Subgroups — C₂×C₄×#11924753 #23750580

Order 9536.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11924753	C₂	1	2	yes	maximal
2	C₄×#11924753	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924753	C₄	1	8	yes	direct product factor
5	C₂×#11924753	C₂²	1	4	yes	—
6	C₂²×Dic₁₄₉	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₄₉	C₄	1	2	yes	—
9	C₄×Dic₁₄₉	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₄₉	C₄	1	1	yes	characteristic
11	#11924753	C₂×C₄	1	8	yes	direct product factor
12	C₂×Dic₁₄₉	C₈	1	4	yes	complemented
13	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₄₉	C₂×C₄	1	4	yes	—
15	C₂×Dic₁₄₉	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
17	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₄₉	C₈	1	4	yes	complemented
19	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
20	C₂²×C₁₄₉	C₄²	1	2	yes	—
21	C₂²×C₁₄₉	C₂×C₈	1	2	yes	—
22	C₂²×C₁₄₉	C₂×C₈	1	2	yes	—
23	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₄₉	C₂×C₈	1	4	yes	complemented
25	Dic₁₄₉	C₄²	1	2	yes	—
26	Dic₁₄₉	C₂×C₈	1	4	yes	complemented
27	Dic₁₄₉	C₂²×C₄	1	2	yes	—
28	C₂×C₁₄₉	C₄×C₈	1	4	yes	complemented
29	C₂×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
31	C₂×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
32	C₁₄₉	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄×C₈	—	149	1	no	maximal, Sylow
34	C₂²×C₈	—	149	2	no	—
35	C₂×C₄²	—	149	1	no	—
36	C₄×C₈	—	149	4	no	—
37	C₂²×C₄	—	149	1	no	—
38	C₂²×C₄	—	149	1	no	—
39	C₂²×C₄	#10597010	1	1	yes	characteristic
40	C₂×C₈	—	149	8	no	—
41	C₂×C₈	—	149	4	no	—
42	C₄²	—	149	2	no	—
43	C₄²	—	149	2	no	—
44	C₂³	C₂×#10597010	1	1	yes	characteristic
45	C₂×C₄	—	149	4	no	—
46	C₂×C₄	—	149	4	no	—
47	C₂×C₄	—	149	1	no	—
48	C₂×C₄	—	149	2	no	—
49	C₂×C₄	—	149	1	no	—
50	C₂×C₄	#11924753	1	4	yes	direct product factor
51	C₂×C₄	C₂×#10597010	1	2	yes	—
52	C₈	—	149	8	no	—
53	C₂²	C₄×#10597010	1	2	yes	—
54	C₂²	C₂×#11924753	1	2	yes	—
55	C₂²	D₁₄₉⋊C₈	1	2	yes	—
56	C₂²	C₂²×#10597010	1	1	yes	characteristic
57	C₄	—	149	2	no	—
58	C₄	—	149	2	no	—
59	C₄	—	149	4	no	—
60	C₄	C₂×#11924753	1	4	yes	direct product factor
61	C₂	C₄×#11924753	1	4	yes	direct product factor
62	C₂	C₂×C₄×#10597010	1	1	yes	characteristic
63	C₂	C₂²×#11924753	1	1	yes	characteristic
64	C₂	C₂×D₁₄₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	#10597010
commutator, hypocenter	C₁₄₉	C₂×C₄×C₈
Frattini	C₂²	C₂²×#10597010
Fitting	C₂²×C₄×C₁₄₉	C₄
socle, prime radical	C₂³×C₁₄₉	C₂×C₄
cosocle	C₂×Dic₁₄₉	C₂³
LCS	G ▷ C₁₄₉
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#11924753	C₂	direct (N × H)
4. C₂×#11924753	C₄	direct (N × H)
11. #11924753	C₂×C₄	direct (N × H)
12. C₂×Dic₁₄₉	C₈	semidirect
18. C₂×C₄×C₁₄₉	C₈	semidirect
24. C₄×C₁₄₉	C₂×C₈	semidirect
26. Dic₁₄₉	C₂×C₈	semidirect
28. C₂×C₁₄₉	C₄×C₈	semidirect
32. C₁₄₉	C₂×C₄×C₈	semidirect
50. C₂×C₄	#11924753	direct (N × H)
60. C₄	C₂×#11924753	direct (N × H)
61. C₂	C₄×#11924753	direct (N × H)

Subgroups — C2×C4×#11924753 #23750580

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×#11924753 #23750580