	1	no	—
36	C₂×C₈	—	149	1	no	—
37	C₄⋊C₄	—	596	1	no	—
38	C₁₆	—	149	1	no	—
39	C₁₆	C₂×#10597010	1	1	yes	characteristic
40	C₂×C₄	—	149	1	no	—
41	C₂×C₄	—	1192	1	no	—
42	C₈	—	149	1	no	—
43	C₈	—	1192	1	no	—
44	C₈	C₄⋊#10597010	1	1	yes	characteristic
45	C₂²	—	149	1	no	—
46	C₄	—	2384	1	no	—
47	C₄	—	149	1	no	—
48	C₄	#18011980	1	1	yes	characteristic
49	C₂	—	298	1	no	—
50	C₂	#23750552	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750552
commutator	C₁₆×C₁₄₉	C₂×C₄
Frattini	C₁₆	C₂×#10597010
Fitting	C₃₂×C₁₄₉	C₄
socle	C₂×C₁₄₉	#367
prime radical	C₂×D₁₄₉	SD₃₂
cosocle	C₁₆×D₁₄₉	C₂²
hypercenter	C₃₂	#10597010
hypocenter	C₁₄₉	#1426
LCS	G ▷ C₁₆×C₁₄₉ ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #18011817	C₄	semidirect
8. C₃₂×C₁₄₉	C₄	semidirect
25. C₁₄₉	#1426	semidirect
34. C₃₂	#10597010	semidirect

Maximal subgroups

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

subgroup	index
#23750554	2
#23750552	2
#23749458	2
#1426	149