Subgroups — #23750540

Order 9536.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#18011982	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011934	C₂	1	1	yes	maximal, characteristic
4	#14558746	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	#14558737	—	2	1	no	—
7	#14558723	—	2	1	no	—
8	D₁₁₉₂	C₄	1	1	yes	characteristic
9	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₄₉	C₄	1	1	yes	characteristic
11	#11924753	—	4	1	no	—
12	D₅₉₆	—	2	1	no	—
13	D₅₉₆	—	4	1	no	—
14	C₄×D₁₄₉	—	4	1	no	—
15	C₄×D₁₄₉	D₄	1	1	yes	characteristic
16	#11924746	D₄	1	1	yes	characteristic
17	Q₈×C₁₄₉	—	2	1	no	—
18	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₄₉	—	4	1	no	—
20	C₂×D₁₄₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₄₉	—	4	1	no	—
22	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₄₉	D₈	1	1	yes	characteristic
24	C₂×C₁₄₉	#102	1	1	yes	characteristic
25	D₁₄₉	—	2	1	no	—
26	D₁₄₉	—	8	1	no	—
27	C₁₄₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	149	1	no	maximal, Sylow
29	#135	—	149	1	no	—
30	C₂×C₁₆	—	149	1	no	—
31	#108	—	149	1	no	—
32	#41	—	298	1	no	—
33	Q₁₆	#10597010	1	1	yes	characteristic
34	SD₁₆	—	298	1	no	—
35	D₈	—	149	1	no	—
36	M₁₆	—	298	1	no	—
37	C₂×C₈	—	149	1	no	—
38	C₁₆	—	298	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	298	1	no	—
41	D₄	—	596	1	no	—
42	C₂×C₄	—	596	1	no	—
43	C₂×C₄	—	149	1	no	—
44	C₈	—	596	1	no	—
45	C₈	—	149	1	no	—
46	C₈	C₂×#10597010	1	1	yes	characteristic
47	C₂²	—	596	1	no	—
48	C₂²	—	149	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	149	1	no	—
51	C₄	C₂²⋊#10597010	1	1	yes	characteristic
52	C₂	—	298	1	no	—
53	C₂	—	1192	1	no	—
54	C₂	#18011973	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#18011973
commutator	C₈×C₁₄₉	C₂×C₄
Frattini	C₈	C₂×#10597010
Fitting	Q₁₆×C₁₄₉	C₄
socle	C₂×C₁₄₉	#102
prime radical	#18011934	C₂
cosocle	C₈×D₁₄₉	C₂²
hypercenter	Q₁₆	#10597010
hypocenter	C₁₄₉	#359
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₁₄₉⋊C₁₆	C₂	semidirect
2. #18011982	C₂	semidirect
27. C₁₄₉	#359	semidirect