Subgroups — #383×C₄₂₁ #41002355

Order 26944.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₄₂₁	C₂	1	1	yes	maximal, characteristic
2	#95×C₄₂₁	C₂	1	6	yes	maximal
3	C₂²×C₄×C₄₂₁	C₂²	1	4	yes	—
4	C₂²×C₄×C₄₂₁	C₂²	1	3	yes	—
5	C₄²×C₄₂₁	C₄	1	4	yes	complemented
6	C₂³×C₄₂₁	C₂³	1	1	yes	characteristic
7	C₂×C₄×C₄₂₁	—	2	6	no	—
8	C₂×C₄×C₄₂₁	—	2	12	no	—
9	C₂×C₄×C₄₂₁	C₂×C₄	1	6	yes	—
10	C₂²×C₄₂₁	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₄₂₁	#41	1	6	yes	—
12	C₄×C₄₂₁	—	2	6	no	—
13	C₄×C₄₂₁	—	4	4	no	—
14	C₂×C₄₂₁	#117	1	3	yes	—
15	C₂×C₄₂₁	#126	1	4	yes	—
16	C₄₂₁	#383	1	1	yes	characteristic, direct product factor, Sylow
17	#383	C₄₂₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₄²	C₂×C₄₂₁	1	1	yes	characteristic
19	#95	C₂×C₄₂₁	1	6	yes	—
20	C₂²×C₄	C₂²×C₄₂₁	1	4	yes	—
21	C₂²×C₄	C₂²×C₄₂₁	1	3	yes	—
22	C₄²	C₄×C₄₂₁	1	4	yes	complemented
23	C₂³	C₂³×C₄₂₁	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	2	12	no	—
26	C₂×C₄	C₂×C₄×C₄₂₁	1	6	yes	—
27	C₂²	C₂²×C₄×C₄₂₁	1	1	yes	characteristic
28	C₂²	#41×C₄₂₁	1	6	yes	—
29	C₄	—	2	6	no	—
30	C₄	—	4	4	no	—
31	C₂	#117×C₄₂₁	1	3	yes	—
32	C₂	#126×C₄₂₁	1	4	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.