Subgroups — C₂²×#20266991 #39910300

Order 26176.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20266991	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#15692543	C₂	1	1	yes	maximal, characteristic
3	#20266991	C₂²	1	4	yes	direct product factor
4	C₂×#15692543	C₄	1	3	yes	—
5	C₂×#15692543	C₂²	1	3	yes	—
6	C₂²×C₄×C₄₀₉	C₄	1	1	yes	characteristic
7	#15692543	C₂×C₄	1	3	yes	—
8	#15692543	C₂³	1	1	yes	characteristic
9	C₂³×C₄₀₉	C₈	1	1	yes	characteristic
10	C₂×C₄×C₄₀₉	C₈	1	3	yes	—
11	C₂×C₄×C₄₀₉	C₂×C₄	1	3	yes	—
12	C₂²×C₄₀₉	C₁₆	1	4	yes	complemented
13	C₂²×C₄₀₉	C₂×C₈	1	3	yes	—
14	C₄×C₄₀₉	C₂×C₈	1	3	yes	—
15	C₄×C₄₀₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄₀₉	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₄₀₉	C₂²×C₈	1	1	yes	characteristic
18	C₄₀₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	409	1	no	maximal, Sylow
20	C₂²×C₈	—	409	1	no	—
21	C₂×C₁₆	—	409	6	no	—
22	C₂²×C₄	#13109888	1	1	yes	characteristic
23	C₂×C₈	—	409	3	no	—
24	C₂×C₈	—	409	3	no	—
25	C₁₆	—	409	4	no	—
26	C₂³	#15692550	1	1	yes	characteristic
27	C₂×C₄	#15692550	1	3	yes	—
28	C₂×C₄	C₂×#13109888	1	3	yes	—
29	C₈	—	409	1	no	—
30	C₈	—	409	3	no	—
31	C₂²	#20266991	1	4	yes	direct product factor
32	C₂²	C₂×#15692550	1	3	yes	—
33	C₄	C₂×#15692550	1	3	yes	—
34	C₄	C₂²×#13109888	1	1	yes	characteristic
35	C₂	C₂×#20266991	1	6	yes	direct product factor
36	C₂	C₂²×#15692550	1	1	yes	characteristic

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

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