Subgroups — #10628

Order 256.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1995	C₂	1	1	yes	maximal, characteristic
2	#1843	C₂	1	1	yes	maximal, characteristic
3	#1542	C₂	1	2	yes	maximal
4	#1301	C₂	1	2	yes	maximal
5	#1274	C₂	1	1	yes	maximal, characteristic
6	#533	C₂²	1	1	yes	characteristic
7	#431	C₂²	1	2	yes	—
8	#423	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₈	—	2	1	no	—
10	C₂×C₄⋊C₈	—	2	1	no	—
11	C₂×C₄⋊C₈	C₂²	1	2	yes	—
12	#376	C₂²	1	1	yes	characteristic
13	#339	—	2	1	no	—
14	#339	—	2	1	no	—
15	#333	—	2	2	no	—
16	#332	—	2	2	no	—
17	C₂×M₁₆	—	2	1	no	—
18	C₂²×C₈	—	2	2	no	—
19	C₄⋊Q₈	D₄	1	2	yes	—
20	#125	—	2	1	no	—
21	C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈	—	2	2	no	—
23	#117	—	2	1	no	—
24	C₂×C₄²	D₄	1	1	yes	characteristic
25	C₂×C₄²	D₄	1	1	yes	characteristic
26	C₂×C₄²	C₂³	1	1	yes	characteristic
27	C₄⋊C₈	—	2	2	no	—
28	C₄⋊C₈	—	2	2	no	—
29	C₄⋊C₈	—	2	2	no	—
30	C₄⋊C₈	—	2	2	no	—
31	C₄⋊C₈	—	4	2	no	—
32	C₄⋊C₈	—	4	2	no	—
33	C₂²⋊C₈	—	2	2	no	—
34	C₄×C₈	—	2	2	no	—
35	#95	—	2	2	no	—
36	C₂×Q₈	—	2	2	no	—
37	C₂²×C₄	—	2	1	no	—
38	C₂²×C₄	—	2	1	no	—
39	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄	#41	1	2	yes	—
41	M₁₆	—	4	1	no	—
42	M₁₆	—	4	1	no	—
43	C₂×C₈	—	4	2	no	—
44	C₂×C₈	—	4	2	no	—
45	C₂×C₈	—	4	1	no	—
46	C₂×C₈	—	4	2	no	—
47	C₂×C₈	—	4	2	no	—
48	C₄⋊C₄	—	2	2	no	—
49	C₄⋊C₄	—	2	2	no	—
50	C₄⋊C₄	—	4	2	no	—
51	C₂²⋊C₄	—	4	1	no	—
52	C₄²	—	2	1	no	—
53	C₄²	—	2	1	no	—
54	C₄²	—	4	1	no	—
55	C₄²	SD₁₆	1	2	yes	—
56	C₄²	Q₁₆	1	2	yes	—
57	C₄²	C₂×D₄	1	1	yes	characteristic
58	C₄²	#41	1	1	yes	characteristic
59	C₄²	#41	1	2	yes	—
60	C₂³	#123	1	1	yes	characteristic
61	Q₈	—	8	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	—	4	2	no	—
68	C₂×C₄	#121	1	1	yes	characteristic
69	C₂×C₄	#123	1	2	yes	—
70	C₂×C₄	#124	1	1	yes	characteristic
71	C₂×C₄	#126	1	2	yes	—
72	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
73	C₂×C₄	C₂×Q₁₆	1	1	yes	characteristic
74	C₂×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
75	C₂×C₄	#137	1	1	yes	characteristic
76	C₈	—	8	2	no	—
77	C₈	—	8	2	no	—
78	C₈	—	8	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	#397	1	1	yes	characteristic
81	C₂²	#483	1	1	yes	characteristic
82	C₂²	#484	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	2	2	no	—
85	C₄	—	4	2	no	—
86	C₄	—	4	2	no	—
87	C₄	—	8	2	no	—
88	C₄	#460	1	1	yes	characteristic
89	C₄	#462	1	1	yes	characteristic
90	C₄	#487	1	1	yes	characteristic
91	C₄	#489	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#2072	1	1	yes	characteristic
95	C₂	#2080	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³
socle	C₂²	#397
prime radical	C₂³	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Maximal subgroups

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

subgroup	index
#1995	2
#1843	2
#1542	2
#1301	2
#1274	2