Subgroups — #23750544

Order 9536.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011986	C₂	1	1	yes	maximal, characteristic
2	#18011981	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#14558746	—	2	1	no	—
5	#14558739	—	2	1	no	—
6	Q₈×D₁₄₉	—	2	1	no	—
7	Dic₅₉₆	C₄	1	1	yes	characteristic
8	#14558726	—	2	1	no	—
9	C₈×D₁₄₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₄₉	C₄	1	1	yes	characteristic
11	#11924753	—	4	1	no	—
12	Dic₂₉₈	—	2	1	no	—
13	Dic₂₉₈	—	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	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₄₉	—	4	1	no	—
21	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₄₉	—	4	1	no	—
23	Dic₁₄₉	D₈	1	1	yes	characteristic
24	C₂×C₁₄₉	#102	1	1	yes	characteristic
25	D₁₄₉	—	2	1	no	—
26	C₁₄₉	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	149	1	no	maximal, Sylow
28	C₂×Q₁₆	—	149	1	no	—
29	M₃₂	—	149	1	no	—
30	#108	—	149	1	no	—
31	C₂×Q₈	—	298	1	no	—
32	Q₁₆	—	298	1	no	—
33	Q₁₆	—	149	1	no	—
34	Q₁₆	#10597010	1	1	yes	characteristic
35	M₁₆	—	298	1	no	—
36	C₂×C₈	—	149	1	no	—
37	C₁₆	—	298	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	298	1	no	—
40	Q₈	—	596	1	no	—
41	C₂×C₄	—	596	1	no	—
42	C₂×C₄	—	149	1	no	—
43	C₈	—	596	1	no	—
44	C₈	—	149	1	no	—
45	C₈	C₂×#10597010	1	1	yes	characteristic
46	C₂²	—	149	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	596	1	no	—
49	C₄	—	149	1	no	—
50	C₄	C₂²⋊#10597010	1	1	yes	characteristic
51	C₂	—	298	1	no	—
52	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	C₂×D₁₄₉	SD₁₆
cosocle	C₈×D₁₄₉	C₂²
hypercenter	Q₁₆	#10597010
hypocenter	C₁₄₉	#362
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
26. C₁₄₉	#362	semidirect