Subgroups — C₄×#16838784 #29508842

Order 15424.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838784	C₂	1	2	yes	maximal
2	C₄×#14515358	C₂	1	1	yes	maximal, characteristic
3	#16838784	C₄	1	4	yes	direct product factor
4	C₂×#14515358	C₄	1	1	yes	characteristic
5	C₂×#14515358	C₂²	1	1	yes	characteristic
6	C₄×#11757210	C₄	1	1	yes	characteristic
7	#14515358	C₈	1	2	yes	—
8	#14515358	C₂×C₄	1	2	yes	—
9	C₂×#11757210	C₈	1	1	yes	characteristic
10	C₂×#11757210	C₂×C₄	1	1	yes	characteristic
11	C₄×D₂₄₁	C₈	1	1	yes	characteristic
12	C₂×D₂₄₁	C₂×C₈	1	1	yes	characteristic
13	#11757210	C₁₆	1	2	yes	complemented
14	#11757210	C₄²	1	1	yes	characteristic
15	#11757210	C₂×C₈	1	1	yes	characteristic
16	C₄×C₂₄₁	C₁₆	1	1	yes	characteristic, complemented
17	Dic₂₄₁	C₁₆	1	1	yes	characteristic, complemented
18	C₂×C₂₄₁	C₂×C₁₆	1	1	yes	characteristic
19	D₂₄₁	C₄×C₈	1	1	yes	characteristic
20	D₂₄₁	C₂×C₁₆	1	1	yes	characteristic
21	C₂₄₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	241	1	no	maximal, Sylow
23	C₂×C₁₆	—	241	2	no	—
24	C₄×C₈	—	241	1	no	—
25	C₂×C₈	—	241	1	no	—
26	C₂×C₈	—	241	1	no	—
27	C₄²	—	241	1	no	—
28	C₁₆	—	241	4	no	—
29	C₂×C₄	—	241	1	no	—
30	C₂×C₄	—	241	1	no	—
31	C₂×C₄	—	241	1	no	—
32	C₈	—	241	2	no	—
33	C₈	—	241	2	no	—
34	C₂²	—	241	1	no	—
35	C₄	—	241	1	no	—
36	C₄	—	241	1	no	—
37	C₄	—	241	2	no	—
38	C₄	—	241	1	no	—
39	C₄	#16838784	1	1	yes	characteristic, direct product factor
40	C₂	—	241	1	no	—
41	C₂	—	241	1	no	—
42	C₂	C₂×#16838784	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.