Subgroups — C₂²×#20294100 #42122864

Order 27712.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294100	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#16812358	C₂	1	1	yes	maximal, characteristic
3	#20294100	C₂²	1	4	yes	direct product factor
4	C₂×#16812358	C₄	1	3	yes	—
5	C₂×#16812358	C₂²	1	3	yes	—
6	C₂²×C₄×C₄₃₃	C₄	1	1	yes	characteristic
7	#16812358	C₂×C₄	1	3	yes	—
8	#16812358	C₂³	1	1	yes	characteristic
9	C₂³×C₄₃₃	C₈	1	1	yes	characteristic
10	C₂×C₄×C₄₃₃	C₈	1	3	yes	—
11	C₂×C₄×C₄₃₃	C₂×C₄	1	3	yes	—
12	C₂²×C₄₃₃	C₁₆	1	4	yes	complemented
13	C₂²×C₄₃₃	C₂×C₈	1	3	yes	—
14	C₄×C₄₃₃	C₂×C₈	1	3	yes	—
15	C₄×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄₃₃	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₄₃₃	C₂²×C₈	1	1	yes	characteristic
18	C₄₃₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	433	1	no	maximal, Sylow
20	C₂²×C₈	—	433	1	no	—
21	C₂×C₁₆	—	433	6	no	—
22	C₂²×C₄	#13181884	1	1	yes	characteristic
23	C₂×C₈	—	433	3	no	—
24	C₂×C₈	—	433	3	no	—
25	C₁₆	—	433	4	no	—
26	C₂³	#16812365	1	1	yes	characteristic
27	C₂×C₄	#16812365	1	3	yes	—
28	C₂×C₄	C₂×#13181884	1	3	yes	—
29	C₈	—	433	1	no	—
30	C₈	—	433	3	no	—
31	C₂²	#20294100	1	4	yes	direct product factor
32	C₂²	C₂×#16812365	1	3	yes	—
33	C₄	C₂×#16812365	1	3	yes	—
34	C₄	C₂²×#13181884	1	1	yes	characteristic
35	C₂	C₂×#20294100	1	6	yes	direct product factor
36	C₂	C₂²×#16812365	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.