Subgroups — C₂⁴×#622 #11918424

Order 1152.

3338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×#622	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵×C₃²	C₄	1	1	yes	characteristic
4	C₂³×C₃⋊Dic₃	C₄	1	15	yes	—
5	C₂³×C₃⋊Dic₃	C₂²	1	15	yes	—
6	C₂²×#622	C₂²	1	140	yes	direct product factor
7	C₂⁴×Dic₃	—	6	2	no	—
8	C₂⁴×C₃²	C₈	1	16	yes	complemented
9	C₂⁴×C₃²	C₂×C₄	1	15	yes	—
10	C₂²×C₃⋊Dic₃	C₂×C₄	1	105	yes	—
11	C₂²×C₃⋊Dic₃	C₂³	1	35	yes	—
12	C₂×#622	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₈	—	9	1	no	maximal, Sylow
14	C₂⁵×C₃	—	2	2	no	—
15	C₂³×Dic₃	—	6	30	no	—
16	C₂³×Dic₃	—	6	30	no	—
17	C₂³×C₃²	C₂×C₈	1	120	yes	complemented
18	C₂³×C₃²	C₂²×C₄	1	35	yes	—
19	C₂×C₃⋊Dic₃	C₂²×C₄	1	105	yes	—
20	C₂×C₃⋊Dic₃	C₂⁴	1	15	yes	—
21	#622	C₂⁴	1	16	yes	direct product factor
22	C₂⁴×C₄	—	9	1	no	—
23	C₂³×C₈	—	9	30	no	—
24	C₂⁴×C₃	—	2	32	no	—
25	C₂⁴×C₃	—	2	30	no	—
26	C₂²×Dic₃	—	6	210	no	—
27	C₂²×Dic₃	—	6	70	no	—
28	C₂²×C₃²	C₂²×C₈	1	140	yes	complemented
29	C₂²×C₃²	C₂³×C₄	1	15	yes	—
30	C₃⋊Dic₃	C₂³×C₄	1	15	yes	—
31	C₃⋊Dic₃	C₂⁵	1	1	yes	characteristic
32	C₂⁵	#157	1	1	yes	characteristic
33	C₂³×C₄	—	9	15	no	—
34	C₂³×C₄	—	9	15	no	—
35	C₂²×C₈	—	9	140	no	—
36	C₂³×C₃	—	2	70	no	—
37	C₂³×C₃	—	2	240	no	—
38	C₂×Dic₃	—	6	210	no	—
39	C₂×Dic₃	—	6	30	no	—
40	C₂×C₃²	C₂³×C₈	1	30	yes	complemented
41	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
42	C₂⁴	#622	1	16	yes	direct product factor
43	C₂⁴	C₂×#157	1	15	yes	—
44	C₂²×C₄	—	9	35	no	—
45	C₂²×C₄	—	9	105	no	—
46	C₂×C₈	—	9	120	no	—
47	C₂²×C₃	—	2	280	no	—
48	C₂²×C₃	—	2	30	no	—
49	Dic₃	—	6	30	no	—
50	Dic₃	—	6	2	no	—
51	C₃²	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
52	C₂³	C₂×#622	1	120	yes	direct product factor
53	C₂³	C₂²×#157	1	35	yes	—
54	C₂×C₄	—	9	15	no	—
55	C₂×C₄	—	9	105	no	—
56	C₈	—	9	16	no	—
57	C₂×C₃	—	2	60	no	—
58	C₂×C₃	—	2	2	no	—
59	C₂²	C₂²×#622	1	140	yes	direct product factor
60	C₂²	C₂³×#157	1	15	yes	—
61	C₄	—	9	1	no	—
62	C₄	—	9	15	no	—
63	C₃	—	2	2	no	—
64	C₂	C₂³×#622	1	30	yes	direct product factor
65	C₂	C₂⁴×#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#157
commutator, hypocenter	C₃²	C₂⁴×C₈
Frattini	C₂	C₂⁴×#157
Fitting, socle, prime radical	C₂⁵×C₃²	C₄
cosocle	C₃⋊Dic₃	C₂⁵
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×#622	C₂	direct (N × H)
6. C₂²×#622	C₂²	direct (N × H)
8. C₂⁴×C₃²	C₈	semidirect
12. C₂×#622	C₂³	direct (N × H)
17. C₂³×C₃²	C₂×C₈	semidirect
21. #622	C₂⁴	direct (N × H)
28. C₂²×C₃²	C₂²×C₈	semidirect
40. C₂×C₃²	C₂³×C₈	semidirect
42. C₂⁴	#622	direct (N × H)
51. C₃²	C₂⁴×C₈	semidirect
52. C₂³	C₂×#622	direct (N × H)
59. C₂²	C₂²×#622	direct (N × H)
64. C₂	C₂³×#622	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₃⋊Dic₃	2
C₂³×#622	2
C₂⁴×C₈	9

Subgroups — C24×#622 #11918424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#622 #11918424