Subgroups — C₂×#28357310 #42122917

Order 27712.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357310	C₂	1	2	yes	maximal, direct product factor
2	C₂×#20294100	C₂	1	1	yes	maximal, characteristic
3	#20294100	C₄	1	1	yes	characteristic
4	#20294100	C₂²	1	1	yes	characteristic
5	C₂×#16812358	C₄	1	1	yes	characteristic
6	#16812358	C₈	1	1	yes	characteristic
7	#16812358	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₄₃₃	C₈	1	1	yes	characteristic
9	C₂²×C₄₃₃	C₁₆	1	1	yes	characteristic
10	C₄×C₄₃₃	C₁₆	1	1	yes	characteristic
11	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₄₃₃	C₃₂	1	2	yes	complemented
13	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
14	C₄₃₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	433	1	no	maximal, Sylow
16	C₂×C₁₆	—	433	1	no	—
17	C₃₂	—	433	2	no	—
18	C₂×C₈	—	433	1	no	—
19	C₁₆	—	433	1	no	—
20	C₁₆	—	433	1	no	—
21	C₂×C₄	#16812367	1	1	yes	characteristic
22	C₈	—	433	1	no	—
23	C₈	—	433	1	no	—
24	C₂²	#20294109	1	1	yes	characteristic
25	C₄	#20294109	1	1	yes	characteristic
26	C₄	C₂×#16812367	1	1	yes	characteristic
27	C₂	#28357310	1	2	yes	direct product factor
28	C₂	C₂×#20294109	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.