Subgroups — #42122914

Order 27712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294109	C₂	1	2	yes	maximal
2	C₄×#16812365	C₂	1	1	yes	maximal, characteristic
3	#20294109	—	2	2	no	—
4	C₂×#16812365	C₄	1	1	yes	characteristic
5	C₂×#16812365	C₂²	1	1	yes	characteristic
6	C₄×Dic₄₃₃	C₄	1	1	yes	characteristic
7	#16812365	—	2	1	no	—
8	#16812365	D₄	1	1	yes	characteristic
9	#16812365	Q₈	1	1	yes	characteristic
10	C₂×Dic₄₃₃	C₈	1	1	yes	characteristic
11	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₃₃	C₈	1	1	yes	characteristic
13	C₂²×C₄₃₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₃₃	—	2	1	no	—
15	Dic₄₃₃	C₁₆	1	2	yes	complemented
16	Dic₄₃₃	C₄⋊C₄	1	1	yes	characteristic
17	Dic₄₃₃	M₁₆	1	1	yes	characteristic
18	C₂×C₄₃₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄₃₃	M₃₂	1	1	yes	characteristic
21	C₄₃₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	433	1	no	maximal, Sylow
23	C₂×C₁₆	—	433	2	no	—
24	C₄×C₈	—	433	1	no	—
25	C₂×C₈	—	433	1	no	—
26	C₂×C₈	—	433	1	no	—
27	C₄²	—	433	1	no	—
28	C₁₆	—	866	2	no	—
29	C₂×C₄	—	433	1	no	—
30	C₂×C₄	—	433	1	no	—
31	C₂×C₄	#16812367	1	1	yes	characteristic
32	C₈	—	866	1	no	—
33	C₈	—	433	1	no	—
34	C₈	—	433	1	no	—
35	C₂²	C₂×#16812367	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	—	433	1	no	—
38	C₄	—	433	1	no	—
39	C₄	—	433	2	no	—
40	C₂	C₄⋊#16812367	1	1	yes	characteristic
41	C₂	#28357315	1	1	yes	characteristic
42	C₂	#28357316	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. Dic₄₃₃	C₁₆	semidirect
21. C₄₃₃	C₄⋊C₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.