Subgroups — #23749430

Order 9536.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₉₆	C₂	1	1	yes	maximal, characteristic
2	#18011845	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₈	—	2	1	no	—
5	Dic₅₉₆	—	2	1	no	—
6	Dic₅₉₆	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₄₉	—	2	1	no	—
8	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₄₉	—	2	1	no	—
10	Dic₂₉₈	—	2	2	no	—
11	Dic₂₉₈	—	4	1	no	—
12	C₂×Dic₁₄₉	—	4	1	no	—
13	C₂×Dic₁₄₉	—	4	1	no	—
14	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
15	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₄₉	D₄	1	1	yes	characteristic
17	C₂²×C₁₄₉	D₈	1	1	yes	characteristic
18	C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₄₉	SD₁₆	1	1	yes	characteristic
20	Dic₁₄₉	—	4	2	no	—
21	Dic₁₄₉	—	8	1	no	—
22	C₂×C₁₄₉	#102	1	1	yes	characteristic
23	C₂×C₁₄₉	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₄₉	Q₃₂	1	1	yes	characteristic
25	C₁₄₉	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	149	1	no	maximal, Sylow
27	C₂×Q₁₆	—	149	1	no	—
28	C₂×C₁₆	D₁₄₉	1	1	yes	characteristic
29	#107	—	149	1	no	—
30	C₂×Q₈	—	298	1	no	—
31	Q₁₆	—	298	1	no	—
32	Q₁₆	—	149	2	no	—
33	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
34	C₄⋊C₄	—	298	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	298	2	no	—
37	Q₈	—	596	1	no	—
38	C₂×C₄	—	596	1	no	—
39	C₂×C₄	—	596	1	no	—
40	C₂×C₄	D₅₉₆	1	1	yes	characteristic
41	C₈	C₄×D₁₄₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₄₉	1	1	yes	characteristic
43	C₂²	D₁₁₉₂	1	1	yes	characteristic
44	C₄	—	596	2	no	—
45	C₄	—	1192	1	no	—
46	C₄	#14558713	1	1	yes	characteristic
47	C₄	#14558725	1	1	yes	characteristic
48	C₂	#18011833	1	1	yes	characteristic
49	C₂	#18011856	1	1	yes	characteristic
50	C₂	Dic₁₁₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₁₉₂
commutator	C₈×C₁₄₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₄₉
Fitting	C₂×C₁₆×C₁₄₉	C₂
socle, prime radical	C₂²×C₁₄₉	D₈
cosocle	C₂×C₈×C₁₄₉	C₂²
hypercenter	C₂×C₁₆	D₁₄₉
hypocenter	C₁₄₉	#358
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₅₉₆	C₄	semidirect
25. C₁₄₉	#358	semidirect