Subgroups — #42122700

Order 27712.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294100	C₂	1	2	yes	maximal
2	C₈×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
3	#20294100	C₄	1	4	yes	complemented
4	C₂×#16812358	C₂²	1	1	yes	characteristic
5	C₄×Dic₄₃₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₄₃₃	C₄	1	1	yes	characteristic
7	C₂×Dic₄₃₃	C₈	1	2	yes	—
8	#16812358	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
10	C₈×C₄₃₃	C₈	1	2	yes	—
11	C₂²×C₄₃₃	C₂×C₈	1	1	yes	characteristic
12	C₄×C₄₃₃	C₄²	1	1	yes	characteristic
13	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
14	Dic₄₃₃	—	2	2	no	—
15	C₂×C₄₃₃	C₄×C₈	1	1	yes	characteristic
16	C₂×C₄₃₃	M₃₂	1	2	yes	—
17	C₄₃₃	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	433	1	no	maximal, Sylow
19	C₂×C₁₆	—	433	2	no	—
20	C₄×C₈	—	433	1	no	—
21	C₂×C₈	—	433	1	no	—
22	C₂×C₈	#13181884	1	1	yes	characteristic
23	C₄²	—	433	1	no	—
24	C₁₆	—	433	4	no	—
25	C₂×C₄	—	433	2	no	—
26	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
27	C₈	—	433	2	no	—
28	C₈	#16812365	1	2	yes	—
29	C₂²	#20294105	1	1	yes	characteristic
30	C₄	—	866	2	no	—
31	C₄	C₄×#13181884	1	1	yes	characteristic
32	C₄	C₂×#16812365	1	1	yes	characteristic
33	C₂	C₄×#16812365	1	1	yes	characteristic
34	C₂	#28357295	1	2	yes	—

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

N	H ≅ G/N	type
3. #20294100	C₄	semidirect
17. C₄₃₃	#346	semidirect

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