Subgroups — C₈×#16812365 #42122651

Order 27712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16812365	C₂	1	2	yes	maximal
2	C₈×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812365	C₄	1	4	yes	—
4	C₂×#16812358	C₄	1	1	yes	characteristic
5	C₄×Dic₄₃₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₃₃	C₄	1	1	yes	characteristic
7	#16812365	C₈	1	8	yes	direct product factor
8	C₂×Dic₄₃₃	C₂×C₄	1	2	yes	—
9	#16812358	C₈	1	2	yes	complemented
10	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₄₃₃	C₈	1	2	yes	complemented
12	C₂²×C₄₃₃	C₄²	1	1	yes	characteristic
13	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
15	Dic₄₃₃	C₂×C₈	1	4	yes	—
16	C₂×C₄₃₃	C₄×C₈	1	2	yes	—
17	C₂×C₄₃₃	C₄×C₈	1	1	yes	characteristic
18	C₄₃₃	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	433	1	no	maximal, Sylow
20	C₄×C₈	—	433	2	no	—
21	C₄×C₈	—	433	1	no	—
22	C₂×C₈	—	433	4	no	—
23	C₂×C₈	—	433	1	no	—
24	C₂×C₈	#13181884	1	1	yes	characteristic
25	C₄²	—	433	1	no	—
26	C₂×C₄	—	433	2	no	—
27	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
28	C₈	—	433	8	no	—
29	C₈	—	433	2	no	—
30	C₈	#16812365	1	2	yes	direct product factor
31	C₂²	C₄×#13181884	1	1	yes	characteristic
32	C₄	—	433	4	no	—
33	C₄	C₂×#16812365	1	1	yes	characteristic
34	C₄	#20294105	1	1	yes	characteristic
35	C₂	C₈×#13181884	1	2	yes	—
36	C₂	C₄×#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.