Subgroups — #34059718

Order 19072.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750547	C₂	1	2	yes	maximal
2	#23749400	C₂	1	1	yes	maximal, characteristic
3	#18011985	—	2	2	no	—
4	C₂×#14558711	C₄	1	1	yes	characteristic
5	C₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₄₉	C₄	1	1	yes	characteristic
7	#14558739	—	4	2	no	—
8	C₂×#11924746	D₄	1	1	yes	characteristic
9	C₄×Dic₁₄₉	Q₈	1	1	yes	characteristic
10	#14558711	—	2	1	no	—
11	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₄₉	C₈	1	2	yes	—
13	C₂×Dic₁₄₉	—	2	1	no	—
14	#11924746	SD₁₆	1	2	yes	—
15	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
18	C₂²×C₁₄₉	#108	1	1	yes	characteristic
19	C₄×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₁₄₉	#106	1	1	yes	characteristic
21	Dic₁₄₉	—	4	1	no	—
22	C₂×C₁₄₉	—	2	1	no	—
23	C₂×C₁₄₉	#334	1	1	yes	characteristic
24	C₁₄₉	#1369	1	1	yes	characteristic, complemented, Sylow
25	#1369	—	149	1	no	maximal, Sylow
26	#364	—	149	2	no	—
27	#346	—	149	1	no	—
28	M₃₂	—	298	2	no	—
29	C₂×C₁₆	—	149	1	no	—
30	C₂×C₁₆	#10597010	1	1	yes	characteristic
31	C₄×C₈	—	149	1	no	—
32	C₂×C₈	—	149	1	no	—
33	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
34	C₄²	—	149	1	no	—
35	C₁₆	—	298	1	no	—
36	C₁₆	—	596	2	no	—
37	C₁₆	#11924753	1	2	yes	—
38	C₂×C₄	—	298	1	no	—
39	C₂×C₄	C₄⋊#10597010	1	1	yes	characteristic
40	C₈	—	149	2	no	—
41	C₈	C₂×#11924753	1	1	yes	characteristic
42	C₈	#14558746	1	1	yes	characteristic
43	C₂²	#18011981	1	1	yes	characteristic
44	C₄	—	596	1	no	—
45	C₄	C₄⋊#11924753	1	1	yes	characteristic
46	C₄	#18011979	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#23750486	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#18011979
commutator	C₈×C₁₄₉	C₂×C₈
Frattini	C₂×C₈	C₂×#10597010
Fitting	C₂×C₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	#334
prime radical	C₂²×C₁₄₉	#108
cosocle	C₈×Dic₁₄₉	C₂²
hypercenter	C₂×C₁₆	#10597010
hypocenter	C₁₄₉	#1369
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₁₄₉	#1369	semidirect

Maximal subgroups

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

subgroup	index
#23750547	2
#23749400	2
#1369	149