Subgroups — #7374

Order 256.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1849	C₂	1	1	yes	maximal, characteristic
2	#1327	C₂	1	2	yes	maximal
3	C₂×#108	—	2	2	no	—
4	#423	C₄	1	1	yes	characteristic
5	#423	C₂²	1	1	yes	characteristic
6	C₂×#97	C₄	1	1	yes	characteristic
7	#349	—	2	2	no	—
8	C₂×M₁₆	—	2	1	no	—
9	C₂×M₁₆	D₄	1	2	yes	—
10	C₂²×C₈	—	2	1	no	—
11	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
12	M₃₂	—	4	2	no	—
13	#108	—	4	4	no	—
14	C₄⋊C₈	—	4	1	no	—
15	C₄⋊C₈	—	4	1	no	—
16	#97	—	2	1	no	—
17	#97	C₈	1	2	yes	—
18	C₂²×C₄	—	2	1	no	—
19	C₂²×C₄	C₂²⋊C₄	1	1	yes	characteristic
20	M₁₆	—	4	2	no	—
21	M₁₆	—	4	2	no	—
22	C₂×C₈	—	2	2	no	—
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	—	2	2	no	—
25	C₂×C₈	—	2	2	no	—
26	C₂×C₈	—	4	1	no	—
27	C₄²	—	2	1	no	—
28	C₄²	C₂×C₈	1	1	yes	characteristic
29	C₄²	M₁₆	1	1	yes	characteristic
30	C₁₆	—	8	2	no	—
31	C₂³	#101	1	1	yes	characteristic
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	8	1	no	—
37	C₂×C₄	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₄	#99	1	1	yes	characteristic
39	C₈	—	2	4	no	—
40	C₈	—	4	2	no	—
41	C₈	—	8	1	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	4	1	no	—
44	C₂²	#324	1	1	yes	characteristic
45	C₄	—	2	1	no	—
46	C₄	—	4	1	no	—
47	C₄	—	4	1	no	—
48	C₄	#353	1	1	yes	characteristic
49	C₄	#356	1	1	yes	characteristic
50	C₂	—	2	1	no	—
51	C₂	—	4	1	no	—
52	C₂	#1325	1	1	yes	characteristic

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

subgroup	index
#1849	2
#1327	2