Subgroups — #37548882

Order 23168.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042205	C₂	1	2	yes	maximal
2	C₃₂×D₁₈₁	C₂	1	1	yes	maximal, characteristic
3	#19153885	—	2	2	no	—
4	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
5	#19153722	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#10624382	—	4	2	no	—
8	C₈×D₁₈₁	D₄	1	1	yes	characteristic
9	#15668424	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
11	C₂×#10624382	—	8	2	no	—
12	C₄×D₁₈₁	D₈	1	1	yes	characteristic
13	#13089678	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₈₁	D₁₆	1	1	yes	characteristic
16	#10624382	—	16	2	no	—
17	C₄×C₁₈₁	#107	1	1	yes	characteristic
18	Dic₁₈₁	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₈₁	#366	1	1	yes	characteristic
20	D₁₈₁	D₃₂	1	1	yes	characteristic
21	D₁₈₁	Q₆₄	1	1	yes	characteristic
22	C₁₈₁	#1423	1	1	yes	characteristic, complemented, Sylow
23	#1423	—	181	1	no	maximal, Sylow
24	C₂×C₃₂	—	181	1	no	—
25	#366	—	181	2	no	—
26	C₂×C₁₆	—	181	1	no	—
27	#107	—	362	2	no	—
28	C₃₂	—	181	1	no	—
29	C₃₂	#10624382	1	1	yes	characteristic, complemented
30	C₂×C₈	—	181	1	no	—
31	C₄⋊C₄	—	724	2	no	—
32	C₁₆	—	181	1	no	—
33	C₁₆	C₂×#10624382	1	1	yes	characteristic
34	C₂×C₄	—	1448	2	no	—
35	C₂×C₄	—	181	1	no	—
36	C₈	—	181	1	no	—
37	C₈	C₄⋊#10624382	1	1	yes	characteristic
38	C₂²	—	181	1	no	—
39	C₄	—	2896	2	no	—
40	C₄	—	181	1	no	—
41	C₄	#19153885	1	1	yes	characteristic
42	C₂	—	181	1	no	—
43	C₂	—	181	1	no	—
44	C₂	#26042205	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.