Subgroups — #13066820

Order 1408.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#10622144	C₂	1	2	yes	maximal
3	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
4	#66883	—	2	2	no	—
5	C₁₁×C₃₂	C₄	1	2	yes	—
6	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
7	#4318	—	4	2	no	—
8	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
10	#1425	—	11	1	no	maximal, Sylow
11	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
12	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
14	C₁₁⋊C₈	—	8	2	no	—
15	C₂×C₃₂	D₁₁	1	1	yes	characteristic
16	#368	—	11	2	no	—
17	C₂²×C₁₁	Q₃₂	1	1	yes	characteristic
18	C₄×C₁₁	#107	1	1	yes	characteristic
19	C₄×C₁₁	D₁₆	1	1	yes	characteristic
20	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
21	#108	—	22	2	no	—
22	C₃₂	Dic₁₁	1	2	yes	—
23	C₂×C₁₁	—	2	1	no	—
24	C₂×C₁₁	#366	1	1	yes	characteristic
25	M₁₆	—	44	2	no	—
26	C₂×C₈	D₄₄	1	1	yes	characteristic
27	C₁₆	Dic₂₂	1	1	yes	characteristic
28	C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
29	C₁₁	#1425	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄	D₈₈	1	1	yes	characteristic
31	C₈	—	88	2	no	—
32	C₈	Dic₄₄	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
34	C₂²	Dic₈₈	1	1	yes	characteristic
35	C₄	D₁₇₆	1	1	yes	characteristic
36	C₄	#66882	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#10622142	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
29. C₁₁	#1425	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.