Subgroups — C₁₁×Dic₇₃₇ #44569832

Order 32428.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor
4	C₁₁×Dic₆₇	—	11	1	no	maximal
5	C₂×C₁₁×C₆₇	—	2	5	no	—
6	C₂×C₁₁×C₆₇	D₁₁	1	1	yes	characteristic
7	C₂×C₁₁×C₆₇	C₂×C₁₁	1	1	yes	characteristic
8	C₁₁×C₆₇	—	2	5	no	—
9	C₁₁×C₆₇	Dic₁₁	1	1	yes	characteristic, complemented
10	C₁₁×C₆₇	C₄×C₁₁	1	1	yes	characteristic, complemented
11	C₁₁×Dic₁₁	—	67	1	no	maximal, Hall
12	Dic₆₇	—	11	1	no	Hall
13	C₂×C₁₁²	D₆₇	1	1	yes	characteristic
14	C₂×C₆₇	C₁₁×D₁₁	1	1	yes	characteristic
15	C₁₁²	Dic₆₇	1	1	yes	characteristic, complemented, Sylow
16	C₆₇	C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₁₁	—	737	1	no	—
18	Dic₁₁	—	67	1	no	—
19	C₂×C₁₁	—	2	5	no	—
20	C₂×C₁₁	C₁₁×D₆₇	1	1	yes	characteristic
21	C₂×C₁₁	D₇₃₇	1	1	yes	characteristic
22	C₁₁	—	2	5	no	—
23	C₁₁	C₁₁×Dic₆₇	1	1	yes	characteristic, complemented
24	C₁₁	Dic₇₃₇	1	1	yes	characteristic, direct product factor
25	C₄	—	737	1	no	Sylow
26	C₂	C₁₁×D₇₃₇	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.