Subgroups — #23750669

Order 9536.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011999	C₂	1	2	yes	maximal, complemented
2	#18011982	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011976	C₂	1	2	yes	maximal, complemented
4	C₈×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
5	#18011934	C₂	1	1	yes	maximal, characteristic
6	#14558746	—	2	2	no	—
7	#14558746	C₂²	1	2	yes	—
8	D₁₄₉⋊C₈	—	2	2	no	—
9	D₁₄₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×#10597010	C₂²	1	1	yes	characteristic
11	#14558737	C₂²	1	2	yes	—
12	#14558723	C₄	1	2	yes	complemented
13	D₁₁₉₂	C₄	1	1	yes	characteristic, complemented
14	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₄₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#10597010	—	2	1	no	—
17	#11924753	—	2	2	no	—
18	#11924753	D₄	1	1	yes	characteristic
19	#11924753	D₄	1	1	yes	characteristic
20	D₅₉₆	—	2	2	no	—
21	D₅₉₆	C₂×C₄	1	2	yes	—
22	C₄×D₁₄₉	—	2	2	no	—
23	C₄×D₁₄₉	C₂³	1	1	yes	characteristic
24	#11924746	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
26	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₄₉	—	2	2	no	—
28	C₂×D₁₄₉	#41	1	1	yes	characteristic
29	#10597010	—	2	2	no	—
30	C₄×C₁₄₉	—	2	2	no	—
31	C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
32	Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
34	D₁₄₉	—	2	1	no	—
35	D₁₄₉	—	4	2	no	—
36	C₁₄₉	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	149	1	no	maximal, Sylow
38	#135	—	149	1	no	—
39	#131	—	149	2	no	—
40	#108	—	149	1	no	—
41	#104	—	149	2	no	—
42	C₄×C₈	—	149	1	no	—
43	#41	—	149	2	no	—
44	Q₁₆	#10597010	1	1	yes	characteristic, complemented
45	SD₁₆	—	149	2	no	—
46	D₈	—	149	1	no	—
47	M₁₆	—	298	2	no	—
48	M₁₆	—	149	2	no	—
49	C₂×C₈	—	298	2	no	—
50	C₂×C₈	—	149	1	no	—
51	C₂×C₈	—	149	1	no	—
52	C₄²	—	149	1	no	—
53	Q₈	C₂×#10597010	1	2	yes	—
54	D₄	—	298	2	no	—
55	D₄	—	149	2	no	—
56	C₂×C₄	—	298	2	no	—
57	C₂×C₄	—	298	1	no	—
58	C₂×C₄	—	149	1	no	—
59	C₈	—	298	2	no	—
60	C₈	—	149	1	no	—
61	C₈	—	149	1	no	—
62	C₈	—	149	1	no	—
63	C₈	C₂×#10597010	1	1	yes	characteristic
64	C₂²	—	298	2	no	—
65	C₂²	—	149	1	no	—
66	C₄	—	2	2	no	—
67	C₄	—	298	2	no	—
68	C₄	—	149	1	no	—
69	C₄	C₂²×#10597010	1	1	yes	characteristic
70	C₂	—	298	1	no	—
71	C₂	—	596	2	no	—
72	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	#18011934	C₂
cosocle	C₄×D₁₄₉	C₂³
hypercenter	Q₁₆	#10597010
hypocenter	C₁₄₉	#443
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
1. #18011999	C₂	semidirect
2. #18011982	C₂	semidirect
3. #18011976	C₂	semidirect
4. C₈×#10597010	C₂	semidirect
12. #14558723	C₄	semidirect
13. D₁₁₉₂	C₄	semidirect
15. Q₁₆×C₁₄₉	C₄	semidirect
36. C₁₄₉	#443	semidirect
44. Q₁₆	#10597010	semidirect