Subgroups — C₂⁴×#376 #72302212

Order 1024.

228053 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄²	C₂	1	3	yes	maximal
2	C₂³×#376	C₂	1	120	yes	maximal, direct product factor
3	C₂⁴×#95	C₂	1	4	yes	maximal
4	C₂⁶×C₄	C₂²	1	6	yes	—
5	C₂⁶×C₄	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄²	C₄	1	192	yes	complemented
7	C₂⁴×C₄²	C₂²	1	180	yes	—
8	C₂²×#376	C₂²	1	2240	yes	direct product factor
9	C₂³×#95	C₂²	1	240	yes	—
10	C₂⁷	C₂³	1	1	yes	characteristic
11	C₂⁵×C₄	—	2	192	no	—
12	C₂⁵×C₄	C₂×C₄	1	192	yes	—
13	C₂⁵×C₄	C₂×C₄	1	96	yes	—
14	C₂⁵×C₄	C₂³	1	180	yes	—
15	C₂⁵×C₄	C₂³	1	30	yes	—
16	C₂³×C₄²	C₂×C₄	1	5760	yes	complemented
17	C₂³×C₄²	C₂³	1	1680	yes	—
18	C₂×#376	C₂³	1	7680	yes	direct product factor
19	C₂²×#95	C₂³	1	2240	yes	—
20	C₂⁶	C₂²×C₄	1	48	yes	—
21	C₂⁶	#41	1	64	yes	—
22	C₂⁶	C₂⁴	1	15	yes	—
23	C₂⁴×C₄	—	2	3072	no	—
24	C₂⁴×C₄	—	2	2880	no	—
25	C₂⁴×C₄	C₄²	1	1024	yes	—
26	C₂⁴×C₄	C₂²×C₄	1	2880	yes	—
27	C₂⁴×C₄	C₂²×C₄	1	1440	yes	—
28	C₂⁴×C₄	C₂⁴	1	840	yes	—
29	C₂⁴×C₄	C₂⁴	1	140	yes	—
30	C₂²×C₄²	C₂²×C₄	1	26880	yes	complemented
31	C₂²×C₄²	C₂⁴	1	2880	yes	—
32	#376	C₂⁴	1	4096	yes	direct product factor
33	C₂×#95	C₂⁴	1	3840	yes	—
34	C₂⁵	C₂×C₄²	1	256	yes	—
35	C₂⁵	#117	1	1536	yes	—
36	C₂⁵	C₂³×C₄	1	360	yes	—
37	C₂⁵	C₂×#41	1	480	yes	—
38	C₂⁵	C₂⁵	1	35	yes	—
39	C₂³×C₄	—	2	23040	no	—
40	C₂³×C₄	—	2	6720	no	—
41	C₂³×C₄	C₂×C₄²	1	7680	yes	—
42	C₂³×C₄	C₂³×C₄	1	6720	yes	—
43	C₂³×C₄	C₂³×C₄	1	3360	yes	—
44	C₂³×C₄	C₂⁵	1	720	yes	—
45	C₂³×C₄	C₂⁵	1	120	yes	—
46	C₂×C₄²	C₂³×C₄	1	23040	yes	complemented
47	C₂×C₄²	C₂⁵	1	768	yes	—
48	#95	C₂⁵	1	1024	yes	—
49	C₂⁴	#376	1	4096	yes	direct product factor
50	C₂⁴	C₂²×C₄²	1	960	yes	—
51	C₂⁴	C₂×#117	1	5760	yes	—
52	C₂⁴	C₂⁴×C₄	1	420	yes	—
53	C₂⁴	C₂²×#41	1	560	yes	—
54	C₂⁴	C₂⁶	1	15	yes	—
55	C₂²×C₄	—	2	2880	no	—
56	C₂²×C₄	—	2	26880	no	—
57	C₂²×C₄	C₂²×C₄²	1	8960	yes	—
58	C₂²×C₄	C₂⁴×C₄	1	2880	yes	—
59	C₂²×C₄	C₂⁴×C₄	1	1440	yes	—
60	C₂²×C₄	C₂⁶	1	96	yes	—
61	C₂²×C₄	C₂⁶	1	16	yes	—
62	C₄²	C₂⁴×C₄	1	3072	yes	complemented
63	C₂³	C₂×#376	1	7680	yes	direct product factor
64	C₂³	C₂³×C₄²	1	560	yes	—
65	C₂³	C₂²×#117	1	3360	yes	—
66	C₂³	C₂⁵×C₄	1	90	yes	—
67	C₂³	C₂³×#41	1	120	yes	—
68	C₂³	C₂⁷	1	1	yes	characteristic
69	C₂×C₄	—	2	192	no	—
70	C₂×C₄	—	2	5760	no	—
71	C₂×C₄	C₂³×C₄²	1	1920	yes	—
72	C₂×C₄	C₂⁵×C₄	1	192	yes	—
73	C₂×C₄	C₂⁵×C₄	1	96	yes	—
74	C₂²	C₂²×#376	1	2240	yes	direct product factor
75	C₂²	C₂⁴×C₄²	1	60	yes	—
76	C₂²	C₂³×#117	1	360	yes	—
77	C₂²	C₂⁶×C₄	1	3	yes	—
78	C₂²	C₂⁴×#41	1	4	yes	—
79	C₄	—	2	192	no	—
80	C₄	C₂⁴×C₄²	1	64	yes	—
81	C₂	C₂³×#376	1	120	yes	direct product factor
82	C₂	C₂⁵×C₄²	1	1	yes	characteristic
83	C₂	C₂⁴×#117	1	6	yes	—

	subgroup	G/H
center, socle	C₂⁶×C₄	C₂²
commutator	C₂	C₂⁵×C₄²
Frattini, cosocle	C₂³	C₂⁷
prime radical	C₂⁷	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂³×#376	C₂	direct (N × H)
6. C₂⁴×C₄²	C₄	semidirect
8. C₂²×#376	C₂²	direct (N × H)
16. C₂³×C₄²	C₂×C₄	semidirect
18. C₂×#376	C₂³	direct (N × H)
30. C₂²×C₄²	C₂²×C₄	semidirect
32. #376	C₂⁴	direct (N × H)
46. C₂×C₄²	C₂³×C₄	semidirect
49. C₂⁴	#376	direct (N × H)
62. C₄²	C₂⁴×C₄	semidirect
63. C₂³	C₂×#376	direct (N × H)
74. C₂²	C₂²×#376	direct (N × H)
81. C₂	C₂³×#376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄²	2
C₂³×#376	2
C₂⁴×#95	2

Subgroups — C24×#376 #72302212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#376 #72302212