Subgroups — #93721

Order 512.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#12883	C₂	1	1	yes	maximal, characteristic
2	#7364	C₂	1	2	yes	maximal
3	#2150	C₄	1	1	yes	characteristic
4	#2150	C₂²	1	1	yes	characteristic
5	C₄²×C₈	C₄	1	1	yes	characteristic
6	#1400	—	2	2	no	—
7	#1376	—	2	2	no	—
8	C₂×M₃₂	—	2	1	no	—
9	C₂×M₃₂	D₄	1	2	yes	—
10	C₂×C₄×C₈	—	2	1	no	—
11	C₂×C₄×C₈	—	2	1	no	—
12	C₂×C₄×C₈	C₈	1	1	yes	characteristic
13	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
14	C₄³	C₈	1	1	yes	characteristic
15	M₆₄	—	4	2	no	—
16	C₄⋊C₁₆	—	4	1	no	—
17	C₄⋊C₁₆	—	4	1	no	—
18	C₂²×C₈	—	2	1	no	—
19	C₂²×C₈	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₈	M₁₆	1	1	yes	characteristic
21	C₂×C₄²	—	2	1	no	—
22	C₂×C₄²	—	4	1	no	—
23	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
24	M₃₂	—	4	2	no	—
25	M₃₂	—	4	2	no	—
26	C₂×C₁₆	—	2	2	no	—
27	C₂×C₁₆	—	4	1	no	—
28	C₄×C₈	—	2	1	no	—
29	C₄×C₈	—	2	1	no	—
30	C₄×C₈	—	2	1	no	—
31	C₄×C₈	—	4	2	no	—
32	C₄×C₈	—	4	1	no	—
33	C₄×C₈	—	4	1	no	—
34	C₄×C₈	C₁₆	1	2	yes	—
35	C₃₂	—	8	2	no	—
36	C₂²×C₄	—	2	1	no	—
37	C₂²×C₄	—	4	1	no	—
38	C₂²×C₄	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	2	1	no	—
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	4	1	no	—
45	C₂×C₈	—	4	1	no	—
46	C₂×C₈	#99	1	1	yes	characteristic
47	C₂×C₈	#101	1	1	yes	characteristic
48	C₄²	—	2	1	no	—
49	C₄²	—	2	2	no	—
50	C₄²	—	4	1	no	—
51	C₄²	—	4	4	no	—
52	C₄²	C₂×C₁₆	1	1	yes	characteristic
53	C₄²	M₃₂	1	1	yes	characteristic
54	C₁₆	—	4	2	no	—
55	C₁₆	—	8	1	no	—
56	C₂³	#349	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	4	2	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	#324	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊C₁₆	1	1	yes	characteristic
66	C₈	—	2	1	no	—
67	C₈	—	4	2	no	—
68	C₈	—	4	1	no	—
69	C₈	#354	1	1	yes	characteristic
70	C₈	#355	1	1	yes	characteristic
71	C₂²	—	2	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	#1322	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	4	no	—
78	C₄	#1324	1	1	yes	characteristic
79	C₄	#1327	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#7062	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#354
commutator	C₄²	C₂×C₁₆
Frattini, cosocle	#2150	C₂²
socle	C₂	#7062
prime radical	C₂³	#349
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #2150 ◁ G
LECS	G ▷ #2150 ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
#12883	2
#7364	2