Subgroups — #13050229

Order 1312.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10620310	C₂	1	1	yes	maximal, characteristic
2	C₄×#4223	C₂	1	1	yes	maximal, characteristic, complemented
3	#10620297	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#4223	—	2	1	no	—
5	Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
6	D₁₆₄	—	2	1	no	—
7	D₁₆₄	C₄	1	1	yes	characteristic, complemented
8	C₄×D₄₁	—	2	1	no	—
9	C₄×D₄₁	C₂²	1	1	yes	characteristic
10	#66493	—	2	1	no	—
11	C₂×D₄₁	—	2	1	no	—
12	C₂×D₄₁	D₄	1	1	yes	characteristic
13	#4223	—	2	2	no	—
14	C₄×C₄₁	—	2	1	no	—
15	C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
16	Dic₄₁	D₄	1	1	yes	characteristic
17	C₂×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
18	D₄₁	—	2	1	no	—
19	D₄₁	—	4	1	no	—
20	C₄₁	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	41	1	no	maximal, Sylow
22	#41	—	41	1	no	—
23	M₁₆	—	41	1	no	—
24	C₄²	—	41	1	no	—
25	Q₈	#4223	1	1	yes	characteristic, complemented
26	D₄	—	41	1	no	—
27	D₄	—	82	1	no	—
28	C₂×C₄	—	41	1	no	—
29	C₂×C₄	—	82	1	no	—
30	C₂×C₄	—	82	1	no	—
31	C₈	—	82	1	no	—
32	C₂²	—	41	1	no	—
33	C₂²	—	82	1	no	—
34	C₄	—	2	1	no	—
35	C₄	—	41	1	no	—
36	C₄	—	82	2	no	—
37	C₄	C₂×#4223	1	1	yes	characteristic
38	C₂	—	82	1	no	—
39	C₂	—	164	1	no	—
40	C₂	C₂²⋊#4223	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.