Subgroups — #42122756

Order 27712.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂×#13181884)⋊C₄	C₂	1	6	yes	maximal
2	C₄²×D₄₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13181884	C₂²	1	4	yes	—
4	C₂×C₄×D₄₃₃	C₂²	1	3	yes	—
5	C₄×Dic₄₃₃	C₄	1	3	yes	complemented
6	C₄²×C₄₃₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#13181884	—	2	12	no	—
8	C₂²×D₄₃₃	C₂³	1	1	yes	characteristic
9	C₂×Dic₄₃₃	C₂×C₄	1	3	yes	—
10	C₄×D₄₃₃	—	2	6	no	—
11	C₂×C₄×C₄₃₃	C₂×C₄	1	3	yes	—
12	C₂²×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×D₄₃₃	#41	1	6	yes	—
14	#13181884	—	4	4	no	—
15	C₄×C₄₃₃	—	2	3	no	—
16	Dic₄₃₃	—	2	3	no	—
17	C₂×C₄₃₃	#117	1	3	yes	—
18	D₄₃₃	#126	1	4	yes	—
19	C₄₃₃	#383	1	1	yes	characteristic, complemented, Sylow
20	#383	—	433	1	no	maximal, Sylow
21	C₂×C₄²	—	433	1	no	—
22	#95	—	433	6	no	—
23	C₂²×C₄	—	433	4	no	—
24	C₂²×C₄	—	433	3	no	—
25	C₄²	—	433	3	no	—
26	C₄²	#13181884	1	1	yes	characteristic, complemented
27	C₂³	—	433	1	no	—
28	C₂×C₄	—	866	6	no	—
29	C₂×C₄	—	866	12	no	—
30	C₂×C₄	—	433	3	no	—
31	C₂×C₄	C₂×#13181884	1	3	yes	—
32	C₂²	—	433	6	no	—
33	C₂²	C₂²×#13181884	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	866	3	no	—
36	C₄	—	1732	4	no	—
37	C₂	—	433	4	no	—
38	C₂	#28357299	1	3	yes	—

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.