Subgroups — #34059724

Order 19072.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750488	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11924753	—	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	C₂×#11924753	—	4	2	no	—
8	C₂×#11924746	Q₈	1	1	yes	characteristic
9	C₄×Dic₁₄₉	D₄	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	complemented
13	#11924753	—	8	2	no	—
14	C₂×Dic₁₄₉	D₈	1	1	yes	characteristic
15	C₂×Dic₁₄₉	Q₁₆	1	1	yes	characteristic
16	#11924746	—	2	1	no	—
17	C₂×C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
20	C₂²×C₁₄₉	#107	1	1	yes	characteristic
21	C₄×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₄₉	#108	1	1	yes	characteristic
23	Dic₁₄₉	—	2	1	no	—
24	Dic₁₄₉	SD₃₂	1	2	yes	—
25	C₂×C₁₄₉	#335	1	1	yes	characteristic
26	C₂×C₁₄₉	#367	1	1	yes	characteristic
27	C₂×C₁₄₉	#368	1	1	yes	characteristic
28	C₁₄₉	#1372	1	1	yes	characteristic, complemented, Sylow
29	#1372	—	149	1	no	maximal, Sylow
30	C₄×C₁₆	—	149	1	no	—
31	#335	—	149	2	no	—
32	C₂×C₁₆	—	149	1	no	—
33	C₂×C₁₆	#10597010	1	1	yes	characteristic
34	C₄⋊C₈	—	298	2	no	—
35	C₄×C₈	—	149	1	no	—
36	C₂×C₈	—	596	2	no	—
37	C₂×C₈	—	149	1	no	—
38	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
39	C₄²	—	149	1	no	—
40	C₁₆	—	298	1	no	—
41	C₁₆	#11924753	1	2	yes	complemented
42	C₂×C₄	—	149	1	no	—
43	C₂×C₄	—	149	1	no	—
44	C₂×C₄	C₄⋊#10597010	1	1	yes	characteristic
45	C₈	—	298	1	no	—
46	C₈	—	1192	2	no	—
47	C₈	C₂×#11924753	1	1	yes	characteristic
48	C₈	#14558746	1	1	yes	characteristic
49	C₂²	#18011980	1	1	yes	characteristic
50	C₄	—	298	1	no	—
51	C₄	—	149	2	no	—
52	C₄	C₄⋊#11924753	1	1	yes	characteristic
53	C₄	#18011982	1	1	yes	characteristic
54	C₂	#23750488	1	1	yes	characteristic
55	C₂	#23750552	1	1	yes	characteristic
56	C₂	#23750554	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#18011980
commutator	C₈×C₁₄₉	C₂×C₈
Frattini	C₂×C₈	C₂×#10597010
Fitting	C₂×C₁₆×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	#107
cosocle	C₈×Dic₁₄₉	C₂²
hypercenter	C₂×C₁₆	#10597010
hypocenter	C₁₄₉	#1372
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₄₉	C₈	semidirect
28. C₁₄₉	#1372	semidirect
41. C₁₆	#11924753	semidirect

Maximal subgroups

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

subgroup	index
#23750488	2
C₁₆×Dic₁₄₉	2
#1372	149