Subgroups — #11924753⋊C₈ #23750467

Order 9536.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11924753	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924753	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924753	C₄	1	2	yes	—
5	C₂×#11924753	C₄	1	2	yes	—
6	C₂×#11924746	C₄	1	1	yes	characteristic
7	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₄₉	C₄	1	1	yes	characteristic
9	#11924753	—	2	2	no	—
10	#11924753	C₈	1	4	yes	complemented
11	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
13	#11924746	—	2	1	no	—
14	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₄₉	—	2	1	no	—
16	C₂²×C₁₄₉	C₄²	1	1	yes	characteristic
17	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
18	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
19	Dic₁₄₉	C₂×C₈	1	2	yes	—
20	Dic₁₄₉	M₁₆	1	2	yes	—
21	C₂×C₁₄₉	C₄×C₈	1	1	yes	characteristic
22	C₂×C₁₄₉	#97	1	1	yes	characteristic
23	C₂×C₁₄₉	#97	1	1	yes	characteristic
24	C₁₄₉	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	149	1	no	maximal, Sylow
26	C₄×C₈	—	149	1	no	—
27	C₄×C₈	—	149	1	no	—
28	C₄×C₈	—	149	1	no	—
29	C₂×C₈	—	149	2	no	—
30	C₂×C₈	—	149	1	no	—
31	C₂×C₈	—	149	2	no	—
32	C₂×C₈	#10597010	1	1	yes	characteristic
33	C₄²	—	149	1	no	—
34	C₂×C₄	—	149	1	no	—
35	C₂×C₄	—	149	1	no	—
36	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	298	2	no	—
39	C₈	—	298	1	no	—
40	C₈	—	149	4	no	—
41	C₂²	C₄×#10597010	1	1	yes	characteristic
42	C₄	—	149	2	no	—
43	C₄	—	149	2	no	—
44	C₄	#14558745	1	1	yes	characteristic
45	C₄	#14558746	1	1	yes	characteristic
46	C₂	C₈×#10597010	1	1	yes	characteristic
47	C₂	#18011965	1	1	yes	characteristic
48	C₂	#18011966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10597010
commutator	C₂×C₁₄₉	C₄×C₈
Fitting	C₂×C₈×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₄²
cosocle	C₄×Dic₁₄₉	C₂²
hypercenter	C₂×C₈	#10597010
hypocenter	C₁₄₉	#322
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #11924753	C₈	semidirect
24. C₁₄₉	#322	semidirect

Subgroups — #11924753⋊C8 #23750467

Conjugacy classes of subgroups

Complements

Subgroups — #11924753⋊C₈ #23750467