Subgroups — #42122702

Order 27712.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357295	C₂	1	1	yes	maximal, characteristic
2	#28357274	C₂	1	1	yes	maximal, characteristic
3	#28357159	C₂	1	1	yes	maximal, characteristic
4	#20294105	C₄	1	1	yes	characteristic
5	C₄×#13181884	C₄	1	1	yes	characteristic
6	#20294100	C₄	1	2	yes	complemented
7	C₈×D₄₃₃	C₂²	1	1	yes	characteristic
8	#20294072	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₄₃₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#13181884	—	2	1	no	—
11	#16812365	—	2	1	no	—
12	C₄×D₄₃₃	C₂×C₄	1	1	yes	characteristic
13	#16812358	C₂×C₄	1	1	yes	characteristic
14	C₈×C₄₃₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₄₃₃	M₁₆	1	1	yes	characteristic
16	#13181884	—	4	1	no	—
17	C₄×C₄₃₃	C₄²	1	1	yes	characteristic
18	Dic₄₃₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄₃₃	#97	1	1	yes	characteristic
20	D₄₃₃	—	2	1	no	—
21	C₄₃₃	#347	1	1	yes	characteristic, complemented, Sylow
22	#347	—	433	1	no	maximal, Sylow
23	M₃₂	—	433	1	no	—
24	M₃₂	—	433	1	no	—
25	#97	—	433	1	no	—
26	C₂×C₈	—	433	1	no	—
27	C₂×C₈	—	433	1	no	—
28	C₄²	—	433	1	no	—
29	C₁₆	—	433	2	no	—
30	C₁₆	—	433	1	no	—
31	C₁₆	#13181884	1	1	yes	characteristic, complemented
32	C₂×C₄	—	866	1	no	—
33	C₂×C₄	—	433	1	no	—
34	C₈	—	866	1	no	—
35	C₈	—	433	1	no	—
36	C₈	C₂×#13181884	1	1	yes	characteristic
37	C₂²	—	433	1	no	—
38	C₄	—	433	1	no	—
39	C₄	—	1732	1	no	—
40	C₄	C₄×#13181884	1	1	yes	characteristic
41	C₂	—	866	1	no	—
42	C₂	#28357274	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.