Subgroups — #23749355

Order 9536.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924746	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₈	C₄	1	1	yes	characteristic
5	C₂×#11924746	—	2	1	no	—
6	C₄⋊Dic₁₄₉	C₄	1	1	yes	characteristic
7	#14558715	—	2	1	no	—
8	C₄×Dic₁₄₉	—	2	1	no	—
9	C₂×C₈×C₁₄₉	—	2	1	no	—
10	C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
11	Dic₂₉₈	—	2	1	no	—
12	Dic₂₉₈	C₈	1	2	yes	complemented
13	C₂×Dic₁₄₉	—	2	1	no	—
14	C₂×Dic₁₄₉	—	2	1	no	—
15	#11924746	—	2	2	no	—
16	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
19	C₈×C₁₄₉	—	4	1	no	—
20	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₄₉	—	2	1	no	—
22	C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
24	C₄×C₁₄₉	SD₁₆	1	1	yes	characteristic
25	C₄×C₁₄₉	Q₁₆	1	1	yes	characteristic
26	Dic₁₄₉	—	2	2	no	—
27	Dic₁₄₉	—	4	1	no	—
28	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₄₉	#103	1	1	yes	characteristic
30	C₂×C₁₄₉	#104	1	1	yes	characteristic
31	C₁₄₉	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	149	1	no	maximal, Sylow
33	C₄×Q₈	—	149	1	no	—
34	C₄⋊C₈	D₁₄₉	1	1	yes	characteristic
35	C₄×C₈	—	149	1	no	—
36	C₂×Q₈	—	149	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	298	1	no	—
39	C₄⋊C₄	—	298	1	no	—
40	C₄⋊C₄	—	149	1	no	—
41	C₄²	—	298	1	no	—
42	C₄²	C₂×D₁₄₉	1	1	yes	characteristic
43	Q₈	—	298	1	no	—
44	Q₈	—	149	2	no	—
45	C₂×C₄	—	298	1	no	—
46	C₂×C₄	—	298	1	no	—
47	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₁₄₉	1	1	yes	characteristic
49	C₂×C₄	D₅₉₆	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	298	2	no	—
52	C₂²	#14558713	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	298	2	no	—
55	C₄	—	596	1	no	—
56	C₄	C₈×D₁₄₉	1	1	yes	characteristic
57	C₄	#14558719	1	1	yes	characteristic
58	C₄	#14558724	1	1	yes	characteristic
59	C₄	#14558726	1	1	yes	characteristic
60	C₂	#18011823	1	1	yes	characteristic
61	C₂	#18011834	1	1	yes	characteristic
62	C₂	#18011837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₄₉
commutator	C₄×C₁₄₉	C₂×C₈
Frattini	C₄²	C₂×D₁₄₉
Fitting	C₄⋊C₈×C₁₄₉	C₂
socle, prime radical	C₂²×C₁₄₉	C₂²⋊C₄
cosocle	C₄²×C₁₄₉	C₂²
hypercenter	C₄⋊C₈	D₁₄₉
hypocenter	C₁₄₉	Q₈⋊C₈
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
12. Dic₂₉₈	C₈	semidirect
31. C₁₄₉	Q₈⋊C₈	semidirect