Subgroups — #23750561

Order 9536.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10597010	C₂	1	2	yes	maximal
2	(C₂×#10597010)⋊C₄	C₂	1	4	yes	maximal
3	C₄²×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10597010	C₂²	1	4	yes	—
5	C₄×#10597010	C₄	1	8	yes	complemented
6	C₂×C₄×D₁₄₉	C₂²	1	2	yes	—
7	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₄₉	C₄	1	2	yes	complemented
9	C₄×Dic₁₄₉	C₄	1	1	yes	characteristic, complemented
10	C₄²×C₁₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#10597010	—	2	8	no	—
12	C₂×#10597010	C₂×C₄	1	8	yes	—
13	C₂²×D₁₄₉	C₂³	1	1	yes	characteristic
14	C₂×Dic₁₄₉	C₂×C₄	1	2	yes	—
15	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₄₉	—	2	4	no	—
17	C₄×D₁₄₉	C₂×C₄	1	4	yes	—
18	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₁₄₉	C₂²×C₄	1	2	yes	—
22	C₂×D₁₄₉	#41	1	4	yes	—
23	#10597010	—	2	8	no	—
24	C₄×C₁₄₉	—	2	2	no	—
25	C₄×C₁₄₉	C₄²	1	2	yes	—
26	Dic₁₄₉	—	2	2	no	—
27	Dic₁₄₉	C₄²	1	2	yes	—
28	C₂×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₁₄₉	#117	1	2	yes	—
30	D₁₄₉	#117	1	4	yes	—
31	C₁₄₉	#376	1	1	yes	characteristic, complemented, Sylow
32	#376	—	149	1	no	maximal, Sylow
33	C₂×C₄²	—	149	2	no	—
34	C₂×C₄²	—	149	1	no	—
35	#95	—	149	4	no	—
36	C₂²×C₄	—	149	4	no	—
37	C₂²×C₄	—	149	2	no	—
38	C₂²×C₄	—	149	1	no	—
39	C₄²	—	149	8	no	—
40	C₄²	—	149	2	no	—
41	C₄²	—	149	1	no	—
42	C₄²	#10597010	1	1	yes	characteristic, complemented
43	C₂³	—	149	1	no	—
44	C₂×C₄	—	298	4	no	—
45	C₂×C₄	—	298	8	no	—
46	C₂×C₄	—	149	8	no	—
47	C₂×C₄	—	149	2	no	—
48	C₂×C₄	—	149	1	no	—
49	C₂×C₄	—	149	4	no	—
50	C₂×C₄	C₂×#10597010	1	2	yes	—
51	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
52	C₂²	—	149	2	no	—
53	C₂²	—	149	4	no	—
54	C₂²	C₂²×#10597010	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	298	8	no	—
57	C₄	—	298	2	no	—
58	C₄	—	149	2	no	—
59	C₄	C₄×#10597010	1	2	yes	—
60	C₂	—	149	4	no	—
61	C₂	C₂×C₄×#10597010	1	1	yes	characteristic
62	C₂	#18011990	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#10597010
commutator	C₂×C₁₄₉	C₂×C₄²
Frattini	C₂²	C₂²×#10597010
Fitting	C₄²×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical, cosocle	C₂²×D₁₄₉	C₂³
hypercenter	C₄²	#10597010
hypocenter	C₁₄₉	#376
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
5. C₄×#10597010	C₄	semidirect
8. C₄×Dic₁₄₉	C₄	semidirect
9. C₄×Dic₁₄₉	C₄	semidirect
10. C₄²×C₁₄₉	C₄	semidirect
31. C₁₄₉	#376	semidirect
42. C₄²	#10597010	semidirect