Subgroups — #23750665

Order 9536.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10597010	C₂	1	2	yes	maximal
2	#18011979	C₂	1	1	yes	maximal, characteristic
3	#18011974	C₂	1	2	yes	maximal
4	#18011965	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic
6	D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊#10597010	—	2	2	no	—
8	C₄⋊#10597010	C₂²	1	2	yes	—
9	C₄×#10597010	—	2	2	no	—
10	C₄×#10597010	C₂²	1	1	yes	characteristic
11	Q₈×D₁₄₉	C₂²	1	2	yes	—
12	Dic₅₉₆	C₄	1	1	yes	characteristic, complemented
13	#14558726	C₄	1	2	yes	complemented
14	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₄₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#10597010	—	2	2	no	—
17	C₂×#10597010	D₄	1	2	yes	—
18	#11924753	—	2	1	no	—
19	Dic₂₉₈	—	2	2	no	—
20	Dic₂₉₈	C₂×C₄	1	2	yes	—
21	C₄×D₁₄₉	—	2	2	no	—
22	C₄×D₁₄₉	C₂³	1	1	yes	characteristic
23	#11924746	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
25	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
26	C₂×D₁₄₉	C₂×D₄	1	1	yes	characteristic
27	#10597010	—	2	2	no	—
28	#10597010	—	4	2	no	—
29	C₄×C₁₄₉	—	2	2	no	—
30	C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₄₉	—	2	2	no	—
32	Dic₁₄₉	#41	1	1	yes	characteristic
33	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
34	D₁₄₉	#137	1	2	yes	—
35	C₁₄₉	#441	1	1	yes	characteristic, complemented, Sylow
36	#441	—	149	1	no	maximal, Sylow
37	C₂×Q₁₆	—	149	1	no	—
38	C₄×Q₈	—	149	2	no	—
39	#106	—	149	1	no	—
40	#103	—	149	2	no	—
41	#97	—	149	1	no	—
42	C₂×Q₈	—	149	2	no	—
43	Q₁₆	—	149	2	no	—
44	Q₁₆	—	149	1	no	—
45	Q₁₆	#10597010	1	1	yes	characteristic, complemented
46	C₂×C₈	—	149	1	no	—
47	C₂×C₈	—	149	1	no	—
48	C₄⋊C₄	—	298	2	no	—
49	C₄⋊C₄	—	149	2	no	—
50	C₄²	—	298	2	no	—
51	C₄²	—	149	1	no	—
52	Q₈	—	298	2	no	—
53	Q₈	—	149	2	no	—
54	Q₈	C₂×#10597010	1	2	yes	—
55	C₂×C₄	—	298	2	no	—
56	C₂×C₄	—	298	2	no	—
57	C₂×C₄	—	149	2	no	—
58	C₂×C₄	—	149	1	no	—
59	C₈	—	298	1	no	—
60	C₈	—	149	1	no	—
61	C₈	C₂×#10597010	1	1	yes	characteristic
62	C₂²	—	149	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	298	2	no	—
65	C₄	—	298	2	no	—
66	C₄	—	596	2	no	—
67	C₄	—	149	1	no	—
68	C₄	C₂²×#10597010	1	1	yes	characteristic
69	C₂	—	149	2	no	—
70	C₂	D₄×#10597010	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10597010
commutator	C₄×C₁₄₉	C₂²×C₄
Frattini	C₄	C₂²×#10597010
Fitting	Q₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₄×D₄
prime radical	C₂×D₁₄₉	C₂×D₄
cosocle	C₄×D₁₄₉	C₂³
hypercenter	Q₁₆	#10597010
hypocenter	C₁₄₉	#441
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₅₉₆	C₄	semidirect
13. #14558726	C₄	semidirect
15. Q₁₆×C₁₄₉	C₄	semidirect
35. C₁₄₉	#441	semidirect
45. Q₁₆	#10597010	semidirect