Subgroups — #42122901

Order 27712.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16812367	C₂	1	2	yes	maximal
2	C₈×#13181884	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812367	—	2	2	no	—
4	#20294105	C₄	1	1	yes	characteristic
5	C₄×#13181884	C₂²	1	1	yes	characteristic
6	C₈×D₄₃₃	C₄	1	1	yes	characteristic
7	#16812367	—	4	2	no	—
8	C₂×#13181884	D₄	1	1	yes	characteristic
9	C₂×#13181884	Q₈	1	1	yes	characteristic
10	#16812365	—	2	1	no	—
11	C₄×D₄₃₃	C₂×C₄	1	1	yes	characteristic
12	#16812358	C₈	1	1	yes	characteristic, complemented
13	C₈×C₄₃₃	C₈	1	1	yes	characteristic, complemented
14	C₂×D₄₃₃	C₄⋊C₄	1	1	yes	characteristic
15	#13181884	—	2	1	no	—
16	#13181884	D₈	1	1	yes	characteristic
17	#13181884	Q₁₆	1	1	yes	characteristic
18	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
19	Dic₄₃₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄₃₃	C₄⋊C₈	1	1	yes	characteristic
21	D₄₃₃	#107	1	1	yes	characteristic
22	D₄₃₃	#108	1	1	yes	characteristic
23	C₄₃₃	#335	1	1	yes	characteristic, complemented, Sylow
24	#335	—	433	1	no	maximal, Sylow
25	C₄⋊C₈	—	433	2	no	—
26	C₄×C₈	—	433	1	no	—
27	C₂×C₈	—	866	2	no	—
28	C₂×C₈	—	433	1	no	—
29	C₂×C₈	—	433	1	no	—
30	C₄²	—	433	1	no	—
31	C₂×C₄	—	433	1	no	—
32	C₂×C₄	—	433	1	no	—
33	C₂×C₄	—	433	1	no	—
34	C₈	—	866	1	no	—
35	C₈	—	433	1	no	—
36	C₈	—	1732	2	no	—
37	C₈	#16812367	1	1	yes	characteristic, complemented
38	C₂²	—	433	1	no	—
39	C₄	—	866	1	no	—
40	C₄	—	433	1	no	—
41	C₄	—	433	1	no	—
42	C₄	—	433	1	no	—
43	C₄	C₂×#16812367	1	1	yes	characteristic
44	C₂	—	433	1	no	—
45	C₂	—	433	1	no	—
46	C₂	C₄⋊#16812367	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.