Subgroups — C₂×#7331 #149497

Order 512.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃₂	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#7331	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃₂	C₄	1	4	yes	—
5	C₂×C₄×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₈²	C₄	1	1	yes	characteristic
8	C₄×C₃₂	C₄	1	4	yes	—
9	C₄×C₃₂	C₂²	1	4	yes	—
10	C₈×C₁₆	C₄	1	2	yes	—
11	C₈×C₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₆	C₈	1	2	yes	—
13	C₂²×C₁₆	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₈	C₈	1	1	yes	characteristic
15	C₂×C₄×C₈	C₈	1	1	yes	characteristic
16	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃₂	—	2	8	no	—
18	C₂×C₃₂	C₂×C₄	1	8	yes	—
19	C₄×C₁₆	C₈	1	2	yes	—
20	C₄×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₄×C₁₆	C₂×C₄	1	2	yes	—
23	C₄×C₁₆	C₂³	1	1	yes	characteristic
24	C₈²	C₈	1	2	yes	—
25	C₈²	C₂×C₄	1	2	yes	—
26	C₂²×C₈	C₁₆	1	2	yes	—
27	C₂²×C₈	C₁₆	1	2	yes	—
28	C₂²×C₈	C₄²	1	1	yes	characteristic
29	C₂²×C₈	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
31	C₂×C₁₆	—	2	4	no	—
32	C₂×C₁₆	C₄²	1	2	yes	—
33	C₂×C₁₆	C₂×C₈	1	4	yes	—
34	C₂×C₁₆	M₁₆	1	8	yes	—
35	C₂×C₁₆	C₂²×C₄	1	2	yes	—
36	C₄×C₈	C₁₆	1	2	yes	—
37	C₄×C₈	C₁₆	1	2	yes	—
38	C₄×C₈	C₄²	1	1	yes	characteristic
39	C₄×C₈	C₂×C₈	1	1	yes	characteristic
40	C₄×C₈	C₂×C₈	1	1	yes	characteristic
41	C₄×C₈	C₂×C₈	1	2	yes	—
42	C₄×C₈	C₂×C₈	1	2	yes	—
43	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
44	C₃₂	—	2	8	no	—
45	C₂²×C₄	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₄	C₂×C₁₆	1	1	yes	characteristic
47	C₂²×C₄	C₂×C₁₆	1	1	yes	characteristic
48	C₂×C₈	—	2	4	no	—
49	C₂×C₈	C₃₂	1	8	yes	complemented
50	C₂×C₈	C₄×C₈	1	1	yes	characteristic
51	C₂×C₈	C₄×C₈	1	1	yes	characteristic
52	C₂×C₈	#97	1	4	yes	—
53	C₂×C₈	C₂×C₁₆	1	4	yes	—
54	C₂×C₈	C₂×C₁₆	1	4	yes	—
55	C₂×C₈	M₃₂	1	4	yes	—
56	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
58	C₄²	C₄×C₈	1	1	yes	characteristic
59	C₄²	C₂×C₁₆	1	1	yes	characteristic
60	C₄²	C₂×C₁₆	1	1	yes	characteristic
61	C₄²	C₂²×C₈	1	1	yes	characteristic
62	C₁₆	—	2	4	no	—
63	C₁₆	#97	1	4	yes	—
64	C₁₆	C₂×M₁₆	1	4	yes	—
65	C₂³	C₄×C₁₆	1	1	yes	characteristic
66	C₂×C₄	#322	1	2	yes	—
67	C₂×C₄	C₄×C₁₆	1	1	yes	characteristic
68	C₂×C₄	C₄×C₁₆	1	1	yes	characteristic
69	C₂×C₄	C₄×C₁₆	1	1	yes	characteristic
70	C₂×C₄	#346	1	2	yes	—
71	C₂×C₄	C₂×C₃₂	1	4	yes	—
72	C₂×C₄	M₆₄	1	4	yes	—
73	C₂×C₄	C₂×C₄×C₈	1	1	yes	characteristic
74	C₂×C₄	C₂²×C₁₆	1	1	yes	characteristic
75	C₂×C₄	C₂²×C₁₆	1	1	yes	characteristic
76	C₈	—	2	4	no	—
77	C₈	#322	1	2	yes	—
78	C₈	#346	1	2	yes	—
79	C₈	C₂×C₃₂	1	8	yes	complemented
80	C₈	C₂×#97	1	2	yes	—
81	C₈	C₂×M₃₂	1	2	yes	—
82	C₂²	#1312	1	2	yes	—
83	C₂²	C₄×C₃₂	1	2	yes	—
84	C₂²	#1397	1	2	yes	—
85	C₂²	C₂×C₄×C₁₆	1	1	yes	characteristic
86	C₄	#1312	1	2	yes	—
87	C₄	C₄×C₃₂	1	2	yes	—
88	C₄	#1397	1	2	yes	—
89	C₄	C₂×#322	1	1	yes	characteristic
90	C₄	C₂×#346	1	1	yes	characteristic
91	C₄	C₂²×C₃₂	1	2	yes	—
92	C₄	C₂×M₆₄	1	2	yes	—
93	C₂	#7331	1	4	yes	direct product factor
94	C₂	C₂×#1312	1	1	yes	characteristic
95	C₂	C₂×C₄×C₃₂	1	1	yes	characteristic
96	C₂	C₂×#1397	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₆	C₂²
commutator	C₂	C₂×C₄×C₃₂
Frattini, cosocle	C₄×C₁₆	C₂³
socle, prime radical	C₂³	C₄×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₆ ◁ G
LECS	G ▷ C₄×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #7331	C₂	direct (N × H)
49. C₂×C₈	C₃₂	semidirect
79. C₈	C₂×C₃₂	semidirect
93. C₂	#7331	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×C₄×C₃₂	2
C₂×C₈×C₁₆	2
#7331	2

Subgroups — C2×#7331 #149497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#7331 #149497