Subgroups — #12892

Order 256.

137 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#346	C₂	1	1	yes	maximal, characteristic
2	#1848	C₂	1	2	yes	maximal
3	#1381	C₂	1	4	yes	maximal
4	C₂²×C₁₆	C₂²	1	2	yes	—
5	C₂×#108	—	2	2	no	—
6	C₂×#108	C₂²	1	4	yes	—
7	#423	—	2	2	no	—
8	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
9	#346	C₄	1	4	yes	—
10	C₂×M₁₆	—	2	4	no	—
11	C₂²×C₈	D₄	1	1	yes	characteristic
12	C₂²×C₈	C₂³	1	1	yes	characteristic
13	C₂×C₄²	D₄	1	1	yes	characteristic
14	C₂×C₁₆	—	2	4	no	—
15	C₂×C₁₆	C₂×C₄	1	4	yes	—
16	#108	—	2	8	no	—
17	#108	—	4	4	no	—
18	C₄⋊C₈	—	4	4	no	—
19	C₄×C₈	C₂×C₄	1	2	yes	—
20	C₄×C₈	Q₈	1	2	yes	—
21	C₂²×C₄	Q₁₆	1	2	yes	—
22	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
23	M₁₆	—	4	4	no	—
24	M₁₆	—	4	4	no	—
25	C₂×C₈	—	4	4	no	—
26	C₂×C₈	C₄⋊C₄	1	2	yes	—
27	C₂×C₈	SD₁₆	1	4	yes	—
28	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₈	#41	1	4	yes	—
31	C₄²	C₄⋊C₄	1	2	yes	—
32	C₄²	D₈	1	2	yes	—
33	C₁₆	—	2	4	no	—
34	C₂³	C₂×Q₁₆	1	1	yes	characteristic
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	#107	1	4	yes	—
37	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄	#124	1	2	yes	—
39	C₂×C₄	C₂×D₈	1	1	yes	characteristic
40	C₂×C₄	C₂×SD₁₆	1	2	yes	—
41	C₈	—	8	4	no	—
42	C₈	#106	1	4	yes	—
43	C₈	#117	1	2	yes	—
44	C₈	#125	1	2	yes	—
45	C₂²	—	2	2	no	—
46	C₂²	C₂×#107	1	1	yes	characteristic
47	C₂²	#487	1	2	yes	—
48	C₄	—	2	4	no	—
49	C₄	#382	1	1	yes	characteristic
50	C₄	C₂×#106	1	1	yes	characteristic
51	C₄	#486	1	2	yes	—
52	C₂	—	2	2	no	—
53	C₂	#1834	1	1	yes	characteristic
54	C₂	#2161	1	2	yes	—

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