Subgroups — C₂³×#16812365 #42122881

Order 27712.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16812365	C₂	1	14	yes	maximal, direct product factor
2	C₂³×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812365	C₂²	1	28	yes	direct product factor
4	C₂²×Dic₄₃₃	C₄	1	7	yes	—
5	C₂²×Dic₄₃₃	C₂²	1	7	yes	—
6	C₂⁴×C₄₃₃	C₄	1	1	yes	characteristic
7	#16812365	C₂³	1	8	yes	direct product factor
8	C₂×Dic₄₃₃	C₂×C₄	1	21	yes	—
9	C₂×Dic₄₃₃	C₂³	1	7	yes	—
10	C₂³×C₄₃₃	C₈	1	8	yes	complemented
11	C₂³×C₄₃₃	C₂×C₄	1	7	yes	—
12	C₂²×C₄₃₃	C₂×C₈	1	28	yes	complemented
13	C₂²×C₄₃₃	C₂²×C₄	1	7	yes	—
14	Dic₄₃₃	C₂²×C₄	1	7	yes	—
15	Dic₄₃₃	C₂⁴	1	1	yes	characteristic
16	C₂×C₄₃₃	C₂²×C₈	1	14	yes	complemented
17	C₂×C₄₃₃	C₂³×C₄	1	1	yes	characteristic
18	C₄₃₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	433	1	no	maximal, Sylow
20	C₂³×C₄	—	433	1	no	—
21	C₂²×C₈	—	433	14	no	—
22	C₂⁴	#13181884	1	1	yes	characteristic
23	C₂²×C₄	—	433	7	no	—
24	C₂²×C₄	—	433	7	no	—
25	C₂×C₈	—	433	28	no	—
26	C₂³	#16812365	1	8	yes	direct product factor
27	C₂³	C₂×#13181884	1	7	yes	—
28	C₂×C₄	—	433	7	no	—
29	C₂×C₄	—	433	21	no	—
30	C₈	—	433	8	no	—
31	C₂²	C₂×#16812365	1	28	yes	direct product factor
32	C₂²	C₂²×#13181884	1	7	yes	—
33	C₄	—	433	1	no	—
34	C₄	—	433	7	no	—
35	C₂	C₂²×#16812365	1	14	yes	direct product factor
36	C₂	C₂³×#13181884	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.