Subgroups — #93995

Order 512.

143 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1398	C₂	1	2	yes	maximal
2	#11405	C₂	1	1	yes	maximal, characteristic
3	C₂×M₆₄	C₄	1	4	yes	—
4	C₄×M₃₂	C₄	1	1	yes	characteristic
5	C₂×#346	C₂²	1	1	yes	characteristic
6	#1450	C₄	1	1	yes	characteristic
7	#1398	—	2	2	no	—
8	#1398	—	2	2	no	—
9	#1313	—	2	2	no	—
10	C₂×M₃₂	—	2	1	no	—
11	C₂²×C₁₆	C₂×C₄	1	2	yes	—
12	#431	—	2	1	no	—
13	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
14	M₆₄	—	2	4	no	—
15	M₆₄	—	2	4	no	—
16	C₂×C₃₂	C₈	1	8	yes	complemented
17	#346	—	2	1	no	—
18	#346	D₄	1	2	yes	—
19	#346	D₄	1	1	yes	characteristic
20	#346	Q₈	1	1	yes	characteristic
21	C₄×C₁₆	C₈	1	2	yes	—
22	#322	—	2	1	no	—
23	C₈²	C₈	1	2	yes	—
24	C₂²×C₈	C₄²	1	1	yes	characteristic
25	C₂²×C₈	M₁₆	1	1	yes	characteristic
26	C₂×C₄²	M₁₆	1	1	yes	characteristic
27	M₃₂	—	4	2	no	—
28	C₂×C₁₆	—	2	2	no	—
29	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
30	C₂×C₁₆	C₄⋊C₄	1	2	yes	—
31	C₂×C₁₆	C₂×C₈	1	4	yes	—
32	C₂×C₁₆	M₁₆	1	4	yes	—
33	C₄⋊C₈	—	4	1	no	—
34	C₂²⋊C₈	—	4	1	no	—
35	C₄×C₈	—	2	2	no	—
36	C₄×C₈	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×C₈	C₄⋊C₄	1	1	yes	characteristic
38	C₄×C₈	C₂×C₈	1	1	yes	characteristic
39	C₄×C₈	C₂×C₈	1	1	yes	characteristic
40	C₃₂	—	2	8	no	—
41	C₂²×C₄	—	2	1	no	—
42	C₂²×C₄	#97	1	1	yes	characteristic
43	C₂×C₈	—	2	2	no	—
44	C₂×C₈	—	4	2	no	—
45	C₂×C₈	#95	1	1	yes	characteristic
46	C₂×C₈	C₄×C₈	1	1	yes	characteristic
47	C₂×C₈	C₄×C₈	1	2	yes	—
48	C₂×C₈	#97	1	2	yes	—
49	C₂×C₈	C₂²⋊C₈	1	1	yes	characteristic
50	C₂×C₈	C₄⋊C₈	1	1	yes	characteristic
51	C₄²	—	2	1	no	—
52	C₄²	C₂²⋊C₈	1	1	yes	characteristic
53	C₄²	C₄⋊C₈	1	1	yes	characteristic
54	C₁₆	—	4	2	no	—
55	C₁₆	C₂²⋊C₈	1	4	yes	—
56	C₁₆	C₄⋊C₈	1	4	yes	—
57	C₂³	#347	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	8	1	no	—
61	C₂×C₄	#322	1	2	yes	—
62	C₂×C₄	#336	1	1	yes	characteristic
63	C₂×C₄	#347	1	1	yes	characteristic
64	C₂×C₄	#347	1	2	yes	—
65	C₈	—	2	1	no	—
66	C₈	—	2	1	no	—
67	C₈	—	8	2	no	—
68	C₈	C₈²	1	1	yes	characteristic
69	C₈	#322	1	1	yes	characteristic
70	C₈	#336	1	2	yes	—
71	C₂²	—	4	1	no	—
72	C₂²	#1313	1	2	yes	—
73	C₂²	#1375	1	1	yes	characteristic
74	C₄	—	4	1	no	—
75	C₄	—	4	1	no	—
76	C₄	#1273	1	1	yes	characteristic
77	C₄	#1313	1	2	yes	—
78	C₄	#1375	1	1	yes	characteristic
79	C₂	—	2	1	no	—
80	C₂	—	2	2	no	—
81	C₂	#7137	1	1	yes	characteristic

	subgroup	G/H
center, commutator	C₈	C₈²
Frattini, cosocle	C₂×#346	C₂²
socle	C₂	#7137
prime radical	C₂³	#347
LCS	G ▷ C₈ ▷ C₁
UCS	C₁ ◁ C₈ ◁ G
LECS	G ▷ C₂×#346 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
16. C₂×C₃₂	C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1398	2
#11405	2