Subgroups — C₄×#1423 #151990

Order 512.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1423	C₂	1	2	yes	maximal
2	C₂×C₄×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₄×#366	C₂	1	2	yes	maximal
4	#7471	C₂	1	2	yes	maximal
5	C₂²×C₃₂	C₂²	1	1	yes	characteristic
6	C₂²×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×#366	C₂²	1	4	yes	—
8	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
9	C₄×#107	—	2	2	no	—
10	#1423	C₄	1	8	yes	direct product factor
11	C₄×C₃₂	C₄	1	4	yes	complemented
12	#1380	—	2	2	no	—
13	C₂²×C₁₆	D₄	1	1	yes	characteristic
14	C₂²×C₁₆	C₂³	1	1	yes	characteristic
15	C₂×#107	—	2	4	no	—
16	C₂×C₄×C₈	D₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄	—	4	2	no	—
18	C₂×C₃₂	—	2	2	no	—
19	C₂×C₃₂	C₂×C₄	1	2	yes	—
20	C₂×C₃₂	C₂×C₄	1	2	yes	—
21	C₂×C₃₂	C₂×C₄	1	4	yes	—
22	#366	—	2	4	no	—
23	#366	C₂×C₄	1	8	yes	—
24	C₄×C₁₆	C₂×C₄	1	2	yes	—
25	C₄×C₁₆	Q₈	1	2	yes	—
26	#340	—	4	2	no	—
27	C₂²×C₈	D₈	1	1	yes	characteristic
28	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄⋊C₄	—	4	4	no	—
30	C₂×C₄²	—	8	2	no	—
31	C₂×C₄²	D₈	1	1	yes	characteristic
32	C₂×C₁₆	—	2	2	no	—
33	C₂×C₁₆	C₄⋊C₄	1	2	yes	—
34	C₂×C₁₆	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₁₆	C₂²×C₄	1	2	yes	—
36	C₂×C₁₆	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₁₆	#41	1	2	yes	—
38	#107	—	2	8	no	—
39	#107	—	4	4	no	—
40	C₄×C₈	C₄⋊C₄	1	2	yes	—
41	C₄×C₈	Q₁₆	1	2	yes	—
42	#95	—	8	2	no	—
43	C₃₂	—	2	2	no	—
44	C₃₂	C₄²	1	4	yes	complemented
45	C₂²×C₄	—	8	4	no	—
46	C₂²×C₄	D₁₆	1	1	yes	characteristic
47	C₂²×C₄	D₁₆	1	1	yes	characteristic
48	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
49	C₂×C₈	—	2	2	no	—
50	C₂×C₈	#107	1	2	yes	—
51	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₈	C₄×D₄	1	2	yes	—
53	C₂×C₈	C₂×Q₁₆	1	1	yes	characteristic
54	C₂×C₈	#135	1	2	yes	—
55	C₄⋊C₄	—	4	8	no	—
56	C₄⋊C₄	—	8	4	no	—
57	C₄²	—	16	4	no	—
58	C₄²	#107	1	2	yes	—
59	C₄²	Q₃₂	1	2	yes	—
60	C₁₆	—	2	2	no	—
61	C₁₆	C₂×C₄²	1	1	yes	characteristic
62	C₁₆	#117	1	1	yes	characteristic
63	C₁₆	C₄×Q₈	1	2	yes	—
64	C₂³	C₂×D₁₆	1	1	yes	characteristic
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	8	8	no	—
67	C₂×C₄	—	16	4	no	—
68	C₂×C₄	—	16	4	no	—
69	C₂×C₄	#366	1	2	yes	—
70	C₂×C₄	#366	1	2	yes	—
71	C₂×C₄	D₃₂	1	2	yes	—
72	C₂×C₄	Q₆₄	1	2	yes	—
73	C₂×C₄	C₂×#107	1	1	yes	characteristic
74	C₂×C₄	C₄×D₈	1	2	yes	—
75	C₂×C₄	C₂×Q₃₂	1	1	yes	characteristic
76	C₂×C₄	#508	1	2	yes	—
77	C₈	—	2	2	no	—
78	C₈	C₄×C₄⋊C₄	1	1	yes	characteristic
79	C₈	#427	1	1	yes	characteristic
80	C₈	C₄×Q₁₆	1	2	yes	—
81	C₂²	C₂×#366	1	1	yes	characteristic
82	C₂²	C₄×D₁₆	1	2	yes	—
83	C₂²	C₂×D₃₂	1	1	yes	characteristic
84	C₂²	C₂×Q₆₄	1	1	yes	characteristic
85	C₂²	#2262	1	2	yes	—
86	C₄	—	2	2	no	—
87	C₄	—	16	8	no	—
88	C₄	#1423	1	4	yes	direct product factor
89	C₄	C₄×#107	1	1	yes	characteristic
90	C₄	#2158	1	1	yes	characteristic
91	C₄	C₄×Q₃₂	1	2	yes	—
92	C₂	C₄×#366	1	1	yes	characteristic
93	C₂	C₂×#1423	1	1	yes	characteristic
94	C₂	#13633	1	1	yes	characteristic
95	C₂	C₄×D₃₂	1	2	yes	—
96	C₂	C₄×Q₆₄	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₁₆
commutator	C₁₆	C₂×C₄²
Frattini, cosocle	C₂²×C₁₆	C₂³
socle, prime radical	C₂³	C₂×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆ ◁ G
LECS	G ▷ C₂²×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
10. #1423	C₄	direct (N × H)
11. C₄×C₃₂	C₄	semidirect
44. C₃₂	C₄²	semidirect
88. C₄	#1423	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#1423	2
C₂×C₄×C₃₂	2
C₄×#366	2
#7471	2

Subgroups — C4×#1423 #151990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#1423 #151990